A health plan to reduce poverty.

PubMed

Weil, Alan

2007-01-01

Noting that the failures of the U.S. health care system are compounding the problems faced by low-income Americans, Alan Weil argues that any strategy to reduce poverty must provide access to health care for all low-income families. Although nearly all children in families with incomes under 200 percent of poverty are eligible for either Medicaid or the State Children's Health Insurance Program (SCHIP), the parents of poor children often lack health insurance. Parents who leave welfare normally get a year of coverage but then lose coverage unless their employer provides it, and many employers of low-wage workers do not offer health insurance. Similarly, parents who take low-paying jobs to avoid welfare usually have no coverage at all. This lack of coverage discourages adults from working and may also affect the health of children because adults without health insurance are less likely to take their children for preventive care. Weil proposes creating a federal earned income health credit (EIHC) and redefining the federal floor of coverage through Medicaid and SCHIP. His aim is to make health insurance affordable for low-income families and to make sure enough options are available that individuals and families can get coverage using a combination of their own, their employer's, and public resources. Weil would expand Medicaid eligibility to include all families whose income falls below the poverty line. The EIHC would be a refundable tax credit that would be available to parents during the year in advance of filing a tax return. The credit, which would be based on taxpayer earnings and family structure, would phase in as earnings increase, reach a plateau, and then phase out farther up the income scale. The credit would be larger for families with dependents. The EIHC would function seamlessly with the employee payroll withholding system. It would be available only to adults who demonstrate that they had health insurance coverage during the year and, for adults with children, only if their eligible dependent children were enrolled in either a private or public insurance program. Weil's proposal would cover individuals who receive coverage from their employer and those who do not. The proposal smooths transitions from public to private coverage, and it anticipates a substantial role for states. Weil estimates that his policy would cost about $45 billion a year.

Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term

NASA Astrophysics Data System (ADS)

Deruelle, Nathalie; Merino, Nelson; Olea, Rodrigo

2018-05-01

We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which uses the Chern-Weil theorem plus a dimensional continuation process, such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The boundary term constructed in this paper allows to deal with a general background and is not equivalent to the Gibbons-Hawking-Myers boundary term. However, we show that they coincide if one replaces the background of the Katz procedure by a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients, the expected mass of the Boulware-Deser black hole.

Typhus-like Fevers of Unknown Ætiology, with Special Reference to the Malay States

PubMed Central

Fletcher, William

1930-01-01

Typhus exanthematicus, Rocky Mountain fever, and the tsutsugamushi disease have been classified in the “typhus group” by Megaw, as louse-typhus, tick-typhus, and mite-typhus. He has added a fourth-class, comprising typhus-like fevers, with unknown vectors. It is the diseases of this class with which this paper is concerned. Endemic typhus (Brill's disease) is very closely related to typhus fever; the Weil-Felix reaction is positive, typhus-like vascular lesions are present, and there is cross-immunity with typhus. In the exanthematic fever of Marseilles the relationship is more superficial; there is neither cross-immunity nor vascular lesion, and the Weil-Felix reaction is negative. Some, e.g., the scrub-typhus of Malaya (vector probably a mite), are more nearly related to tsutsugamushi than to typhus; others, e.g., Indian “tick-typhus” (vector probably a tick), to Rocky Mountain fever. All are non-contagious, non-epidemic, warm-weather diseases. They are unassociated with dirt, squalor, or lice, and are restricted to definite foci. Probably rodents or other animals are the reservoirs of the virus. On the question of identity with typhus, health authorities decide that notification is unnecessary; typhus introduced into America spreads, Brill's disease does not. These typhus-like diseases are not the same in all the countries where they occur. There are two main groups: (1) an urban group, more closely related to typhus, in which the Weil-Felix reaction is positive; (2) a rural group, more closely related to tsutsugamushi and Rocky Mountain fever, in which the Weil-Felix reaction is negative. There is a special non-indologenic strain of B. proteus, which is agglutinated in some of the fevers belonging to the second group. Tropical typhus in the Malay States: (1) urban form, or “shop-typhus,” resembling Brill's disease; (2) rural form or “scrub-typhus.” Peculiar association with oil-palms and coarse grass. PMID:19987538

Revised estimates for continuous shoreline fumigation: a PDF approach.

PubMed

Nazir, Muddassir; Khan, Faisal I; Husain, Tahir

2005-02-14

A probability density function (PDF) fumigation model is presented here to study the dispersion of air pollutants emitted from a tall stack on the shoreline. This work considers dispersion of the pollutants in the stable layer and within the thermal internal boundary layer (TIBL) proceeds independently. The growth of TIBL is considered parabolic with distance inland. Turbulence is taken as homogeneous and stationary. Dispersion of particles (contaminant) in lateral and vertical directions is assumed independent of each other. This assumption allows us to consider the position of particles in both directions as independent random variables. The lateral dispersion distribution within the TIBL is considered as Gaussian and independent of height. A skewed bi-Gaussian vertical velocity PDF is used to account for the physics of dispersion due to different characteristics of updrafts and downdrafts within the TIBL. We have used Weil (J.C. Weil, A diagnosis of the asymmetry in top-down and bottom-up diffusion using a Lagrangian stochastic model, J. Atmos. Sci., 47 (1990) 501-515) solutions to find out the parameters of this PDF. Incorporating finite Lagrangian integral time scale for the vertical velocity component, it is observed that it reduces the vertical dispersion in the beginning and moves the point of maximum concentration further downwind. Due to little dispersion in the beginning, there is more plume to be dispersed causing higher concentrations at large distances. The model has considered Weil and Brower's (J.C. Weil, P.R. Brower, Estimating convective boundary layer parameters for diffusion applications, Maryland Power Plant Siting Program Rep. PPSP-MP-48, Department of Natural Resources, Annapolis, MD, 1985, 37 pp.) convective limit to analyze dispersion characteristics within TIBL. The revised model discussed here is evaluated with the data available from the Nanticoke field experiment on fumigation conducted in summer of 1978 in Ontario, Canada. The results of revised model are in good agreement with the observed data.

Case series of 17 modified Weil's osteotomies for Freiberg's and Köhler's II AVN, with AOFAS scoring pre- and post-operatively.

PubMed

Edmondson, M C; Sherry, K R; Afolayan, J; Armitage, A R; Skyrme, A D

2011-03-01

Treatment for metatarsal head avascular necrosis is largely conservative. For severe or refractory cases there are various surgical options. We have performed a 'modified Weil's osteotomy' of the distal metatarsal in order to manage this problem. We present the largest case series, to our knowledge, with 17 such cases. The patients were scored pre- and post-operatively using the AOFAS Forefoot scoring system. We found that this procedure provided a mean score improvement of 36 points, with a complication rate of 5.9%. We would advocate this modified osteotomy as an effective, reliable and safe treatment option. Copyright © 2009 European Foot and Ankle Society. Published by Elsevier Ltd. All rights reserved.

21 CFR 866.3410 - Proteus spp. (Weil-Felix) serological reagents.

Code of Federal Regulations, 2011 CFR

2011-04-01

... fluorescent dye (immunofluorescent reagents), derived from the bacterium Proteus vulgaris used in... (virus-like bacteria) in serum. Test results aid in the diagnosis of diseases caused by bacteria...

21 CFR 866.3410 - Proteus spp. (Weil-Felix) serological reagents.

Code of Federal Regulations, 2010 CFR

2010-04-01

... fluorescent dye (immunofluorescent reagents), derived from the bacterium Proteus vulgaris used in... (virus-like bacteria) in serum. Test results aid in the diagnosis of diseases caused by bacteria...

Leptospirosis

MedlinePlus

... trail biking in warm areas Household exposure -- pet dogs, domesticated livestock, rainwater catchment systems, and infected rodents Weil disease is rare in the continental United States. Hawaii has the highest number of cases in the United States.

Destruction of the hepatocyte junction by intercellular invasion of Leptospira causes jaundice in a hamster model of Weil's disease

PubMed Central

Miyahara, Satoshi; Saito, Mitsumasa; Kanemaru, Takaaki; Villanueva, Sharon Y A M; Gloriani, Nina G; Yoshida, Shin-ichi

2014-01-01

Weil's disease, the most severe form of leptospirosis, is characterized by jaundice, haemorrhage and renal failure. The mechanisms of jaundice caused by pathogenic Leptospira remain unclear. We therefore aimed to elucidate the mechanisms by integrating histopathological changes with serum biochemical abnormalities during the development of jaundice in a hamster model of Weil's disease. In this work, we obtained three-dimensional images of infected hamster livers using scanning electron microscope together with freeze-cracking and cross-cutting methods for sample preparation. The images displayed the corkscrew-shaped bacteria, which infiltrated the Disse's space, migrated between hepatocytes, detached the intercellular junctions and disrupted the bile canaliculi. Destruction of bile canaliculi coincided with the elevation of conjugated bilirubin, aspartate transaminase and alkaline phosphatase levels in serum, whereas serum alanine transaminase and γ-glutamyl transpeptidase levels increased slightly, but not significantly. We also found in ex vivo experiments that pathogenic, but not non-pathogenic leptospires, tend to adhere to the perijunctional region of hepatocyte couplets isolated from hamsters and initiate invasion of the intercellular junction within 1 h after co-incubation. Our results suggest that pathogenic leptospires invade the intercellular junctions of host hepatocytes, and this invasion contributes in the disruption of the junction. Subsequently, bile leaks from bile canaliculi and jaundice occurs immediately. Our findings revealed not only a novel pathogenicity of leptospires, but also a novel mechanism of jaundice induced by bacterial infection. PMID:24945433

Flexor digitorum brevis transfer for floating toe prevention after Weil osteotomy: a cadaveric study.

PubMed

Lee, Lydia C; Charlton, Timothy P; Thordarson, David B

2013-12-01

A floating toe deformity occurs in many patients who undergo Weil osteotomies. It is likely caused by the failure of the windlass mechanism in shortening the metatarsal. For patients who require a proximal interphalangeal (PIP) joint arthroplasty or fusion in addition to a Weil osteotomy, the transfer of the flexor digitorum brevis (FDB) tendon to the PIP joint might restore the windlass mechanism and decrease the incidence of floating toes. Fourteen cadaveric foot specimens were examined to determine the effects of changing metatarsal length as well as tensioning the FDB tendon on the angle of the metatarsophalangeal (MTP) joint as a measure of a floating toe. Shortening and lengthening the second metatarsal resulted in a significant change in MTP angle (P = .03 and .02, respectively), though there was no clear relationship found between the amount of change in metatarsal length and the change in MTP angle. Transferring the FDB to a PIP arthroplasty site plantarflexed the MTP joint and corrected floating toes; the change in angle was significant compared with the control and shortening groups (P = .0001 and .002, respectively). This study supports the theory that change in length of the metatarsal, possibly via the windlass mechanism, plays a role in the pathophysiology of the floating toe deformity. Tensioning and transferring the FDB tendon into the PIP joint helped prevent the floating toe deformity in this cadaveric model. Continued research in this subject will help to refine methods of prevention and correction of the floating toe deformity.

Dissecting Dissection.

ERIC Educational Resources Information Center

AV Magazine, 1996

1996-01-01

This journal features articles covering various aspects of dissection. "Biology--The Study of Life" (George Russell) offers students experiments that do not require using invasive procedures. "Animal Cruelty--Behind the Scenes" (Zoe Weil) describes sources of laboratory animals. "Doing without Dissection" (Juliana…

Systeme mit veränderlicher Teilchenzahl, Gasentartung

NASA Astrophysics Data System (ADS)

Heintze, Joachim

Bisher haben wir die Zustandsgrößen ν (Zahl der Mole) und N (Zahl der Teilchen im System) als konstant betrachtet. In diesem Kapitel wollen wir untersuchen, wie sich Veränderungen von ν bzw. von N beschreiben lassen. Dazu werden wir eine neue thermodynamische Größe einführen, das chemische Potential μ. Als Beispiele für die Veränderung von Teilchenzahlen werden wir diffusive Prozesse und chemische Reaktionen betrachten. Am Ende des Kapitels werden wir die quantenmechanische Gasentartung diskutieren, bei der das chemische Potential ebenfalls eine Rolle spielt. Wir werden feststellen, dass es nicht schwierig ist, einige Eigenschaften dieses interessanten Materiezustands zu verstehen. Wir behandeln das Thema bereits hier und nicht erst in der Quantenphysik am Ende des Buches, weil es in die Wärmelehre gehört und weil auf dieser Grundlage die elektrischen Eigenschaften von Metallen in Bd. III/9 leicht diskutiert werden können.

Enracinement or the earth, the originary ark, does not move: on the phenomenological (historical and ontogenetic) origin of common and scientific sense and the genetic method of teaching (for) understanding

NASA Astrophysics Data System (ADS)

Roth, Wolff-Michael

2015-06-01

For many students, the experience with science tends to be alienating and uprooting. In this study, I take up Simone Weil's concepts of enracinement (rooting) and déracinement (uprooting) to theorize the root of this alienation, the confrontation between children's familiarity with the world and unfamiliar/strange scientific conceptions. I build on the works of the phenomenological philosopher Edmund Husserl and the German physics educator Martin Wagenschein (who directly refers to Weil's concepts) to make a case for the rooting function of original/originary experiences and the genetic method to science teaching. The genetic approach allows students to retain their foundational familiarity with the world and their descriptions thereof all the while evolving other (more scientific) ways of explaining natural phenomena.

Tall sections from non-minimal transformations

DOE PAGES

Morrison, David R.; Park, Daniel S.

2016-10-10

In previous study, we have shown that elliptic fibrations with two sections, or Mordell-Weil rank one, can always be mapped birationally to a Weierstrass model of a certain form, namely, the Jacobian of a P 112 model. Most constructions of elliptically fibered Calabi-Yau manifolds with two sections have been carried out assuming that the image of this birational map was a “minimal” Weierstrass model. In this paper, we show that for some elliptically fibered Calabi-Yau manifolds with Mordell-Weil rank-one, the Jacobian of the P 112 model is not minimal. Said another way, starting from a Calabi-Yau Weierstrass model, the totalmore » space must be blown up (thereby destroying the “Calabi-Yau” property) in order to embed the model into P 112. In particular, we show that the elliptic fibrations studied recently by Klevers and Taylor fall into this class of models.« less

Destruction of the hepatocyte junction by intercellular invasion of Leptospira causes jaundice in a hamster model of Weil's disease.

PubMed

Miyahara, Satoshi; Saito, Mitsumasa; Kanemaru, Takaaki; Villanueva, Sharon Y A M; Gloriani, Nina G; Yoshida, Shin-ichi

2014-08-01

Weil's disease, the most severe form of leptospirosis, is characterized by jaundice, haemorrhage and renal failure. The mechanisms of jaundice caused by pathogenic Leptospira remain unclear. We therefore aimed to elucidate the mechanisms by integrating histopathological changes with serum biochemical abnormalities during the development of jaundice in a hamster model of Weil's disease. In this work, we obtained three-dimensional images of infected hamster livers using scanning electron microscope together with freeze-cracking and cross-cutting methods for sample preparation. The images displayed the corkscrew-shaped bacteria, which infiltrated the Disse's space, migrated between hepatocytes, detached the intercellular junctions and disrupted the bile canaliculi. Destruction of bile canaliculi coincided with the elevation of conjugated bilirubin, aspartate transaminase and alkaline phosphatase levels in serum, whereas serum alanine transaminase and γ-glutamyl transpeptidase levels increased slightly, but not significantly. We also found in ex vivo experiments that pathogenic, but not non-pathogenic leptospires, tend to adhere to the perijunctional region of hepatocyte couplets isolated from hamsters and initiate invasion of the intercellular junction within 1 h after co-incubation. Our results suggest that pathogenic leptospires invade the intercellular junctions of host hepatocytes, and this invasion contributes in the disruption of the junction. Subsequently, bile leaks from bile canaliculi and jaundice occurs immediately. Our findings revealed not only a novel pathogenicity of leptospires, but also a novel mechanism of jaundice induced by bacterial infection. © 2014 The Authors. International Journal of Experimental Pathology © 2014 International Journal of Experimental Pathology.

76 FR 22078 - Sunshine Act Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2011-04-20

.... Richard Lobo, Director of the International Broadcasting Bureau. Maryjean Buhler, BBG Chief Financial Officer. Paul Kollmer-Dorsey, BBG Deputy General Counsel. Lynne Weil, Senior Advisor to the Under Secretary for Public Diplomacy and Public Affairs. Oanh Tran, BBG Special Projects Officer. CONTACT PERSON...

Multiobjective Topology Optimization of Energy Absorbing Materials

DTIC Science & Technology

2015-08-01

absorbing liner for equestrian helmets. Part I: layered foam liner . Mater Des 30(9):3405–3413 Sethian J, Wiegmann A (2000) Structural boundary design via...Army Research Laboratory Wildman RA, Weile DS (2007) Geometry reconstruction of conduct- ing cylinders using genetic programming. IEEE Trans Antennas

[Spotted fever and the invention of its serodiagnosis and vaccination in the Austro-Hungarian army in World War I].

PubMed

Flamm, Heinz

2015-04-01

After description of the medical institutions and epidemiological situations of the Austro-Hungarian army in World War I the provisions against spotted fever focused on louse control are discussed. The letter specified for the army had to be adjusted for the local populations. 1915 in the k.u.k. military service in Galicia Edmund Weil and Arthur Felix cultivated Proteus strains from urine of soldiers with spotted fever. As sera of such patients agglutinated these bacteria in considerable titers the investigators developed the reliable diagnostic "Weil-Felix-Test" used still today. In the same military area and time Rudolf Weigl invented the anal infection of lice. This enabled him to harvest a great amount of louse intestines containing the spotted fever Rickettsiae in their epithelial cells. Lots with defined numbers of intestines were homogenized, sterilized and used with success as vaccine for medical staff. This sort of vaccine still was used in World War II.

Musical Hunger: A Philosophical Testimonial of Miseducation

ERIC Educational Resources Information Center

Laird, Susan

2009-01-01

Reflecting upon Simone Weil's conception of beauty as food, this essay proposes musical hunger as a metaphoric way of understanding a particular species of "cultural miseducation" as conceived by Jane Roland Martin, that disadvantages children musically and perhaps therefore also spiritually. It examines such musical miseducation with regard to an…

Stem Cell-Based Therapies for Epidermolysis Bullosa

DTIC Science & Technology

2014-10-01

of human hematopoietic cells for extracellular matrix protein deficiency in epidermolysis bullosa. Stem Cells 2011, 29:900–906. 18. Di Nicola M...promotes cardiogenic gene expression in mesenchymal stem cells. Stem Cell Res Ther 2013, 4:43. 57. Herrmann JL, Wang Y, Abarbanell AM, Weil BR, Tan J

Moral Attention: A Comparative Philosophical Study

ERIC Educational Resources Information Center

Gendron, Claude

2016-01-01

The notion of moral attention allows the recognition of fundamental aspects of ethical life ignored or neglected by mainstream ethical theories. It is central to the theories of several notable female ethicists and many of them identify the French philosopher Simone Weil as the source of the contemporary use of this concept which invites…

Long-term effects of wetland harvesting practices on productivity and carbon pools

Treesearch

Scott McKee; Mike Aust; John Seiler; Brian Strahm

2012-01-01

Forested wetlands are valued for social and ecological benefits including filtering sediments, uptake of nutrients, carbon storage, reduction of flood depths, protection of shorelines and streambanks, and provision of terrestrial and aquatic wildlife habitat (Walbridge 1993, Kellison and Young 1997, Brady and Weil 2002). Although the importance of wetland functions are...

Private Philanthropy and Basic Research in Mid-Twentieth Century America: The Hickrill Chemical Research Foundation.

PubMed

Gortler, Leon; Weininger, Stephen J

2017-02-01

The Hickrill Chemical Research Foundation, located north of New York City on the estate of its patrons, Sylvan and Ruth Alice Norman Weil, had a short (1948-59) but productive life. Ruth Alice Weil received a Ph.D. in organic chemistry in 1947, directed by William von Eggers Doering of Columbia University. She intended that Hickrill contribute to cancer chemotherapy while providing resources for Doering's more speculative research. Ultimately, Doering's commitment to theoretical organic chemistry set Hickrill's research agenda. Lawrence Knox, an African American with a Harvard Ph.D., supervised the laboratory's daily activities. Hickrill's two dozen postdoctoral fellows produced path-breaking results in Hückel aromatic theory and reactive intermediate chemistry, fostering the postwar emphasis on "basic science." This essay places the Laboratory's successes in the wider context of postwar politics and scientific priorities. Private philanthropic support of basic science arose because it received little pre-World War II government support. In the immediate postwar period, modest organisations like Hickrill still met a need, but the increasing governmental defence- and non-defence-related support for science eventually rendered them unnecessary.

Leptospirosis in South-western Spain.

PubMed

Rodríguez-Vidigal, F F; Vera-Tomé, A; Nogales-Muñoz, N; Muñoz-García-Borruel, M; Muñoz-Sanz, A

2014-01-01

Leptospirosis is a zoonosis of worldwide distribution and tropical predominance. Its incidence could be underestimated in template regions. We describe the manifestations of leptospirosis in an area of Southwestern Spain. Eighty-six cases of leptospirosis (April 1997-April 2013) were retrospectively analyzed. The diagnosis was based in clinical and serological (Leptospira IgM ELISA) judgement. Epidemiological, clinical, laboratory, and prognostic dates were recorded. The mean age was 43.1 ± 13.8 years (84.9% males). The mean annual incidence was 1.99/100.000. There were activities of risk in 94%: 82.5% contact with animals (57.4% pigs, 38.1% dogs, 31.7% cows, 22.2% sheeps), and 31.7% contact with pooled water. The most frequent symptoms were fever (94.1%), arthromyalgias (60.7%), and cephalalgia (53.3%). The main laboratory alterations were hypertransaminemia (48%), renal insufficiency (26.3%), and thrombocytopenia (16.9%). A lymphocytic meningitis was associated in 11 cases (12.5%) and a picture of Weil's disease was observed in 13 patients (15.1%). The patients with meningitis were younger (31.2 ± 9.2 versus 44.8 ± 15.2, p=0.004). The patients with Weil's disease were older (53.5 ± 15.8 versus 41.2 ± 14.5, p=0.007). Fifty seven patients were hospitalized (66.3%) and 6 patients died (7.0%). Factors independently associated with mortality were age >60 years (odds ratio [OR] 45.0, confidence interval 95% [CI95%] 4.7-434.6) and diagnosis of Weil's disease (OR 15.8, CI95% 2.5-98.7). In our experience, leptospirosis have a not despicable incidence and tends to show fever and arthromyalgias in men with risk activities. Leptospirosis should be included in the differential diagnosis of lymphocytic meningitis. Mortality is associated with older age. Copyright © 2013 Elsevier España, S.L. All rights reserved.

Contemplation, Attention, and the Distinctive Nature of Catholic Education

ERIC Educational Resources Information Center

Van Nieuwenhove, Rik

2016-01-01

Catholic education should be primarily understood in terms of the contemplative disposition it fosters among students, i.e., a theocentric focus of knowing and loving God, rather than in terms of values. This argument will be developed by drawing on the Thomist understanding of contemplation (as knowing and loving God), and Simone Weil's notion of…

A Health Plan to Reduce Poverty

ERIC Educational Resources Information Center

Weil, Alan

2007-01-01

Noting that the failures of the U.S. health care system are compounding the problems faced by low-income Americans, Alan Weil argues that any strategy to reduce poverty must provide access to health care for all low-income families. Although nearly all children in families with incomes under 200 percent of poverty are eligible for either Medicaid…

The competitive health care marketplace: bringing new challenges to a changing field.

PubMed

Jeppson, D H

1986-07-01

This article, in response to Dr. Weil's article (beginning on page 4), explores the changing health care industry from a different perspective. Stressed here is the need fro hospitals to join an integrated regional network of providers. Also discussed is the responsibility of not-for-profit hospitals to provide indigent care, despite the trend toward prepaid, discounted health plans.

Improving the Signal for U.S. Navy Officer Productivity

DTIC Science & Technology

2014-12-01

American Economic Review, 93(1), 216–240. Retrieved from http://www.jstor.org/stable/3132169 Mankiw , G., Romer, D., & Weil, D. (1992). A contribution...individual perfonnance appraisal system to optimally signal officer productivity. This paper utilizes the economics literature on individual perfonnance...signal officer productivity. This paper utilizes the economics literature on individual performance appraisals and promotion systems as the lens

The Effect of Education on Economic Growth in Greece over the 1960-2000 Period

ERIC Educational Resources Information Center

Tsamadias, Constantinos; Prontzas, Panagiotis

2012-01-01

This paper examines the impact of education on economic growth in Greece over the period 1960-2000 by applying the model introduced by Mankiw, Romer, and Weil. The findings of the empirical analysis reveal that education had a positive and statistically significant effect on economic growth in Greece over the period 1960-2000. The econometric…

"Weil Man da Uber Seine Probleme Reden Kann . . ." Partielle Geschlechtertrennung aus der Sicht der Schulerinnen und Schuler ("Because There, You can Talk about Your Problems . . ." Partial Separation by Gender from the Perspective of Male and Female Students).

ERIC Educational Resources Information Center

Biskup, Claudia; Pfister, Gertrud; Robke, Cathrin

1998-01-01

Examines the results of interviews with elementary school children that gauged the attitudes towards and reasons for a partial separation by gender. Proposes an occassional separation of girls and boys for special pedogogical intervention. Discusses the findings. (CMK)

Transfer Learning in Integrated Cognitive Systems

DTIC Science & Technology

2010-09-01

Psychology Press. 2. Falkenhainer, B ., Forbus, K . D., and Gentner, D. (1989). The Structure-mapping Engine: Algorithm and Examples. Artificial...Kaps, A.; Lemcke, K .; Mannhaupt, G.; Pfeiffer, F.; Schuller, C.; Stocker, S. & Weil, B ., "MIPS: A Database for Genomes and Protein Sequences...NAME OF RESPONSIBLE PERSON Deborah A. Cerino a. REPORT U b . ABSTRACT U c. THIS PAGE U 19b. TELEPHONE NUMBER (Include area code) N/A

"Enracinement" or the Earth, the Originary Ark, Does Not Move: On the Phenomenological (Historical and Ontogenetic) Origin of Common and Scientific Sense and the Genetic Method of Teaching (For) Understanding

ERIC Educational Resources Information Center

Roth, Wolff-Michael

2015-01-01

For many students, the experience with science tends to be alienating and uprooting. In this study, I take up Simone Weil's concepts of "enracinement" (rooting) and "déracinement" (uprooting) to theorize the root of this alienation, the confrontation between children's familiarity with the world and unfamiliar/strange…

Installation Restoration Program. Phase 2. Confirmation/Quantification. Stage 1. Air Force Plant 4, Fort Worth, Texas. Volume 9. Appendices F-K.

DTIC Science & Technology

1987-12-01

mineralogy and igneous petrology . Consultant to Shield Energy. Inc.; performed mudlogging and well site geology duties on 4,670’ wildcat weil in...Taylor County, Texas. Evaluated prospects for hydrocarbon potential. Prepared geologic reports for drilling prospectus. Geologist, Wold Minerals...Exploration Company; conducted geologic and geophysi- cal mapping in Precambrian metamorphic terrain of West Texas for talc depos- its. Supervised the drilling

Radioactivity of the Cooling Water

DOE R&D Accomplishments Database

Wigner, E. P.

1943-03-01

The most important source of radioactivity at the exit manifold of the pile will be due to O{sup 19}, formed by neutron absorption of O{sup 18}. A recent measurement of Fermi and Weil permits to estimate that it will be safe to stay about 80 minutes daily close to the exit manifolds without any shield. Estimates are given for the radioactivities from other sources both in the neighborhood and farther away from the pile.

Nation Building as a Determinent of Economic Growth

DTIC Science & Technology

2010-05-18

Consortium for Political and Social Reserch (2007). Mankiw , N. Gregory, David Romer, and David N. Weil. “A Contribution to the Empirics of Economic Growth...Determinent of Economic Growth 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6 . AUTHOR(S) 5d. PROJECT NUMBER Creasey. Ellyn Ann 5e. TASK NUMBER 51...J ss istance and econom ic aid impact the development process. The primary resu lts suggest a 1% increase in spending on nation building result s

Block-circulant matrices with circulant blocks, Weil sums, and mutually unbiased bases. II. The prime power case

DOE Office of Scientific and Technical Information (OSTI.GOV)

Combescure, Monique

2009-03-15

In our previous paper [Combescure, M., 'Circulant matrices, Gauss sums and the mutually unbiased bases. I. The prime number case', Cubo A Mathematical Journal (unpublished)] we have shown that the theory of circulant matrices allows to recover the result that there exists p+1 mutually unbiased bases in dimension p, p being an arbitrary prime number. Two orthonormal bases B, B{sup '} of C{sup d} are said mutually unbiased if for all b(set-membership sign)B, for all b{sup '}(set-membership sign)B{sup '} one has that |b{center_dot}b{sup '}|=1/{radical}(d) (b{center_dot}b{sup '} Hermitian scalar product in C{sup d}). In this paper we show that the theorymore » of block-circulant matrices with circulant blocks allows to show very simply the known result that if d=p{sup n} (p a prime number and n any integer) there exists d+1 mutually unbiased bases in C{sup d}. Our result relies heavily on an idea of Klimov et al. [''Geometrical approach to the discrete Wigner function,'' J. Phys. A 39, 14471 (2006)]. As a subproduct we recover properties of quadratic Weil sums for p{>=}3, which generalizes the fact that in the prime case the quadratic Gauss sum properties follow from our results.« less

Non-Destructive Impermeability Testing of Land-Based Sewage Systems (zerstoerungsfreie dichtheitspruefung con grundstuecksentwaesserungsleitungen)

DTIC Science & Technology

2001-01-01

CYberdeckungsh6he zunehmen. Ffr die Stabilitdt des Str ~mungszustandes ist dagegen ein weniger empfindlicher Ansaugstutzen von Vorteil, weil geringe Schwankungen im...Gerinnestr() mung mit einem Laser-Doppler- Anemometer und einem Pitot-Rohr Ltd. BD Dipl.-Ing. B. Ftirmaier M6glichkeiten der Verwertung von HausmUll und...GrundstticksentwAsserungsleitungen ISBN 3-486-26517-2 * diese Hefte k6nnen beim Oldenbourg Industrieverlag GmbH, Rosenheimer Str . 145, 81671 MUnchen bezogen werden (Preis pro Heft: 35,00 DM, Stand 2001)

Fever, jaundice and acute renal failure.

PubMed

O'Toole, Sam M; Pathak, Neha; Toms, Graham C; Gelding, Susan V; Sivaprakasam, Venkat

2015-02-01

Leptospirosis is an uncommon infectious disease that has protean clinical manifestations ranging from an innocuous 'flu-like' illness to potentially life-threatening multi-organ failure. Here we describe a case of Weil's disease that presented on the acute medical take with fever, jaundice and acute renal failure. We highlight the importance of careful history taking at the time of admission and how understanding the epidemiology and pathophysiology of leptospirosis enables a definitive diagnosis to be reached. © 2015 Royal College of Physicians.

Water Resources Data, California, Water Year 1989. Volume 5. Ground-Water Data

USGS Publications Warehouse

Lamb, C.E.; Johnson, J.A.; Fogelman, R.P.; Grillo, D.A.

1990-01-01

Water resources data for the 1989 water year for California consist of records of stage, discharge, and water quality of streams; stage and contents in lakes and reservoirs; and water levels and water quality in weils. Volume 5 contains water levels for 1,037 observation wells and water-quality data for 254 monitoring wells. These data represent that part of the National Water Data System operated by the U.S. Geological Survey and cooperatine State and Federal agencies in California.

General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure

DOE PAGES

Cvetic, Mirjam; Klevers, Denis; Piragua, Hernan; ...

2015-11-30

We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)×U(1) gauge symmetry. Generic U(1)×U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)×SU(2)×SU(3), SU(2) 3×SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. Wemore » give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. In conclusion, the construction suggests a generalization to U(1) k factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups.« less

[Lesser toe deformities. Definition, pathogenesis, and options for surgical correction].

PubMed

Arnold, H

2005-08-01

Whereas in the past resection arthroplasty was - in analogy to hallux valgus surgery - the preferred therapy to correct lesser toe deformities, the point of view has undergone a change. Much interest is directed toward functional aspects that require reconstructive management. Whenever possible the integrity of joint play should be saved. Above all the metatarsophalangeal joint of the lesser toes is worth being preserved to prevent a severe disturbance of the biomechanics of the foot. Tendon transfers and subtle corrective osteotomies such as the Weil procedure allow restricting resection procedures to contraction deformities.

Fifth Metatarsal Osteotomies.

PubMed

Weil, Lowell; Consul, Devon

2015-07-01

A tailor's bunion or bunionette deformity is a combination of osseous and soft tissue bursitis on the lateral aspect of the fifth metatarsal head. This article discusses 7 corrective measures: medial oblique sliding osteotomy with fixation, medial oblique slide osteotomy-minimal incision procedure without fixation, SERI (simple, effective, rapid, inexpensive) with fixation, chevron with or without fixation, closing, lateral wedge osteotomy at the metatarsal neck or proximal diaphysis, Weil osteotomy, and scarfette. These evidence-based techniques can be used by practitioners for medical management of their patients through evaluation, diagnosis, and prognosis. Complications are also addressed. Copyright © 2015 Elsevier Inc. All rights reserved.

Metatarsal Osteotomies: Complications.

PubMed

Reddy, Veerabhadra Babu

2018-03-01

Metatarsal osteotomies can be divided into proximal and distal. The proximal osteotomies, such as the oblique, segmental, set cut, and Barouk-Rippstein-Toullec (BRT) osteotomy, all provide the ability to significantly change the position of the metatarsal head without violating the joint. These osteotomies, however, have a high rate of nonunion when done without internal fixation and can lead to transfer metatarsalgia when done without regard to the parabola of metatarsal head position. Distal osteotomies such as the Weil and Helal offer superior healing but have an increased incidence of recurrent metatarsalgia, joint stiffness, and floating toe. Copyright © 2017 Elsevier Inc. All rights reserved.

Origin of Abelian gauge symmetries in heterotic/F-theory duality

DOE PAGES

Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; ...

2016-04-07

Here, we study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, and also derive both the Calabi-Yau geometry and the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in theirmore » low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. And while the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stuckelberg mechanism in the lower-dimensional effective theory. Finally, in geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.« less

Atomic Basic Blocks

NASA Astrophysics Data System (ADS)

Scheler, Fabian; Mitzlaff, Martin; Schröder-Preikschat, Wolfgang

Die Entscheidung, einen zeit- bzw. ereignisgesteuerten Ansatz für ein Echtzeitsystem zu verwenden, ist schwierig und sehr weitreichend. Weitreichend vor allem deshalb, weil diese beiden Ansätze mit äußerst unterschiedlichen Kontrollflussabstraktionen verknüpft sind, die eine spätere Migration zum anderen Paradigma sehr schwer oder gar unmöglich machen. Wir schlagen daher die Verwendung einer Zwischendarstellung vor, die unabhängig von der jeweils verwendeten Kontrollflussabstraktion ist. Für diesen Zweck verwenden wir auf Basisblöcken basierende Atomic Basic Blocks (ABB) und bauen darauf ein Werkzeug, den Real-Time Systems Compiler (RTSC) auf, der die Migration zwischen zeit- und ereignisgesteuerten Systemen unterstützt.

A risk hedging strategy under the nonparallel-shift yield curve

NASA Astrophysics Data System (ADS)

Gong, Pu; He, Xubiao

2005-08-01

Under the assumption of the movement of rigid, a nonparallel-shift model in the term structure of interest rates is developed by introducing Fisher & Weil duration which is a well-known concept in the area of interest risk management. This paper has studied the hedge and replication for portfolio immunization to minimize the risk exposure. Throughout the experiment of numerical simulation, the risk exposures of the portfolio under the different risk hedging strategies are quantitatively evaluated by the method of value at risk (VaR) order statistics (OS) estimation. The results show that the risk hedging strategy proposed in this paper is very effective for the interest risk management of the default-free bond.

The Epidemiology of Weil's Disease

PubMed Central

Alston, J. M.; Brown, H. C.

1937-01-01

Adolf Weil defined the disease as a clinical entity in 1886, and Leptospira ictero-hæmorrhagiæ was found to be the causative organism in 1915 by Inada et al. in Japan, and confirmed by Hübener and Reiter in Germany. The infection has been found in most countries, and recently there has been a great increase in the number of instances reported. In most parts of the world rats and other small rodents harbour the organism and excrete it in the urine. This is almost always the direct or indirect source of infection of man, but natural infection of dogs and foxes takes place, and is at least a potential danger to human beings. Infection is usually related to occupation in coal-mines, field work of all sorts, sewers, fish-cleaning, and to bathing in fresh water. The organism quickly dies in an acid medium, in strong sunlight and in salt water. These facts accord with the presence of the disease in certain situations. The route of infection of man is usually by contact of the abraded or sodden skin with infected mud or water, but it may be by inhalation of water and by bites of rats, dogs, and ferrets. Men are much more exposed to infection than women, but in fish-cleaners the incidence is equal in the sexes. Children are sometimes infected by bathing and in houses. The incubation time may be four to nineteen days, and is usually seven to thirteen days. By serological methods many unjaundiced and subclinical infections can be detected among people who are often at risk, and these correct the rather high fatality rates which are derived from jaundiced cases only. During the last three and a half years 142 authenticated instances of the disease in an obvious clinical form have been reported in the British Isles. Twenty-one occupations or circumstances were involved, and the case fatality rate was 15 per cent. ImagesFig. 1Fig. 2Fig. 3 PMID:19991094

[Clinical features of four atypical pediatric cases of endemic typhus with pneumonia].

PubMed

Liu, Jin-rong; Xu, Bao-ping; Li, Shao-gang; Liu, Jun; Tian, Bao-lin; Zhao, Shun-ying

2013-10-01

To analyze clinical manifestations, treatment and prognosis of 4 cases with endemic typhus. The clinical data of four endemic typhus patients in prognosis were retrospectively analyzed. These four atypical cases of endemic typhus with pneumonia were treated in our department from October 2011 to March 2012. They were all male, with an age range of 15 months to 7 years. The four patients had long history, mild respiratory symptom and no improvement was found after treatment with cephalosporins. There were no evidences of bacterial, viral, or fungal infections and we thought they might have infection with other pathogen. Three were from rural areas. Routine blood tests, Weil-Felix reaction, blood smear (Giemsa staining) , and indirect immunofluorescence assay were performed. Blood smear and IFA tests showed evidences for endemic typhus. The clinical presentations were atypical, the patients had no headache, but all had fever, rash, and pneumonia of varying severity. None of the patients had a severe cough, but bronchial casts were observed in one case. Recurrent fever was reported in three cases. Physical examinations showed no eschars, but one patient had a subconjunctival hemorrhage, and one had skin scratches, cervical lymphadenopathy, pleural effusion, pericardial effusion, and cardiac dilatation. Two patients had remarkably increased peripheral blood leukocyte counts; both these patients also had high alanine aminotransferase (ALT) levels and one had a high C-reactive protein (CRP) level. Weil-Felix testing was negative or the OX19 titer was low. The peripheral blood smear (Giemsa stain) showed intracellular pathogens in all four cases. After combined therapy with doxycycline and macrolide antibiotics, all four patients recovered well. The endemic typhus children often come from rural areas. The clinical presentations were atypical, they usually have no headache, but have fever (often Periodic fever) , rash, and pneumonia of varying severity in these four cases. Combined therapy with doxycycline and macrolide antibiotics was effective in all four patients.

Abundance & distribution of trombiculid mites & Orientia tsutsugamushi, the vectors & pathogen of scrub typhus in rodents & shrews collected from Puducherry & Tamil Nadu, India.

PubMed

Candasamy, Sadanandane; Ayyanar, Elango; Paily, Kummankottil; Karthikeyan, Patricia Anitha; Sundararajan, Agatheswaran; Purushothaman, Jambulingam

2016-12-01

Human cases of scrub typhus are reported every year from Puducherry and adjoining areas in southern India. However, information on the presence of causative agent, Orientia tsutsugamushi, and its vectors is lacking. Hence, the objective of the study was to find out the vector as well as pathogen distribution in rodents and shrews present in the scrub typhus-reported areas in southern India. Trombiculid mites were collected by combing rats and shrews collected using Sherman traps and identified to species level following standard taxonomical keys. The serum samples of the animals were used for Weil-Felix test and the clots containing blood cells were used for DNA extraction and polymerase chain reaction (PCR). A total of 181 animals comprising four rodent species and one shrew species were collected from 12 villages. High proportion of chiggers was collected from the shrew, Suncus murinus (79.1%) and Rattus rattus (47.6%). A total of 10,491 trombiculid mites belonging to nine species were collected. Leptotrombidium deliense, the known vector of scrub typhus pathogen, was the predominant species (71.0%) and the chigger (L. deliense) index was 41.1 per animal. Of the 50 animals screened for the pathogen, 28 showed agglutination against OX-K in Weil-Felix test indicating the presence of antibodies against O. tsutsugamushi, the causative agent of scrub typhus. PCR carried out with the DNA extracted from blood samples of two of the animals were positive for GroEl gene of O. tsutsugamushi. L. deliense index was well above the critical limit of chigger load, indicating that all the villages were receptive for high risk of transmission of scrub typhus to human. Pathogen positivity was higher among animals collected from villages recorded for higher chigger indices due to active transmission between the chigger mites and reservoir host animals. The results are suggestive of routine vector/pathogen surveillance at hot spots to initiate timely preventive measures.

Der Organismus der Mathematik - mikro-, makro- und mesoskopisch betrachtet

NASA Astrophysics Data System (ADS)

Winkler, Reinhard

Meist enden ähnliche Gespräche über Mathematik etwa an diesem Punkt, ohne dass der Nichtmathematiker von der Sinnhaftigkeit mathematischer Forschung, ja mathematischer Tätigkeit generell überzeugt werden konnte. Ich glaube nicht, dass dem Laien Blindheit für die Großartigkeit unserer Wissenschaft vorzuwerfen ist, wenn hier keine befriedigendere Kommunikation zustande kommt. Ich sehe als Ursache eher ein stark verkürztes Bild von der Mathematik, welches auch Fachleute oft zeichnen, weil ihnen eine angemessenere Darstellung ihres Faches zu viel Mühe macht - und das obwohl Mathematik nur betreiben kann, wer geistige Mühen sonst keineswegs scheut. Ich will versuchen, den Ursachen dieses eigentümlichen Phänomens auf den Grund zu gehen.

SOME DUALITY THEOREMS FOR CYCLOTOMIC \\Gamma-EXTENSIONS OF ALGEBRAIC NUMBER FIELDS OF CM TYPE

NASA Astrophysics Data System (ADS)

Kuz'min, L. V.

1980-06-01

For an odd prime l and a cyclotomic \\Gamma{-}l-extension k_\\infty/k of a field k of CM type, a compact periodic \\Gamma-module A_l(k), analogous to the Tate module of a function field, is defined. The analog of the Weil scalar product is constructed on the module A_l(k). The properties of this scalar product are examined, and certain other duality relations are determined on A_l(k). It is proved that, in a finite l-extension k'/k of CM type, the \\mathbf{Z}_l-ranks of A_l(k) and A_l(k') are connected by a relation similar to the Hurwitz formula for the genus of a curve.Bibliography: 7 titles.

Soils: An Introduction, Fifth Edition

NASA Astrophysics Data System (ADS)

Baisden, W. Troy

Understanding the links among global biogeochemical cycles, ecology, hydrology and climate demands a knowledge base that has traditionally been considered soil science. However, for soil science to play a role in this understanding, geologists, hydrologists, ecologists, climatologists, and many others must have a fundamental understanding of soil science. Do introductory soil science texts speak to this audience?To address this question, I reviewed the fifth edition of a textbook that set out in its original edition to accomplish just this goal—to be the introductory soil science text for students outside the discipline of soil science. As such, Singer and Munns' Soils:An Introduction must be compared to The Nature and Properties of Soils by N.C. Brady and R.R. Weil, a standard text directly descended from a first edition published in 1922.

Weil's Disease from a Local New Orleans Bar.

PubMed

Kahn, H P; Bateman, L

2017-01-01

Leptospirosis is a zoonotic infection that typically presents with fever, myalgias, nausea, and vomiting after contact with contaminated waters or infected animals (typically rodents); and their excrements. Conditions favorable to the transmission of leptospirosis are common in LA and, without treatment, leptospirosis can lead to both liver and renal failure, meningitis, pulmonary hemorrhage and ultimately death. A 56 year old woman with no past medical history presented to the Emergency Department with weakness, myalgias, jaundice and decreased urine output for one week. On arrival, she appeared septic with a heart rate of 130 and fever. Her exam was significant for significant jaundice and diffuse abdominal pain. Laboratory studies were notable for WBC 14, hemoglobin of 12 and platelet count of 63. Creatinine was 8.5mg/dL with a blood-urea nitrogen of 96mg/dl. Total bilirubin was 19.4mg/dL and direct bilirubin was 13.7mg/dL. AST/ALT were 69/38 U/L, respectively and the alkaline phosphate was 160U/L. The patient was admitted to the hospital medicine wards for sepsis and multi-organ failure. She was started on broad spectrum antibiotics but her clinical condition continued to worsen with progressive decline in her hemoglobin and thrombocytopenia and worsening liver failure. She quickly became anuric necessitating dialysis and developed respiratory distress with bilateral pulmonary infiltrates and hemoptysis. Additional history was obtained from her employer that she works at a local New Orleans bar and had been cleaning out rats from the kitchen. Leptospirosis antibody was sent, which returned as positive. Her antibiotics were de-escalated to IV Ceftriaxone. She made a slow recovery over the next two-week period. Since 1987, there has been an average of 3 cases of Leptospirosis diagnosed per year, most of which have been from southeast LA. This case illustrates the importance of considering the diagnosis of Leptospirosis and Weil's Disease in patients in the southeast region of LA who present with multi-organ failure. In addition, our patient's occupational exposure was key to her diagnosis which emphasizes the importance of a detailed history in clinical decision making and patient outcomes.

[Melorheostosis of the foot: a case report of a rare entity].

PubMed

Craiovan, B; Zeiler, G; Delling, G; Schuh, A

2006-12-01

Melorheostosis is a rare bony dysplasia and often recognised just sporadically by chance. We present a case of a 15 year old girl who presented a melorheostosis of the left foot. After birth there was recognized a shortening and deformity of the 2nd toe on the left foot. Furthermore she had an interphalangeal hallux valgus that displaced the 2nd toe increasingly. Thus in the last years there were more and more difficulties to wear normal shoes. Conservative therapy was not successful. We performed a lengthening extending osteotomy of the 2nd toe (a modified Weil osteotomy) and an Akin osteotomy of the interphalangeal hallux valgus. Since the surgical procedure the patient is out of any complaints. We demonstrate the radiologic and histologic findings and discuss the relevant literature and possible etiology.

Cryptococcal meningitis in an immunocompetent child: a case report and literature review.

PubMed

Othman, Norlijah; Abdullah, Nor Atiqah Ng; Wahab, Zubaidah Abdul

2004-12-01

An immunocompetent 5 year-old girl presented with pyrexia of unknown origin associated with headache. Initial investigations showed leukocytosis and an increased erythrocyte sedimentation rate. A Widal-Weil Felix test, blood film for malarial parasites, mycoplasma IgM antibody, cultures from blood and urine, full blood picture, Mantoux test, and chest x-ray were all negative. A lumbar puncture was done as part of a work-up for pyrexia of unknown origin. Cryptococcus neoformans was seen on India ink examination and confirmed on culture. She was treated with 10 weeks of intravenous amphotericin B and 8 weeks of fluconazole. Further immunological tests did not reveal any defect in the cell-mediated immune system. C. neoformans meningitis may present with non-specific symptoms and should be considered in a work-up for pyrexia of unknown origin.

Diagnosis of scrub typhus.

PubMed

Janardhanan, Jeshina; Trowbridge, Paul; Varghese, George M

2014-12-01

Scrub typhus is an acute febrile illness that, if untreated, can result in considerable morbidity and mortality. One of the primary reasons for delays in the treatment of this potentially fatal infection is the difficulty in diagnosing the condition. Diagnosis is often complicated because of the combination of non-specific symptoms that overlap with other infections commonly found in endemic areas and the poor available diagnostics. In the majority of the endemic settings, diagnosis still relies on the Weil-Felix test, which is neither sensitive nor specific. Other methods of testing have become available, but at this time, these remain insufficient to provide the rapid point-of-care diagnostics that would be necessary to significantly change the management of this infection by providers in endemic areas. This article reviews the currently available diagnostic tools for scrub typhus and their utility in the clinical setting.

Oxidative Stress Markers Correlate with Renal Dysfunction and Thrombocytopenia in Severe Leptospirosis

PubMed Central

Araújo, Alan M.; Reis, Eliana A. G.; Athanazio, Daniel A.; Ribeiro, Guilherme S.; Hagan, José E.; Araujo, Guilherme C.; Damião, Alcineia O.; Couto, Nicolli S.; Ko, Albert I.; Noronha-Dutra, Alberto; Reis, Mitermayer G.

2014-01-01

Leptospirosis is a zoonotic disease that causes severe manifestations such as Weil's disease and pulmonary hemorrhage syndrome. The aim of this study was to evaluate whether reactive oxygen species (ROS) production and antioxidant reduced glutathione (GSH) levels are related to complications in patients hospitalized with leptospirosis. The ROS production and GSH levels were measured in blood samples of 12 patients and nine healthy controls using chemiluminescence and absorbance assays. We found that ROS production was higher and GSH levels were lower in leptospirosis patients compared with healthy individuals. Among patients, GSH depletion was correlated with thrombocytopenia and elevated serum creatinine, whereas a strong positive correlation was observed between ROS production and elevated serum potassium. Additional investigation of the biological significance of ROS production and GSH levels is warranted as they may guide the development of novel adjuvant therapies for leptospirosis targeting oxidative stress. PMID:24493675

Geometric and Topological Methods for Quantum Field Theory

NASA Astrophysics Data System (ADS)

Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.

2013-05-01

Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.

Rocky Mountain spotted fever: a disease in need of microbiological concern.

PubMed Central

Walker, D H

1989-01-01

Rocky Mountain spotted fever, a life-threatening tick-transmitted infection, is the most prevalent rickettsiosis in the United States. This zoonosis is firmly entrenched in the tick host, which maintains the rickettsiae in nature by transovarian transmission. Although the incidence of disease fluctuates in various regions and nationwide, the problems of a deceptively difficult clinical diagnosis and little microbiologic diagnostic effort persist. Many empiric antibiotic regimens lack antirickettsial activity. There is neither an effective vaccine nor a generally available assay that is diagnostic during the early stages of illness, when treatment is most effective. Microbiology laboratories that offer only the archaic retrospective Weil-Felix serologic tests should review the needs of their patients. Research microbiologists who tackle these challenging organisms have an array of questions to address regarding rickettsial surface composition, structure-function analysis, and pathogenic and immune mechanisms, as well as laboratory diagnosis. PMID:2504480

Coherent states for quantum compact groups

NASA Astrophysics Data System (ADS)

Jurĉo, B.; Ŝťovíĉek, P.

1996-12-01

Coherent states are introduced and their properties are discussed for simple quantum compact groups A l, Bl, Cl and D l. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested.

Leptospira interrogans in Rodents from Cape Verde.

PubMed

Plata-Luis, Josué; Foronda, Pilar; Martín-Alonso, Aaron; Feliu, Carlos; Alves, Joana; Gil, Horacio; Valladares, Basilio

2016-11-01

Leptospirosis is an important worldwide zoonotic disease that can infect both animals and humans. In most cases, leptospirosis is a nonspecific self-limiting illness, but some patients can develop a severe form with a high mortality. This study was carried out in Santiago Island, Cape Verde, in 2012-2013. A total of 62 wild rodents (Rattus rattus and Mus domesticus) were analyzed. The lipL32 gene, present only in pathogenic Leptospira spp., was amplified by PCR, and 16 samples were positive (25.8%). In both rodent species, Leptospira interrogans was identified. The results show the presence of pathogenic Leptospira in the three localities analyzed in Santiago. The presence of L. interrogans demonstrates a serious health risk for the population, since this species has been associated with the most severe form of leptospirosis, the Weil's disease in humans, a severe infection with jaundice, renal failure, and hemorrhage.

Geometric engineering on flops of length two

NASA Astrophysics Data System (ADS)

Collinucci, Andrés; Fazzi, Marco; Valandro, Roberto

2018-04-01

Type IIA on the conifold is a prototype example for engineering QED with one charged hypermultiplet. The geometry admits a flop of length one. In this paper, we study the next generation of geometric engineering on singular geometries, namely flops of length two such as Laufer's example, which we affectionately think of as the conifold 2.0. Type IIA on the latter geometry gives QED with higher-charge states. In type IIB, even a single D3-probe gives rise to a nonabelian quiver gauge theory. We study this class of geometries explicitly by leveraging their quiver description, showing how to parametrize the exceptional curve, how to see the flop transition, and how to find the noncompact divisors intersecting the curve. With a view towards F-theory applications, we show how these divisors contribute to the enhancement of the Mordell-Weil group of the local elliptic fibration defined by Laufer's example.

PREFACE: Symmetries and Integrability of Difference Equations

NASA Astrophysics Data System (ADS)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane

2007-10-01

The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of Kent in Canterbury, UK (1996), in Sabaudia near Rome, Italy (1998), at the University of Tokyo, Japan (2000), in Giens, France (2002), and in Helsinki, Finland (2004). The SIDE VII meeting was held at the University of Melbourne from 10-14 July 2006. The scientific committee consisted of Nalini Joshi (The University of Sydney), Frank W Nijhoff (University of Leeds), Reinout Quispel (La Trobe University) and Colin Rogers (University of New South Wales). The local organization was in the hands of John A G Roberts and Wolfgang K Schief. Proceedings of all the previous SIDE meetings have been published; the 1994 and 1988 meetings (edited respectively by D Levi, L Vinet and P Winternitz, and by D Levi and O Ragnisco) as volumes of the CRM Proceedings and Lecture Notes (AMS Publications), the 1996 meeting (edited by P Clarkson and F W Nijhoff) as Volume 255 in the LMS Lecture Note Series. Starting from the 1996 meeting the formula of publication has been changed to include rather selected refereed contributions submitted in response to a call for papers issued after the meetings and not restricted to their participants. Thus publications reflecting the scope of the 1996 meeting (edited by J Hietarinta, F W Nijhoff and J Satsuma) appeared in Journal of Physics A: Mathematical and General 34 48 (special issue), and of the 1998 and 2000 meetings (edited respectively by F W Nijhoff, Yu B Suris and C-M Viallet, and by J F van Diejen and R Halburd) in Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2). The aim of this special issue is to benefit from the occasion offered by the SIDE VII meeting, producing an issue containing papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. This special issue features high quality research papers and invited reviews which deal with themes that were covered by the SIDE VII conference. These are in alphabetical order: Algebraic-geometric approaches to integrability. The first section contains a paper by T Hamamoto and K Kajiwara on hypergeometric solutions to the q-Painlevé equation of type A4(1). Discrete geometry. In this category there are three papers. J Cielinski offers a geometric definition and a spectral approach on pseudospherical surfaces on time scales, while A Doliwa considers generalized isothermic lattices. The paper by U Pinkall, B Springborn and S Weiss mann is concerned with a new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow. Integrable systems in statistical physics. Under this heading there is a paper by R J Baxter on corner transfer matrices in statistical mechanics, and a paper by S Boukraa, S Hassani, J-M Maillard, B M McCoy, J-A Weil and N Zenine where the authors consider Fuchs-Painlevé elliptic representation of the Painlevé VI equation. KP lattices and differential-difference hierarchies. In this section we have seven articles. C R Gilson, J J C Nimmo and Y Ohta consider quasideterminant solutions of a non-Abelian Hirota-Miwa equation, while B Grammaticos, A Ramani, V Papageorgiou, J Satsuma and R Willox discuss the construction of lump-like solutions of the Hirota-Miwa equation. J Hietarinta and C Viallet analyze the factorization process for lattice maps searching for integrable cases, the paper by X-B Hu and G-F Yu is concerned with integrable discretizations of the (2+1)-dimensional sinh-Gordon equation, and K Kajiwara, M Mazzocco and Y Ohta consider the Hankel determinant formula of the tau-functions of the Toda equation. Finally, V G Papageorgiou and A G Tongas study Yang-Baxter maps and multi-field integrable lattice equations, and H-Y Wang, X-B Hu and H-W Tam consider the two-dimensional Leznov lattice equation with self-consistent sources. Quantum integrable systems. This category contains a paper on q-extended eigenvectors of the integral and finite Fourier transforms by N M Atakishiyev, J P Rueda and K B Wolf, and an article by S M Sergeev on quantization of three-wave equations. Random matrix theory. This section contains a paper by A V Kitaev on the boundary conditions for scaled random matrix ensembles in the bulk of the spectrum. Symmetries and conservation laws. In this section we have five articles. H Gegen, X-B Hu, D Levi and S Tsujimoto consider a difference-analogue of Davey-Stewartson system giving its discrete Gram-type determinant solution and Lax pair. The paper by D Levi, M Petrera, and C Scimiterna is about the lattice Schwarzian KDV equation and its symmetries, while O G Rasin and P E Hydon study the conservation laws for integrable difference equations. S Saito and N Saitoh discuss recurrence equations associated with invariant varieties of periodic points, and P H van der Kamp presents closed-form expressions for integrals of MKDV and sine-Gordon maps. Ultra-discrete systems. This final category contains an article by C Ormerod on connection matrices for ultradiscrete linear problems. We would like to express our sincerest thanks to all contributors, and to everyone involved in compiling this special issue.

Population growth, interest rate, and housing tax in the transitional China

NASA Astrophysics Data System (ADS)

He, Ling-Yun; Wen, Xing-Chun

2017-03-01

This paper combines and develops the models in Lastrapes (2002) and Mankiw and Weil (1989), which enables us to analyze the effects of interest rate and population growth shocks on housing price in one integrated framework. Based on this model, we carry out policy simulations to examine whether the housing (stock or flow) tax reduces the housing price fluctuations caused by interest rate or population growth shocks. Simulation results imply that the choice of housing tax tools depends on the kind of shock that housing market faces. In the situation where the housing price volatility is caused by the population growth shock, the flow tax can reduce the volatility of housing price while the stock tax makes no difference to it. If the shock is resulting from the interest rate, the policy maker should not impose any kind of the housing taxes. Furthermore, the effect of one kind of the housing tax can be strengthened by that of the other type of housing tax.

The toric SO(10) F-theory landscape

NASA Astrophysics Data System (ADS)

Buchmüller, W.; Dierigl, M.; Oehlmann, P.-K.; Rühle, F.

2017-12-01

Supergravity theories in more than four dimensions with grand unified gauge symmetries are an important intermediate step towards the ultraviolet completion of the Standard Model in string theory. Using toric geometry, we classify and analyze six-dimensional F-theory vacua with gauge group SO(10) taking into account Mordell-Weil U(1) and discrete gauge factors. We determine the full matter spectrum of these models, including charged and neutral SO(10) singlets. Based solely on the geometry, we compute all matter multiplicities and confirm the cancellation of gauge and gravitational anomalies independent of the base space. Particular emphasis is put on symmetry enhancements at the loci of matter fields and to the frequent appearance of superconformal points. They are linked to non-toric Kähler deformations which contribute to the counting of degrees of freedom. We compute the anomaly coefficients for these theories as well by using a base-independent blow-up procedure and superconformal matter transitions. Finally, we identify six-dimensional supergravity models which can yield the Standard Model with high-scale supersymmetry by further compactification to four dimensions in an Abelian flux background.

Revisiting arithmetic solutions to the W =0 condition

NASA Astrophysics Data System (ADS)

Kanno, Keita; Watari, Taizan

2017-11-01

The gravitino mass is expected not to be much smaller than the Planck scale for a large fraction of vacua in flux compactifications. There is no continuous parameter to tune even by hand, and it seems that the gravitino mass can be small only as a result of accidental cancellation among period integrals weighted by integer-valued flux quanta. DeWolfe et al. [J. High Energy Phys. 02 (2005) 037, 10.1088/1126-6708/2005/02/037] proposed paying close attention to vacua where the Hodge decomposition is possible within a number field, so that the precise cancellation takes place as a result of algebra. We focus on a subclass of those vacua—those with complex multiplication—and explore more on the idea in this article. It turns out, in Type IIB compactifications, that those vacua admit nontrivial supersymmetric flux configurations if and only if the reflex field of the Weil intermediate Jacobian is isomorphic to the quadratic imaginary field generated by the axidilaton vacuum expectation value. We also found that flux statistics are highly enriched on such vacua, as F-term conditions become linearly dependent.

Effect of methylmercury on the rat mast cell degranulation

NASA Astrophysics Data System (ADS)

Graevskaya, E. E.; Yasutake, A.; Aramai, R.; Rubin, A. B.

2003-05-01

Methylmercury is the well-known neurotoxicant as weil as a modulator of the immune system. We investigated the effects of MeHg on the rat mast cell degranulation induced by nonimmunological stimuli (the selective liberator of histamine, compound 48/80, and calcium ionophore A23187) both in vivo and in vitro. In 8, 12 and 15 days afterthe final administration of MeHg we observed the suppression of calcium ionophore A23187-and 48/80-induced histamine release, which enhanced with time. In experiments in vitro incubation of peritoneal mast cells with MeHg alone in the dose range 10^{-8} to 10^{-6} did not induce mast cell degranulation, however modified the activation of mast cells by compound 48/80, and calcium ionophore A23187. We observed activation of stimulated secretion by preliminary incubation with low dose of MeHg 10^{-8} M and inhibition by dose of MeHg 10^{-6} M. These results show that MeHg treatment can modify mast cell function in vivo and in vitro and provide insight into the understanding what role this cell has in the pathogenesis of Minamata disease-comlected disorders.

Human leptospirosis in Croatia: current status of epidemiology and clinical characteristics.

PubMed

Topic, Mirjana Balen; Habus, Josipa; Milas, Zoran; Tosev, Elvira Celjuska; Stritof, Zrinka; Turk, Nenad

2010-03-01

This study presents the current status of human leptospirosis in Croatia from an epidemiological and clinical viewpoint. Data from annual reports of the Croatian Institute for Public Health as well as archives of the University Hospital for Infectious Diseases 'Dr Fran Mihaljevic' (UHID) in Zagreb were used in this retrospective cohort analysis. The mean yearly incidence of leptospirosis from 1990 to 2007 was 1.83/100 000 inhabitants, with an incidence >2.5/100 000 inhabitants recorded approximately every 3-4 years, making Croatia one of the countries with the highest incidence of human leptospirosis in Europe. In addition to the majority of sporadic cases, two minor outbreaks were recorded. The clinical burden and more detailed epidemiology of 130 patients hospitalised at UHID in the period 1997-2007 were also studied. Clinical presentations were as expected, with an overall case fatality rate (CFR) of 0.77%. The most commonly established infective serovars were Australis followed by Saxkoebing and Grippotyphosa. In comparison with previous periods, the mean yearly number of patients with leptospirosis hospitalised at UHID decreased, but among them a rather higher rate of patients with Weil's disease and a higher CFR was observed.

Differential geometric invariants for time-reversal symmetric Bloch-bundles: The “Real” case

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Nittis, Giuseppe, E-mail: gidenittis@mat.puc.cl; Gomi, Kiyonori, E-mail: kgomi@math.shinshu-u.ac.jp

2016-05-15

Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related “Real” (resp. “Quaternionic”) Bloch-bundles. If from one side the topological classification of these time-reversal vector bundle theories has been completely described in De Nittis and Gomi [J. Geom. Phys. 86, 303–338 (2014)] for the “Real” case and in De Nittis and Gomi [Commun. Math. Phys. 339, 1–55 (2015)] for the “Quaternionic” case, from the other side it seems that a classification in terms of differential geometric invariants is still missing in the literature. With this article and its companion [G. Demore » Nittis and K. Gomi (unpublished)] we want to cover this gap. More precisely, we extend in an equivariant way the theory of connections on principal bundles and vector bundles endowed with a time-reversal symmetry. In the “Real” case we generalize the Chern-Weil theory and we show that the assignment of a “Real” connection, along with the related differential Chern class and its holonomy, suffices for the classification of “Real” vector bundles in low dimensions.« less

Diagnostic evaluation of rapid tests for scrub typhus in the Indian population is needed.

PubMed

Shivalli, Siddharudha

2016-05-12

Owing to frequent outbreaks witnessed in different parts of the country in the recent past, scrub typhus is being described as a re-emerging infectious disease in India. Differentiating scrub typhus from other endemic diseases like malaria, leptospirosis, dengue fever, typhoid, etc. is difficult due to overlapping clinical features and a lower positivity for eschars in Asian populations. Hence, the diagnosis heavily relies on laboratory tests. Costs and the need of technical expertise limit the wide use of indirect immunoperoxidase or immunofluorescence assays, ELISA and PCR. The Weil-Felix test is the most commonly used and least expensive serological test, but lacks both sensitivity and specificity. Hence, the diagnosis of scrub typhus is often delayed or overlooked. With due consideration of the cost, rapidity, single test result and simplicity of interpretation, rapid diagnostic tests have come into vogue. However, evaluation of rapid diagnostic tests for scrub typhus in the Indian population is needed to justify or discourage their use. Research studies are needed to find the most suitable test in terms of the rapidity of the result, simplicity of the procedure, ease of interpretation and cost to be used in the Indian populace.

Commonly used severity scores are not good predictors of mortality in sepsis from severe leptospirosis: a series of ten patients.

PubMed

Velissaris, Dimitrios; Karanikolas, Menelaos; Flaris, Nikolaos; Fligou, Fotini; Marangos, Markos; Filos, Kriton S

2012-01-01

Introduction. Severe leptospirosis, also known as Weil's disease, can cause multiorgan failure with high mortality. Scoring systems for disease severity have not been validated for leptospirosis, and there is no documented method to predict mortality. Methods. This is a case series on 10 patients admitted to ICU for multiorgan failure from severe leptospirosis. Data were collected retrospectively, with approval from the Institution Ethics Committee. Results. Ten patients with severe leptospirosis were admitted in the Patras University Hospital ICU in a four-year period. Although, based on SOFA scores, predicted mortality was over 80%, seven of 10 patients survived and were discharged from the hospital in good condition. There was no association between SAPS II or SOFA scores and mortality, but survivors had significantly lower APACHE II scores compared to nonsurvivors. Conclusion. Commonly used severity scores do not seem to be useful in predicting mortality in severe leptospirosis. Early ICU admission and resuscitation based on a goal-directed therapy protocol are recommended and may reduce mortality. However, this study is limited by retrospective data collection and small sample size. Data from large prospective studies are needed to validate our findings.

From Philharmonic Hall to number theory: The way to more diffusion

NASA Astrophysics Data System (ADS)

Schroeder, Manfred R.

2005-09-01

In September 1962, in the presence of Mrs. Jacqueline Kennedy, Philharmonic Hall in New York was inaugurated-the first building of the new Lincoln Center for the Performing Arts. To address the soon-apparent acoustic problems, Lincoln Center turned to Bell Laboratories for help, and I was asked to join a ``committee of experts,'' chaired by Vern O. Knudsen of UCLA. My work on Philharmonic Hall, assisted by B.S. Atal, G.M. Sessler, and J.E. West, and later, after my move to Göttingen, by my students D. Gottlob, F.K. Siebrasse, and U. Eysholdt, indicated a need for energetic early lateral sound. It was clear that better lateral diffusion could improve the acoustic quality and the feeling of ``envelopment'' by the sound. Knowing some Galois field mathematics, I lucked upon the design of diffusors which scattered incident waves into broad lateral patterns-but only for a single musical octave. Then, in 1977, during a celebration of the 200th anniversary of Gauss's birth, I heard a talk by André Weil on Gauss sums and quadratic residues and, in a flash, it became clear to me that diffusors based on quadratic residues were the answer to broadly scattering waves comprising many musical octaves.

A case Study of Applying Object-Relational Persistence in Astronomy Data Archiving

NASA Astrophysics Data System (ADS)

Yao, S. S.; Hiriart, R.; Barg, I.; Warner, P.; Gasson, D.

2005-12-01

The NOAO Science Archive (NSA) team is developing a comprehensive domain model to capture the science data in the archive. Java and an object model derived from the domain model weil address the application layer of the archive system. However, since RDBMS is the best proven technology for data management, the challenge is the paradigm mismatch between the object and the relational models. Transparent object-relational mapping (ORM) persistence is a successful solution to this challenge. In the data modeling and persistence implementation of NSA, we are using Hibernate, a well-accepted ORM tool, to bridge the object model in the business tier and the relational model in the database tier. Thus, the database is isolated from the Java application. The application queries directly on objects using a DBMS-independent object-oriented query API, which frees the application developers from the low level JDBC and SQL so that they can focus on the domain logic. We present the detailed design of the NSA R3 (Release 3) data model and object-relational persistence, including mapping, retrieving and caching. Persistence layer optimization and performance tuning will be analyzed. The system is being built on J2EE, so the integration of Hibernate into the EJB container and the transaction management are also explored.

On a personal note: a music therapist's reflections on working with those who are living with a terminal illness.

PubMed

Hartley, N A

2001-01-01

Music therapists are constantly called upon to justify their work through research projects and evaluation processes. Rarely do we get the opportunity to talk personally about our work, the effects it has on us as music therapists, indeed, as human beings. This paper traces my own journey as a music therapist working with the terminally ill. Using audio extracts of music improvised with patients at the end of their lives, the concept of "attention" in music is addressed and explored. The paper will investigate: a) What is the difference between the quality of attention that is available to ourselves and our patients "in" music, as opposed to other ways of being together?; b) What does musical experience, particularly when achieved through improvisation, enable us and our patients to be that we cannot achieve in other ways?; c) Can "being in music" with another person fulfill a sense of longing that is evident in people at the end of their lives? In her book Waiting For God, Simone Weil suggests, "Those who are unhappy have no need for anything else in this world other than people capable of giving them their attention..." (1). Can the improvisation of music offer a unique and uncomplicated medium for being close?

Leptospirosis risk around a potential source of infection

NASA Astrophysics Data System (ADS)

Loaiza-Echeverry, Erica; Hincapié-Palacio, Doracelly; Ochoa Acosta, Jesús; Ospina Giraldo, Juan

2015-05-01

Leptospirosis is a bacterial zoonosis with world distribution and multiform clinical spectrum in men and animals. The etiology of this disease is the pathogenic species of Leptospira, which cause diverse manifestations of the disease, from mild to serious, such as the Weil disease and the lung hemorrhagic syndrome with lethal proportions of 10% - 50%. This is an emerging problem of urban health due to the growth of marginal neighborhoods without basic sanitary conditions and an increased number of rodents. The presence of rodents and the probability of having contact with their urine determine the likelihood for humans to get infected. In this paper, we simulate the spatial distribution of risk infection of human leptospirosis according to the proximity to rodent burrows considered as potential source of infection. The Bessel function K0 with an r distance from the potential point source, and the scale parameter α in meters was used. Simulation inputs were published data of leptospirosis incidence rate (range of 5 to 79 x 10 000), and a distance of 100 to 5000 meters from the source of infection. We obtained an adequate adjustment between the function and the simulated data. The risk of infection increases with the proximity of the potential source. This estimation can become a guide to propose effective measures of control and prevention.

[Benefit of rotational exercises for patients with Meniere's syndrome, method used by the ENT department of St-Luc university clinic].

PubMed

Nyabenda, A; Briart, C; Deggouj, N; Gersdorff, M

2003-12-01

To date, the effectiveness of balanced rehabilitation for patients with Meniere's syndrome has not been unanimously acknowledged by all physicians and physiotherapists. The purpose of this study is to assess the therapeutic efficacy of rotational exercises in the treatment of disequilibrium for patients with unilateral Meniere's syndrome. Rotational stimuli were used to symmetrize and reduce postrotatory nystagmic response. Three reference sources were used to assess the efficacy of this management: vestibulospinal function tests: pre- and post-treatment results at the Romberg test, the Unterberger-Fukuda stepping test, the Babinski-Weil test, and gait testing with eyes closed; rotational tests: pre- and post-treatment results; and the self-perceived impact of vertigo: assessed by the Dizziness Handicap Inventory (DHI) and a scale based on the guidelines of the Japanese Society of Equilibrium Research (JSER, 1993). The JSER scale provides quantitative vertigo evaluation; the DHI reflects the patient's perceptual evaluation of handicap. Patients required 11 sessions (mean value) to attain subjective improvement. Of the 23 patients, only seven required optokinetic stimulation (mean requirement: three sessions). Rotational tests and dynamic tests of the vestibulospinal function improved. The DHI and JSER results show that patients' post-rehabilitation perceptual evaluation significantly improved. The objective and subjective measures of disequilibrium in patients with unilateral Meniere's syndrome were significantly improved.

Making direct use of canopy profiles in vegetation - atmosphere coupling

NASA Astrophysics Data System (ADS)

Ryder, James; Polcher, Jan; Peylin, Philippe; Ottlé, Catherine; Chen, Yiying; van Gorsel, Eva; Haverd, Vanessa; McGrath, Matthew; Naudts, Kim; Otto, Juliane; Valade, Aude; Luyssaert, Sebastiaan

2015-04-01

Most coupled land-surface regional models use the 'big-leaf' approach for simulating the sensible and latent heat fluxes of different vegetation types. However, there has been a progression in the types of questions being asked of these models, such as the consequences of land-use change or the behaviour of BVOCs and aerosol. In addition, recent years has seen growth in the availability of in-canopy datasets across a broaded range of species, with which to calibrate these simulations. Hence, there is now an argument for transferring some of the techniques and processes previously used in local, site-based land surface models to the land surface components of models which operate on a regional or even global scale. We describe here the development and evaluation of a vertical canopy energy budget model (Ryder, J et al., 2014) that can be coupled to an atmospheric model such as LMDz. Significantly, the model preserves the implicit coupling of the land-surface to atmosphere interface, which means that run-time efficiences are preserved. This is acheived by means of an interface based on the approach of Polcher et al. (1998) and Best et al. (2004), but newly developed for a canopy column. The model makes use of techniques from site-based models, such as the calculation of vertical turbulence statistics using a second-order closure model (Massman & Weil, 1999), and the distribution of long-wave and short-wave radiation over the profile, the latter using an innovate multilayer albedo scheme (McGrath et al., in prep.). Complete profiles of atmospheric temperature and specific humidity are now calculated, in order to simulate sensible and latent heat fluxes, as well as the leaf temperature at each level in the model. The model is shown to perform stably, and reproduces well flux measurements at an initial test site, across a time period of several days, or over the course of a year. Further applications of the model might be to simulate mixed canopies, the light-stimulated emission of chemical species, or the ecological consequences of changes to temperature profile as a results of changes to stand structure. References: Best, M. J., Beljaars, A. C. M., Polcher, J., & Viterbo, P. (2004). A proposed structure for coupling tiled surfaces with the planetary boundary layer. Journal of Hydrometeorology, 5, 1271-1278. Massman, W. J., & Weil, J. C., 1999. 'An analytical one-dimensional second-order closure model of turbulence statistics and the lagrangian time scale within and above plant canopies of arbitrary structure', Boundary-Layer Meteorology, 91, 81-107. Mcgrath, M. J., Pinty, B., Ryder, J., Otto, J., & Luyssaert, S., in prep. A multilevel canopy radiative transfer scheme based on a domain-averaged structure factor Polcher, J., McAvaney, B., Viterbo, P., Gaertner, M., Hahmann, A., Mahfouf, J.-F., Noilhan, J., Phillips, T.J., Pitman, A. J., Schlosser, C. A., Schulz, J-P, Timbal, B., Verseghy, D. L., Xue, Y. (1998). A proposal for a general interface between land surface schemes and general circulation models. Global and Planetary Change, 19, 261-276. Ryder, J., J. Polcher, P. Peylin, C. Ottlé, Y. Chen, E. Van Gorsel, V. Haverd, M. J. McGrath, K.Naudts, J. Otto, A. Valade, and S. Luyssaert, 2014. 'A multi-layer land surface energy budget model for implicit coupling with global atmospheric simulations', Geosci. Model Dev. Discuss. 7, 8649-8701

Loss of locality in gravitational correlators with a large number of insertions

NASA Astrophysics Data System (ADS)

Ghosh, Sudip; Raju, Suvrat

2017-09-01

We review lessons from the AdS/CFT correspondence that indicate that the emergence of locality in quantum gravity is contingent upon considering observables with a small number of insertions. Correlation functions, where the number of insertions scales with a power of the central charge of the CFT, are sensitive to nonlocal effects in the bulk theory, which arise from a combination of the effects of the bulk Gauss law and a breakdown of perturbation theory. To examine whether a similar effect occurs in flat space, we consider the scattering of massless particles in the bosonic string and the superstring in the limit, where the number of external particles, n, becomes very large. We use estimates of the volume of the Weil-Petersson moduli space of punctured Riemann surfaces to argue that string amplitudes grow factorially in this limit. We verify this factorial behavior through an extensive numerical analysis of string amplitudes at large n. Our numerical calculations rely on the observation that, in the large n limit, the string scattering amplitude localizes on the Gross-Mende saddle points, even though individual particle energies are small. This factorial growth implies the breakdown of string perturbation theory for n ˜(M/plE ) d -2 in d dimensions, where E is the typical individual particle energy. We explore the implications of this breakdown for the black hole information paradox. We show that the loss of locality suggested by this breakdown is precisely sufficient to resolve the cloning and strong subadditivity paradoxes.

Mutually unbiased phase states, phase uncertainties, and Gauss sums

NASA Astrophysics Data System (ADS)

Planat, M.; Rosu, H.

2005-10-01

Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is a constant equal to 1/sqrt{d}, with d the dimension of the finite Hilbert space, are becoming more and more studied for applications such as quantum tomography and cryptography, and in relation to entangled states and to the Heisenberg-Weil group of quantum optics. Complete sets of MUBs of cardinality d+1 have been derived for prime power dimensions d=pm using the tools of abstract algebra. Presumably, for non prime dimensions the cardinality is much less. Here we reinterpret MUBs as quantum phase states, i.e. as eigenvectors of Hermitian phase operators generalizing those introduced by Pegg and Barnett in 1989. We relate MUB states to additive characters of Galois fields (in odd characteristic p) and to Galois rings (in characteristic 2). Quantum Fourier transforms of the components in vectors of the bases define a more general class of MUBs with multiplicative characters and additive ones altogether. We investigate the complementary properties of the above phase operator with respect to the number operator. We also study the phase probability distribution and variance for general pure quantum electromagnetic states and find them to be related to the Gauss sums, which are sums over all elements of the field (or of the ring) of the product of multiplicative and additive characters. Finally, we relate the concepts of mutual unbiasedness and maximal entanglement. This allows to use well studied algebraic concepts as efficient tools in the study of entanglement and its information aspects.

Five-year analysis of rickettsial fevers in children in South India: Clinical manifestations and complications.

PubMed

Thomas, Rwituja; Puranik, Preeti; Kalal, Bhuvanesh; Britto, Carl; Kamalesh, Savitha; Rego, Sylvan; Shet, Anita

2016-06-30

Rickettsial infections are re-emerging in the Indian subcontinent, especially among children. Understanding geographical and clinical epidemiology will facilitate early diagnosis and management. Children aged <18yrs hospitalized with clinically-diagnosed rickettsial fever were reviewed retrospectively. Frequency distributions and odds ratios were calculated from tabulated data. Among 262 children hospitalized between January 2008-December 2012, median age was five years, and 61% were male children. Hospitalized cases increased steadily every year, with the highest burden (74%) occurring between September and January each year. Mean duration of fever was 11.5 days. Rash was present in 54.2% (142/262) of children, with 37.0% involving palms and soles. Prevalence of malnutrition was high (45% of children were underweight and 28% had stunting). Retinal vasculitis was seen in 13.7% (36/262), and the risk appeared higher in females. Severe complications were seen in 29% (purpura fulminans, 7.6%; meningitis and meningoencephalitis, 28%; septic shock, 1.9%; acute respiratory distress syndrome, 1.1%). Complications were more likely to occur in anemic children. Positive Weil-Felix test results (titers ≥1:160) were seen in 70% of cases. Elevated OX-K titers suggestive of scrub typhus were seen in 80% (147/184). Patients were treated with chloramphenicol (32%) or doxycycline (68%). Overall mortality among hospitalised children was 1.9%. This five-year analysis from southern India shows a high burden and increasing trend of rickettsial infections among children. The occurrence of retinal vasculitis and a high rate of severe complications draw attention to the need for early diagnosis and management of these infections.

Validation of Geno-Sen's Scrub Typhus Real Time Polymerase Chain Reaction Kit by its Comparison with a Serological ELISA Test

PubMed Central

Anitharaj, Velmurugan; Stephen, Selvaraj; Pradeep, Jothimani; Pooja, Pratheesh; Preethi, Sridharan

2017-01-01

Background: In the recent past, scrub typhus (ST) has been reported from different parts of India, based on Weil-Felix/enzyme-linked immunosorbent assay (ELISA)/indirect immunofluorescence assay (IFA). Molecular tests are applied only by a few researchers. Aims: Evaluation of a new commercial real time polymerase chain reaction (PCR) kit for molecular diagnosis of ST by comparing it with the commonly used IgM ELISA is our aim. Settings and Design: ST has been reported all over India including Puducherry and surrounding Tamil Nadu and identified as endemic for ST. This study was designed to correlate antibody detection by IgM ELISA and Orientia tsutsugamushi DNA in real time PCR. Materials and Methods: ST IgM ELISA (InBios Inc., USA) was carried out for 170 consecutive patients who presented with the symptoms of acute ST during 11 months (November, 2015– September, 2016). All 77 of these patients with IgM ELISA positivity and 49 of 93 IgM ELISA negative patients were subjected to real time PCR (Geno-Sen's ST real time PCR, Himachal Pradesh, India). Statistical Analysis: Statistical analysis for clinical and laboratory results was performed using IBM SPSS Statistics 17 for Windows (SPSS Inc., Chicago, USA). Chi-square test with Yates correction (Fisher's test) was employed for a small number of samples. Results and Conclusion: Among 77 suspected cases of acute ST with IgM ELISA positivity and 49 IgM negative patients, 42 and 7 were positive, respectively, for O. tsutsugamushi 56-kDa type-specific gene in real time PCR kit. Until ST IFA, the gold standard diagnostic test, is properly validated in India, diagnosis of acute ST will depend on both ELISA and quantitative PCR. PMID:28878522

Large-scale purification and in vitro characterization of the assembly of MreB from Leptospira interrogans.

PubMed

Barkó, Szilvia; Szatmári, Dávid; Bódis, Emőke; Türmer, Katalin; Ujfalusi, Zoltán; Popp, David; Robinson, Robert C; Nyitrai, Miklós

2016-09-01

Weil's syndrome is caused by Leptospira interrogans infections, a Gram negative bacterium with a distinct thin corkscrew cell shape. The molecular basis for this unusual morphology is unknown. In many bacteria, cell wall synthesis is orchestrated by the actin homolog, MreB. Here we have identified the MreB within the L. interrogans genome and expressed the His-tagged protein product of the synthesized gene (Li-MreB) in Escherichia coli. Li-MreB did not purify under standard nucleotide-free conditions used for MreBs from other species, requiring the continual presence of ATP to remain soluble. Covalent modification of Li-MreB free thiols with Alexa488 produced a fluorescent version of Li-MreB. We developed native and denaturing/refolding purification schemes for Li-MreB. The purified product was shown to assemble and disassemble in MgCl2 and KCl dependent manners, as monitored by light scattering and sedimentation studies. The fluorescence spectrum of labeled Li-MreB-Alexa488 showed cation-induced changes in line with an activation process followed by a polymerization phase. The resulting filaments appeared as bundles and sheets under the fluorescence microscope. Finally, since the Li-MreB polymerization was cation dependent, we developed a simple method to measure monovalent cation concentrations within a test case prokaryote, E. coli. We have identified and initially characterized the cation-dependent polymerization properties of a novel MreB from a non-rod shaped bacterium and developed a method to measure cation concentrations within prokaryotes. This initial characterization of Li-MreB will enable future structural determination of the MreB filament from this corkscrew-shaped bacterium. Copyright © 2016 Elsevier B.V. All rights reserved.

Stochastic Geometry and Quantum Gravity: Some Rigorous Results

NASA Astrophysics Data System (ADS)

Zessin, H.

The aim of these lectures is a short introduction into some recent developments in stochastic geometry which have one of its origins in simplicial gravity theory (see Regge Nuovo Cimento 19: 558-571, 1961). The aim is to define and construct rigorously point processes on spaces of Euclidean simplices in such a way that the configurations of these simplices are simplicial complexes. The main interest then is concentrated on their curvature properties. We illustrate certain basic ideas from a mathematical point of view. An excellent representation of this area can be found in Schneider and Weil (Stochastic and Integral Geometry, Springer, Berlin, 2008. German edition: Stochastische Geometrie, Teubner, 2000). In Ambjørn et al. (Quantum Geometry Cambridge University Press, Cambridge, 1997) you find a beautiful account from the physical point of view. More recent developments in this direction can be found in Ambjørn et al. ("Quantum gravity as sum over spacetimes", Lect. Notes Phys. 807. Springer, Heidelberg, 2010). After an informal axiomatic introduction into the conceptual foundations of Regge's approach the first lecture recalls the concepts and notations used. It presents the fundamental zero-infinity law of stochastic geometry and the construction of cluster processes based on it. The second lecture presents the main mathematical object, i.e. Poisson-Delaunay surfaces possessing an intrinsic random metric structure. The third and fourth lectures discuss their ergodic behaviour and present the two-dimensional Regge model of pure simplicial quantum gravity. We terminate with the formulation of basic open problems. Proofs are given in detail only in a few cases. In general the main ideas are developed. Sufficiently complete references are given.

Serological Diagnosis of Acute Scrub Typhus in Southern India: Evaluation of InBios Scrub Typhus Detect IgM Rapid Test and Comparison with other Serological Tests.

PubMed

Anitharaj, Velmurugan; Stephen, Selvaraj; Pradeep, Jothimani; Park, Sungman; Kim, Seung-Han; Kim, Young Jin; Kim, Eun-Ye; Kim, Yoon-Won

2016-11-01

Scrub Typhus (ST) is being reported from different parts of India in the recent past. However, the diagnosis and confirmation of ST cases require specific serological and molecular diagnostic tests. Both rapid and conventional ELISA tests need to be properly evaluated. Evaluation of a new ST IgM Immunochromatography (ICT) test kit (InBios Scrub Typhus Detect IgM Rapid Test) and compare it with another rapid kit, conventional ELISA kit and Weil-Felix (WF) test. This prospective study was carried out in Mahatma Gandhi Medical College and Research Institute, Puducherry, during November 2015 to June 2016. Clinically suspected 220 ST patients were examined by a new kit, InBios Scrub Typhus Detect IgM Rapid Test, taking the conventional InBios Scrub Typhus Detect IgM ELISA as reference. Additional comparison was made with ImmuneMed Scrub Typhus Rapid, and WF test (single OXK titers ≥1:320). Statistical analysis was performed (Chi-square, Spearman's correlation and Kappa) using IBM SPSS Statistics 17 for Windows (SPSS Inc; Chicago, USA). Percentage Sensitivity, Specificity, Positive Predictive and Negative Predictive Values for InBios, ImmuneMed and WF were 99.25, 93.02, 95.68, 98.77; 94.87, 94.19, 96.21, 92.05 and 50.38, 95.51, 94.29, 56.67 respectively. A total of 134 patients were positive in reference standard InBios IgM ELISA. This new rapid ST IgM kit validated for the first time in India, showed good sensitivity and specificity. As a Point-of-Care (PoC) test, the kit would be helpful in both urban and remote rural parts of India.

Validation of Geno-Sen's Scrub Typhus Real Time Polymerase Chain Reaction Kit by its Comparison with a Serological ELISA Test.

PubMed

Anitharaj, Velmurugan; Stephen, Selvaraj; Pradeep, Jothimani; Pooja, Pratheesh; Preethi, Sridharan

2017-01-01

In the recent past, scrub typhus (ST) has been reported from different parts of India, based on Weil-Felix/enzyme-linked immunosorbent assay (ELISA)/indirect immunofluorescence assay (IFA). Molecular tests are applied only by a few researchers. Evaluation of a new commercial real time polymerase chain reaction (PCR) kit for molecular diagnosis of ST by comparing it with the commonly used IgM ELISA is our aim. ST has been reported all over India including Puducherry and surrounding Tamil Nadu and identified as endemic for ST. This study was designed to correlate antibody detection by IgM ELISA and Orientia tsutsugamushi DNA in real time PCR. ST IgM ELISA (InBios Inc., USA) was carried out for 170 consecutive patients who presented with the symptoms of acute ST during 11 months (November, 2015- September, 2016). All 77 of these patients with IgM ELISA positivity and 49 of 93 IgM ELISA negative patients were subjected to real time PCR (Geno-Sen's ST real time PCR, Himachal Pradesh, India). Statistical analysis for clinical and laboratory results was performed using IBM SPSS Statistics 17 for Windows (SPSS Inc., Chicago, USA). Chi-square test with Yates correction (Fisher's test) was employed for a small number of samples. Among 77 suspected cases of acute ST with IgM ELISA positivity and 49 IgM negative patients, 42 and 7 were positive, respectively, for O. tsutsugamushi 56-kDa type-specific gene in real time PCR kit. Until ST IFA, the gold standard diagnostic test, is properly validated in India, diagnosis of acute ST will depend on both ELISA and quantitative PCR.

Serological Diagnosis of Acute Scrub Typhus in Southern India: Evaluation of InBios Scrub Typhus Detect IgM Rapid Test and Comparison with other Serological Tests

PubMed Central

Anitharaj, Velmurugan; Pradeep, Jothimani; Park, Sungman; Kim, Seung-Han; Kim, Young Jin; Kim, Eun-Ye; Kim, Yoon-Won

2016-01-01

Introduction Scrub Typhus (ST) is being reported from different parts of India in the recent past. However, the diagnosis and confirmation of ST cases require specific serological and molecular diagnostic tests. Both rapid and conventional ELISA tests need to be properly evaluated. Aim Evaluation of a new ST IgM Immunochromatography (ICT) test kit (InBios Scrub Typhus Detect IgM Rapid Test) and compare it with another rapid kit, conventional ELISA kit and Weil-Felix (WF) test. Materials and Methods This prospective study was carried out in Mahatma Gandhi Medical College and Research Institute, Puducherry, during November 2015 to June 2016. Clinically suspected 220 ST patients were examined by a new kit, InBios Scrub Typhus Detect IgM Rapid Test, taking the conventional InBios Scrub Typhus Detect IgM ELISA as reference. Additional comparison was made with ImmuneMed Scrub Typhus Rapid, and WF test (single OXK titers ≥1:320). Statistical analysis was performed (Chi-square, Spearman’s correlation and Kappa) using IBM SPSS Statistics 17 for Windows (SPSS Inc; Chicago, USA). Results Percentage Sensitivity, Specificity, Positive Predictive and Negative Predictive Values for InBios, ImmuneMed and WF were 99.25, 93.02, 95.68, 98.77; 94.87, 94.19, 96.21, 92.05 and 50.38, 95.51, 94.29, 56.67 respectively. A total of 134 patients were positive in reference standard InBios IgM ELISA. Conclusion This new rapid ST IgM kit validated for the first time in India, showed good sensitivity and specificity. As a Point-of-Care (PoC) test, the kit would be helpful in both urban and remote rural parts of India. PMID:28050364

[Genotyping and evaluation of infection dynamics in a Colombian isolate of Leptospira santarosai in hamster as an experimental model].

PubMed

Agudelo-Flórez, Piedad; Durango, Harold; Aranzazu, Diego; Rodas, Juan David; Travi, Bruno

2014-01-01

Is necessary to develop models for the study of leptospirosis. To genotype a Colombian strain of Leptospira isolated from a human with Weil´s syndrome and to evaluate its infection dynamics in the hamster experimental model. Genotyping was performed by amplification and sequence analysis of the rrs 16S and lipL32 genes. The median lethal dose was determined in intraperitoneally inoculated hamsters. The patterns of clinical chemistry, the duration of leptospiremia, leptospiruria and pathological findings were studied and compared in the same animal model infected with L. interrogans (Fiocruz L1-130). Molecular typing revealed that the isolate corresponded to the pathogenic species L. santarosai, which was recovered from hamsters´ kidneys and lungs and detected by lipL32 PCR from day 3 post-infection in these organs. There was a marked increase of C-reactive protein in animals at day 5 post-infection (3.25 mg/dl; normal value: 0.3 mg/dl) with decreases by day 18 (2.60 mg/dl: normal value: 0.8 mg/dl). Biomarkers of urea showed changes consistent with possible renal acute failure (day 5 post-infection: 49.01 mg/dl and day 18 post-infection: 53.71 mg/dl). Histopathological changes included interstitial pneumonia with varying degrees of hemorrhage and interstitial nephritis. The pathogenic species L. santarosai was identified in Colombia. Its pathogenicity as determined by tropism to lung and kidney was comparable to that of L. interrogans Fiocruz L1-130, well known for its virulence and pulmonar tropism. The biological aspects studied here had never before been evaluated in an autochthonous isolate.

Characterizing Clinical Genetic Counselors' Countertransference Experiences: an Exploratory Study.

PubMed

Reeder, Rebecca; Veach, Patricia McCarthy; MacFarlane, Ian M; LeRoy, Bonnie S

2017-10-01

Countertransference (CT) refers to conscious and unconscious emotions, fantasies, behaviors, perceptions, and psychological defenses genetic counselors experience in response to any aspect of genetic counseling situations (Weil 2010). Some authors theorize about the importance of recognizing and managing CT, but no studies solely aim to explore genetic counselors' experiences of the phenomenon. This study examined the extent to which clinical genetic counselors' perceive themselves as inclined to experience CT, gathered examples of CT encountered in clinical situations, and assessed their CT management strategies. An anonymous online survey, sent to NSGC members, yielded 127 usable responses. Participants completed Likert-type items rating their CT propensities; 57 of these individuals also provided examples of CT they experienced in their practice. Factor analysis of CT propensities tentatively suggested four factors: Control, Conflict Avoidance, Directiveness, and Self-Regulation, accounting for 38.5% of response variance. Thematic analysis of CT examples yielded five common triggers: general similarity to patient, medical/genetic similarity, angry patients, patient behaves differently from counselor expectations, and disclosing bad news; six common manifestations: being self-focused, projecting feelings onto the patient, intense emotional reaction to patient, being overly invested, disengagement, and physical reaction; five CT effects: disruption in rapport building, repaired empathy, over-identification, conversation does not reach fullest potential, and counselor is drained emotionally; and three management strategies: recognizing CT as it occurs, self-reflection, and consultation. Results suggest CT is a common experience, occurring in both "routine" and emotionally complex cases. Training programs, continuing education, and peer supervision might include discussion of CT, informed by examples from the present study, to increase genetic counselor awareness and skills for managing the phenomenon.

Scrub typhus and spotted fever among hospitalised children in South India: Clinical profile and serological epidemiology.

PubMed

Kalal, B S; Puranik, P; Nagaraj, S; Rego, S; Shet, A

2016-01-01

Rickettsial infections are re-emerging. In India, they are now being reported from several areas where they were previously unknown. The objective of this study was to describe the epidemiology, clinical profile and outcome of serologically-confirmed scrub typhus and spotted fever among children in a tertiary care hospital in Bengaluru. Hospitalised children aged <18 years, with clinical features suggestive of rickettsial disease admitted between January 2010 and October 2012 were included prospectively. Diagnosis was based on scrub typhus and spotted fever-specific IgM and IgG by enzyme-linked immunosorbent assay (ELISA). Of 103 children with clinical features suggestive of rickettsial illness, ELISA test confirmed 53 cases for scrub typhus, 23 cases for spotted fever group and 14 with mixed infection. The average age was 7.3 (±3.9) years and 44 (71.0%) children were male. Majority of cases were from Karnataka (50%), Andhra Pradesh (32.3%) and Tamil Nadu (17.7%). Common clinical features included fever (100%, average duration 11 days), nausea and vomiting (44%), rash (36%); eschar was rare. Compared to the ELISA test, Weil-Felix test (OX-K titre of 1:80) had a sensitivity and specificity of 88.7% and 43.9%, respectively. Treatment with chloramphenicol or doxycycline was given to the majority of the children. Complications included meningoencephalitis (28%), shock (10%), retinal vasculitis (10%) and purpura fulminans (7%). These findings suggest that the burden of rickettsial infection among children in India is high, with a substantially high complication rate. Rickettsial-specific ELISA tests can help in early diagnosis and early institution of appropriate treatment that may prevent life-threatening complications.

Tsutsugamushi Disease (Scrub Typhus) Meningoencephalitis in North Eastern India: A Prospective Study.

PubMed

Sharma, S R; Masaraf, H; Lynrah, K G; Lyngdoh, M

2015-01-01

Scrub typhus is rampant in northern, eastern, and southern India. Central nervous system involvement in the form of meningitis or meningoencephalitis is common in scrub typhus. As specific laboratory methods remain inadequate or inaccessible in developing countries, prompt diagnosis is often difficult. The aim of this study was to characterize neurological complications in scrub typhus from northeastern region of India. We did a prospective study of scrub meningoencephalitis at North Eastern Indira Gandhi Regional Institute of Medical Sciences among patients admitted to hospital between October 2009 and November 2011. The diagnosis was made based on the clinical pictures, presence of an eschar, and a positive Weil-Felix test (WFT) with a titer of >1:160 and if required a positive scrub IgM enzyme-linked immunosorbent assay. Lumbar puncture was performed in patients with headache, nuchal rigidity, altered sensorium or cranial nerve deficits, and magnetic resonance imaging (MRI) brain performed if needed. Twenty-three patients of scrub typhus meningitis that were serologically confirmed were included in the study. There were 13 males and 10 females. Fever ≥1 week was the most common manifestation (39.1%). Interestingly, none had an eschar. Median cerebrospinal fluid (CSF) cell count, lymphocyte percentage, CSF protein, CSF glucose/blood glucose, CSF ADA were 17 cells/μL, 90%, 86 mg/dL, 0.6605 and 3.6 U/mL, respectively. All patients were treated with doxycycline. There was no mortality in our study. Absence of Eschar does not rule out scrub typhus. Clinical features and CSF findings can mimic tuberculous meningitis so misdiagnosis may lead to unwarranted prolonged empirical antituberculous therapy in cases of lymphocytic meningoencephalitis. Delay in treatment can be potentially fatal. WFT still serves as a useful and affordable diagnostic tool for this disease in resource-poor countries.

Kinetic energy equations for the average-passage equation system

NASA Technical Reports Server (NTRS)

Johnson, Richard W.; Adamczyk, John J.

1989-01-01

Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.

The chemical (not mechanical) paradigm of thermodynamics of colloid and interface science.

PubMed

Kaptay, George

2018-06-01

In the most influential monograph on colloid and interfacial science by Adamson three fundamental equations of "physical chemistry of surfaces" are identified: the Laplace equation, the Kelvin equation and the Gibbs adsorption equation, with a mechanical definition of surface tension by Young as a starting point. Three of them (Young, Laplace and Kelvin) are called here the "mechanical paradigm". In contrary it is shown here that there is only one fundamental equation of the thermodynamics of colloid and interface science and all the above (and other) equations of this field follow as its derivatives. This equation is due to chemical thermodynamics of Gibbs, called here the "chemical paradigm", leading to the definition of surface tension and to 5 rows of equations (see Graphical abstract). The first row is the general equation for interfacial forces, leading to the Young equation, to the Bakker equation and to the Laplace equation, etc. Although the principally wrong extension of the Laplace equation formally leads to the Kelvin equation, using the chemical paradigm it becomes clear that the Kelvin equation is generally incorrect, although it provides right results in special cases. The second row of equations provides equilibrium shapes and positions of phases, including sessile drops of Young, crystals of Wulff, liquids in capillaries, etc. The third row of equations leads to the size-dependent equations of molar Gibbs energies of nano-phases and chemical potentials of their components; from here the corrected versions of the Kelvin equation and its derivatives (the Gibbs-Thomson equation and the Freundlich-Ostwald equation) are derived, including equations for more complex problems. The fourth row of equations is the nucleation theory of Gibbs, also contradicting the Kelvin equation. The fifth row of equations is the adsorption equation of Gibbs, and also the definition of the partial surface tension, leading to the Butler equation and to its derivatives, including the Langmuir equation and the Szyszkowski equation. Positioning the single fundamental equation of Gibbs into the thermodynamic origin of colloid and interface science leads to a coherent set of correct equations of this field. The same provides the chemical (not mechanical) foundation of the chemical (not mechanical) discipline of colloid and interface science. Copyright © 2018 Elsevier B.V. All rights reserved.

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Allan; Vine, Edward L.

The incidence of commercial buildings with poor indoor air quality (IAQ), and the frequency of litigation over the effects of poor IAQ is increasing. If so, these increases have ramifications for insurance carriers, which pay for many of the costs of health care and general commercial liability. However, little is known about the actual costs to insurance companies from poor IAQ in buildings. This paper reports on the results of a literature search of buildings-related, business and legal databases, and interviews with insurance and risk management representatives aimed at finding information on the direct costs to the insurance industry ofmore » poor building IAQ, as well as the costs of litigation. The literature search and discussions with insurance and risk management professionals reported in this paper turned up little specific information about the costs of IAQ-related problems to insurance companies. However, those discussions and certain articles in the insurance industry press indicate that there is a strong awareness and growing concern over the "silent crisis" of IAQ and its potential to cause large industry losses, and that a few companies are taking steps to address this issue. The source of these losses include both direct costs to insurers from paying health insurance and professional liability claims, as weIl as the cost of litigation. In spite of the lack of data on how IAQ-related health problems affect their business, the insurance industry has taken the anecdotal evidence about their reality seriously enough to alter their policies in ways that have lessened their exposure. We conclude by briefly discussing four activities that need to be addressed in the near future: (1) quantifying IAQ-related insurance costs by sector, (2) educating the insurance industry about the importance of IAQ issues, (3) examining IAQ impacts on the insurance industry in the residential sector, and (4) evaluating the relationship between IAQ improvements and their impact on energy use.« less

A Model System for Studying the Transcriptomic and Physiological Changes Associated with Mammalian Host-Adaptation by Leptospira interrogans Serovar Copenhageni

PubMed Central

Caimano, Melissa J.; Sivasankaran, Sathesh K.; Allard, Anna; Hurley, Daniel; Hokamp, Karsten; Grassmann, André A.; Hinton, Jay C. D.; Nally, Jarlath E.

2014-01-01

Leptospirosis, an emerging zoonotic disease with worldwide distribution, is caused by spirochetes belonging to the genus Leptospira. More than 500,000 cases of severe leptospirosis are reported annually, with >10% of these being fatal. Leptospires can survive for weeks in suitably moist conditions before encountering a new host. Reservoir hosts, typically rodents, exhibit little to no signs of disease but shed large numbers of organisms in their urine. Transmission occurs when mucosal surfaces or abraded skin come into contact with infected urine or urine-contaminated water or soil. In humans, leptospires can cause a variety of clinical manifestations, ranging from asymptomatic or mild fever to severe icteric (Weil's) disease and pulmonary haemorrhage. Currently, little is known about how Leptospira persist within a reservoir host. Prior in vitro studies have suggested that leptospires alter their transcriptomic and proteomic profiles in response to environmental signals encountered during mammalian infection. However, no study has examined gene expression by leptospires within a mammalian host-adapted state. To obtain a more faithful representation of how leptospires respond to host-derived signals, we used RNA-Seq to compare the transcriptome of L. interrogans cultivated within dialysis membrane chambers (DMCs) implanted into the peritoneal cavities of rats with that of organisms grown in vitro. In addition to determining the relative expression levels of “core” housekeeping genes under both growth conditions, we identified 166 genes that are differentially-expressed by L. interrogans in vivo. Our analyses highlight physiological aspects of host adaptation by leptospires relating to heme uptake and utilization. We also identified 11 novel non-coding transcripts that are candidate small regulatory RNAs. The DMC model provides a facile system for studying the transcriptional and antigenic changes associated with mammalian host-adaption, selection of targets for mutagenesis, and the identification of previously unrecognized virulence determinants. PMID:24626166

Outbreak of scrub typhus in Puducherry & Tamil Nadu during cooler months

PubMed Central

Stephen, Selvaraj; Sangeetha, Balakrishnan; Ambroise, Stanley; Sarangapani, Kengamuthu; Gunasekaran, Dhandapany; Hanifah, Mohamed; Somasundaram, Subramanian

2015-01-01

Background & objectives: The southern part of India has witnessed an increase in scrub typhus (ST) during the past ten years. ST outbreaks occurred during winter months but at intervals of one to three years. With only a few reports of ST in Puducherry, this study was undertaken to look for the persistence of ST cases in Puducherry and Tamil Nadu in the winter months. Methods: During relatively cooler months of September, 2012 to March, 2013, a total of 45 patients with fever and clinical suspicion of ST and who provided both acute and convalescent blood samples were included. Total WBC, platelet counts, serum creatinine, liver enzymes levels and a rapid immunochromatographic test (RICT) for ST were first done. Paired serum samples were analysed by two specific tests - ST IgM and IgG ELISA- and a non-specific, but widely used Weil-Felix (WF) test. Results: Of the 45 patients, 21 adults and seven children were confirmed as ST based on clinical and laboratory findings, and positivity in specific serological test(s). Setting ST IgM and IgG ELISA as reference, the sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) for RICT were 91.67, 85.71 per cent; 90.48, 100 per cent; 91.67, 100 per cent and 90.48, 80.95 per cent, respectively. Similarly, for WF the values were 83.33, 75 per cent; 95.24, 100 per cent; 95.24, 100 per cent and 83.33, 70.83 per cent, respectively. Interpretation & conclusions: ST continues to persist in the cooler months in Puducherry and neighbouring Tamil Nadu with fever and myalgia as prominent features. None of the tests evaluated in this study was found to be ideal, but ST IgM/IgG ELISA was useful for batch testing and the non-specific WF test can be used in resource poor settings. PMID:26658595

F-theory on all toric hypersurface fibrations and its Higgs branches

DOE PAGES

Klevers, Denis; Mayorga Pena, Damian Kaloni; Oehlmann, Paul-Konstantin; ...

2015-01-27

We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces inmore » $$\\mathbb P^{2}$$, $$\\mathbb P^{1}$$ × $$\\mathbb P^{1}$$ and the recently studied $$\\mathbb P^{2}$$ (1,1, 2) , yield F-theory realizations of SUGRA theories with discrete gauge groups $$\\mathbb Z$$ 3, $$\\mathbb Z$$ 2 and $$\\mathbb Z$$ 4.This opens up a whole new arena for model building with discrete global symmetries in F-theory. In these three manifolds, we also find codimension two I 2-fibers supporting matter charged only under these discrete gauge groups. Their 6D matter multiplicities are computed employing ideal techniques and the associated Jacobian fibrations. Here, we also show that the Jacobian of the biquadric fibration has one rational section, yielding one U(1)-gauge field in F-theory. Furthermore, the elliptically fibered Calabi-Yau manifold based on dP 1 has a U(1)-gauge field induced by a non-toric rational section. In this model, we find the first F-theory realization of matter with U(1)-charge q = 3.« less

An Electroencephalography Network and Connectivity Analysis for Deception in Instructed Lying Tasks

PubMed Central

Wang, Yue; Ng, Wu Chun; Ng, Khoon Siong; Yu, Ke; Wu, Tiecheng; Li, Xiaoping

2015-01-01

Deception is an impactful social event that has been the focus of an abundance of researches over recent decades. In this paper, an electroencephalography (EEG) study is presented regarding the cognitive processes of an instructed liar/truth-teller during the time window of stimulus (question) delivery period (SDP) prior to their deceptive/truthful responses towards questions related to authentic (WE: with prior experience) and fictional experience (NE: no prior experience). To investigate deception in non-experienced events, the subjects were given stimuli in a mock interview scenario that induced them to fabricate lies. To analyze the data, frequency domain network and connectivity analysis was performed in the source space in order to provide a more systematic level understanding of deception during SDP. This study reveals several groups of neuronal generators underlying both the instructed lying (IL) and the instructed truth-telling (IT) conditions for both tasks during the SDP. Despite the similarities existed in these group components, significant differences were found in the intra- and inter-group connectivity between the IL and IT conditions in either task. Additionally, the response time was found to be positively correlated with the clustering coefficient of the inferior frontal gyrus (44R) in the WE-IL condition and positively correlated with the clustering coefficient of the precuneus (7L) and the angular gyrus (39R) in the WE-IT condition. However, the response time was found to be marginally negatively correlated with the clustering coefficient of the secondary auditory cortex (42L) in the NE-IL condition and negatively correlated with the clustering coefficient of the somatosensory association cortex (5L, R) in the NE-IT condition. Therefore, these results provide complementary and intuitive evidence for the differences between the IL and IT conditions in SDP for two types of deception tasks, thus elucidating the electrophysiological mechanisms underlying SDP of deception from regional, inter-regional, network, and inter-network scale analyses. PMID:25679784

A History of Soil Science Education in the United States

NASA Astrophysics Data System (ADS)

Brevik, Eric C.

2017-04-01

The formal study of soil science is a fairly recent undertaking in academics. Fields like biology, chemistry, and physics date back hundreds of years, but the scientific study of soils only dates to the late 1800s. Academic programs to train students in soil science are even more recent, with the first such programs only developing in the USA in the early 1900s. Some of the first schools to offer soil science training at the university level included the University of North Carolina (UNC), Earlham College (EC), and Cornell University. The first modern soil science textbook published in the United States was "Soils, Their Properties and Management" by Littleton Lyon, Elmer Fippin and Harry Buckman in 1909. This has evolved over time into the popular modern textbook "The Nature and Properties of Soils", most recently authored by Raymond Weil and Nyle Brady. Over time soil science education moved away from liberal arts schools such as UNC and EC and became associated primarily with land grant universities in their colleges of agriculture. There are currently about 71 colleges and universities in the USA that offer bachelors level soil science degree programs, with 54 of these (76%) being land grant schools. In the 1990s through the early 2000s enrollment in USA soil science programs was on the decline, even as overall enrollment at USA colleges and universities increased. This caused considerable concern in the soil science community. More recently there is evidence that soil science student numbers may be increasing, although additional information on this potential trend is desirable. One challenge soil science faces in the modern USA is finding an academic home, as soils are taught by a wide range of fields and soils classes are taken by students in many fields of study, including soil science, a range of agricultural programs, environmental science, environmental health, engineering, geology, geography, and others.

Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny-Lin equation

NASA Astrophysics Data System (ADS)

Rashidi, Saeede; Hejazi, S. Reza

This paper investigates the invariance properties of the time fractional Benny-Lin equation with Riemann-Liouville and Caputo derivatives. This equation can be reduced to the Kawahara equation, fifth-order Kdv equation, the Kuramoto-Sivashinsky equation and Navier-Stokes equation. By using the Lie group analysis method of fractional differential equations (FDEs), we derive Lie symmetries for the Benny-Lin equation. Conservation laws for this equation are obtained with the aid of the concept of nonlinear self-adjointness and the fractional generalization of the Noether’s operators. Furthermore, by means of the invariant subspace method, exact solutions of the equation are also constructed.

Nonintegrable semidiscrete Hirota equation: gauge-equivalent structures and dynamical properties.

PubMed

Ma, Li-Yuan; Zhu, Zuo-Nong

2014-09-01

In this paper, we investigate nonintegrable semidiscrete Hirota equations, including the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation. We focus on the topics on gauge-equivalent structures and dynamical behaviors for the two nonintegrable semidiscrete equations. By using the concept of the prescribed discrete curvature, we show that, under the discrete gauge transformations, the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation are, respectively, gauge equivalent to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We prove that the two discrete gauge transformations are reversible. We study the dynamical properties for the two nonintegrable semidiscrete Hirota equations. The exact spatial period solutions of the two nonintegrable semidiscrete Hirota equations are obtained through the constructions of period orbits of the stationary discrete Hirota equations. We discuss the topic regarding whether the spatial period property of the solution to the nonintegrable semidiscrete Hirota equation is preserved to that of the corresponding gauge-equivalent nonintegrable semidiscrete equations under the action of discrete gauge transformation. By using the gauge equivalent, we obtain the exact solutions to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We also give the numerical simulations for the stationary discrete Hirota equations. We find that their dynamics are much richer than the ones of stationary discrete nonlinear Schrödinger equations.

A Comparative Analysis of Pre-Equating and Post-Equating in a Large-Scale Assessment, High Stakes Examination

ERIC Educational Resources Information Center

Ojerinde, Dibu; Popoola, Omokunmi; Onyeneho, Patrick; Egberongbe, Aminat

2016-01-01

Statistical procedure used in adjusting test score difficulties on test forms is known as "equating". Equating makes it possible for various test forms to be used interchangeably. In terms of where the equating method fits in the assessment cycle, there are pre-equating and post-equating methods. The major benefits of pre-equating, when…

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

Basic lubrication equations

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1981-01-01

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

Computation techniques and computer programs to analyze Stirling cycle engines using characteristic dynamic energy equations

NASA Technical Reports Server (NTRS)

Larson, V. H.

1982-01-01

The basic equations that are used to describe the physical phenomena in a Stirling cycle engine are the general energy equations and equations for the conservation of mass and conversion of momentum. These equations, together with the equation of state, an analytical expression for the gas velocity, and an equation for mesh temperature are used in this computer study of Stirling cycle characteristics. The partial differential equations describing the physical phenomena that occurs in a Stirling cycle engine are of the hyperbolic type. The hyperbolic equations have real characteristic lines. By utilizing appropriate points along these curved lines the partial differential equations can be reduced to ordinary differential equations. These equations are solved numerically using a fourth-fifth order Runge-Kutta integration technique.

THE STABILITY OF THE PINCH WITH ANISOTROPIC PRESSURE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jaggi, R.K.

1961-12-01

A dispersion equation was obtained for the stability of the pinch from the hydromagnetic equations supplemented by an equation for the pressure tensor of the ions. The dispersion equation was obtained for the marginal instability case only. It was observed that this dispersion equation coincides with the dispersion equation obtained from the Chew, Goldberger, and Low equations for the marginal instability case. It was concluded that the region of stability predicted from the equations that were used is slightly more than given by the kinetic equation used by Chandrasekhar, Kaufmann, and Watson. (auth)

Critical spaces for quasilinear parabolic evolution equations and applications

NASA Astrophysics Data System (ADS)

Prüss, Jan; Simonett, Gieri; Wilke, Mathias

2018-02-01

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.

Construction of Chained True Score Equipercentile Equatings under the Kernel Equating (KE) Framework and Their Relationship to Levine True Score Equating. Research Report. ETS RR-09-24

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2009-01-01

In this paper, we develop a new chained equipercentile equating procedure for the nonequivalent groups with anchor test (NEAT) design under the assumptions of the classical test theory model. This new equating is named chained true score equipercentile equating. We also apply the kernel equating framework to this equating design, resulting in a…

A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

ERIC Educational Resources Information Center

Chen, Haiwen

2012-01-01

In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2018-07-01

A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified KdV equation (MKdV-nMKdV). The complete integrability of this equation is confirmed by showing that it nicely possesses the Painlevé property. We obtain multiple soliton solutions for the newly developed integrable equation. Moreover, this equation enjoys a variety of solutions which include solitons, peakons, cuspons, negaton, positon, complexiton and other solutions.

How to Obtain the Covariant Form of Maxwell's Equations from the Continuity Equation

ERIC Educational Resources Information Center

Heras, Jose A.

2009-01-01

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

Bifurcations of solitary wave solutions for (two and three)-dimensional nonlinear partial differential equation in quantum and magnetized plasma by using two different methods

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-06-01

In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.

Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.; Matinelli, L.

1994-01-01

The steady state solution of the system of equations consisting of the full Navier-Stokes equations and two turbulence equations has been obtained using a multigrid strategy of unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time-stepping scheme with a stability-bound local time step, while turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positivity. Low-Reynolds-number modifications to the original two-equation model are incorporated in a manner which results in well-behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.

A numerical study of the 3-periodic wave solutions to KdV-type equations

NASA Astrophysics Data System (ADS)

Zhang, Yingnan; Hu, Xingbiao; Sun, Jianqing

2018-02-01

In this paper, by using the direct method of calculating periodic wave solutions proposed by Akira Nakamura, we present a numerical process to calculate the 3-periodic wave solutions to several KdV-type equations: the Korteweg-de Vries equation, the Sawada-Koterra equation, the Boussinesq equation, the Ito equation, the Hietarinta equation and the (2 + 1)-dimensional Kadomtsev-Petviashvili equation. Some detailed numerical examples are given to show the existence of the three-periodic wave solutions numerically.

Turbulent fluid motion 3: Basic continuum equations

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1991-01-01

A derivation of the continuum equations used for the analysis of turbulence is given. These equations include the continuity equation, the Navier-Stokes equations, and the heat transfer or energy equation. An experimental justification for using a continuum approach for the study of turbulence is given.

p-Euler equations and p-Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

Some Properties of the Fractional Equation of Continuity and the Fractional Diffusion Equation

NASA Astrophysics Data System (ADS)

Fukunaga, Masataka

2006-05-01

The fractional equation of continuity (FEC) and the fractional diffusion equation (FDE) show peculiar behaviors that are in the opposite sense to those expected from the equation of continuity and the diffusion equation, respectively. The behaviors are interpreted in terms of the memory effect of the fractional time derivatives included in the equations. Some examples are given by solutions of the FDE.

An efficient computational method for the approximate solution of nonlinear Lane-Emden type equations arising in astrophysics

NASA Astrophysics Data System (ADS)

Singh, Harendra

2018-04-01

The key purpose of this article is to introduce an efficient computational method for the approximate solution of the homogeneous as well as non-homogeneous nonlinear Lane-Emden type equations. Using proposed computational method given nonlinear equation is converted into a set of nonlinear algebraic equations whose solution gives the approximate solution to the Lane-Emden type equation. Various nonlinear cases of Lane-Emden type equations like standard Lane-Emden equation, the isothermal gas spheres equation and white-dwarf equation are discussed. Results are compared with some well-known numerical methods and it is observed that our results are more accurate.

Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.; Martinelli, L.

1991-01-01

The system of equations consisting of the full Navier-Stokes equations and two turbulence equations was solved for in the steady state using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time stepping scheme with a stability bound local time step, while the turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positively. Low Reynolds number modifications to the original two equation model are incorporated in a manner which results in well behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved for, initializing all quantities with uniform freestream values, and resulting in rapid and uniform convergence rates for the flow and turbulence equations.

Double-Plate Penetration Equations

NASA Technical Reports Server (NTRS)

Hayashida, K. B.; Robinson, J. H.

2000-01-01

This report compares seven double-plate penetration predictor equations for accuracy and effectiveness of a shield design. Three of the seven are the Johnson Space Center original, modified, and new Cour-Palais equations. The other four are the Nysmith, Lundeberg-Stern-Bristow, Burch, and Wilkinson equations. These equations, except the Wilkinson equation, were derived from test results, with the velocities ranging up to 8 km/sec. Spreadsheet software calculated the projectile diameters for various velocities for the different equations. The results were plotted on projectile diameter versus velocity graphs for the expected orbital debris impact velocities ranging from 2 to 15 km/sec. The new Cour-Palais double-plate penetration equation was compared to the modified Cour-Palais single-plate penetration equation. Then the predictions from each of the seven double-plate penetration equations were compared to each other for a chosen shield design. Finally, these results from the equations were compared with test results performed at the NASA Marshall Space Flight Center. Because the different equations predict a wide range of projectile diameters at any given velocity, it is very difficult to choose the "right" prediction equation for shield configurations other than those exactly used in the equations' development. Although developed for various materials, the penetration equations alone cannot be relied upon to accurately predict the effectiveness of a shield without using hypervelocity impact tests to verify the design.

A critical review and database of biomass and volume allometric equation for trees and shrubs of Bangladesh

NASA Astrophysics Data System (ADS)

Mahmood, H.; Siddique, M. R. H.; Akhter, M.

2016-08-01

Estimations of biomass, volume and carbon stock are important in the decision making process for the sustainable management of a forest. These estimations can be conducted by using available allometric equations of biomass and volume. Present study aims to: i. develop a compilation with verified allometric equations of biomass, volume, and carbon for trees and shrubs of Bangladesh, ii. find out the gaps and scope for further development of allometric equations for different trees and shrubs of Bangladesh. Key stakeholders (government departments, research organizations, academic institutions, and potential individual researchers) were identified considering their involvement in use and development of allometric equations. A list of documents containing allometric equations was prepared from secondary sources. The documents were collected, examined, and sorted to avoid repetition, yielding 50 documents. These equations were tested through a quality control scheme involving operational verification, conceptual verification, applicability, and statistical credibility. A total of 517 allometric equations for 80 species of trees, shrubs, palm, and bamboo were recorded. In addition, 222 allometric equations for 39 species were validated through the quality control scheme. Among the verified equations, 20%, 12% and 62% of equations were for green-biomass, oven-dried biomass, and volume respectively and 4 tree species contributed 37% of the total verified equations. Five gaps have been pinpointed for the existing allometric equations of Bangladesh: a. little work on allometric equation of common tree and shrub species, b. most of the works were concentrated on certain species, c. very little proportion of allometric equations for biomass estimation, d. no allometric equation for belowground biomass and carbon estimation, and d. lower proportion of valid allometric equations. It is recommended that site and species specific allometric equations should be developed and consistency in field sampling, sample processing, data recording and selection of allometric equations should be maintained to ensure accuracy in estimation of biomass, volume, and carbon stock in different forest types of Bangladesh.

Darboux transformation and explicit solutions for some (2+1)-dimensional equations

NASA Astrophysics Data System (ADS)

Wang, Yan; Shen, Lijuan; Du, Dianlou

2007-06-01

Three systems of (2+1)-dimensional soliton equations and their decompositions into the (1+1)-dimensional soliton equations are proposed. These equations include KPI, CKP, MKPI. With the help of Darboux transformation of (1+1)-dimensional equations, we get the explicit solutions of the (2+1)-dimensional equations.

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

2018-03-01

We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

Minimizing Secular J2 Perturbation Effects on Satellite Formations

DTIC Science & Technology

2008-03-01

linear set of differential equations describing the relative motion was established by Hill as well as Clohessy and Wiltshire , with a slightly... Wiltshire (CW) equations, and Hill- Clohessy - Wiltshire (HCW) equations. In the simplest form these differential equations can be expressed as: 2 2 2 3 2...different orientation. Because these equations are much alike, the differential equations established are referred to as Hill’s equations, Clohessy

Dichotomies for generalized ordinary differential equations and applications

NASA Astrophysics Data System (ADS)

Bonotto, E. M.; Federson, M.; Santos, F. L.

2018-03-01

In this work we establish the theory of dichotomies for generalized ordinary differential equations, introducing the concepts of dichotomies for these equations, investigating their properties and proposing new results. We establish conditions for the existence of exponential dichotomies and bounded solutions. Using the correspondences between generalized ordinary differential equations and other equations, we translate our results to measure differential equations and impulsive differential equations. The fact that we work in the framework of generalized ordinary differential equations allows us to manage functions with many discontinuities and of unbounded variation.

Method of mechanical quadratures for solving singular integral equations of various types

NASA Astrophysics Data System (ADS)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

A discrete model of a modified Burgers' partial differential equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.; Shoosmith, J. N.

1990-01-01

A new finite-difference scheme is constructed for a modified Burger's equation. Three special cases of the equation are considered, and the 'exact' difference schemes for the space- and time-independent forms of the equation are presented, along with the diffusion-free case of Burger's equation modeled by a difference equation. The desired difference scheme is then obtained by imposing on any difference model of the initial equation the requirement that, in the appropriate limits, its difference scheme must reduce the results of the obtained equations.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

PubMed

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

Investigation of a Coupled Arrhenius-Type/Rossard Equation of AH36 Material.

PubMed

Qin, Qin; Tian, Ming-Liang; Zhang, Peng

2017-04-13

High-temperature tensile testing of AH36 material in a wide range of temperatures (1173-1573 K) and strain rates (10 -4 -10 -2 s -1 ) has been obtained by using a Gleeble system. These experimental stress-strain data have been adopted to develop the constitutive equation. The constitutive equation of AH36 material was suggested based on the modified Arrhenius-type equation and the modified Rossard equation respectively. The results indicate that the constitutive equation is strongly influenced by temperature and strain, especially strain. Moreover, there is a good agreement between the predicted data of the modified Arrhenius-type equation and the experimental results when the strain is greater than 0.02. There is also good agreement between the predicted data of the Rossard equation and the experimental results when the strain is less than 0.02. Therefore, a coupled equation where the modified Arrhenius-type equation and Rossard equation are combined has been proposed to describe the constitutive equation of AH36 material according to the different strain values in order to improve the accuracy. The correlation coefficient between the computed and experimental flow stress data was 0.998. The minimum value of the average absolute relative error shows the high accuracy of the coupled equation compared with the two modified equations.

Impact of switching from Caucasian to Indian reference equations for spirometry interpretation.

PubMed

Chhabra, S K; Madan, M

2018-03-01

In the absence of ethnically appropriate prediction equations, spirometry data in Indian subjects are often interpreted using equations for other ethnic populations. To evaluate the impact of switching from Caucasian (National Health and Nutrition Examination Survey III [NHANES III] and Global Lung Function Initiative [GLI]) equations to the recently published North Indian equations on spirometric interpretation, and to examine the suitability of GLI-Mixed equations for this population. Spirometry data on 12 323 North Indian patients were analysed using the North Indian equations as well as NHANES III, GLI-Caucasian and GLI-Mixed equations. Abnormalities and ventilatory patterns were categorised and agreement in interpretation was evaluated. The NHANES III and GLI-Caucasian equations and, to a lesser extent, the GLI-Mixed equations, predicted higher values and labelled more measurements as abnormal. In up to one third of the patients, these differed from Indian equations in the categorisation of ventilatory patterns, with more patients classified as having restrictive and mixed disease. The NHANES III and GLI-Caucasian equations substantially overdiagnose abnormalities and misclassify ventilatory patterns on spirometry in Indian patients. Such errors of interpretation, although less common with the GLI-Mixed equations, remain substantial and are clinically unacceptable. A switch to Indian equations will have a major impact on interpretation.

The applicability of eGFR equations to different populations.

PubMed

Delanaye, Pierre; Mariat, Christophe

2013-09-01

The Cockcroft-Gault equation for estimating glomerular filtration rate has been learnt by every generation of medical students over the decades. Since the publication of the Modification of Diet in Renal Disease (MDRD) study equation in 1999, however, the supremacy of the Cockcroft-Gault equation has been relentlessly disputed. More recently, the Chronic Kidney Disease Epidemiology (CKD-EPI) consortium has proposed a group of novel equations for estimating glomerular filtration rate (GFR). The MDRD and CKD-EPI equations were developed following a rigorous process, are expressed in a way in which they can be used with standardized biomarkers of GFR (serum creatinine and/or serum cystatin C) and have been evaluated in different populations of patients. Today, the MDRD Study equation and the CKD-EPI equation based on serum creatinine level have supplanted the Cockcroft-Gault equation. In many regards, these equations are superior to the Cockcroft-Gault equation and are now specifically recommended by international guidelines. With their generalized use, however, it has become apparent that those equations are not infallible and that they fail to provide an accurate estimate of GFR in certain situations frequently encountered in clinical practice. After describing the processes that led to the development of the new GFR-estimating equations, this Review discusses the clinical situations in which the applicability of these equations is questioned.

Predictive Temperature Equations for Three Sites at the Grand Canyon

NASA Astrophysics Data System (ADS)

McLaughlin, Katrina Marie Neitzel

Climate data collected at a number of automated weather stations were used to create a series of predictive equations spanning from December 2009 to May 2010 in order to better predict the temperatures along hiking trails within the Grand Canyon. The central focus of this project is how atmospheric variables interact and can be combined to predict the weather in the Grand Canyon at the Indian Gardens, Phantom Ranch, and Bright Angel sites. Through the use of statistical analysis software and data regression, predictive equations were determined. The predictive equations are simple or multivariable best fits that reflect the curvilinear nature of the data. With data analysis software curves resulting from the predictive equations were plotted along with the observed data. Each equation's reduced chi2 was determined to aid the visual examination of the predictive equations' ability to reproduce the observed data. From this information an equation or pair of equations was determined to be the best of the predictive equations. Although a best predictive equation for each month and season was determined for each site, future work may refine equations to result in a more accurate predictive equation.

A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

PubMed

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

PubMed Central

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method. PMID:25973605

Symmetry investigations on the incompressible stationary axisymmetric Euler equations with swirl

NASA Astrophysics Data System (ADS)

Frewer, M.; Oberlack, M.; Guenther, S.

2007-08-01

We discuss the incompressible stationary axisymmetric Euler equations with swirl, for which we derive via a scalar stream function an equivalent representation, the Bragg-Hawthorne equation [Bragg, S.L., Hawthorne, W.R., 1950. Some exact solutions of the flow through annular cascade actuator discs. J. Aero. Sci. 17, 243]. Despite this obvious equivalence, we will show that under a local Lie point symmetry analysis the Bragg-Hawthorne equation exposes itself as not being fully equivalent to the original Euler equations. This is reflected in the way that it possesses additional symmetries not being admitted by its counterpart. In other words, a symmetry of the Bragg-Hawthorne equation is in general not a symmetry of the Euler equations. Not the differential Euler equations but rather a set of integro-differential equations attains full equivalence to the Bragg-Hawthorne equation. For these intermediate Euler equations, it is interesting to note that local symmetries of the Bragg-Hawthorne equation transform to local as well as to nonlocal symmetries. This behaviour, on the one hand, is in accordance with Zawistowski's result [Zawistowski, Z.J., 2001. Symmetries of integro-differential equations. Rep. Math. Phys. 48, 269; Zawistowski, Z.J., 2004. General criterion of invariance for integro-differential equations. Rep. Math. Phys. 54, 341] that it is possible for integro-differential equations to admit local Lie point symmetries. On the other hand, with this transformation process we collect symmetries which cannot be obtained when carrying out a usual local Lie point symmetry analysis. Finally, the symmetry classification of the Bragg-Hawthorne equation is used to find analytical solutions for the phenomenon of vortex breakdown.

FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

NASA Astrophysics Data System (ADS)

Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

2010-11-01

In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

Equating Multidimensional Tests under a Random Groups Design: A Comparison of Various Equating Procedures

ERIC Educational Resources Information Center

Lee, Eunjung

2013-01-01

The purpose of this research was to compare the equating performance of various equating procedures for the multidimensional tests. To examine the various equating procedures, simulated data sets were used that were generated based on a multidimensional item response theory (MIRT) framework. Various equating procedures were examined, including…

Comparison of Kernel Equating and Item Response Theory Equating Methods

ERIC Educational Resources Information Center

Meng, Yu

2012-01-01

The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

PubMed

Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

2017-06-01

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

Soliton evolution and radiation loss for the sine-Gordon equation.

PubMed

Smyth, N F; Worthy, A L

1999-08-01

An approximate method for describing the evolution of solitonlike initial conditions to solitons for the sine-Gordon equation is developed. This method is based on using a solitonlike pulse with variable parameters in an averaged Lagrangian for the sine-Gordon equation. This averaged Lagrangian is then used to determine ordinary differential equations governing the evolution of the pulse parameters. The pulse evolves to a steady soliton by shedding dispersive radiation. The effect of this radiation is determined by examining the linearized sine-Gordon equation and loss terms are added to the variational equations derived from the averaged Lagrangian by using the momentum and energy conservation equations for the sine-Gordon equation. Solutions of the resulting approximate equations, which include loss, are found to be in good agreement with full numerical solutions of the sine-Gordon equation.

Multi-Hamiltonian structure of equations of hydrodynamic type

NASA Astrophysics Data System (ADS)

Gümral, H.; Nutku, Y.

1990-11-01

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama's generalization of the shallow-water equations admits bi-Hamiltonian structure.

Elliptic Painlevé equations from next-nearest-neighbor translations on the E_8^{(1)} lattice

NASA Astrophysics Data System (ADS)

Joshi, Nalini; Nakazono, Nobutaka

2017-07-01

The well known elliptic discrete Painlevé equation of Sakai is constructed by a standard translation on the E_8(1) lattice, given by nearest neighbor vectors. In this paper, we give a new elliptic discrete Painlevé equation obtained by translations along next-nearest-neighbor vectors. This equation is a generic (8-parameter) version of a 2-parameter elliptic difference equation found by reduction from Adler’s partial difference equation, the so-called Q4 equation. We also provide a projective reduction of the well known equation of Sakai.

From differential to difference equations for first order ODEs

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Walker, Kevin P.

1991-01-01

When constructing an algorithm for the numerical integration of a differential equation, one should first convert the known ordinary differential equation (ODE) into an ordinary difference equation. Given this difference equation, one can develop an appropriate numerical algorithm. This technical note describes the derivation of two such ordinary difference equations applicable to a first order ODE. The implicit ordinary difference equation has the same asymptotic expansion as the ODE itself, whereas the explicit ordinary difference equation has an asymptotic that is similar in structure but different in value when compared with that of the ODE.

Influence of the dispersive and dissipative scales alpha and beta on the energy spectrum of the Navier-Stokes alphabeta equations.

PubMed

Chen, Xuemei; Fried, Eliot

2008-10-01

Lundgren's vortex model for the intermittent fine structure of high-Reynolds-number turbulence is applied to the Navier-Stokes alphabeta equations and specialized to the Navier-Stokes alpha equations. The Navier-Stokes alphabeta equations involve dispersive and dissipative length scales alpha and beta, respectively. Setting beta equal to alpha reduces the Navier-Stokes alphabeta equations to the Navier-Stokes alpha equations. For the Navier-Stokes alpha equations, the energy spectrum is found to obey Kolmogorov's -5/3 law in a range of wave numbers identical to that determined by Lundgren for the Navier-Stokes equations. For the Navier-Stokes alphabeta equations, Kolmogorov's -5/3 law is also recovered. However, granted that beta < alpha, the range of wave numbers for which this law holds is extended by a factor of alphabeta . This suggests that simulations based on the Navier-Stokes alphabeta equations may have the potential to resolve features smaller than those obtainable using the Navier-Stokes alpha equations.

Fast sweeping method for the factored eikonal equation

NASA Astrophysics Data System (ADS)

Fomel, Sergey; Luo, Songting; Zhao, Hongkai

2009-09-01

We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.

A procedure to construct exact solutions of nonlinear fractional differential equations.

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ho, C.-L.; Lee, C.-C., E-mail: chieh.no27@gmail.com

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

Single wall penetration equations

NASA Technical Reports Server (NTRS)

Hayashida, K. B.; Robinson, J. H.

1991-01-01

Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

Investigation of a Coupled Arrhenius-Type/Rossard Equation of AH36 Material

PubMed Central

Qin, Qin; Tian, Ming-Liang; Zhang, Peng

2017-01-01

High-temperature tensile testing of AH36 material in a wide range of temperatures (1173–1573 K) and strain rates (10−4–10−2 s−1) has been obtained by using a Gleeble system. These experimental stress-strain data have been adopted to develop the constitutive equation. The constitutive equation of AH36 material was suggested based on the modified Arrhenius-type equation and the modified Rossard equation respectively. The results indicate that the constitutive equation is strongly influenced by temperature and strain, especially strain. Moreover, there is a good agreement between the predicted data of the modified Arrhenius-type equation and the experimental results when the strain is greater than 0.02. There is also good agreement between the predicted data of the Rossard equation and the experimental results when the strain is less than 0.02. Therefore, a coupled equation where the modified Arrhenius-type equation and Rossard equation are combined has been proposed to describe the constitutive equation of AH36 material according to the different strain values in order to improve the accuracy. The correlation coefficient between the computed and experimental flow stress data was 0.998. The minimum value of the average absolute relative error shows the high accuracy of the coupled equation compared with the two modified equations. PMID:28772767

A Graphical Approach to Evaluating Equating Using Test Characteristic Curves

ERIC Educational Resources Information Center

Wyse, Adam E.; Reckase, Mark D.

2011-01-01

An essential concern in the application of any equating procedure is determining whether tests can be considered equated after the tests have been placed onto a common scale. This article clarifies one equating criterion, the first-order equity property of equating, and develops a new method for evaluating equating that is linked to this…

Simple taper: Taper equations for the field forester

Treesearch

David R. Larsen

2017-01-01

"Simple taper" is set of linear equations that are based on stem taper rates; the intent is to provide taper equation functionality to field foresters. The equation parameters are two taper rates based on differences in diameter outside bark at two points on a tree. The simple taper equations are statistically equivalent to more complex equations. The linear...

Optimization of one-way wave equations.

USGS Publications Warehouse

Lee, M.W.; Suh, S.Y.

1985-01-01

The theory of wave extrapolation is based on the square-root equation or one-way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square-root equation represents waves propagating in one direction only. A new optimization method presented here improves the dispersion relation of the one-way wave equation. -from Authors

Standard Errors of Equating for the Percentile Rank-Based Equipercentile Equating with Log-Linear Presmoothing

ERIC Educational Resources Information Center

Wang, Tianyou

2009-01-01

Holland and colleagues derived a formula for analytical standard error of equating using the delta-method for the kernel equating method. Extending their derivation, this article derives an analytical standard error of equating procedure for the conventional percentile rank-based equipercentile equating with log-linear smoothing. This procedure is…

Conservational PDF Equations of Turbulence

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2010-01-01

Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application

GFR Estimation: From Physiology to Public Health

PubMed Central

Levey, Andrew S.; Inker, Lesley A.; Coresh, Josef

2014-01-01

Estimating glomerular filtration rate (GFR) is essential for clinical practice, research, and public health. Appropriate interpretation of estimated GFR (eGFR) requires understanding the principles of physiology, laboratory medicine, epidemiology and biostatistics used in the development and validation of GFR estimating equations. Equations developed in diverse populations are less biased at higher GFR than equations developed in CKD populations and are more appropriate for general use. Equations that include multiple endogenous filtration markers are more precise than equations including a single filtration marker. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations are the most accurate GFR estimating equations that have been evaluated in large, diverse populations and are applicable for general clinical use. The 2009 CKD-EPI creatinine equation is more accurate in estimating GFR and prognosis than the 2006 Modification of Diet in Renal Disease (MDRD) Study equation and provides lower estimates of prevalence of decreased eGFR. It is useful as a “first” test for decreased eGFR and should replace the MDRD Study equation for routine reporting of serum creatinine–based eGFR by clinical laboratories. The 2012 CKD-EPI cystatin C equation is as accurate as the 2009 CKD-EPI creatinine equation in estimating eGFR, does not require specification of race, and may be more accurate in patients with decreased muscle mass. The 2012 CKD-EPI creatinine–cystatin C equation is more accurate than the 2009 CKD-EPI creatinine and 2012 CKD-EPI cystatin C equations and is useful as a confirmatory test for decreased eGFR as determined by an equation based on serum creatinine. Further improvement in GFR estimating equations will require development in more broadly representative populations, including diverse racial and ethnic groups, use of multiple filtration markers, and evaluation using statistical techniques to compare eGFR to “true GFR”. PMID:24485147

Receptor binding kinetics equations: Derivation using the Laplace transform method.

PubMed

Hoare, Sam R J

Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time-dependent pharmacological activities. Copyright © 2017 Elsevier Inc. All rights reserved.

Superposition of elliptic functions as solutions for a large number of nonlinear equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khare, Avinash; Saxena, Avadh

2014-03-15

For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ{sup 4}, the discrete MKdV as well asmore » for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn{sup 2}(x, m), it also admits solutions in terms of dn {sup 2}(x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations.« less

Lax representations for matrix short pulse equations

NASA Astrophysics Data System (ADS)

Popowicz, Z.

2017-10-01

The Lax representation for different matrix generalizations of Short Pulse Equations (SPEs) is considered. The four-dimensional Lax representations of four-component Matsuno, Feng, and Dimakis-Müller-Hoissen-Matsuno equations are obtained. The four-component Feng system is defined by generalization of the two-dimensional Lax representation to the four-component case. This system reduces to the original Feng equation, to the two-component Matsuno equation, or to the Yao-Zang equation. The three-component version of the Feng equation is presented. The four-component version of the Matsuno equation with its Lax representation is given. This equation reduces the new two-component Feng system. The two-component Dimakis-Müller-Hoissen-Matsuno equations are generalized to the four-parameter family of the four-component SPE. The bi-Hamiltonian structure of this generalization, for special values of parameters, is defined. This four-component SPE in special cases reduces to the new two-component SPE.

Modified equations, rational solutions, and the Painleve property for the Kadomtsev--Petviashvili and Hirota--Satsuma equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weiss, J.

1985-09-01

We propose a method for finding the Lax pairs and rational solutions of integrable partial differential equations. That is, when an equation possesses the Painleve property, a Baecklund transformation is defined in terms of an expansion about the singular manifold. This Baecklund transformation obtains (1) a type of modified equation that is formulated in terms of Schwarzian derivatives and (2) a Miura transformation from the modified to the original equation. By linearizing the (Ricati-type) Miura transformation the Lax pair is found. On the other hand, consideration of the (distinct) Baecklund transformations of the modified equations provides a method for themore » iterative construction of rational solutions. This also obtains the Lax pairs for the modified equations. In this paper we apply this method to the Kadomtsev--Petviashvili equation and the Hirota--Satsuma equations.« less

Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

Rui, Wenjuan; Zhang, Xiangzhi

2016-05-01

This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation

NASA Astrophysics Data System (ADS)

Ormerod, Christopher M.

2014-01-01

We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with E_6^{(1)} symmetry. We present a description of a set of symmetries of the reduced equations and their relations to the symmetries of the discrete Painlevé equation. Finally, we exploit the simple symmetric form of the reduced equations to find rational and hypergeometric solutions of this discrete Painlevé equation.

The Effectiveness of Circular Equating as a Criterion for Evaluating Equating.

ERIC Educational Resources Information Center

Wang, Tianyou; Hanson, Bradley A.; Harris, Deborah J.

Equating a test form to itself through a chain of equatings, commonly referred to as circular equating, has been widely used as a criterion to evaluate the adequacy of equating. This paper uses both analytical methods and simulation methods to show that this criterion is in general invalid in serving this purpose. For the random groups design done…

Brownian motion from Boltzmann's equation.

NASA Technical Reports Server (NTRS)

Montgomery, D.

1971-01-01

Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.

A Comparison of the Kernel Equating Method with Traditional Equating Methods Using SAT[R] Data

ERIC Educational Resources Information Center

Liu, Jinghua; Low, Albert C.

2008-01-01

This study applied kernel equating (KE) in two scenarios: equating to a very similar population and equating to a very different population, referred to as a distant population, using SAT[R] data. The KE results were compared to the results obtained from analogous traditional equating methods in both scenarios. The results indicate that KE results…

New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2010-01-01

In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2017-01-01

We introduce a so-called coprimeness-preserving non-integrable extension to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equations defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.

Generalized Thomas-Fermi equations as the Lampariello class of Emden-Fowler equations

NASA Astrophysics Data System (ADS)

Rosu, Haret C.; Mancas, Stefan C.

2017-04-01

A one-parameter family of Emden-Fowler equations defined by Lampariello's parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.

Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.

2011-03-01

We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping

2016-10-01

Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.

Investigation of two and three parameter equations of state for cryogenic fluids

NASA Technical Reports Server (NTRS)

Jenkins, Susan L.; Majumdar, Alok K.; Hendricks, Robert C.

1990-01-01

Two-phase flows are a common occurrence in cryogenic engines and an accurate evaluation of the heat-transfer coefficient in two-phase flow is of significant importance in their analysis and design. The thermodynamic equation of state plays a key role in calculating the heat transfer coefficient which is a function of thermodynamic and thermophysical properties. An investigation has been performed to study the performance of two- and three-parameter equations of state to calculate the compressibility factor of cryogenic fluids along the saturation loci. The two-parameter equations considered here are van der Waals and Redlich-Kwong equations of state. The three-parameter equation represented here is the generalized Benedict-Webb-Rubin (BWR) equation of Lee and Kesler. Results have been compared with the modified BWR equation of Bender and the extended BWR equations of Stewart. Seven cryogenic fluids have been tested; oxygen, hydrogen, helium, nitrogen, argon, neon, and air. The performance of the generalized BWR equation is poor for hydrogen and helium. The van der Waals equation is found to be inaccurate for air near the critical point. For helium, all three equations of state become inaccurate near the critical point.

Compressible Flow Toolbox

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

The Compressible Flow Toolbox is primarily a MATLAB-language implementation of a set of algorithms that solve approximately 280 linear and nonlinear classical equations for compressible flow. The toolbox is useful for analysis of one-dimensional steady flow with either constant entropy, friction, heat transfer, or Mach number greater than 1. The toolbox also contains algorithms for comparing and validating the equation-solving algorithms against solutions previously published in open literature. The classical equations solved by the Compressible Flow Toolbox are as follows: The isentropic-flow equations, The Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), The Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section), The normal-shock equations, The oblique-shock equations, and The expansion equations.

Evaluation of equations that estimate glomerular filtration rate in renal transplant recipients.

PubMed

De Alencastro, M G; Veronese, F V; Vicari, A R; Gonçalves, L F; Manfro, R C

2014-03-01

The accuracy of equations that estimate the glomerular filtration rate (GFR) in renal transplant patients has not been established; thus their performance was assessed in stable renal transplant patients. Renal transplant patients (N.=213) with stable graft function were enrolled. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation was used as the reference method and compared with the Cockcroft-Gault (CG), Modification of Diet in Renal Disease (MDRD), Mayo Clinic (MC) and Nankivell equations. Bias, accuracy and concordance rates were determined for all equation relative to CKD-EPI. Mean estimated GFR values of the equations differed significantly from the CKD-EPI values, though the correlations with the reference method were significant. Values of MDRD differed from the CG, MC and Nankivell estimations. The best agreement to classify the chronic kidney disease (CKD) stages was for the MDRD (Kappa=0.649, P<0.001), and for the other equations the agreement was moderate. The MDRD had less bias and narrower agreement limits but underestimated the GFR at levels above 60 mL/min/1.73 m2. Conversely, the CG, MC and Nankivell equations overestimated the GFR, and the Nankivell equation had the worst performance. The MDRD equation P15 and P30 values were higher than those of the other equations (P<0.001). Despite their correlations, equations estimated the GFR and CKD stage differently. The MDRD equation was the most accurate, but the sub-optimal performance of all the equations precludes their accurate use in clinical practice.

Reduction of lattice equations to the Painlevé equations: PIV and PV

NASA Astrophysics Data System (ADS)

Nakazono, Nobutaka

2018-02-01

In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

An Evaluation of Kernel Equating: Parallel Equating with Classical Methods in the SAT Subject Tests[TM] Program. Research Report. ETS RR-09-06

ERIC Educational Resources Information Center

Grant, Mary C.; Zhang, Lilly; Damiano, Michele

2009-01-01

This study investigated kernel equating methods by comparing these methods to operational equatings for two tests in the SAT Subject Tests[TM] program. GENASYS (ETS, 2007) was used for all equating methods and scaled score kernel equating results were compared to Tucker, Levine observed score, chained linear, and chained equipercentile equating…

Smoothing and Equating Methods Applied to Different Types of Test Score Distributions and Evaluated with Respect to Multiple Equating Criteria. Research Report. ETS RR-11-20

ERIC Educational Resources Information Center

Moses, Tim; Liu, Jinghua

2011-01-01

In equating research and practice, equating functions that are smooth are typically assumed to be more accurate than equating functions with irregularities. This assumption presumes that population test score distributions are relatively smooth. In this study, two examples were used to reconsider common beliefs about smoothing and equating. The…

A Comparison of Kernel Equating and Traditional Equipercentile Equating Methods and the Parametric Bootstrap Methods for Estimating Standard Errors in Equipercentile Equating

ERIC Educational Resources Information Center

Choi, Sae Il

2009-01-01

This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response…

Prediction equation of resting energy expenditure in an adult Spanish population of obese adult population.

PubMed

de Luis, D A; Aller, R; Izaola, O; Romero, E

2006-01-01

The aim of our study was to evaluate the accuracy of the equations to estimate REE in obese patents and develop a new equation in our obese population. A population of 200 obesity outpatients was analyzed in a prospective way. The following variables were specifically recorded: age, weight, body mass index (BMI), waist circumference, and waist-to-hip ratio. Basal glucose, insulin, and TSH (thyroid-stimulating hormone) were measured. An indirect calorimetry and a tetrapolar electrical bioimpedance were performed. REE measured by indirect calorimetry was compared with REE obtained by prediction equations to obese or nonobese patients. The mean age was 44.8 +/- 16.81 years and the mean BMI 34.4 +/- 5.3. Indirect calorimetry showed that, as compared to women, men had higher resting energy expenditure (REE) (1,998.1 +/- 432 vs. 1,663.9 +/- 349 kcal/day; p < 0.05) and oxygen consumption (284.6 +/- 67.7 vs. 238.6 +/- 54.3 ml/min; p < 0.05). Correlation analysis among REE obtained by indirect calorimetry and REE predicted by prediction equations showed the next data; Berstein's equation (r = 0.65; p < 0.05), Harris Benedict's equation (r = 0.58; p < 0.05), Owen's equation (r = 0.56; p < 0.05), Ireton's equation (r = 0.58; p < 0.05) and WHO's equation (r = 0.57; p < 0.05). Both the Berstein's and the Ireton's equations overpredicted REE and showed nonsignificant mean differences form measured REE. The Owen's, WHO's, and Harris Benedict's equations underpredicted REE. Our male prediction equation was REE = 58.6 + (6.1 x weight (kg)) + (1,023.7 x height (m)) - (9.5 x age). The female model was REE = 1,272.5 + (9.8 x weight (kg)) - (61.6 x height (m)) - (8.2 x age). Our prediction equations showed a nonsignificant difference with REE measured (-3.7 kcal/day) with a significant correlation coefficient (r = 0.67; p < 0.05). Previously developed prediction equations overestimated and underestimated REE measured. WHO equation developed in normal weight individuals provided the closest values. The two new equations (male and female equations) developed in our study had a good accuracy. Copyright 2006 S. Karger AG, Basel.

Revised techniques for estimating peak discharges from channel width in Montana

USGS Publications Warehouse

Parrett, Charles; Hull, J.A.; Omang, R.J.

1987-01-01

This study was conducted to develop new estimating equations based on channel width and the updated flood frequency curves of previous investigations. Simple regression equations for estimating peak discharges with recurrence intervals of 2, 5, 10 , 25, 50, and 100 years were developed for seven regions in Montana. The standard errors of estimates for the equations that use active channel width as the independent variables ranged from 30% to 87%. The standard errors of estimate for the equations that use bankfull width as the independent variable ranged from 34% to 92%. The smallest standard errors generally occurred in the prediction equations for the 2-yr flood, 5-yr flood, and 10-yr flood, and the largest standard errors occurred in the prediction equations for the 100-yr flood. The equations that use active channel width and the equations that use bankfull width were determined to be about equally reliable in five regions. In the West Region, the equations that use bankfull width were slightly more reliable than those based on active channel width, whereas in the East-Central Region the equations that use active channel width were slightly more reliable than those based on bankfull width. Compared with similar equations previously developed, the standard errors of estimate for the new equations are substantially smaller in three regions and substantially larger in two regions. Limitations on the use of the estimating equations include: (1) The equations are based on stable conditions of channel geometry and prevailing water and sediment discharge; (2) The measurement of channel width requires a site visit, preferably by a person with experience in the method, and involves appreciable measurement errors; (3) Reliability of results from the equations for channel widths beyond the range of definition is unknown. In spite of the limitations, the estimating equations derived in this study are considered to be as reliable as estimating equations based on basin and climatic variables. Because the two types of estimating equations are independent, results from each can be weighted inversely proportional to their variances, and averaged. The weighted average estimate has a variance less than either individual estimate. (Author 's abstract)

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

NASA Astrophysics Data System (ADS)

Rivera, R.; Villarroel, D.

2002-10-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

Chemical Equation Balancing.

ERIC Educational Resources Information Center

Blakley, G. R.

1982-01-01

Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

Nonlocal nonlinear Schrödinger equations and their soliton solutions

NASA Astrophysics Data System (ADS)

Gürses, Metin; Pekcan, Aslı

2018-05-01

We study standard and nonlocal nonlinear Schrödinger (NLS) equations obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur (AKNS) equations) by using standard and nonlocal reductions, respectively. By using the Hirota bilinear method, we first find soliton solutions of the coupled NLS system of equations; then using the reduction formulas, we find the soliton solutions of the standard and nonlocal NLS equations. We give examples for particular values of the parameters and plot the function |q(t, x)|2 for the standard and nonlocal NLS equations.

From nonlinear Schrödinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

NASA Astrophysics Data System (ADS)

Yang, Xiao; Du, Dianlou

2010-08-01

The Poisson structure on CN×RN is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schrödinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

Symmetry methods for option pricing

NASA Astrophysics Data System (ADS)

Davison, A. H.; Mamba, S.

2017-06-01

We obtain a solution of the Black-Scholes equation with a non-smooth boundary condition using symmetry methods. The Black-Scholes equation along with its boundary condition are first transformed into the one dimensional heat equation and an initial condition respectively. We then find an appropriate general symmetry generator of the heat equation using symmetries and the fundamental solution of the heat equation. The symmetry generator is chosen such that the boundary condition is left invariant; the symmetry can be used to solve the heat equation and hence the Black-Scholes equation.

On the Connection Between One-and Two-Equation Models of Turbulence

NASA Technical Reports Server (NTRS)

Menter, F. R.; Rai, Man Mohan (Technical Monitor)

1994-01-01

A formalism will be presented that allows the transformation of two-equation eddy viscosity turbulence models into one-equation models. The transformation is based on an assumption that is widely accepted over a large range of boundary layer flows and that has been shown to actually improve predictions when incorporated into two-equation models of turbulence. Based on that assumption, a new one-equation turbulence model will be derived. The new model will be tested in great detail against a previously introduced one-equation model and against its parent two-equation model.

On the continuum limit for a semidiscrete Hirota equation

PubMed Central

Pickering, Andrew; Zhao, Hai-qiong

2016-01-01

In this paper, we propose a new semidiscrete Hirota equation which yields the Hirota equation in the continuum limit. We focus on the topic of how the discrete space step δ affects the simulation for the soliton solution to the Hirota equation. The Darboux transformation and explicit solution for the semidiscrete Hirota equation are constructed. We show that the continuum limit for the semidiscrete Hirota equation, including the Lax pair, the Darboux transformation and the explicit solution, yields the corresponding results for the Hirota equation as δ→0. PMID:27956884

A new modified CKD-EPI equation for Chinese patients with type 2 diabetes.

PubMed

Liu, Xun; Gan, Xiaoliang; Chen, Jinxia; Lv, Linsheng; Li, Ming; Lou, Tanqi

2014-01-01

To improve the performance of glomerular filtration rate (GFR) estimating equation in Chinese type 2 diabetic patients by modification of the CKD-EPI equation. A total of 1196 subjects were enrolled. Measured GFR was calibrated to the dual plasma sample 99mTc-DTPA-GFR. GFRs estimated by the re-expressed 4-variable MDRD equation, the CKD-EPI equation and the Asian modified CKD-EPI equation were compared in 351 diabetic/non-diabetic pairs. And a new modified CKD-EPI equation was reconstructed in a total of 589 type 2 diabetic patients. In terms of both precision and accuracy, GFR estimating equations all achieved better results in the non-diabetic cohort comparing with those in the type 2 diabetic cohort (30% accuracy, P≤0.01 for all comparisons). In the validation data set, the new modified equation showed less bias (median difference, 2.3 ml/min/1.73 m2 for the new modified equation vs. ranged from -3.8 to -7.9 ml/min/1.73 m2 for the other 3 equations [P<0.001 for all comparisons]), as was precision (IQR of the difference, 24.5 ml/min/1.73 m2 vs. ranged from 27.3 to 30.7 ml/min/1.73 m2), leading to a greater accuracy (30% accuracy, 71.4% vs. 55.2% for the re-expressed 4 variable MDRD equation and 61.0% for the Asian modified CKD-EPI equation [P = 0.001 and P = 0.02]). A new modified CKD-EPI equation for type 2 diabetic patients was developed and validated. The new modified equation improves the performance of GFR estimation.

Performance of Creatinine and Cystatin C GFR Estimating Equations in an HIV-positive population on Antiretrovirals

PubMed Central

INKER, Lesley A; WYATT, Christina; CREAMER, Rebecca; HELLINGER, James; HOTTA, Matthew; LEPPO, Maia; LEVEY, Andrew S; OKPARAVERO, Aghogho; GRAHAM, Hiba; SAVAGE, Karen; SCHMID, Christopher H; TIGHIOUART, Hocine; WALLACH, Fran; KRISHNASAMI, Zipporah

2013-01-01

Objective To evaluate the performance of CKD-EPI creatinine, cystatin C and creatinine-cystatin C estimating equations in HIV-positive patients. Methods We evaluated the performance of the MDRD Study and CKD-EPI creatinine 2009, CKD-EPI cystatin C 2012 and CKD-EPI creatinine-cystatin C 2012 glomerular filtration rate (GFR) estimating equations compared to GFR measured using plasma clearance of iohexol in 200 HIV-positive patients on stable antiretroviral therapy. Creatinine and cystatin C assays were standardized to certified reference materials. Results Of the 200 participants, median (IQR) CD4 count was 536 (421) and 61% had an undetectable HIV-viral load. Mean (SD) measured GFR (mGFR) was 87 (26) ml/min/1.73m2. All CKD-EPI equations performed better than the MDRD Study equation. All three CKD-EPI equations had similar bias and precision. The cystatin C equation was not more accurate than the creatinine equation. The creatinine-cystatin C equation was significantly more accurate than the cystatin C equation and there was a trend toward greater accuracy than the creatinine equation. Accuracy was equal or better in most subgroups with the combined equation compared to either alone. Conclusions The CKD-EPI cystatin C equation does not appear to be more accurate than the CKD-EPI creatinine equation in patients who are HIV-positive, supporting the use of the CKD-EPI creatinine equation for routine clinical care for use in North American populations with HIV. The use of both filtration markers together as a confirmatory test for decreased estimated GFR based on creatinine in individuals who are HIV-positive requires further study. PMID:22842844

Universal equation for estimating ideal body weight and body weight at any BMI1

PubMed Central

Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B

2016-01-01

Background: Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. Objective: For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. Design: With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Results: Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5–0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Conclusions: Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. PMID:27030535

Universal equation for estimating ideal body weight and body weight at any BMI.

PubMed

Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B

2016-05-01

Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5-0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. © 2016 American Society for Nutrition.

Evaluation of pier-scour equations for coarse-bed streams

USGS Publications Warehouse

Chase, Katherine J.; Holnbeck, Stephen R.

2004-01-01

Streambed scour at bridge piers is among the leading causes of bridge failure in the United States. Several pier-scour equations have been developed to calculate potential scour depths at existing and proposed bridges. Because many pier-scour equations are based on data from laboratory flumes and from cohesionless silt- and sand-bottomed streams, they tend to overestimate scour for piers in coarse-bed materials. Several equations have been developed to incorporate the mitigating effects of large particle sizes on pier scour, but further investigations are needed to evaluate how accurately pier-scour depths calculated by these equations match measured field data. This report, prepared in cooperation with the Montana Department of Transportation, describes the evaluation of five pier-scour equations for coarse-bed streams. Pier-scour and associated bridge-geometry, bed-material, and streamflow-measurement data at bridges over coarse-bed streams in Montana, Alaska, Maryland, Ohio, and Virginia were selected from the Bridge Scour Data Management System. Pier scour calculated using the Simplified Chinese equation, the Froehlich equation, the Froehlich design equation, the HEC-18/Jones equation and the HEC-18/Mueller equation for flood events with approximate recurrence intervals of less than 2 to 100 years were compared to 42 pier-scour measurements. Comparison of results showed that pier-scour depths calculated with the HEC-18/Mueller equation were seldom smaller than measured pier-scour depths. In addition, pier-scour depths calculated using the HEC-18/Mueller equation were closer to measured scour than for the other equations that did not underestimate pier scour. However, more data are needed from coarse-bed streams and from less frequent flood events to further evaluate pier-scour equations.

Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.

PubMed

Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail

2014-01-01

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

The Geochemistry of Mass Extinction

NASA Astrophysics Data System (ADS)

Kump, L. R.

2003-12-01

The course of biological evolution is inextricably linked to that of the environment through an intricate network of feedbacks that span all scales of space and time. Disruptions to the environment have biological consequences, and vice versa. Fossils provide the prima facie evidence for biotic disruptions: catastrophic losses of global biodiversity at various times in the Phanerozoic. However, the forensic evidence for the causes and environmental consequences of these mass extinctions resides primarily in the geochemical composition of sedimentary rocks deposited during the extinction intervals. Thus, advancement in our understanding of mass extinctions requires detailed knowledge obtained from both paleontological and geochemical records.This chapter reviews the state of knowledge concerning the geochemistry of the "big five" extinctions of the Phanerozoic (e.g., Sepkoski, 1993): the Late Ordovician (Hirnantian; 440 Ma), the Late Devonian (an extended or multiple event with its apex at the Frasnian-Famennian (F-F) boundary; 367 Ma), the Permian-Triassic (P-Tr; 251 Ma), the Triassic-Jurassic (Tr-J; 200 Ma), and the Cretaceous-Tertiary (K-T; 65 Ma). The focus on the big five is a matter of convenience, as there is a continuum in extinction rates from "background" to "mass extinction." Although much of the literature on extinctions centers on the causes and extents of biodiversity loss, in recent years paleontologists have begun to focus on recoveries (see, e.g., Hart, 1996; Kirchner and Weil, 2000; Erwin, 2001 and references therein).To the extent that the duration of the recovery interval may reflect a slow relaxation of the environment from perturbation, analysis of the geochemical record of recovery is an integral part of this effort. In interpreting the geochemical and biological records of recovery, we need to maintain a clear distinction among the characteristics of the global biota: their biodiversity (affected by differences in origination and extinction rates) and ecosystem function (guild structure, complexity of interactions, productivity). Geochemical records reflect attributes of ecosystem function, not biodiversity; low-diversity recovery faunas and floras may support pre-event productivities. Thus, geochemical and biodiversity recovery intervals are interdependent but not equivalent, and may not be of equal duration.From the biological point of view, there is an inevitable lag between peak extinction rates and peak origination rates, and the durations and underlying causes of the lags are topics of debate. Both intrinsic (e.g., the fact that ecospace is created as biodiversity increases producing positive feedback) and external (environmental) constraints are possible. Kirchner and Weil (2000) performed a time-series analysis of extinction and origination-rate data, and concluded that the lag is ˜10 Myr and independent of the magnitude of the event. Erwin (2001) raised the possibility that the 10 Myr lag may be an artifact of the coarseness of the timescales utilized, and discussed possible environmental and ecological limits on rate of recovery from mass extinction.The comparison of the geochemical records of the five major mass extinctions of the Phanerozoic reveals few commonalities. Most, but not all, exhibit sharp drops in the carbon isotopic composition (δ13C) of the surface ocean, indicating substantial disruptions to the global carbon cycle. The P-Tr and F-F events are associated with indicators of widespread anoxia and enhanced pyrite burial (positive δ34S excursions), whereas the Late Ordovician extinction occurred during a brief interlude of oxic conditions from general anoxia. Some are associated with sea-level transgressions from previous lowstands (P-Tr, Tr-J, K-T), but the Late Ordovician and F-F occurred during sea-level falls. Long-term climates change across all events, but span major coolings (Late Ordovician, F-F) to prominent warmings (P-Tr, Tr-J, K-T).Evidence for extraterrestrial influence is strong for the K-T, suggestive for the Tr-J and Late Permian, and missing for the F-F and Late Ordovician. What these times have in common is that all were times of biotic and environmental change. Long-term trends toward extreme environmental conditions presaged the Late Ordovician, F-F, and P-Tr events, whereas the Tr-J and K-T seem to have been abrupt shocks to the Earth system, perhaps belying their extraterrestrial cause. However, even for the K-T extinction there is indication of environmental and biotic change before the known impact event and mass extinction (e.g., Keller et al., 1993; Barrera, 1994; Abramovich and Keller, 2002).

Classifying bilinear differential equations by linear superposition principle

NASA Astrophysics Data System (ADS)

Zhang, Lijun; Khalique, Chaudry Masood; Ma, Wen-Xiu

2016-09-01

In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota bilinear equations possessing this specific sub-class of N-wave solutions is presented. We apply this result to find N-wave solutions to the (2+1)-dimensional KP equation, a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation, a (3+1)-dimensional generalized BKP equation and the (2+1)-dimensional BKP equation. The inverse question, i.e., constructing Hirota Bilinear equations possessing N-wave solutions, is considered and a refined 3-step algorithm is proposed. As examples, we construct two very general kinds of Hirota bilinear equations of order 4 possessing N-wave solutions among which one satisfies dispersion relation and another does not satisfy dispersion relation.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

Bianchi transformation between the real hyperbolic Monge-Ampère equation and the Born-Infeld equation

NASA Astrophysics Data System (ADS)

Mokhov, O. I.; Nutku, Y.

1994-10-01

By casting the Born-Infeld equation and the real hyperbolic Monge-Ampère equation into the form of equations of hydrodynamic type, we find that there exists an explicit transformation between them. This is Bianchi transformation.

Axisymmetric ideal MHD stellar wind flow

NASA Technical Reports Server (NTRS)

Heinemann, M.; Olbert, S.

1978-01-01

The ideal MHD equations are reduced to a single equation under the assumption of axisymmetric flow. A variational principle from which the equation is derivable is given. The characteristics of the equation are briefly discussed. The equation is used to rederive the theorem of Gussenhoven and Carovillano.

Teaching Modeling with Partial Differential Equations: Several Successful Approaches

ERIC Educational Resources Information Center

Myers, Joseph; Trubatch, David; Winkel, Brian

2008-01-01

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Optimal Control for Stochastic Delay Evolution Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

Wave equations in conformal gravity

NASA Astrophysics Data System (ADS)

Du, Juan-Juan; Wang, Xue-Jing; He, You-Biao; Yang, Si-Jiang; Li, Zhong-Heng

2018-05-01

We study the wave equation governing massless fields of all spins (s = 0, 1 2, 1, 3 2 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

Stochastic modification of the Schrödinger-Newton equation

NASA Astrophysics Data System (ADS)

Bera, Sayantani; Mohan, Ravi; Singh, Tejinder P.

2015-07-01

The Schrödinger-Newton (SN) equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the SN equation. However, the equation itself lacks a decoherence mechanism, because it does not possess any stochastic feature. In the present work we derive a stochastic modification of the Schrödinger-Newton equation, starting from the Einstein-Langevin equation in the theory of stochastic semiclassical gravity. We specialize this equation to the case of a single massive point particle, and by using Karolyhazy's phase variance method, we derive the Diósi-Penrose criterion for the decoherence time. We obtain a (nonlinear) master equation corresponding to this stochastic SN equation. This equation is, however, linear at the level of the approximation we use to prove decoherence; hence, the no-signaling requirement is met. Lastly, we use physical arguments to obtain expressions for the decoherence length of extended objects.

A family of wave equations with some remarkable properties.

PubMed

da Silva, Priscila Leal; Freire, Igor Leite; Sampaio, Júlio Cesar Santos

2018-02-01

We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation. This transformation, on the other hand, enables us to obtain solutions of the equation from the kernel of a Schrödinger operator with potential parametrized by the solutions of the KdV equation. In particular, this allows us to exhibit a kink solution to the completely integrable equation from the 1-soliton solution of the KdV equation. Finally, peakon-type solutions are also found for a certain choice of the parameters, although for this particular case the equation is reduced to a homogeneous second-order nonlinear evolution equation.

Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

NASA Astrophysics Data System (ADS)

Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

2016-12-01

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

Methods for Equating Mental Tests.

DTIC Science & Technology

1984-11-01

1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth

An Exploration of Kernel Equating Using SAT® Data: Equating to a Similar Population and to a Distant Population. Research Report. ETS RR-07-17

ERIC Educational Resources Information Center

Liu, Jinghua; Low, Albert C.

2007-01-01

This study applied kernel equating (KE) in two scenarios: equating to a very similar population and equating to a very different population, referred to as a distant population, using SAT® data. The KE results were compared to the results obtained from analogous classical equating methods in both scenarios. The results indicate that KE results are…

Multiscale functions, scale dynamics, and applications to partial differential equations

NASA Astrophysics Data System (ADS)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

Thermodynamic properties of oxygen and nitrogen III

NASA Technical Reports Server (NTRS)

Stewart, R. B.; Jacobsen, R. T.; Myers, A. F.

1972-01-01

The final equation for nitrogen was determined. In the work on the equation of state for nitrogen, coefficients were determined by constraining the critical point to selected critical point parameters. Comparisons of this equation with all the P-density-T data were made, as well as comparisons to all other thermodynamic data reported in the literature. The extrapolation of the equation of state was studied for vapor to higher temperatures and lower temperatures, and for the liquid surface to the saturated liquid and the fusion lines. A new vapor pressure equation was also determined which was constrained to the same critical temperature, pressure, and slope (dP/dT) as the equation of state. Work on the equation of state for oxygen included studies for improving the equation at the critical point. Comparisons of velocity of sound data for oxygen were also made between values calculated with a preliminary equation of state and experimental data. Functions for the calculation of the derived thermodynamic properties using the equation of state are given, together with the derivative and integral functions for the calculation of the thermodynamic properties using the equations of state. Summary tables of the thermodynamic properties of nitrogen and oxygen are also included to serve as a check for those preparing computer programs using the equations of state.

The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation

NASA Astrophysics Data System (ADS)

Meng, Fei; Liu, Fang

2018-03-01

In this paper, we study the Fourier transforms for two equations arising in the kinetic theory. The first equation is the spatially homogeneous Boltzmann equation. The Fourier transform of the spatially homogeneous Boltzmann equation has been first addressed by Bobylev (Sov Sci Rev C Math Phys 7:111-233, 1988) in the Maxwellian case. Alexandre et al. (Arch Ration Mech Anal 152(4):327-355, 2000) investigated the Fourier transform of the gain operator for the Boltzmann operator in the cut-off case. Recently, the Fourier transform of the Boltzmann equation is extended to hard or soft potential with cut-off by Kirsch and Rjasanow (J Stat Phys 129:483-492, 2007). We shall first establish the relation between the results in Alexandre et al. (2000) and Kirsch and Rjasanow (2007) for the Fourier transform of the Boltzmann operator in the cut-off case. Then we give the Fourier transform of the spatially homogeneous Boltzmann equation in the non cut-off case. It is shown that our results cover previous works (Bobylev 1988; Kirsch and Rjasanow 2007). The second equation is the spatially homogeneous Landau equation, which can be obtained as a limit of the Boltzmann equation when grazing collisions prevail. Following the method in Kirsch and Rjasanow (2007), we can also derive the Fourier transform for Landau equation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheviakov, Alexei F., E-mail: chevaikov@math.usask.ca

Partial differential equations of the form divN=0, N{sub t}+curl M=0 involving two vector functions in R{sup 3} depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R{sup 4}(t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations,more » it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented.« less

Comparison of Eight Equations That Predict Percent Body Fat Using Skinfolds in American Youth

PubMed Central

Roberts, Amy; Cai, Jianwen; Berge, Jerica M.; Stevens, June

2016-01-01

Abstract Background: Skinfolds are often used in equations to predict percent body fat (PBF) in youth. Although there are numerous such equations published, there is limited information to help researchers determine which equation to use for their sample. Methods: Using data from the 1999–2006 National Health and Nutrition Examination Surveys (NHANES), we compared eight published equations for prediction of PBF. These published equations all included triceps and/or subscapular skinfold measurements. We examined the PBF equations in a nationally representative sample of American youth that was matched by age, sex, and race/ethnicity to the original equation development population and a full sample of 8- to 18-year-olds. We compared the equation-predicted PBF to the dual-emission X-ray absorptiometry (DXA)-measured PBF. The adjusted R2, root mean square error (RMSE), and mean signed difference (MSD) were compared. The MSDs were used to examine accuracy and differential bias by age, sex, and race/ethnicity. Results: When applied to the full range of 8- 18-year-old youth, the R2 values ranged from 0.495 to 0.738. The MSD between predicted and DXA-measured PBF indicated high average accuracy (MSD between −1.0 and 1.0) for only three equations (Bray subscapular equation and Dezenberg equations [with and without race/ethnicity]). The majority of the equations showed differential bias by sex, race/ethnicity, weight status, or age. Conclusions: These findings indicate that investigators should use caution in the selection of an equation to predict PBF in youth given that results may vary systematically in important subgroups. PMID:27045618

Comparison of Eight Equations That Predict Percent Body Fat Using Skinfolds in American Youth.

PubMed

Truesdale, Kimberly P; Roberts, Amy; Cai, Jianwen; Berge, Jerica M; Stevens, June

2016-08-01

Skinfolds are often used in equations to predict percent body fat (PBF) in youth. Although there are numerous such equations published, there is limited information to help researchers determine which equation to use for their sample. Using data from the 1999-2006 National Health and Nutrition Examination Surveys (NHANES), we compared eight published equations for prediction of PBF. These published equations all included triceps and/or subscapular skinfold measurements. We examined the PBF equations in a nationally representative sample of American youth that was matched by age, sex, and race/ethnicity to the original equation development population and a full sample of 8- to 18-year-olds. We compared the equation-predicted PBF to the dual-emission X-ray absorptiometry (DXA)-measured PBF. The adjusted R(2), root mean square error (RMSE), and mean signed difference (MSD) were compared. The MSDs were used to examine accuracy and differential bias by age, sex, and race/ethnicity. When applied to the full range of 8- 18-year-old youth, the R(2) values ranged from 0.495 to 0.738. The MSD between predicted and DXA-measured PBF indicated high average accuracy (MSD between -1.0 and 1.0) for only three equations (Bray subscapular equation and Dezenberg equations [with and without race/ethnicity]). The majority of the equations showed differential bias by sex, race/ethnicity, weight status, or age. These findings indicate that investigators should use caution in the selection of an equation to predict PBF in youth given that results may vary systematically in important subgroups.

Futile transmembrane NH4+ cycling: A cellular hypothesis to explain ammonium toxicity in plants

PubMed Central

Britto, Dev T.; Siddiqi, M. Yaeesh; Glass, Anthony D. M.; Kronzucker, Herbert J.

2001-01-01

Most higher plants develop severe toxicity symptoms when grown on ammonium (NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document}) as the sole nitrogen source. Recently, NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document} toxicity has been implicated as a cause of forest decline and even species extinction. Although mechanisms underlying NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document} toxicity have been extensively sought, the primary events conferring it at the cellular level are not understood. Using a high-precision positron tracing technique, we here present a cell-physiological characterization of NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document} acquisition in two major cereals, barley (Hordeum vulgare), known to be susceptible to toxicity, and rice (Oryza sativa), known for its exceptional tolerance to even high levels of NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document}. We show that, at high external NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document} concentration ([NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document}]o), barley root cells experience a breakdown in the regulation of NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document} influx, leading to the accumulation of excessive amounts of NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document} in the cytosol. Measurements of NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document} efflux, combined with a thermodynamic analysis of the transmembrane electrochemical potential for NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document}, reveal that, at elevated [NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document}]o, barley cells engage a high-capacity NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document}-efflux system that supports outward NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document} fluxes against a sizable gradient. Ammonium efflux is shown to constitute as much as 80% of primary influx, resulting in a never-before-documented futile cycling of nitrogen across the plasma membrane of root cells. This futile cycling carries a high energetic cost (we record a 40% increase in root respiration) that is independent of N metabolism and is accompanied by a decline in growth. In rice, by contrast, a cellular defense strategy has evolved that is characterized by an energetically neutral, near-Nernstian, equilibration of NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document} at high [NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document}]o. Thus our study has characterized the primary events in NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document} nutrition at the cellular level that may constitute the fundamental cause of NH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\mathrm{_{4}^{+}}}\\end{equation*}\\end{document} toxicity in plants. PMID:11274450

A Bayesian Nonparametric Approach to Test Equating

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2009-01-01

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

Dark soliton solution of Sasa-Satsuma equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohta, Y.

2010-03-08

The Sasa-Satsuma equation is a higher order nonlinear Schroedinger type equation which admits bright soliton solutions with internal freedom. We present the dark soliton solutions for the equation by using Gram type determinant. The dark solitons have no internal freedom and exist for both defocusing and focusing equations.

The Complexity of One-Step Equations

ERIC Educational Resources Information Center

Ngu, Bing

2014-01-01

An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…

Simple Derivation of the Lindblad Equation

ERIC Educational Resources Information Center

Pearle, Philip

2012-01-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…

On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

ERIC Educational Resources Information Center

Savoye, Philippe

2009-01-01

In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

On the solution of the generalized wave and generalized sine-Gordon equations

NASA Technical Reports Server (NTRS)

Ablowitz, M. J.; Beals, R.; Tenenblat, K.

1986-01-01

The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.

Local Discontinuous Galerkin Methods for the Cahn-Hilliard Type Equations

DTIC Science & Technology

2007-01-01

Kuramoto-Sivashinsky equations , the Ito-type coupled KdV equa- tions, the Kadomtsev - Petviashvili equation , and the Zakharov-Kuznetsov equation . A common...Local discontinuous Galerkin methods for the Cahn-Hilliard type equations Yinhua Xia∗, Yan Xu† and Chi-Wang Shu ‡ Abstract In this paper we develop...local discontinuous Galerkin (LDG) methods for the fourth-order nonlinear Cahn-Hilliard equation and system. The energy stability of the LDG methods is

Symmetries and BI-Hamiltonian Structures of 2+1 Dimensional Systems,

DTIC Science & Technology

1986-01-01

and 0 aisociated with the Kadomtsev - 12 12 Petviashvili (KP) equation 2 -1qtq + 6qqx+ 3aD-q, (1.2) we have developed the theory associated with...generalized to equations in muLtidimensions. Applications to physically relevant equations like the Kadomcsev- Petviashvili equation are illustrated...integro-differenrial evo- lucion equations like the Benjamin-Ono equation are shown to be also described by this generalized V theory. IDSTEBO STP8 3

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Cellular Automata for Spatiotemporal Pattern Formation from Reaction-Diffusion Partial Differential Equations

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.

Nonlinear acoustic wave equations with fractional loss operators.

PubMed

Prieur, Fabrice; Holm, Sverre

2011-09-01

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America

Infinite hierarchy of nonlinear Schrödinger equations and their solutions.

PubMed

Ankiewicz, A; Kedziora, D J; Chowdury, A; Bandelow, U; Akhmediev, N

2016-01-01

We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that "even- order" equations in the set affect phase and "stretching factors" in the solutions, while "odd-order" equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.

On a new class of completely integrable nonlinear wave equations. I. Infinitely many conservation laws

NASA Astrophysics Data System (ADS)

Nutku, Y.

1985-06-01

We point out a class of nonlinear wave equations which admit infinitely many conserved quantities. These equations are characterized by a pair of exact one-forms. The implication that they are closed gives rise to equations, the characteristics and Riemann invariants of which are readily obtained. The construction of the conservation laws requires the solution of a linear second-order equation which can be reduced to canonical form using the Riemann invariants. The hodograph transformation results in a similar linear equation. We discuss also the symplectic structure and Bäcklund transformations associated with these equations.

Reduction operators of Burgers equation.

PubMed

Pocheketa, Oleksandr A; Popovych, Roman O

2013-02-01

The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.

Reduction operators of Burgers equation

PubMed Central

Pocheketa, Oleksandr A.; Popovych, Roman O.

2013-01-01

The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special “no-go” case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf–Cole transformation to a parameterized family of Lie reductions of the linear heat equation. PMID:23576819

The suitability of common compressibility equations for characterizing plasticity of diverse powders.

PubMed

Paul, Shubhajit; Sun, Changquan Calvin

2017-10-30

The analysis of powder compressibility data yields useful information for characterizing compaction behavior and mechanical properties of powders, especially plasticity. Among the many compressibility equations proposed in powder compaction research, the Heckel equation and the Kawakita equation are the most commonly used, despite their known limitations. Systematic evaluation of the performance in analyzing compressibility data suggested the Kuentz-Leuenberger equation is superior to both the Heckel equation and the Kawakita equation for characterizing plasticity of powders exhibiting a wide range of mechanical properties. Copyright © 2017 Elsevier B.V. All rights reserved.

A viscous flow analysis for the tip vortex generation process

NASA Technical Reports Server (NTRS)

Shamroth, S. J.; Briley, W. R.

1979-01-01

A three dimensional, forward-marching, viscous flow analysis is applied to the tip vortex generation problem. The equations include a streamwise momentum equation, a streamwise vorticity equation, a continuity equation, and a secondary flow stream function equation. The numerical method used combines a consistently split linearized scheme for parabolic equations with a scalar iterative ADI scheme for elliptic equations. The analysis is used to identify the source of the tip vortex generation process, as well as to obtain detailed flow results for a rectangular planform wing immersed in a high Reynolds number free stream at 6 degree incidence.

Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique

NASA Technical Reports Server (NTRS)

Nordmann, R.; Weiser, P.

1989-01-01

The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.

Algebraic methods for the solution of some linear matrix equations

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.

A Variational Assimilation Method for Satellite and Conventional Data: Development of Basic Model for Diagnosis of Cyclone Systems

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Scott, Robert W.; Chen, J.

1991-01-01

A summary is presented of the progress toward the completion of a comprehensive diagnostic objective analysis system based upon the calculus of variations. The approach was to first develop the objective analysis subject to the constraints that the final product satisfies the five basic primitive equations for a dry inviscid atmosphere: the two nonlinear horizontal momentum equations, the continuity equation, the hydrostatic equation, and the thermodynamic equation. Then, having derived the basic model, there would be added to it the equations for moist atmospheric processes and the radiative transfer equation.

Some Exact Solutions of a Nonintegrable Toda-type Equation

NASA Astrophysics Data System (ADS)

Kim, Chanju

2018-05-01

We study a Toda-type equation with two scalar fields which is not integrable and construct two families of exact solutions which are expressed in terms of rational functions. The equation appears in U(1) Chern-Simons theories coupled to two nonrelativistic matter fields with opposite charges. One family of solutions is a trivial embedding of Liouville-type solutions. The other family is obtained by transforming the equation into the Taubes vortex equation on the hyperbolic space. Though the Taubes equation is not integrable, a trivial vacuum solution provides nontrivial solutions to the original Toda-type equation.

On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Masood Khalique, Chaudry

2018-05-01

In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham-Broer-Kaup-Like Equations

NASA Astrophysics Data System (ADS)

Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian

2017-03-01

In this article, a generalised Whitham-Broer-Kaup-Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham-Broer-Kaup-Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.

On integrability of the Killing equation

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

New Equations for Calculating Principal and Fine-Structure Atomic Spectra for Single and Multi-Electron Atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Surdoval, Wayne A.; Berry, David A.; Shultz, Travis R.

A set of equations are presented for calculating atomic principal spectral lines and fine-structure energy splits for single and multi-electron atoms. Calculated results are presented and compared to the National Institute of Science and Technology database demonstrating very good accuracy. The equations do not require fitted parameters. The only experimental parameter required is the Ionization energy for the electron of interest. The equations have comparable accuracy and broader applicability than the single electron Dirac equation. Three Appendices discuss the origin of the new equations and present calculated results. New insights into the special relativistic nature of the Dirac equation andmore » its relationship to the new equations are presented.« less

Dynamical systems theory for nonlinear evolution equations.

PubMed

Choudhuri, Amitava; Talukdar, B; Das, Umapada

2010-09-01

We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as K(n,m) equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated with the equations. We treat the resulting Hamiltonian equations by the dynamical systems theory and present a phase-space analysis of their stable points. The results of our study demonstrate that the equations can, in general, support both compacton and soliton solutions. For the K(2,2) and K(3,3) cases one type of solutions can be obtained from the other by continuously varying a parameter of the equations. This is not true for the K(3,2) equation for which the parameter can take only negative values. The K(2,3) equation does not have any stable point and, in the language of mechanics, represents a particle moving with constant acceleration.

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

PubMed Central

Motsa, S. S.; Magagula, V. M.; Sibanda, P.

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

PubMed

Motsa, S S; Magagula, V M; Sibanda, P

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

A fully vectorized numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Patel, N.

1983-01-01

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

A two-phase micromorphic model for compressible granular materials

NASA Astrophysics Data System (ADS)

Paolucci, Samuel; Li, Weiming; Powers, Joseph

2009-11-01

We introduce a new two-phase continuum model for compressible granular material based on micromorphic theory and treat it as a two-phase mixture with inner structure. By taking an appropriate number of moments of the local micro scale balance equations, the average phase balance equations result from a systematic averaging procedure. In addition to equations for mass, momentum and energy, the balance equations also include evolution equations for microinertia and microspin tensors. The latter equations combine to yield a general form of a compaction equation when the material is assumed to be isotropic. When non-linear and inertial effects are neglected, the generalized compaction equation reduces to that originally proposed by Bear and Nunziato. We use the generalized compaction equation to numerically model a mixture of granular high explosive and interstitial gas. One-dimensional shock tube and piston-driven solutions are presented and compared with experimental results and other known solutions.

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Manafian, Jalil

2018-03-01

This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

The Effect of Tutoring With Nonstandard Equations for Students With Mathematics Difficulty.

PubMed

Powell, Sarah R; Driver, Melissa K; Julian, Tyler E

2015-01-01

Students often misinterpret the equal sign (=) as operational instead of relational. Research indicates misinterpretation of the equal sign occurs because students receive relatively little exposure to equations that promote relational understanding of the equal sign. No study, however, has examined effects of nonstandard equations on the equation solving and equal-sign understanding of students with mathematics difficulty (MD). In the present study, second-grade students with MD (n = 51) were randomly assigned to standard equations tutoring, combined tutoring (standard and nonstandard equations), and no-tutoring control. Combined tutoring students demonstrated greater gains on equation-solving assessments and equal-sign tasks compared to the other two conditions. Standard tutoring students demonstrated improved skill on equation solving over control students, but combined tutoring students' performance gains were significantly larger. Results indicate that exposure to and practice with nonstandard equations positively influence student understanding of the equal sign. © Hammill Institute on Disabilities 2013.

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

PubMed

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations

DOE PAGES

Shao, Xuan-Min

2016-04-12

The fundamental electromagnetic equations used by lightning researchers were introduced in a seminal paper by Uman, McLain, and Krider in 1975. However, these equations were derived for an infinitely thin, one-dimensional source current, and not for a general three-dimensional current distribution. In this paper, we introduce a corresponding pair of generalized equations that are determined from a three-dimensional, time-dependent current density distribution based on Jefimenko's original electric and magnetic equations. To do this, we derive the Jefimenko electric field equation into a new form that depends only on the time-dependent current density similar to that of Uman, McLain, and Krider,more » rather than on both the charge and current densities in its original form. The original Jefimenko magnetic field equation depends only on current, so no further derivation is needed. We show that the equations of Uman, McLain, and Krider can be readily obtained from the generalized equations if a one-dimensional source current is considered. For the purpose of practical applications, we discuss computational implementation of the new equations and present electric field calculations for a three-dimensional, conical-shape discharge.« less

An approach to rogue waves through the cnoidal equation

NASA Astrophysics Data System (ADS)

Lechuga, Antonio

2014-05-01

Lately it has been realized the importance of rogue waves in some events happening in open seas. Extreme waves and extreme weather could explain some accidents, but not all of them. Every now and then inflicted damages on ships only can be reported to be caused by anomalous and elusive waves, such as rogue waves. That's one of the reason why they continue attracting considerable interest among researchers. In the frame of the Nonlinear Schrödinger equation(NLS), Witham(1974) and Dingemans and Otta (2001)gave asymptotic solutions in moving coordinates that transformed the NLS equation in a ordinary differential equation that is the Duffing or cnoidal wave equation. Applying the Zakharov equation, Stiassnie and Shemer(2004) and Shemer(2010)got also a similar equation. It's well known that this ordinary equation can be solved in elliptic functions. The main aim of this presentation is to sort out the domains of the solutions of this equation, that, of course, are linked to the corresponding solutions of the partial differential equations(PDEs). That being, Lechuga(2007),a simple way to look for anomalous waves as it's the case with some "chaotic" solutions of the Duffing equation.

Resting Energy Expenditure Prediction in Recreational Athletes of 18–35 Years: Confirmation of Cunningham Equation and an Improved Weight-Based Alternative

PubMed Central

ten Haaf, Twan; Weijs, Peter J. M.

2014-01-01

Introduction Resting energy expenditure (REE) is expected to be higher in athletes because of their relatively high fat free mass (FFM). Therefore, REE predictive equation for recreational athletes may be required. The aim of this study was to validate existing REE predictive equations and to develop a new recreational athlete specific equation. Methods 90 (53M, 37F) adult athletes, exercising on average 9.1±5.0 hours a week and 5.0±1.8 times a week, were included. REE was measured using indirect calorimetry (Vmax Encore n29), FFM and FM were measured using air displacement plethysmography. Multiple linear regression analysis was used to develop a new FFM-based and weight-based REE predictive equation. The percentage accurate predictions (within 10% of measured REE), percentage bias, root mean square error and limits of agreement were calculated. Results The Cunningham equation and the new weight-based equation and the new FFM-based equation performed equally well. De Lorenzo's equation predicted REE less accurate, but better than the other generally used REE predictive equations. Harris-Benedict, WHO, Schofield, Mifflin and Owen all showed less than 50% accuracy. Conclusion For a population of (Dutch) recreational athletes, the REE can accurately be predicted with the existing Cunningham equation. Since body composition measurement is not always possible, and other generally used equations fail, the new weight-based equation is advised for use in sports nutrition. PMID:25275434

Turning Equations Into Stories: Using "Equation Dictionaries" in an Introductory Geophysics Class

NASA Astrophysics Data System (ADS)

Caplan-Auerbach, J.

2008-12-01

To students with math fear, equations can be intimidating and overwhelming. This discomfort is reflected in some of the frequent questions heard in introductory geophysics: "which equation should I use?" and "does T stand for travel time or period?" Questions such as these indicate that many students view equations as a series of variables and operators rather than as a representation of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume that it meets their needs, rather than selecting an equation that represents the appropriate physical process. These issues can be addressed by encouraging students to think of equations as stories, and to describe them in prose. This is the goal of the Equation Dictionary project, used in Western Washington University's introductory geophysics course. Throughout the course, students create personal equation dictionaries, adding an entry each time an equation is introduced. Entries consist of (a) the equation itself, (b) a brief description of equation variables, (c) a prose description of the physical process described by the equation, and (d) any additional notes that help them understand the equation. Thus, rather than simply writing down the equations for the velocity of body waves, a student might write "The speed of a seismic body wave is controlled by the material properties of the medium through which it passes." In a study of gravity a student might note that the International Gravity Formula describes "the expected value of g at a given latitude, correcting for Earth's shape and rotation." In writing these definitions students learn that equations are simplified descriptions of physical processes, and that understanding the process is more useful than memorizing a sequence of variables. Dictionaries also serve as formula sheets for exams, which encourages students to write definitions that are meaningful to them, and to organize their thoughts clearly. Finally, instructor review of the dictionaries is an excellent way to identify student misconceptions and learn how well they understand derivations and lectures.

An effective rate equation approach to reaction kinetics in small volumes: theory and application to biochemical reactions in nonequilibrium steady-state conditions.

PubMed

Grima, R

2010-07-21

Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the regions of parameter space in which there are maximum differences between the solutions of the master equation and the corresponding rate equations. We show that these differences depend sensitively on the Fano factors and on the inherent structure and topology of the chemical network. The theory of effective mesoscopic rate equations generalizes the conventional rate equations of physical chemistry to describe kinetics in systems of mesoscopic size such as biological cells.

[Equating scores using bridging stations on the clinical performance examination].

PubMed

Yoo, Dong-Mi; Han, Jae-Jin

2013-06-01

This study examined the use of the Tucker linear equating method in producing an individual student's score in 3 groups with bridging stations over 3 consecutive days of the clinical performance examination (CPX) and compared the differences in scoring patterns by bridging number. Data were drawn from 88 examinees from 3 different CPX groups-DAY1, DAY2, and DAY3-each of which comprised of 6 stations. Each group had 3 common stations, and each group had 2 or 3 stations that differed from other groups. DAY1 and DAY3 were equated to DAY2. Equated mean scores and standard deviations were compared with the originals. DAY1 and DAY3 were equated again, and the differences in scores (equated score-raw score) were compared between the 3 sets of equated scores. By equating to DAY2, DAY1 decreased in mean score from 58.188 to 56.549 and in standard deviation from 4.991 to 5.046, and DAY3 fell in mean score from 58.351 to 58.057 and in standard deviation from 5.546 to 5.856, which demonstrates that the scores of examinees in DAY1 and DAY2 were accentuated after use of the equation. The patterns in score differences between the equated sets to DAY1, DAY2, and DAY3 yielded information on the soundness of the equating results from individual and overall comparisons. To generate equated scores between 3 groups on 3 consecutive days of the CPX, we applied the Tucker linear equating method. We also present a method of equating reciprocal days to the anchoring day as much as bridging stations.

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

DOE PAGES

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris; ...

2018-04-23

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Propagation of Finite Amplitude Sound in Multiple Waveguide Modes.

NASA Astrophysics Data System (ADS)

van Doren, Thomas Walter

1993-01-01

This dissertation describes a theoretical and experimental investigation of the propagation of finite amplitude sound in multiple waveguide modes. Quasilinear analytical solutions of the full second order nonlinear wave equation, the Westervelt equation, and the KZK parabolic wave equation are obtained for the fundamental and second harmonic sound fields in a rectangular rigid-wall waveguide. It is shown that the Westervelt equation is an acceptable approximation of the full nonlinear wave equation for describing guided sound waves of finite amplitude. A system of first order equations based on both a modal and harmonic expansion of the Westervelt equation is developed for waveguides with locally reactive wall impedances. Fully nonlinear numerical solutions of the system of coupled equations are presented for waveguides formed by two parallel planes which are either both rigid, or one rigid and one pressure release. These numerical solutions are compared to finite -difference solutions of the KZK equation, and it is shown that solutions of the KZK equation are valid only at frequencies which are high compared to the cutoff frequencies of the most important modes of propagation (i.e., for which sound propagates at small grazing angles). Numerical solutions of both the Westervelt and KZK equations are compared to experiments performed in an air-filled, rigid-wall, rectangular waveguide. Solutions of the Westervelt equation are in good agreement with experiment for low source frequencies, at which sound propagates at large grazing angles, whereas solutions of the KZK equation are not valid for these cases. At higher frequencies, at which sound propagates at small grazing angles, agreement between numerical solutions of the Westervelt and KZK equations and experiment is only fair, because of problems in specifying the experimental source condition with sufficient accuracy.

Comparison of the MDRD study and CKD-EPI equations for the estimation of the glomerular filtration rate in the Korean general population: the fifth Korea National Health and Nutrition Examination Survey (KNHANES V-1), 2010.

PubMed

Jeong, Tae-Dong; Lee, Woochang; Chun, Sail; Lee, Sang Koo; Ryu, Jin-Sook; Min, Won-Ki; Park, Jung Sik

2013-01-01

We compared the accuracy of the Modification of Diet in Renal Disease (MDRD) study and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations in Korean patients and evaluated the difference in CKD prevalence determined using the two equations in the Korean general population. The accuracy of the two equations was evaluated in 607 patients who underwent a chromium-51-ethylenediaminetetraacetic acid GFR measurement. Additionally, we compared the difference in CKD prevalence determined by the two equations among 5,822 participants in the fifth Korea National Health and Nutrition Examination Survey, 2010. Among the 607 subjects, the median bias of the CKD-EPI equation was significantly lower than that of the MDRD study equation (0.9 vs. 2.2, p=0.020). The accuracy of the two equations was not significantly different in patients with mGFR <60 mL/min/1.73m(2); however, the accuracy of the CKD-EPI equation was significantly higher than that of the MDRD study equation in patients with GFR ≥60 mL/min/1.73m(2). The prevalences of the CKD stages 1, 2 and 3 in the Korean general population were 47.56, 49.23, and 3.07%, respectively, for the MDRD study equation; and were 68.48, 28.89, and 2.49%, respectively, for the CKD-EPI equation. These data suggest that the CKD-EPI equation might be more useful in clinical practice than the MDRD study equation in Koreans. © 2013 S. Karger AG, Basel.

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

On the solution of the complex eikonal equation in acoustic VTI media: A perturbation plus optimization scheme

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Jianguo; Greenhalgh, Stewart

2018-04-01

We present methods for obtaining numerical and analytic solutions of the complex eikonal equation in inhomogeneous acoustic VTI media (transversely isotropic media with a vertical symmetry axis). The key and novel point of the method for obtaining numerical solutions is to transform the problem of solving the highly nonlinear acoustic VTI eikonal equation into one of solving the relatively simple eikonal equation for the background (isotropic) medium and a system of linear partial differential equations. Specifically, to obtain the real and imaginary parts of the complex traveltime in inhomogeneous acoustic VTI media, we generalize a perturbation theory, which was developed earlier for solving the conventional real eikonal equation in inhomogeneous anisotropic media, to the complex eikonal equation in such media. After the perturbation analysis, we obtain two types of equations. One is the complex eikonal equation for the background medium and the other is a system of linearized partial differential equations for the coefficients of the corresponding complex traveltime formulas. To solve the complex eikonal equation for the background medium, we employ an optimization scheme that we developed for solving the complex eikonal equation in isotropic media. Then, to solve the system of linearized partial differential equations for the coefficients of the complex traveltime formulas, we use the finite difference method based on the fast marching strategy. Furthermore, by applying the complex source point method and the paraxial approximation, we develop the analytic solutions of the complex eikonal equation in acoustic VTI media, both for the isotropic and elliptical anisotropic background medium. Our numerical results demonstrate the effectiveness of our derivations and illustrate the influence of the beam widths and the anisotropic parameters on the complex traveltimes.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Hou, G. J.-W.; Tiwari, S. N. (Principal Investigator)

1996-01-01

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Estimating Glomerular Filtration Rate in Kidney Transplant Recipients: Comparing a Novel Equation With Commonly Used Equations in this Population

PubMed Central

Salvador, Cathrin L.; Hartmann, Anders; Åsberg, Anders; Bergan, Stein; Rowe, Alexander D.; Mørkrid, Lars

2017-01-01

Background Assessment of glomerular filtration rate (GFR) is important in kidney transplantation. The aim was to develop a kidney transplant specific equation for estimating GFR and evaluate against published equations commonly used for GFR estimation in these patients. Methods Adult kidney recipients (n = 594) were included, and blood samples were collected 10 weeks posttransplant. GFR was measured by 51Cr-ethylenediaminetetraacetic acid clearance. Patients were randomized into a reference group (n = 297) to generate a new equation and a test group (n = 297) for comparing it with 7 alternative equations. Results Two thirds of the test group were males. The median (2.5-97.5 percentile) age was 52 (23-75) years, cystatin C, 1.63 (1.00-3.04) mg/L; creatinine, 117 (63-220) μmol/L; and measured GFR, 51 (29-78) mL/min per 1.73 m2. We also performed external evaluation in 133 recipients without the use of trimethoprim, using iohexol clearance for measured GFR. The Modification of Diet in Renal Disease equation was the most accurate of the creatinine-equations. The new equation, estimated GFR (eGFR) = 991.15 × (1.120sex/([age0.097] × [cystatin C0.306] × [creatinine0.527]); where sex is denoted: 0, female; 1, male, demonstrating a better accuracy with a low bias as well as good precision compared with reference equations. Trimethoprim did not influence the performance of the new equation. Conclusions The new equation demonstrated superior accuracy, precision, and low bias. The Modification of Diet in Renal Disease equation was the most accurate of the creatinine-based equations. PMID:29536033

Equivalent equations of motion for gravity and entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (1)].

PubMed

Murase, Kenya

2014-01-01

Utilization of differential equations and methods for solving them in medical physics are presented. First, the basic concept and the kinds of differential equations were overviewed. Second, separable differential equations and well-known first-order and second-order differential equations were introduced, and the methods for solving them were described together with several examples. In the next issue, the symbolic and series expansion methods for solving differential equations will be mainly introduced.

Variational objective analysis for cyclone studies

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.

1989-01-01

Significant accomplishments during 1987 to 1988 are summarized with regard to each of the major project components. Model 1 requires satisfaction of two nonlinear horizontal momentum equations, the integrated continuity equation, and the hydrostatic equation. Model 2 requires satisfaction of model 1 plus the thermodynamic equation for a dry atmosphere. Model 3 requires satisfaction of model 2 plus the radiative transfer equation. Model 4 requires satisfaction of model 3 plus a moisture conservation equation and a parameterization for moist processes.

Group foliation of finite difference equations

NASA Astrophysics Data System (ADS)

Thompson, Robert; Valiquette, Francis

2018-06-01

Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

Equivalent equations of motion for gravity and entropy

DOE PAGES

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; ...

2017-02-01

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

Variational symmetries, conserved quantities and identities for several equations of mathematical physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donchev, Veliko, E-mail: velikod@ie.bas.bg

2014-03-15

We find variational symmetries, conserved quantities and identities for several equations: envelope equation, Böcher equation, the propagation of sound waves with losses, flow of a gas with losses, and the nonlinear Schrödinger equation with losses or gains, and an electro-magnetic interaction. Most of these equations do not have a variational description with the classical variational principle and we find such a description with the generalized variational principle of Herglotz.

A Computational Examination of Detonation Physics and Blast Chemistry

DTIC Science & Technology

2011-08-01

Equation of State 5 3 Detonation and Shock Hugoniots for TNT using the JWL Equation of State 6 4 Detonation and Shock Hugoniots for HMX using the... JWL Equation of State 6 5 Detonation and Shock Hugoniots for Composition C-4 using the JWL Equation of State 7 6 Detonation and...Shock Hugoniots for PBX-9502 using the JWL Equation of State 7 7 Detonation and Shock Hugoniots for PETN using the JWL Equation of State 8

Relations between nonlinear Riccati equations and other equations in fundamental physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-10-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.

Nonlocal Reformulations of Water and Internal Waves and Asymptotic Reductions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.

2009-09-01

Nonlocal reformulations of the classical equations of water waves and two ideal fluids separated by a free interface, bounded above by either a rigid lid or a free surface, are obtained. The kinematic equations may be written in terms of integral equations with a free parameter. By expressing the pressure, or Bernoulli, equation in terms of the surface/interface variables, a closed system is obtained. An advantage of this formulation, referred to as the nonlocal spectral (NSP) formulation, is that the vertical component is eliminated, thus reducing the dimensionality and fixing the domain in which the equations are posed. The NSP equations and the Dirichlet-Neumann operators associated with the water wave or two-fluid equations can be related to each other and the Dirichlet-Neumann series can be obtained from the NSP equations. Important asymptotic reductions obtained from the two-fluid nonlocal system include the generalizations of the Benney-Luke and Kadomtsev-Petviashvili (KP) equations, referred to as intermediate-long wave (ILW) generalizations. These 2+1 dimensional equations possess lump type solutions. In the water wave problem high-order asymptotic series are obtained for two and three dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known hyperbolic secant squared solution of the KdV equation; in three dimensions, the first term is the rational lump solution of the KP equation.

Neglected transport equations: extended Rankine-Hugoniot conditions and J -integrals for fracture

NASA Astrophysics Data System (ADS)

Davey, K.; Darvizeh, R.

2016-09-01

Transport equations in integral form are well established for analysis in continuum fluid dynamics but less so for solid mechanics. Four classical continuum mechanics transport equations exist, which describe the transport of mass, momentum, energy and entropy and thus describe the behaviour of density, velocity, temperature and disorder, respectively. However, one transport equation absent from the list is particularly pertinent to solid mechanics and that is a transport equation for movement, from which displacement is described. This paper introduces the fifth transport equation along with a transport equation for mechanical energy and explores some of the corollaries resulting from the existence of these equations. The general applicability of transport equations to discontinuous physics is discussed with particular focus on fracture mechanics. It is well established that bulk properties can be determined from transport equations by application of a control volume methodology. A control volume can be selected to be moving, stationary, mass tracking, part of, or enclosing the whole system domain. The flexibility of transport equations arises from their ability to tolerate discontinuities. It is insightful thus to explore the benefits derived from the displacement and mechanical energy transport equations, which are shown to be beneficial for capturing the physics of fracture arising from a displacement discontinuity. Extended forms of the Rankine-Hugoniot conditions for fracture are established along with extended forms of J -integrals.

Local Linear Observed-Score Equating

ERIC Educational Resources Information Center

Wiberg, Marie; van der Linden, Wim J.

2011-01-01

Two methods of local linear observed-score equating for use with anchor-test and single-group designs are introduced. In an empirical study, the two methods were compared with the current traditional linear methods for observed-score equating. As a criterion, the bias in the equated scores relative to true equating based on Lord's (1980)…

Cognitive Load in Algebra: Element Interactivity in Solving Equations

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Chung, Siu Fung; Yeung, Alexander Seeshing

2015-01-01

Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side…

Multi-Hamiltonian structure of the Born-Infeld equation

NASA Astrophysics Data System (ADS)

Arik, Metin; Neyzi, Fahrünisa; Nutku, Yavuz; Olver, Peter J.; Verosky, John M.

1989-06-01

The multi-Hamiltonian structure, conservation laws, and higher order symmetries for the Born-Infeld equation are exhibited. A new transformation of the Born-Infeld equation to the equations of a Chaplygin gas is presented and explored. The Born-Infeld equation is distinguished among two-dimensional hyperbolic systems by its wealth of such multi-Hamiltonian structures.

Generalized Spencer-Lewis equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Filippone, W.L.

The Spencer-Lewis equation, which describes electron transport in homogeneous media when continuous slowing down theory is valid, is derived from the Boltzmann equation. Also derived is a time-dependent generalized Spencer-Lewis equation valid for inhomogeneous media. An independent verification of this last equation is obtained for the one-dimensional case using particle balance considerations.

Standard Errors of Equating Differences: Prior Developments, Extensions, and Simulations

ERIC Educational Resources Information Center

Moses, Tim; Zhang, Wenmin

2011-01-01

The purpose of this article was to extend the use of standard errors for equated score differences (SEEDs) to traditional equating functions. The SEEDs are described in terms of their original proposal for kernel equating functions and extended so that SEEDs for traditional linear and traditional equipercentile equating functions can be computed.…

The Missing Data Assumptions of the NEAT Design and Their Implications for Test Equating

ERIC Educational Resources Information Center

Sinharay, Sandip; Holland, Paul W.

2010-01-01

The Non-Equivalent groups with Anchor Test (NEAT) design involves "missing data" that are "missing by design." Three nonlinear observed score equating methods used with a NEAT design are the "frequency estimation equipercentile equating" (FEEE), the "chain equipercentile equating" (CEE), and the "item-response-theory observed-score-equating" (IRT…

Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

ERIC Educational Resources Information Center

Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen

2012-01-01

This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

Proposed solution methodology for the dynamically coupled nonlinear geared rotor mechanics equations

NASA Technical Reports Server (NTRS)

Mitchell, L. D.; David, J. W.

1983-01-01

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher-KPP equation

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.; Trifonov, A. Yu.

A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP) equation under the supposition of weak diffusion. In terms of the semiclassical formalism developed, the original nonlinear equation is reduced to an associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation with a given accuracy of the asymptotic parameter. The solutions of the nonlinear equation are constructed from the solutions of both the linear equation and the algebraic equations. The solutions of the linear problem are found with the use of symmetry operators. A countable family of the leading terms of the semiclassical asymptotics is constructed in explicit form. The semiclassical asymptotics are valid by construction in a finite time interval. We construct asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher-KPP equation at large times. In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure.

Multi-Component Diffusion with Application To Computational Aerothermodynamics

NASA Technical Reports Server (NTRS)

Sutton, Kenneth; Gnoffo, Peter A.

1998-01-01

The accuracy and complexity of solving multicomponent gaseous diffusion using the detailed multicomponent equations, the Stefan-Maxwell equations, and two commonly used approximate equations have been examined in a two part study. Part I examined the equations in a basic study with specified inputs in which the results are applicable for many applications. Part II addressed the application of the equations in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) computational code for high-speed entries in Earth's atmosphere. The results showed that the presented iterative scheme for solving the Stefan-Maxwell equations is an accurate and effective method as compared with solutions of the detailed equations. In general, good accuracy with the approximate equations cannot be guaranteed for a species or all species in a multi-component mixture. 'Corrected' forms of the approximate equations that ensured the diffusion mass fluxes sum to zero, as required, were more accurate than the uncorrected forms. Good accuracy, as compared with the Stefan- Maxwell results, were obtained with the 'corrected' approximate equations in defining the heating rates for the three Earth entries considered in Part II.

Prediction of unsteady transonic flow around missile configurations

NASA Technical Reports Server (NTRS)

Nixon, D.; Reisenthel, P. H.; Torres, T. O.; Klopfer, G. H.

1990-01-01

This paper describes the preliminary development of a method for predicting the unsteady transonic flow around missiles at transonic and supersonic speeds, with the final goal of developing a computer code for use in aeroelastic calculations or during maneuvers. The basic equations derived for this method are an extension of those derived by Klopfer and Nixon (1989) for steady flow and are a subset of the Euler equations. In this approach, the five Euler equations are reduced to an equation similar to the three-dimensional unsteady potential equation, and a two-dimensional Poisson equation. In addition, one of the equations in this method is almost identical to the potential equation for which there are well tested computer codes, allowing the development of a prediction method based in part on proved technology.

Use of digital land-cover data from the Landsat satellite in estimating streamflow characteristics in the Cumberland Plateau of Tennessee

USGS Publications Warehouse

Hollyday, E.F.; Hansen, G.R.

1983-01-01

Streamflow may be estimated with regression equations that relate streamflow characteristics to characteristics of the drainage basin. A statistical experiment was performed to compare the accuracy of equations using basin characteristics derived from maps and climatological records (control group equations) with the accuracy of equations using basin characteristics derived from Landsat data as well as maps and climatological records (experimental group equations). Results show that when the equations in both groups are arranged into six flow categories, there is no substantial difference in accuracy between control group equations and experimental group equations for this particular site where drainage area accounts for more than 90 percent of the variance in all streamflow characteristics (except low flows and most annual peak logarithms). (USGS)

Solution of the Burnett equations for hypersonic flows near the continuum limit

NASA Technical Reports Server (NTRS)

Imlay, Scott T.

1992-01-01

The INCA code, a three-dimensional Navier-Stokes code for analysis of hypersonic flowfields, was modified to analyze the lower reaches of the continuum transition regime, where the Navier-Stokes equations become inaccurate and Monte Carlo methods become too computationally expensive. The two-dimensional Burnett equations and the three-dimensional rotational energy transport equation were added to the code and one- and two-dimensional calculations were performed. For the structure of normal shock waves, the Burnett equations give consistently better results than Navier-Stokes equations and compare reasonably well with Monte Carlo methods. For two-dimensional flow of Nitrogen past a circular cylinder the Burnett equations predict the total drag reasonably well. Care must be taken, however, not to exceed the range of validity of the Burnett equations.

Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes

NASA Astrophysics Data System (ADS)

Da Rocha, R.; Capelas Oliveira, E.

2009-01-01

The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of generalized Laguerre polynomials and hypergeometric confluent functions.

On the exterior Dirichlet problem for Hessian quotient equations

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Li, Zhisu

2018-06-01

In this paper, we establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for Hessian quotient equations with prescribed asymptotic behavior at infinity. This extends the previous related results on the Monge-Ampère equations and on the Hessian equations, and rearranges them in a systematic way. Based on the Perron's method, the main ingredient of this paper is to construct some appropriate subsolutions of the Hessian quotient equation, which is realized by introducing some new quantities about the elementary symmetric polynomials and using them to analyze the corresponding ordinary differential equation related to the generalized radially symmetric subsolutions of the original equation.

Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves

NASA Astrophysics Data System (ADS)

Grava, T.; Klein, C.; Pitton, G.

2018-02-01

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

Brownian motion of classical spins: Anomalous dissipation and generalized Langevin equation

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Malay; Jayannavar, A. M.

2017-10-01

In this work, we derive the Langevin equation (LE) of a classical spin interacting with a heat bath through momentum variables, starting from the fully dynamical Hamiltonian description. The derived LE with anomalous dissipation is analyzed in detail. The obtained LE is non-Markovian with multiplicative noise terms. The concomitant dissipative terms obey the fluctuation-dissipation theorem. The Markovian limit correctly produces the Kubo and Hashitsume equation. The perturbative treatment of our equations produces the Landau-Lifshitz equation and the Seshadri-Lindenberg equation. Then we derive the Fokker-Planck equation corresponding to LE and the concept of equilibrium probability distribution is analyzed.

Alfvén wave interactions in the solar wind

NASA Astrophysics Data System (ADS)

Webb, G. M.; McKenzie, J. F.; Hu, Q.; le Roux, J. A.; Zank, G. P.

2012-11-01

Alfvén wave mixing (interaction) equations used in locally incompressible turbulence transport equations in the solar wind are analyzed from the perspective of linear wave theory. The connection between the wave mixing equations and non-WKB Alfven wave driven wind theories are delineated. We discuss the physical wave energy equation and the canonical wave energy equation for non-WKB Alfven waves and the WKB limit. Variational principles and conservation laws for the linear wave mixing equations for the Heinemann and Olbert non-WKB wind model are obtained. The connection with wave mixing equations used in locally incompressible turbulence transport in the solar wind are discussed.

Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Islam, S M Rayhanul

2014-01-01

In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. Then these exact solutions correspond to solitary waves for particular values of the parameters. 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg.

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

Karney, C. F. F.

1977-01-01

Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

Technique for handling wave propagation specific effects in biological tissue: mapping of the photon transport equation to Maxwell's equations.

PubMed

Handapangoda, Chintha C; Premaratne, Malin; Paganin, David M; Hendahewa, Priyantha R D S

2008-10-27

A novel algorithm for mapping the photon transport equation (PTE) to Maxwell's equations is presented. Owing to its accuracy, wave propagation through biological tissue is modeled using the PTE. The mapping of the PTE to Maxwell's equations is required to model wave propagation through foreign structures implanted in biological tissue for sensing and characterization of tissue properties. The PTE solves for only the magnitude of the intensity but Maxwell's equations require the phase information as well. However, it is possible to construct the phase information approximately by solving the transport of intensity equation (TIE) using the full multigrid algorithm.

Stable boundary conditions and difference schemes for Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Dutt, P.

1985-01-01

The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.

[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].

PubMed

Murase, Kenya

2015-01-01

In this issue, symbolic methods for solving differential equations were firstly introduced. Of the symbolic methods, Laplace transform method was also introduced together with some examples, in which this method was applied to solving the differential equations derived from a two-compartment kinetic model and an equivalent circuit model for membrane potential. Second, series expansion methods for solving differential equations were introduced together with some examples, in which these methods were used to solve Bessel's and Legendre's differential equations. In the next issue, simultaneous differential equations and various methods for solving these differential equations will be introduced together with some examples in medical physics.

Alternatives for the Bedside Schwartz Equation to Estimate Glomerular Filtration Rate in Children.

PubMed

Pottel, Hans; Dubourg, Laurence; Goffin, Karolien; Delanaye, Pierre

2018-01-01

The bedside Schwartz equation has long been and still is the recommended equation to estimate glomerular filtration rate (GFR) in children. However, this equation is probably best suited to estimate GFR in children with chronic kidney disease (reduced GFR) but is not optimal for children with GFR >75 mL/min/1.73 m 2 . Moreover, the Schwartz equation requires the height of the child, information that is usually not available in the clinical laboratory. This makes automatic reporting of estimated glomerular filtration rate (eGFR) along with serum creatinine impossible. As the majority of children (even children referred to nephrology clinics) have GFR >75 mL/min/1.73 m 2 , it might be interesting to evaluate possible alternatives to the bedside Schwartz equation. The pediatric form of the Full Age Spectrum (FAS) equation offers an alternative to Schwartz, allowing automatic reporting of eGFR since height is not necessary. However, when height is involved in the FAS equation, the equation is essentially equal to the Schwartz equation for children, but there are large differences for adolescents. Combining standardized biomarkers increases the prediction performance of eGFR equations for children, reaching P10 ≈ 45% and P30 ≈ 90%. There are currently good and simple alternatives to the bedside Schwartz equation, but the more complex equations combining serum creatinine, serum cystatin C, and height show the highest accuracy and precision. Copyright © 2017 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.

Group-kinetic theory of turbulence

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1986-01-01

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

Skinfold Prediction Equations Fail to Provide an Accurate Estimate of Body Composition in Elite Rugby Union Athletes of Caucasian and Polynesian Ethnicity.

PubMed

Zemski, Adam J; Broad, Elizabeth M; Slater, Gary J

2018-01-01

Body composition in elite rugby union athletes is routinely assessed using surface anthropometry, which can be utilized to provide estimates of absolute body composition using regression equations. This study aims to assess the ability of available skinfold equations to estimate body composition in elite rugby union athletes who have unique physique traits and divergent ethnicity. The development of sport-specific and ethnicity-sensitive equations was also pursued. Forty-three male international Australian rugby union athletes of Caucasian and Polynesian descent underwent surface anthropometry and dual-energy X-ray absorptiometry (DXA) assessment. Body fat percent (BF%) was estimated using five previously developed equations and compared to DXA measures. Novel sport and ethnicity-sensitive prediction equations were developed using forward selection multiple regression analysis. Existing skinfold equations provided unsatisfactory estimates of BF% in elite rugby union athletes, with all equations demonstrating a 95% prediction interval in excess of 5%. The equations tended to underestimate BF% at low levels of adiposity, whilst overestimating BF% at higher levels of adiposity, regardless of ethnicity. The novel equations created explained a similar amount of variance to those previously developed (Caucasians 75%, Polynesians 90%). The use of skinfold equations, including the created equations, cannot be supported to estimate absolute body composition. Until a population-specific equation is established that can be validated to precisely estimate body composition, it is advocated to use a proven method, such as DXA, when absolute measures of lean and fat mass are desired, and raw anthropometry data routinely to derive an estimate of body composition change.

Necessary and sufficient conditions for the stability of a sleeping top described by three forms of dynamic equations

NASA Astrophysics Data System (ADS)

Ge, Zheng-Ming

2008-04-01

Necessary and sufficient conditions for the stability of a sleeping top described by dynamic equations of six state variables, Euler equations, and Poisson equations, by a two-degree-of-freedom system, Krylov equations, and by a one-degree-of-freedom system, nutation angle equation, is obtained by the Lyapunov direct method, Ge-Liu second instability theorem, an instability theorem, and a Ge-Yao-Chen partial region stability theorem without using the first approximation theory altogether.

Asymptotic of the Solutions of Hyperbolic Equations with a Skew-Symmetric Perturbation

NASA Astrophysics Data System (ADS)

Gallagher, Isabelle

1998-12-01

Using methods introduced by S. Schochet inJ. Differential Equations114(1994), 476-512, we compute the first term of an asymptotic expansion of the solutions of hyperbolic equations perturbated by a skew-symmetric linear operator. That result is first applied to two systems describing the motion of geophysic fluids: the rotating Euler equations and the primitive system of the quasigeostrophic equations. Finally in the last part, we study the slightly compressible Euler equations by application of that same result.

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics: Building Blocks for a Higher Order Method

DTIC Science & Technology

2006-09-30

equation known as the Kadomtsev - Petviashvili (KP) equation ): (ηt + coηx +αηηx + βη )x +γηyy = 0 (4) where γ = co / 2 . The KdV equation ...using the spectral formulation of the Kadomtsev - Petviashvili equation , a standard equation for nonlinear, shallow water wave dynamics that is a... Petviashvili and nonlinear Schroedinger equations and higher order corrections have been developed as prerequisites to coding the Boussinesq and Euler

New conditions for obtaining the exact solutions of the general Riccati equation.

PubMed

Bougoffa, Lazhar

2014-01-01

We propose a direct method for solving the general Riccati equation y' = f(x) + g(x)y + h(x)y(2). We first reduce it into an equivalent equation, and then we formulate the relations between the coefficients functions f(x), g(x), and h(x) of the equation to obtain an equivalent separable equation from which the previous equation can be solved in closed form. Several examples are presented to demonstrate the efficiency of this method.

van der Waals-Tonks-type equations of state for hard-hypersphere fluids in four and five dimensions

NASA Astrophysics Data System (ADS)

Wang, Xian-Zhi

2004-04-01

Recently, we developed accurate van der Waals-Tonks-type equations of state for hard-disk and hard-sphere fluids by using the known virial coefficients. In this paper, we derive the van der Waals-Tonks-type equations of state. We further apply these equations of state to hard-hypersphere fluids in four and five dimensions. In the low-density fluid regime, these equations of state are in good agreement with the simulation results and existing equations of state.

On symmetries, conservation laws and exact solutions of the nonlinear Schrödinger-Hirota equation

NASA Astrophysics Data System (ADS)

Akbulut, Arzu; Taşcan, Filiz

2018-04-01

In this paper, conservation laws and exact solution are found for nonlinear Schrödinger-Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger-Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering.

Oscillation of a class of fractional differential equations with damping term.

PubMed

Qin, Huizeng; Zheng, Bin

2013-01-01

We investigate the oscillation of a class of fractional differential equations with damping term. Based on a certain variable transformation, the fractional differential equations are converted into another differential equations of integer order with respect to the new variable. Then, using Riccati transformation, inequality, and integration average technique, some new oscillatory criteria for the equations are established. As for applications, oscillation for two certain fractional differential equations with damping term is investigated by the use of the presented results.

Analytic solution for the space-time fractional Klein-Gordon and coupled conformable Boussinesq equations

NASA Astrophysics Data System (ADS)

Shallal, Muhannad A.; Jabbar, Hawraz N.; Ali, Khalid K.

2018-03-01

In this paper, we constructed a travelling wave solution for space-time fractional nonlinear partial differential equations by using the modified extended Tanh method with Riccati equation. The method is used to obtain analytic solutions for the space-time fractional Klein-Gordon and coupled conformable space-time fractional Boussinesq equations. The fractional complex transforms and the properties of modified Riemann-Liouville derivative have been used to convert these equations into nonlinear ordinary differential equations.

Nonlinear and dissipative constitutive equations for coupled first-order acoustic field equations that are consistent with the generalized Westervelt equation

NASA Astrophysics Data System (ADS)

Verweij, Martin D.; Huijssen, Jacob

2006-05-01

In diagnostic medical ultrasound, it has become increasingly important to evaluate the nonlinear field of an acoustic beam that propagates in a weakly nonlinear, dissipative medium and that is steered off-axis up to very wide angles. In this case, computations cannot be based on the widely used KZK equation since it applies only to small angles. To benefit from successful computational schemes from elastodynamics and electromagnetics, we propose to use two first-order acoustic field equations, accompanied by two constitutive equations, as an alternative basis. This formulation quite naturally results in the contrast source formalism, makes a clear distinction between fundamental conservation laws and medium behavior, and allows for a straightforward inclusion of any medium inhomogenities. This paper is concerned with the derivation of relevant constitutive equations. We take a pragmatic approach and aim to find those constitutive equations that represent the same medium as implicitly described by the recognized, full wave, nonlinear equations such as the generalized Westervelt equation. We will show how this is achieved by considering the nonlinear case without attenuation, the linear case with attenuation, and the nonlinear case with attenuation. As a result we will obtain surprisingly simple constitutive equations for the full wave case.

An Alternative to the Stay/Switch Equation Assessed When Using a Changeover-Delay

PubMed Central

MacDonall, James S.

2015-01-01

An alternative to the generalized matching equation for understanding concurrent performances is the stay/switch model. For the stay/switch model, the important events are the contingencies and behaviors at each alternative. The current experiment compares the descriptions by two stay/switch equations, the original, empirically derived stay/switch equation and a more theoretically derived equation based on ratios of stay to switch responses matching ratios of stay to switch reinforcers. The present experiment compared descriptions by the original stay/switch equation when using and not using a changeover delay. It also compared descriptions by the more theoretical equation with and without a changeover delay. Finally, it compared descriptions of the concurrent performances by these two equations. Rats were trained in 15 conditions on identical concurrent random-interval schedules in each component of a multiple schedule. A COD operated in only one component. There were no consistent differences in the variance accounted for by each equation of concurrent performances whether or not a COD was used. The simpler equation found greater sensitivity to stay than to switch reinforcers. It also found a COD eliminated the influence of switch reinforcers. Because estimates of parameters were more meaningful when using the more theoretical stay/switch equation it is preferred. PMID:26299548

An alternative to the stay/switch equation assessed when using a changeover-delay.

PubMed

MacDonall, James S

2015-11-01

An alternative to the generalized matching equation for understanding concurrent performances is the stay/switch model. For the stay/switch model, the important events are the contingencies and behaviors at each alternative. The current experiment compares the descriptions by two stay/switch equations, the original, empirically derived stay/switch equation and a more theoretically derived equation based on ratios of stay to switch responses matching ratios of stay to switch reinforcers. The present experiment compared descriptions by the original stay/switch equation when using and not using a changeover delay. It also compared descriptions by the more theoretical equation with and without a changeover delay. Finally, it compared descriptions of the concurrent performances by these two equations. Rats were trained in 15 conditions on identical concurrent random-interval schedules in each component of a multiple schedule. A COD operated in only one component. There were no consistent differences in the variance accounted for by each equation of concurrent performances whether or not a COD was used. The simpler equation found greater sensitivity to stay than to switch reinforcers. It also found a COD eliminated the influence of switch reinforcers. Because estimates of parameters were more meaningful when using the more theoretical stay/switch equation it is preferred. Copyright © 2015 Elsevier B.V. All rights reserved.

Protein electrostatics: a review of the equations and methods used to model electrostatic equations in biomolecules--applications in biotechnology.

PubMed

Neves-Petersen, Maria Teresa; Petersen, Steffen B

2003-01-01

The molecular understanding of the initial interaction between a protein and, e.g., its substrate, a surface or an inhibitor is essentially an understanding of the role of electrostatics in intermolecular interactions. When studying biomolecules it is becoming increasingly evident that electrostatic interactions play a role in folding, conformational stability, enzyme activity and binding energies as well as in protein-protein interactions. In this chapter we present the key basic equations of electrostatics necessary to derive the equations used to model electrostatic interactions in biomolecules. We will also address how to solve such equations. This chapter is divided into two major sections. In the first part we will review the basic Maxwell equations of electrostatics equations called the Laws of Electrostatics that combined will result in the Poisson equation. This equation is the starting point of the Poisson-Boltzmann (PB) equation used to model electrostatic interactions in biomolecules. Concepts as electric field lines, equipotential surfaces, electrostatic energy and when can electrostatics be applied to study interactions between charges will be addressed. In the second part we will arrive at the electrostatic equations for dielectric media such as a protein. We will address the theory of dielectrics and arrive at the Poisson equation for dielectric media and at the PB equation, the main equation used to model electrostatic interactions in biomolecules (e.g., proteins, DNA). It will be shown how to compute forces and potentials in a dielectric medium. In order to solve the PB equation we will present the continuum electrostatic models, namely the Tanford-Kirkwood and the modified Tandord-Kirkwood methods. Priority will be given to finding the protonation state of proteins prior to solving the PB equation. We also present some methods that can be used to map and study the electrostatic potential distribution on the molecular surface of proteins. The combination of graphical visualisation of the electrostatic fields combined with knowledge about the location of key residues on the protein surface allows us to envision atomic models for enzyme function. Finally, we exemplify the use of some of these methods on the enzymes of the lipase family.

Every Equation Tells a Story: Using Equation Dictionaries in Introductory Geophysics

ERIC Educational Resources Information Center

Caplan-Auerbach, Jacqueline

2009-01-01

Many students view equations as a series of variables and operators into which numbers should be plugged rather than as representative of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume it meets their needs, rather than selecting an equation that represents the appropriate physical…

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

FIA's volume-to-biomass conversion method (CRM) generally underestimates biomass in comparison to published equations

Treesearch

David. C. Chojnacky

2012-01-01

An update of the Jenkins et al. (2003) biomass estimation equations for North American tree species resulted in 35 generalized equations developed from published equations. These 35 equations, which predict aboveground biomass of individual species grouped according to a taxa classification (based on genus or family and sometimes specific gravity), generally predicted...

Nonlinear Waves.

DTIC Science & Technology

1988-02-01

in Multi- dimensions II, P.M. Santini and A.S. Fokas, preprint INS#67, 1986. The Recursion Operator of the Kadomtsev - Petviashvili Equation and the...solitons, multidimensional inverse problems, Painleve equations , direct linearizations of certain nonlinear wave equations , DBAR problems, Riemann...the Navy is (a) the recent discovery that many of the equations describing ship hydrodynamics in channels of finite depth obey nonlinear equations

A Versatile Technique for Solving Quintic Equations

ERIC Educational Resources Information Center

Kulkarni, Raghavendra G.

2006-01-01

In this paper we present a versatile technique to solve several types of solvable quintic equations. In the technique described here, the given quintic is first converted to a sextic equation by adding a root, and the resulting sextic equation is decomposed into two cubic polynomials as factors in a novel fashion. The resultant cubic equations are…

Comparing the IRT Pre-equating and Section Pre-equating: A Simulation Study.

ERIC Educational Resources Information Center

Hwang, Chi-en; Cleary, T. Anne

The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

The Examination of the Classification of Students into Performance Categories by Two Different Equating Methods

ERIC Educational Resources Information Center

Keller, Lisa A.; Keller, Robert R.; Parker, Pauline A.

2011-01-01

This study investigates the comparability of two item response theory based equating methods: true score equating (TSE), and estimated true equating (ETE). Additionally, six scaling methods were implemented within each equating method: mean-sigma, mean-mean, two versions of fixed common item parameter, Stocking and Lord, and Haebara. Empirical…

Encouraging Students to Think Strategically when Learning to Solve Linear Equations

ERIC Educational Resources Information Center

Robson, Daphne; Abell, Walt; Boustead, Therese

2012-01-01

Students who are preparing to study science and engineering need to understand equation solving but adult students returning to study can find this difficult. In this paper, the design of an online resource, Equations2go, for helping students learn to solve linear equations is investigated. Students learning to solve equations need to consider…

Middle School Students' Conceptual Understanding of Equations: Evidence From Writing Story Problems. WCER Working Paper No. 2009-3

ERIC Educational Resources Information Center

Alibali, Martha W.; Kao, Yvonne S.; Brown, Alayna N.; Nathan, Mitchell J.; Stephens, Ana C.

2009-01-01

This study investigated middle school students' conceptual understanding of algebraic equations. Participants in the study--257 sixth- and seventh-grade students--were asked to solve one set of algebraic equations and to generate story problems corresponding with another set of equations. Structural aspects of the equations, including the number…

Using the Kernel Method of Test Equating for Estimating the Standard Errors of Population Invariance Measures

ERIC Educational Resources Information Center

Moses, Tim

2008-01-01

Equating functions are supposed to be population invariant, meaning that the choice of subpopulation used to compute the equating function should not matter. The extent to which equating functions are population invariant is typically assessed in terms of practical difference criteria that do not account for equating functions' sampling…

Performance of bed-load transport equations relative to geomorphic significance: Predicting effective discharge and its transport rate

Treesearch

Jeffrey J. Barry; John M. Buffington; Peter Goodwin; John .G. King; William W. Emmett

2008-01-01

Previous studies assessing the accuracy of bed-load transport equations have considered equation performance statistically based on paired observations of measured and predicted bed-load transport rates. However, transport measurements were typically taken during low flows, biasing the assessment of equation performance toward low discharges, and because equation...

Computational Algorithms or Identification of Distributed Parameter Systems

DTIC Science & Technology

1993-04-24

delay-differential equations, Volterra integral equations, and partial differential equations with memory terms . In particular we investigated a...tested for estimating parameters in a Volterra integral equation arising from a viscoelastic model of a flexible structure with Boltzmann damping. In...particular, one of the parameters identified was the order of the derivative in Volterra integro-differential equations containing fractional

Small-Sample Equating with Prior Information. Research Report. ETS RR-09-25

ERIC Educational Resources Information Center

Livingston, Samuel A.; Lewis, Charles

2009-01-01

This report proposes an empirical Bayes approach to the problem of equating scores on test forms taken by very small numbers of test takers. The equated score is estimated separately at each score point, making it unnecessary to model either the score distribution or the equating transformation. Prior information comes from equatings of other…

A novel unsplit perfectly matched layer for the second-order acoustic wave equation.

PubMed

Ma, Youneng; Yu, Jinhua; Wang, Yuanyuan

2014-08-01

When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach. Copyright © 2014 Elsevier B.V. All rights reserved.

Explicit solution of integrated 1 - exp equation for predicting accumulation and decline of concentrations for drugs obeying nonlinear saturation kinetics.

PubMed

Keller, Frieder; Hartmann, Bertram; Czock, David

2009-12-01

To describe nonlinear, saturable pharmacokinetics, the Michaelis-Menten equation is frequently used. However, the Michaelis-Menten equation has no integrated solution for concentrations but only for the time factor. Application of the Lambert W function was proposed recently to obtain an integrated solution of the Michaelis-Menten equation. As an alternative to the Michaelis-Menten equation, a 1 - exp equation has been used to describe saturable kinetics, with the advantage that the integrated 1 - exp equation has an explicit solution for concentrations. We used the integrated 1 - exp equation to predict the accumulation kinetics and the nonlinear concentration decline for a proposed fictive drug. In agreement with the recently proposed method, we found that for the integrated 1 - exp equation no steady state is obtained if the maximum rate of change in concentrations (Vmax) within interval (Tau) is less than the difference between peak and trough concentrations (Vmax x Tau < C peak - C trough).

The fifth-order partial differential equation for the description of the α + β Fermi-Pasta-Ulam model

NASA Astrophysics Data System (ADS)

Kudryashov, Nikolay A.; Volkov, Alexandr K.

2017-01-01

We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the Fermi-Pasta-Ulam model. We use the potential of interaction between neighbouring masses with both quadratic and cubic terms. The equation is derived using the continuous limit. Unlike the previous works, we take into account higher order terms in the Taylor series expansions. We investigate the equation using the Painlevé approach. We show that the equation does not pass the Painlevé test and can not be integrated by the inverse scattering transform. We use the logistic function method and the Laurent expansion method to find travelling wave solutions of the fifth-order equation. We use the pseudospectral method for the numerical simulation of wave processes, described by the equation.

A Variational Formalism for the Radiative Transfer Equation and a Geostrophic, Hydrostatic Atmosphere: Prelude to Model 3

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.

1991-01-01

The second step in development of MODEL III is summarized. It combines the four radiative transfer equations of the first step with the equations for a geostrophic and hydrostatic atmosphere. This step is intended to bring radiance into a three dimensional balance with wind, height, and temperature. The use of the geostrophic approximation in place of the full set of primitive equations allows for an easier evaluation of how the inclusion of the radiative transfer equation increases the complexity of the variational equations. Seven different variational formulations were developed for geostrophic, hydrostatic, and radiative transfer equations. The first derivation was too complex to yield solutions that were physically meaningful. For the remaining six derivations, the variational method gave the same physical interpretation (the observed brightness temperatures could provide no meaningful input to a geostrophic, hydrostatic balance) at least through the problem solving methodology used in these studies. The variational method is presented and the Euler-Lagrange equations rederived for the geostrophic, hydrostatic, and radiative transfer equations.

Cotton-type and joint invariants for linear elliptic systems.

PubMed

Aslam, A; Mahomed, F M

2013-01-01

Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results.

The equations of motion of a secularly precessing elliptical orbit

NASA Astrophysics Data System (ADS)

Casotto, S.; Bardella, M.

2013-01-01

The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular perturbations in the node, the argument of pericentre and the mean motion. Usually this is done in connection with Encke's method to ensure minimal rectification frequency. Similar equations are already available in the literature, but they are either given based on the true anomaly as the independent variable or in mixed mode with respect to time through the use of a supporting equation to track the anomaly. The equations developed here form a complete and independent set of six equations in time. Reformulations both of Escobal's and Kyner and Bennett's equations are also provided which lead to a more concise form.

Evaluation of abutment scour prediction equations with field data

USGS Publications Warehouse

Benedict, S.T.; Deshpande, N.; Aziz, N.M.

2007-01-01

The U.S. Geological Survey, in cooperation with FHWA, compared predicted abutment scour depths, computed with selected predictive equations, with field observations collected at 144 bridges in South Carolina and at eight bridges from the National Bridge Scour Database. Predictive equations published in the 4th edition of Evaluating Scour at Bridges (Hydraulic Engineering Circular 18) were used in this comparison, including the original Froehlich, the modified Froehlich, the Sturm, the Maryland, and the HIRE equations. The comparisons showed that most equations tended to provide conservative estimates of scour that at times were excessive (as large as 158 ft). Equations also produced underpredictions of scour, but with less frequency. Although the equations provide an important resource for evaluating abutment scour at bridges, the results of this investigation show the importance of using engineering judgment in conjunction with these equations.

A Multiparameter Thermal Conductivity Equation for 1,1-Difluoroethane (R152a) with an Optimized Functional Form

NASA Astrophysics Data System (ADS)

Scalabrin, G.; Marchi, P.; Finezzo, F.

2006-11-01

The application of an optimization technique to the available experimental data has led to the development of a new multiparameter equation λ = λ ( T,ρ ) for the representation of the thermal conductivity of 1,1-difluoroethane (R152a). The region of validity of the proposed equation covers the temperature range from 220 to 460 K and pressures up to 55 MPa, including the near-critical region. The average absolute deviation of the equation with respect to the selected 939 primary data points is 1.32%. The proposed equation represents therefore a significant improvement with respect to the literature conventional equation. The density value required by the equation is calculated at the chosen temperature and pressure conditions using a high accuracy equation of state for the fluid.

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

Global-in-time solutions for the isothermal Matovich-Pearson equations

NASA Astrophysics Data System (ADS)

Feireisl, Eduard; Laurençot, Philippe; Mikelić, Andro

2011-01-01

In this paper we study the Matovich-Pearson equations describing the process of glass fibre drawing. These equations may be viewed as a 1D-reduction of the incompressible Navier-Stokes equations including free boundary, valid for the drawing of a long and thin glass fibre. We concentrate on the isothermal case without surface tension. Then the Matovich-Pearson equations represent a nonlinearly coupled system of an elliptic equation for the axial velocity and a hyperbolic transport equation for the fluid cross-sectional area. We first prove existence of a local solution, and, after constructing appropriate barrier functions, we deduce that the fluid radius is always strictly positive and that the local solution remains in the same regularity class. This estimate leads to the global existence and uniqueness result for this important system of equations.

Cotton-Type and Joint Invariants for Linear Elliptic Systems

PubMed Central

Aslam, A.; Mahomed, F. M.

2013-01-01

Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results. PMID:24453871

Evolution of nonlinear waves in a blood-filled artery with an aneurysm

NASA Astrophysics Data System (ADS)

Nikolova, E. V.; Jordanov, I. P.; Dimitrova, Z. I.; Vitanov, N. K.

2017-10-01

We discuss propagation of traveling waves in a blood-filled hyper-elastic artery with a local dilatation (an aneurysm). The processes in the injured artery are modeled by an equation of the motion of the arterial wall and by equations of the motion of the fluid (the blood). Taking into account the specific arterial geometry and applying the reductive perturbation method in long-wave approximation we reduce the model equations to a version of the perturbed Korteweg-de Vries kind equation with variable coefficients. Exact traveling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is numerically simulated and discussed from the point of view of arterial disease mechanics.

Application of a New Spirometric Reference Equation and Its Impact on the Staging of Korean Chronic Obstructive Pulmonary Disease Patients

PubMed Central

Hwang, Yong Il; Kim, Eun Ji; Lee, Chang Youl; Park, Sunghoon; Choi, Jeong Hee; Park, Yong Bum; Jang, Seung Hun; Kim, Cheol Hong; Shin, Tae Rim; Park, Sang Myeon; Kim, Dong-Gyu; Lee, Myung-Goo; Hyun, In-Gyu

2012-01-01

Purpose A new spirometric reference equation was recently developed from the first national chronic obstructive pulmonary disease (COPD) survey in Korea. However, Morris' equation has been preferred for evaluating spirometric values instead. The objective of this study was to evaluate changes in severity staging in Korean COPD patients by adopting the newly developed Korean equation. Materials and Methods We evaluated the spirometric data of 441 COPD patients. The presence of airflow limitation was defined as an observed post-bronchodilator forced expiratory volume in one second/forced vital capacity (FEV1/FVC) less than 0.7, and the severity of airflow limitation was assessed according to GOLD stages. Spirometric values were reassessed using the new Korean equation, Morris' equation and other reference equations. Results The severity of airflow limitation was differently graded in 143 (32.4%) patients after application of the new Korean equation when compared with Morris' equation. All 143 patients were reallocated into more severe stages (49 at mild stage, 65 at moderate stage, and 29 at severe stage were changed to moderate, severe and very severe stages, respectively). Stages according to other reference equations were changed in 18.6-49.4% of the patients. Conclusion These results indicate that equations from different ethnic groups do not sufficiently reflect the airflow limitation of Korean COPD patients. The Korean reference equation should be used for Korean COPD patients in order to administer proper treatment. PMID:22318825

Characterization of Free Phenytoin Concentrations in End-Stage Renal Disease Using the Winter-Tozer Equation.

PubMed

Soriano, Vincent V; Tesoro, Eljim P; Kane, Sean P

2017-08-01

The Winter-Tozer (WT) equation has been shown to reliably predict free phenytoin levels in healthy patients. In patients with end-stage renal disease (ESRD), phenytoin-albumin binding is altered and, thus, affects interpretation of total serum levels. Although an ESRD WT equation was historically proposed for this population, there is a lack of data evaluating its accuracy. The objective of this study was to determine the accuracy of the ESRD WT equation in predicting free serum phenytoin concentration in patients with ESRD on hemodialysis (HD). A retrospective analysis of adult patients with ESRD on HD and concurrent free and total phenytoin concentrations was conducted. Each patient's true free phenytoin concentration was compared with a calculated value using the ESRD WT equation and a revised version of the ESRD WT equation. A total of 21 patients were included for analysis. The ESRD WT equation produced a percentage error of 75% and a root mean square error of 1.76 µg/mL. Additionally, 67% of the samples had an error >50% when using the ESRD WT equation. A revised equation was found to have high predictive accuracy, with only 5% of the samples demonstrating >50% error. The ESRD WT equation was not accurate in predicting free phenytoin concentration in patients with ESRD on HD. A revised ESRD WT equation was found to be significantly more accurate. Given the small study sample, further studies are required to fully evaluate the clinical utility of the revised ESRD WT equation.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.

PubMed

Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio

2014-10-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

Constrained multibody system dynamics: An automated approach

NASA Technical Reports Server (NTRS)

Kamman, J. W.; Huston, R. L.

1982-01-01

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations

PubMed Central

Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio

2014-01-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

PubMed

Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

2015-12-01

The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

Soliton, rational, and periodic solutions for the infinite hierarchy of defocusing nonlinear Schrödinger equations.

PubMed

Ankiewicz, Adrian

2016-07-01

Analysis of short-pulse propagation in positive dispersion media, e.g., in optical fibers and in shallow water, requires assorted high-order derivative terms. We present an infinite-order "dark" hierarchy of equations, starting from the basic defocusing nonlinear Schrödinger equation. We present generalized soliton solutions, plane-wave solutions, and periodic solutions of all orders. We find that "even"-order equations in the set affect phase and "stretching factors" in the solutions, while "odd"-order equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are complex. There are various applications in optics and water waves.

Exact traveling wave solutions for system of nonlinear evolution equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

2016-01-01

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Liouvillian propagators, Riccati equation and differential Galois theory

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo; Suazo, Erwin

2013-11-01

In this paper a Galoisian approach to building propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schrödinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation. As the main application of this approach we solve Ince’s differential equation through the Hamiltonian algebrization procedure and the Kovacic algorithm to find the propagator for a generalized harmonic oscillator. This propagator has applications which describe the process of degenerate parametric amplification in quantum optics and light propagation in a nonlinear anisotropic waveguide. Toy models of propagators inspired by integrable Riccati equations and integrable characteristic equations are also presented.

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Approach to the origin of turbulence on the basis of two-point kinetic theory

NASA Technical Reports Server (NTRS)

Tsuge, S.

1974-01-01

Equations for the fluctuation correlation in an incompressible shear flow are derived on the basis of kinetic theory, utilizing the two-point distribution function which obeys the BBGKY hierarchy equation truncated with the hypothesis of 'ternary' molecular chaos. The step from the molecular to the hydrodynamic description is accomplished by a moment expansion which is a two-point version of the thirteen-moment method, and which leads to a series of correlation equations, viz., the two-point counterparts of the continuity equation, the Navier-Stokes equation, etc. For almost parallel shearing flows the two-point equation is separable and reduces to two Orr-Sommerfeld equations with different physical implications.

Consistent description of kinetic equation with triangle anomaly

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pu Shi; Gao Jianhua; Wang Qun

2011-05-01

We provide a consistent description of the kinetic equation with a triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an anomalous source term is necessary to ensure that the equations for the charge and energy-momentum conservation are satisfied and that the correction terms of distribution functions are compatible to these equations. The constraining equations from the entropy principle are derived for the anomaly-induced leading order corrections to the particle distribution functions. The correction terms can be determined for the minimum number of unknown coefficients in onemore » charge and two charge cases by solving the constraining equations.« less

Truncated Painlevé expansion: Tanh-traveling wave solutions and reduction of sine-Poisson equation to a quadrature for stationary and nonstationary three-dimensional collisionless cold plasma

NASA Astrophysics Data System (ADS)

Ibrahim, R. S.; El-Kalaawy, O. H.

2006-10-01

The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painlevé expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model.

7 CFR 610.12 - Equations for predicting soil loss due to water erosion.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 7 Agriculture 6 2012-01-01 2012-01-01 false Equations for predicting soil loss due to water... ASSISTANCE Soil Erosion Prediction Equations § 610.12 Equations for predicting soil loss due to water erosion. (a) The equation for predicting soil loss due to erosion for both the USLE and the RUSLE is A = R × K...

7 CFR 610.12 - Equations for predicting soil loss due to water erosion.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 6 2014-01-01 2014-01-01 false Equations for predicting soil loss due to water... ASSISTANCE Soil Erosion Prediction Equations § 610.12 Equations for predicting soil loss due to water erosion. (a) The equation for predicting soil loss due to erosion for both the USLE and the RUSLE is A = R × K...

7 CFR 610.12 - Equations for predicting soil loss due to water erosion.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 7 Agriculture 6 2011-01-01 2011-01-01 false Equations for predicting soil loss due to water... ASSISTANCE Soil Erosion Prediction Equations § 610.12 Equations for predicting soil loss due to water erosion. (a) The equation for predicting soil loss due to erosion for both the USLE and the RUSLE is A = R × K...

7 CFR 610.12 - Equations for predicting soil loss due to water erosion.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 7 Agriculture 6 2013-01-01 2013-01-01 false Equations for predicting soil loss due to water... ASSISTANCE Soil Erosion Prediction Equations § 610.12 Equations for predicting soil loss due to water erosion. (a) The equation for predicting soil loss due to erosion for both the USLE and the RUSLE is A = R × K...

7 CFR 610.12 - Equations for predicting soil loss due to water erosion.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 6 2010-01-01 2010-01-01 false Equations for predicting soil loss due to water... ASSISTANCE Soil Erosion Prediction Equations § 610.12 Equations for predicting soil loss due to water erosion. (a) The equation for predicting soil loss due to erosion for both the USLE and the RUSLE is A = R × K...

Tangent Lines without Derivatives for Quadratic and Cubic Equations

ERIC Educational Resources Information Center

Carroll, William J.

2009-01-01

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

ERIC Educational Resources Information Center

Ozdemir, Burhanettin

2017-01-01

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

Fault Tolerant Optimal Control.

DTIC Science & Technology

1982-08-01

subsystem is modelled by deterministic or stochastic finite-dimensional vector differential or difference equations. The parameters of these equations...is no partial differential equation that must be solved. Thus we can sidestep the inability to solve the Bellman equation for control problems with x...transition models and cost functionals can be reduced to the search for solutions of nonlinear partial differential equations using ’verification

Evaluating revised biomass equations: are some forest types more equivalent than others?

Treesearch

Coeli M. Hoover; James E. Smith

2016-01-01

Background: In 2014, Chojnacky et al. published a revised set of biomass equations for trees of temperate US forests, expanding on an existing equation set (published in 2003 by Jenkins et al.), both of which were developed from published equations using a meta-analytical approach. Given the similarities in the approach to developing the equations, an examination of...

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

ERIC Educational Resources Information Center

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

Choice of Target Population Weights in Rater Comparability Scoring and Equating. Research Report. ETS RR-13-03

ERIC Educational Resources Information Center

Puhan, Gautam

2013-01-01

The purpose of this study was to demonstrate that the choice of sample weights when defining the target population under poststratification equating can be a critical factor in determining the accuracy of the equating results under a unique equating scenario, known as "rater comparability scoring and equating." The nature of data…

Stem Profile for Southern Equations for Southern Tree Species

Treesearch

Alexander Clark; Ray A. Souter; Bryce E. Schlaegel

1991-01-01

Form-class segmented-profile equations for 58 southern tree species and species groups are presented.The profile equations are based on taper data for 13,469 trees sampled in natural stands in many locations across the South.The profile equations predict diameter at any given height, height to give diameter, and volume between two heights.Equation coefficients for use...

The physics behind Van der Burgh's empirical equation, providing a new predictive equation for salinity intrusion in estuaries

NASA Astrophysics Data System (ADS)

Zhang, Zhilin; Savenije, Hubert H. G.

2017-07-01

The practical value of the surprisingly simple Van der Burgh equation in predicting saline water intrusion in alluvial estuaries is well documented, but the physical foundation of the equation is still weak. In this paper we provide a connection between the empirical equation and the theoretical literature, leading to a theoretical range of Van der Burgh's coefficient of 1/2 < K < 2/3 for density-driven mixing which falls within the feasible range of 0 < K < 1. In addition, we developed a one-dimensional predictive equation for the dispersion of salinity as a function of local hydraulic parameters that can vary along the estuary axis, including mixing due to tide-driven residual circulation. This type of mixing is relevant in the wider part of alluvial estuaries where preferential ebb and flood channels appear. Subsequently, this dispersion equation is combined with the salt balance equation to obtain a new predictive analytical equation for the longitudinal salinity distribution. Finally, the new equation was tested and applied to a large database of observations in alluvial estuaries, whereby the calibrated K values appeared to correspond well to the theoretical range.

Coupled radial Schrödinger equations written as Dirac-type equations: application to an amplitude-phase approach

NASA Astrophysics Data System (ADS)

Thylwe, Karl-Erik; McCabe, Patrick

2012-04-01

The classical amplitude-phase method due to Milne, Wilson, Young and Wheeler in the 1930s is known to be a powerful computational tool for determining phase shifts and energy eigenvalues in cases where a sufficiently slowly varying amplitude function can be found. The key for the efficient computations is that the original single-state radial Schrödinger equation is transformed to a nonlinear equation, the Milne equation. Such an equation has solutions that may or may not oscillate, depending on boundary conditions, which then requires a robust recipe for locating the (optimal) ‘almost constant’ solutions for its use in the method. For scattering problems the solutions of the amplitude equations always approach constants as the radial distance r tends to infinity, and there is no problem locating the ‘optimal’ amplitude functions from a low-order semiclassical approximation. In the present work, the amplitude-phase approach is generalized to two coupled Schrödinger equations similar to an earlier generalization to radial Dirac equations. The original scalar amplitude then becomes a vector quantity, and the original Milne equation is generalized accordingly. Numerical applications to resonant electron-atom scattering are illustrated.

Molar mass, radius of gyration and second virial coefficient from new static light scattering equations for dilute solutions: application to 21 (macro)molecules.

PubMed

Illien, Bertrand; Ying, Ruifeng

2009-05-11

New static light scattering (SLS) equations for dilute binary solutions are derived. Contrarily to the usual SLS equations [Carr-Zimm (CZ)], the new equations have no need for the experimental absolute Rayleigh ratio of a reference liquid and solely rely on the ratio of scattered intensities of solutions and solvent. The new equations, which are based on polarizability equations, take into account the usual refractive index increment partial differential n/partial differential rho(2) complemented by the solvent specific polarizability and a term proportional to the slope of the solution density rho versus the solute mass concentration rho(2) (density increment). Then all the equations are applied to 21 (macro)molecules with a wide range of molar mass (0.2500 kg mol(-1)), for which the scattered intensity is no longer independent of the scattering angle, the new equations give the same value of the radius of gyration as the CZ equation and consistent values of the second virial coefficient.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

Validity of Bioelectrical Impedance Analysis to Estimation Fat-Free Mass in the Army Cadets.

PubMed

Langer, Raquel D; Borges, Juliano H; Pascoa, Mauro A; Cirolini, Vagner X; Guerra-Júnior, Gil; Gonçalves, Ezequiel M

2016-03-11

Bioelectrical Impedance Analysis (BIA) is a fast, practical, non-invasive, and frequently used method for fat-free mass (FFM) estimation. The aims of this study were to validate predictive equations of BIA to FFM estimation in Army cadets and to develop and validate a specific BIA equation for this population. A total of 396 males, Brazilian Army cadets, aged 17-24 years were included. The study used eight published predictive BIA equations, a specific equation in FFM estimation, and dual-energy X-ray absorptiometry (DXA) as a reference method. Student's t-test (for paired sample), linear regression analysis, and Bland-Altman method were used to test the validity of the BIA equations. Predictive BIA equations showed significant differences in FFM compared to DXA (p < 0.05) and large limits of agreement by Bland-Altman. Predictive BIA equations explained 68% to 88% of FFM variance. Specific BIA equations showed no significant differences in FFM, compared to DXA values. Published BIA predictive equations showed poor accuracy in this sample. The specific BIA equations, developed in this study, demonstrated validity for this sample, although should be used with caution in samples with a large range of FFM.

Derivation of a generalized Schrödinger equation from the theory of scale relativity

NASA Astrophysics Data System (ADS)

Chavanis, Pierre-Henri

2017-06-01

Using Nottale's theory of scale relativity relying on a fractal space-time, we derive a generalized Schrödinger equation taking into account the interaction of the system with the external environment. This equation describes the irreversible evolution of the system towards a static quantum state. We first interpret the scale-covariant equation of dynamics stemming from Nottale's theory as a hydrodynamic viscous Burgers equation for a potential flow involving a complex velocity field and an imaginary viscosity. We show that the Schrödinger equation can be directly obtained from this equation by performing a Cole-Hopf transformation equivalent to the WKB transformation. We then introduce a friction force proportional and opposite to the complex velocity in the scale-covariant equation of dynamics in a way that preserves the local conservation of the normalization condition. We find that the resulting generalized Schrödinger equation, or the corresponding fluid equations obtained from the Madelung transformation, involve not only a damping term but also an effective thermal term. The friction coefficient and the temperature are related to the real and imaginary parts of the complex friction coefficient in the scale-covariant equation of dynamics. This may be viewed as a form of fluctuation-dissipation theorem. We show that our generalized Schrödinger equation satisfies an H-theorem for the quantum Boltzmann free energy. As a result, the probability distribution relaxes towards an equilibrium state which can be viewed as a Boltzmann distribution including a quantum potential. We propose to apply this generalized Schrödinger equation to dark matter halos in the Universe, possibly made of self-gravitating Bose-Einstein condensates.

Validity of one-repetition maximum predictive equations in men with spinal cord injury.

PubMed

Ribeiro Neto, F; Guanais, P; Dornelas, E; Coutinho, A C B; Costa, R R G

2017-10-01

Cross-sectional study. The study aimed (a) to test the cross-validation of current one-repetition maximum (1RM) predictive equations in men with spinal cord injury (SCI); (b) to compare the current 1RM predictive equations to a newly developed equation based on the 4- to 12-repetition maximum test (4-12RM). SARAH Rehabilitation Hospital Network, Brasilia, Brazil. Forty-five men aged 28.0 years with SCI between C6 and L2 causing complete motor impairment were enrolled in the study. Volunteers were tested, in a random order, in 1RM test or 4-12RM with 2-3 interval days. Multiple regression analysis was used to generate an equation for predicting 1RM. There were no significant differences between 1RM test and the current predictive equations. ICC values were significant and were classified as excellent for all current predictive equations. The predictive equation of Lombardi presented the best Bland-Altman results (0.5 kg and 12.8 kg for mean difference and interval range around the differences, respectively). The two created equation models for 1RM demonstrated the same and a high adjusted R 2 (0.971, P<0.01), but different SEE of measured 1RM (2.88 kg or 5.4% and 2.90 kg or 5.5%). All 1RM predictive equations are accurate to assess individuals with SCI at the bench press exercise. However, the predictive equation of Lombardi presented the best associated cross-validity results. A specific 1RM prediction equation was also elaborated for individuals with SCI. The created equation should be tested in order to verify whether it presents better accuracy than the current ones.

Resting energy expenditure prediction in recreational athletes of 18-35 years: confirmation of Cunningham equation and an improved weight-based alternative.

PubMed

ten Haaf, Twan; Weijs, Peter J M

2014-01-01

Resting energy expenditure (REE) is expected to be higher in athletes because of their relatively high fat free mass (FFM). Therefore, REE predictive equation for recreational athletes may be required. The aim of this study was to validate existing REE predictive equations and to develop a new recreational athlete specific equation. 90 (53 M, 37 F) adult athletes, exercising on average 9.1 ± 5.0 hours a week and 5.0 ± 1.8 times a week, were included. REE was measured using indirect calorimetry (Vmax Encore n29), FFM and FM were measured using air displacement plethysmography. Multiple linear regression analysis was used to develop a new FFM-based and weight-based REE predictive equation. The percentage accurate predictions (within 10% of measured REE), percentage bias, root mean square error and limits of agreement were calculated. Results: The Cunningham equation and the new weight-based equation REE(kJ / d) = 49.940* weight(kg) + 2459.053* height(m) - 34.014* age(y) + 799.257* sex(M = 1,F = 0) + 122.502 and the new FFM-based equation REE(kJ / d) = 95.272*FFM(kg) + 2026.161 performed equally well. De Lorenzo's equation predicted REE less accurate, but better than the other generally used REE predictive equations. Harris-Benedict, WHO, Schofield, Mifflin and Owen all showed less than 50% accuracy. For a population of (Dutch) recreational athletes, the REE can accurately be predicted with the existing Cunningham equation. Since body composition measurement is not always possible, and other generally used equations fail, the new weight-based equation is advised for use in sports nutrition.

Shock formation in the dispersionless Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Grava, T.; Klein, C.; Eggers, J.

2016-04-01

The dispersionless Kadomtsev-Petviashvili (dKP) equation {{≤ft({{u}t}+u{{u}x}\\right)}x}={{u}yy} is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation numerically we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation {{u}t}+u{{u}x}=0 . We show numerically that the solutions to the transformed equation stays regular for longer times than the solution of the dKP equation. This permits us to extend the dKP solution as the graph of a multivalued function beyond the critical time when the gradients blow up. This overturned solution is multivalued in a lip shape region in the (x, y) plane, where the solution of the dKP equation exists in a weak sense only, and a shock front develops. A local expansion reveals the universal scaling structure of the shock, which after a suitable change of coordinates corresponds to a generic cusp catastrophe. We provide a heuristic derivation of the shock front position near the critical point for the solution of the dKP equation, and study the solution of the dKP equation when a small amount of dissipation is added. Using multiple-scale analysis, we show that in the limit of small dissipation and near the critical point of the dKP solution, the solution of the dissipative dKP equation converges to a Pearcey integral. We test and illustrate our results by detailed comparisons with numerical simulations of both the regularized equation, the dKP equation, and the asymptotic description given in terms of the Pearcey integral.

A fast marching algorithm for the factored eikonal equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Treister, Eran, E-mail: erantreister@gmail.com; Haber, Eldad, E-mail: haber@math.ubc.ca; Department of Mathematics, The University of British Columbia, Vancouver, BC

The eikonal equation is instrumental in many applications in several fields ranging from computer vision to geoscience. This equation can be efficiently solved using the iterative Fast Sweeping (FS) methods and the direct Fast Marching (FM) methods. However, when used for a point source, the original eikonal equation is known to yield inaccurate numerical solutions, because of a singularity at the source. In this case, the factored eikonal equation is often preferred, and is known to yield a more accurate numerical solution. One application that requires the solution of the eikonal equation for point sources is travel time tomography. Thismore » inverse problem may be formulated using the eikonal equation as a forward problem. While this problem has been solved using FS in the past, the more recent choice for applying it involves FM methods because of the efficiency in which sensitivities can be obtained using them. However, while several FS methods are available for solving the factored equation, the FM method is available only for the original eikonal equation. In this paper we develop a Fast Marching algorithm for the factored eikonal equation, using both first and second order finite-difference schemes. Our algorithm follows the same lines as the original FM algorithm and requires the same computational effort. In addition, we show how to obtain sensitivities using this FM method and apply travel time tomography, formulated as an inverse factored eikonal equation. Numerical results in two and three dimensions show that our algorithm solves the factored eikonal equation efficiently, and demonstrate the achieved accuracy for computing the travel time. We also demonstrate a recovery of a 2D and 3D heterogeneous medium by travel time tomography using the eikonal equation for forward modeling and inversion by Gauss–Newton.« less

Unified approach for incompressible flows

NASA Astrophysics Data System (ADS)

Chang, Tyne-Hsien

1993-12-01

An unified approach for solving both compressible and incompressible flows was investigated in this study. The difference in CFD code development between incompressible and compressible flows is due to the mathematical characteristics. However, if one can modify the continuity equation for incompressible flows by introducing pseudocompressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of a compressible flow code to solve incompressible flows becomes feasible. Among numerical algorithms developed for compressible flows, the Centered Total Variation Diminishing (CTVD) schemes possess better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that CTVD schemes can equally well solve incompressible flows. In this study, the governing equations for incompressible flows include the continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the boundary conditions including physical and numerical boundary conditions must be properly specified to obtain accurate solution. The CFD code for this research is currently in progress. Flow past a circular cylinder will be used for numerical experiments to determine the accuracy and efficiency of the code before applying this code to more specific applications.

Alternative Regression Equations for Estimation of Annual Peak-Streamflow Frequency for Undeveloped Watersheds in Texas using PRESS Minimization

USGS Publications Warehouse

Asquith, William H.; Thompson, David B.

2008-01-01

The U.S. Geological Survey, in cooperation with the Texas Department of Transportation and in partnership with Texas Tech University, investigated a refinement of the regional regression method and developed alternative equations for estimation of peak-streamflow frequency for undeveloped watersheds in Texas. A common model for estimation of peak-streamflow frequency is based on the regional regression method. The current (2008) regional regression equations for 11 regions of Texas are based on log10 transformations of all regression variables (drainage area, main-channel slope, and watershed shape). Exclusive use of log10-transformation does not fully linearize the relations between the variables. As a result, some systematic bias remains in the current equations. The bias results in overestimation of peak streamflow for both the smallest and largest watersheds. The bias increases with increasing recurrence interval. The primary source of the bias is the discernible curvilinear relation in log10 space between peak streamflow and drainage area. Bias is demonstrated by selected residual plots with superimposed LOWESS trend lines. To address the bias, a statistical framework based on minimization of the PRESS statistic through power transformation of drainage area is described and implemented, and the resulting regression equations are reported. Compared to log10-exclusive equations, the equations derived from PRESS minimization have PRESS statistics and residual standard errors less than the log10 exclusive equations. Selected residual plots for the PRESS-minimized equations are presented to demonstrate that systematic bias in regional regression equations for peak-streamflow frequency estimation in Texas can be reduced. Because the overall error is similar to the error associated with previous equations and because the bias is reduced, the PRESS-minimized equations reported here provide alternative equations for peak-streamflow frequency estimation.

Estimating equations for glomerular filtration rate in the era of creatinine standardization: a systematic review.

PubMed

Earley, Amy; Miskulin, Dana; Lamb, Edmund J; Levey, Andrew S; Uhlig, Katrin

2012-06-05

Clinical laboratories are increasingly reporting estimated glomerular filtration rate (GFR) by using serum creatinine assays traceable to a standard reference material. To review the performance of GFR estimating equations to inform the selection of a single equation by laboratories and the interpretation of estimated GFR by clinicians. A systematic search of MEDLINE, without language restriction, between 1999 and 21 October 2011. Cross-sectional studies in adults that compared the performance of 2 or more creatinine-based GFR estimating equations with a reference GFR measurement. Eligible equations were derived or reexpressed and validated by using creatinine measurements traceable to the standard reference material. Reviewers extracted data on study population characteristics, measured GFR, creatinine assay, and equation performance. Eligible studies compared the MDRD (Modification of Diet in Renal Disease) Study and CKD-EPI (Chronic Kidney Disease Epidemiology Collaboration) equations or modifications thereof. In 12 studies in North America, Europe, and Australia, the CKD-EPI equation performed better at higher GFRs (approximately >60 mL/min per 1.73 m(2)) and the MDRD Study equation performed better at lower GFRs. In 5 of 8 studies in Asia and Africa, the equations were modified to improve their performance by adding a coefficient derived in the local population or removing a coefficient. Methods of GFR measurement and study populations were heterogeneous. Neither the CKD-EPI nor the MDRD Study equation is optimal for all populations and GFR ranges. Using a single equation for reporting requires a tradeoff to optimize performance at either higher or lower GFR ranges. A general practice and public health perspective favors the CKD-EPI equation. Kidney Disease: Improving Global Outcomes.

Hammett equation and generalized Pauling's electronegativity equation.

PubMed

Liu, Lei; Fu, Yao; Liu, Rui; Li, Rui-Qiong; Guo, Qing-Xiang

2004-01-01

Substituent interaction energy (SIE) was defined as the energy change of the isodesmic reaction X-spacer-Y + H-spacer-H --> X-spacer-H + H-spacer-Y. It was found that this SIE followed a simple equation, SIE(X,Y) = -ksigma(X)sigma(Y), where k was a constant dependent on the system and sigma was a certain scale of electronic substituent constant. It was demonstrated that the equation was applicable to disubstituted bicyclo[2.2.2]octanes, benzenes, ethylenes, butadienes, and hexatrienes. It was also demonstrated that Hammett's equation was a derivative form of the above equation. Furthermore, it was found that when spacer = nil the above equation was mathematically the same as Pauling's electronegativity equation. Thus it was shown that Hammett's equation was a derivative form of the generalized Pauling's electronegativity equation and that a generalized Pauling's electronegativity equation could be utilized for diverse X-spacer-Y systems. In addition, the total electronic substituent effects were successfully separated into field/inductive and resonance effects in the equation SIE(X,Y) = -k(1)F(X)F(Y) - k(2)R(X)R(Y) - k(3)(F(X)R(Y) + R(X)F(Y)). The existence of the cross term (i.e., F(X)R(Y) and R(X)F(Y)) suggested that the field/inductive effect was not orthogonal to the resonance effect because the field/inductive effect from one substituent interacted with the resonance effect from the other. Further studies on multi-substituted systems suggested that the electronic substituent effects should be pairwise and additive. Hence, the SIE in a multi-substituted system could be described using the equation SIE(X1, X2, ..., Xn) = Sigma(n-1)(i=1)Sigma(n)(j=i+1)k(ij)sigma(X)isigma(X)j.

The mechanical and chemical equations of motion of muscle contraction

NASA Astrophysics Data System (ADS)

Shiner, J. S.; Sieniutycz, Stanislaw

1997-11-01

Up to now no formulation of muscle contraction has provided both the chemical kinetic equations for the reactions responsible for the contraction and the mechanical equation of motion for the muscle. This has most likely been due to the lack of general formalisms for nonlinear systems with chemical-nonchemical coupling valid under the far from equilibrium conditions under which muscle operates physiologically. We have recently developed such formalisms and apply them here to the formulation of muscle contraction to obtain both the chemical and the mechanical equations. The standard formulation up to now has yielded only the dynamic equations for the chemical variables and has considered these to be functions of both time and an appropriate mechanical variable. The macroscopically observable quantities were then obtained by averaging over the mechanical variable. When attempting to derive the dynamics equations for both the chemistry and mechanics this choice of variables leads to conflicting results for the mechanical equation of motion when two different general formalisms are applied. The conflict can be resolved by choosing the variables such that both the chemical variables and the mechanical variables are considered to be functions of time alone. This adds one equation to the set of differential equations to be solved but is actually a simplification of the problem, since these equations are ordinary differential equations, not the partial differential equations of the now standard formulation, and since in this choice of variables the variables themselves are the macroscopic observables the procedure of averaging over the mechanical variable is eliminated. Furthermore, the parameters occurring in the equations at this level of description should be accessible to direct experimental determination.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

Selection of site specific vibration equation by using analytic hierarchy process in a quarry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalayci, Ulku, E-mail: ukalayci@istanbul.edu.tr; Ozer, Umit, E-mail: uozer@istanbul.edu.tr

This paper presents a new approach for the selection of the most accurate SSVA (Site Specific Vibration Attenuation) equation for blasting processes in a quarry located near settlements in Istanbul, Turkey. In this context, the SSVA equations obtained from the same study area in the literature were considered in terms of distance between the shot points and buildings and the amount of explosive charge. In this purpose, 11 different SSVA equations obtained from the study area in the past 12 years, forecasting capabilities according to designated new conditions, using 102 vibration records as test data obtained from the study areamore » was investigated. In this study, AHP (Analytic Hierarchy Process) was selected as an analysis method in order to determine the most accurate equation among 11 SSAV equations, and the parameters such as year, distance, charge, and r{sup 2} of the equations were used as criteria for AHP. Finally, the most appropriate equation was selected among the existing ones, and the process of selecting according to different target criteria was presented. Furthermore, it was noted that the forecasting results of the selected equation is more accurate than that formed using the test results. - Highlights: • The optimum Site Specific Vibration Attenuation equation for blasting in a quarry located near settlements was determined. • It is indicated that SSVA equations changing over the years don’t give always accurate estimates at changing conditions. • Selection of the blast induced SSVA equation was made using AHP. • Equation selection method was highlighted based on parameters such as charge, distance, and quarry geometry changes (year).« less

Introducing Chemical Formulae and Equations.

ERIC Educational Resources Information Center

Dawson, Chris; Rowell, Jack

1979-01-01

Discusses when the writing of chemical formula and equations can be introduced in the school science curriculum. Also presents ways in which formulae and equations learning can be aided and some examples for balancing and interpreting equations. (HM)

Measurement of testicular volume in smaller testes: how accurate is the conventional orchidometer?

PubMed

Lin, Chih-Chieh; Huang, William J S; Chen, Kuang-Kuo

2009-01-01

The aim of this study was to evaluate the accuracy of different methods, including the Seager orchidometer (SO) and ultrasonography (US), for assessing testicular volume of smaller testes (testes volume less than 18 mL). Moreover, the equations used for the calculations--the Hansen formula (length [L] x width [W](2) x 0.52, equation A), the prolate ellipsoid formula (L x W x height [H] x 0.52, equation B), and the Lambert equation (L x W x H x 0.71, equation C)--were also examined and compared with the gold standard testicular volume obtained by water displacement (Archimedes principle). In this study, 30 testes from 15 men, mean age 75.3 (+/-8.3) years, were included. They all had advanced prostate cancer and were admitted for orchiectomy. Before the procedure, all the testes were assessed using SO and US. The dimensions were then input into each equation to obtain the volume estimates. The testicular volume by water displacement was 8.1 +/- 3.5 mL. Correlation coefficients (R(2)) of the 2 different methods (SO, US) to the gold standard were 0.70 and 0.85, respectively. The calculated testicular volumes were 9.2 +/- 3.9 mL (measured by SO, equation A), 11.9 +/- 5.2 mL (measured by SO, equation C), 7.3 +/- 4.2 mL (measured by US, equation A), 6.5 +/- 3.3 mL (measured by US, equation B) and 8.9 +/- 4.5 mL (measured by US, equation C). Only the mean size measured by US and volume calculated with the Hansen equation (equation A) and the mean size measured by US and volume calculated with the Lambert equation (equation C) showed no significant differences when compared with the volumes estimated by water displacement (mean difference 0.81 mL, P = .053, and 0.81 mL, P = .056, respectively). Based on our measurements, we categorized testicular volume by different cutoff values (7.0 mL, 7.5 mL, 8.0 mL, and 8.5 mL) to calculate a new constant for use in the Hansen equation. The new constant was 0.59. We then reexamined the equations using the new 0.59 constant, and found that the equation Volume (V) = L x W(2) x 0.59 was the best for describing testicular volume among our subjects (difference between the new equation and the gold standard of water displacement = 0.19 mL, P = .726). We also found that US was more precise in measuring testicular dimensions. We propose a new formula, V = L x W(2) x 0.59, to assess the volumes of smaller testes.

The eight tetrahedron equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hietarinta, J.; Nijhoff, F.

1997-07-01

In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that represents integrable structures in three dimensions generalizing the Yang{endash}Baxter equation. Under additional restrictions this system reduces to the usual tetrahedron equation in the vertex form. Most known solutions fall under this class, but it is by no means necessary. Comparison is made with the work on braided monoidal 2-categories also leading to eight tetrahedron equations. {copyright} {ital 1997 American Institute of Physics.}

New nonlinear evolution equations from surface theory

NASA Astrophysics Data System (ADS)

Gürses, Metin; Nutku, Yavuz

1981-07-01

We point out that the connection between surfaces in three-dimensional flat space and the inverse scattering problem provides a systematic way for constructing new nonlinear evolution equations. In particular we study the imbedding for Guichard surfaces which gives rise to the Calapso-Guichard equations generalizing the sine-Gordon (SG) equation. Further, we investigate the geometry of surfaces and their imbedding which results in the Korteweg-deVries (KdV) equation. Then by constructing a family of applicable surfaces we obtain a generalization of the KdV equation to a compressible fluid.

Partner symmetries and non-invariant solutions of four-dimensional heavenly equations

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2004-07-01

We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetries and derive the relations between them. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate Legendre transformation. The solutions of these linear equations are generically non-invariant. As a consequence we obtain explicitly new classes of heavenly metrics without Killing vectors.

The method of Ritz applied to the equation of Hamilton. [for pendulum systems

NASA Technical Reports Server (NTRS)

Bailey, C. D.

1976-01-01

Without any reference to the theory of differential equations, the initial value problem of the nonlinear, nonconservative double pendulum system is solved by the application of the method of Ritz to the equation of Hamilton. Also shown is an example of the reduction of the traditional eigenvalue problem of linear, homogeneous, differential equations of motion to the solution of a set of nonhomogeneous algebraic equations. No theory of differential equations is used. Solution of the time-space path of the linear oscillator is demonstrated and compared to the exact solution.

Note on Solutions to a Class of Nonlinear Singular Integro-Differential Equations,

DTIC Science & Technology

1986-08-01

KdV) ut + 2uu x +Uxx x a 0, (1) the sine-Gordon equation Uxt a sin u, (2) and the Kadomtsev - Petviashvili (KP) equation (Ut + 2uu x + UXXx)x -3a 2u yy...SOUIN OA LSFNN ! /" / M.. \\boiz A.S ::-:- and ,M.O.. .- :1/1 / NOTE ON SOLUTIONS TO A CLASS OF NON \\ / LINEAR SINGULAR INTEGRO-DIFFERENTIA[ EQUATIONS by...important nonlinear evolution equations which can be linearized. Many of these equations fall into the category of linearization via soliton theory and

On the integration of a class of nonlinear systems of ordinary differential equations

NASA Astrophysics Data System (ADS)

Talyshev, Aleksandr A.

2017-11-01

For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.

On the exact solutions of high order wave equations of KdV type (I)

NASA Astrophysics Data System (ADS)

Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

2014-12-01

In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

Conservation laws and symmetries of a generalized Kawahara equation

NASA Astrophysics Data System (ADS)

Gandarias, Maria Luz; Rosa, Maria; Recio, Elena; Anco, Stephen

2017-06-01

The generalized Kawahara equation ut = a(t)uxxxxx + b(t)uxxx + c(t) f (u)ux appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which includes as a special case the usual Kawahara equation ut = αuux + βu2ux + γuxxx + μuxxxxx. A general connection between conservation laws and symmetries for the generalized Kawahara equation is derived through the Hamiltonian structure of this equation and its relationship to Noether's theorem using a potential formulation.

Symmetry analysis of the high-order equations for the description of the Fermi - Pasta - Ulam problem

NASA Astrophysics Data System (ADS)

Kudryashov, N. A.; Volkov, A. K.

2017-01-01

Recently some new nonlinear equations for the description of the Fermi - Pasta - Ulam problem have been derived. The main aim of this work is to use the symmetry test to investigate these equations. We consider equations for the description of the α and α + β Fermi - Pasta - Ulam model. We find the infinitesimal operators and Lie groups, admitted by the equations. Using the groups we find the self-similar variables as well as the reductions to the ordinary differential equations. Some exact solutions are also constructed.

Dissipative Relativistic Fluid Dynamics: A New Way to Derive the Equations of Motion from Kinetic Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Denicol, G. S.; Koide, T.; Rischke, D. H.

2010-10-15

We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.

Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

PubMed

Reck, Kasper; Thomsen, Erik V; Hansen, Ole

2011-01-31

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

Renal function assessment in atrial fibrillation: Usefulness of chronic kidney disease epidemiology collaboration vs re-expressed 4 variable modification of diet in renal disease.

PubMed

Abumuaileq, Rami Riziq-Yousef; Abu-Assi, Emad; López-López, Andrea; Raposeiras-Roubin, Sergio; Rodríguez-Mañero, Moisés; Martínez-Sande, Luis; García-Seara, Francisco Javier; Fernandez-López, Xesus Alberte; González-Juanatey, Jose Ramón

2015-10-26

To compare the performance of the re-expressed Modification of Diet in Renal Disease equation vs the new Chronic Kidney Disease Epidemiology Collaboration equation in patients with non-valvular atrial fibrillation. We studied 911 consecutive patients with non-valvular atrial fibrillation on vitamin-K antagonist. The performance of the re-expressed Modification of Diet in Renal Disease equation vs the new Chronic Kidney Disease Epidemiology Collaboration equation in patients with non-valvular atrial fibrillation with respect to either a composite endpoint of major bleeding, thromboembolic events and all-cause mortality or each individual component of the composite endpoint was assessed using continuous and categorical ≥ 60, 59-30, and < 30 mL/min per 1.73 m(2) estimated glomerular filtration rate. During 10 ± 3 mo, the composite endpoint occurred in 98 (10.8%) patients: 30 patients developed major bleeding, 18 had thromboembolic events, and 60 died. The new equation provided lower prevalence of renal dysfunction < 60 mL/min per 1.73 m(2) (32.9%), compared with the re-expressed equation (34.1%). Estimated glomerular filtration rate from both equations was independent predictor of composite endpoint (HR = 0.98 and 0.97 for the re-expressed and the new equation, respectively; P < 0.0001) and all-cause mortality (HR = 0.98 for both equations, P < 0.01). Strong association with thromboembolic events was observed only when estimated glomerular filtration rate was < 30 mL/min per 1.73 m(2): HR is 5.1 for the re-expressed equation, and HR = 5.0 for the new equation. No significant association with major bleeding was observed for both equations. The new equation reduced the prevalence of renal dysfunction. Both equations performed similarly in predicting major adverse outcomes.

Modified Maturity Offset Prediction Equations: Validation in Independent Longitudinal Samples of Boys and Girls.

PubMed

Kozieł, Sławomir M; Malina, Robert M

2018-01-01

Predicted maturity offset and age at peak height velocity are increasingly used with youth athletes, although validation studies of the equations indicated major limitations. The equations have since been modified and simplified. The objective of this study was to validate the new maturity offset prediction equations in independent longitudinal samples of boys and girls. Two new equations for boys with chronological age and sitting height and chronological age and stature as predictors, and one equation for girls with chronological age and stature as predictors were evaluated in serial data from the Wrocław Growth Study, 193 boys (aged 8-18 years) and 198 girls (aged 8-16 years). Observed age at peak height velocity for each youth was estimated with the Preece-Baines Model 1. The original prediction equations were included for comparison. Predicted age at peak height velocity was the difference between chronological age at prediction and maturity offset. Predicted ages at peak height velocity with the new equations approximated observed ages at peak height velocity in average maturing boys near the time of peak height velocity; a corresponding window for average maturing girls was not apparent. Compared with observed age at peak height velocity, predicted ages at peak height velocity with the new and original equations were consistently later in early maturing youth and earlier in late maturing youth of both sexes. Predicted ages at peak height velocity with the new equations had reduced variation compared with the original equations and especially observed ages at peak height velocity. Intra-individual variation in predicted ages at peak height velocity with all equations was considerable. The new equations are useful for average maturing boys close to the time of peak height velocity; there does not appear to be a clear window for average maturing girls. The new and original equations have major limitations with early and late maturing boys and girls.

Drift-free kinetic equations for turbulent dispersion

NASA Astrophysics Data System (ADS)

Bragg, A.; Swailes, D. C.; Skartlien, R.

2012-11-01

The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.

Drift-free kinetic equations for turbulent dispersion.

PubMed

Bragg, A; Swailes, D C; Skartlien, R

2012-11-01

The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.

Peak flow regression equations For small, ungaged streams in Maine: Comparing map-based to field-based variables

USGS Publications Warehouse

Lombard, Pamela J.; Hodgkins, Glenn A.

2015-01-01

Regression equations to estimate peak streamflows with 1- to 500-year recurrence intervals (annual exceedance probabilities from 99 to 0.2 percent, respectively) were developed for small, ungaged streams in Maine. Equations presented here are the best available equations for estimating peak flows at ungaged basins in Maine with drainage areas from 0.3 to 12 square miles (mi2). Previously developed equations continue to be the best available equations for estimating peak flows for basin areas greater than 12 mi2. New equations presented here are based on streamflow records at 40 U.S. Geological Survey streamgages with a minimum of 10 years of recorded peak flows between 1963 and 2012. Ordinary least-squares regression techniques were used to determine the best explanatory variables for the regression equations. Traditional map-based explanatory variables were compared to variables requiring field measurements. Two field-based variables—culvert rust lines and bankfull channel widths—either were not commonly found or did not explain enough of the variability in the peak flows to warrant inclusion in the equations. The best explanatory variables were drainage area and percent basin wetlands; values for these variables were determined with a geographic information system. Generalized least-squares regression was used with these two variables to determine the equation coefficients and estimates of accuracy for the final equations.

Generalization of Einstein's gravitational field equations

NASA Astrophysics Data System (ADS)

Moulin, Frédéric

2017-12-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

A vector-dyadic development of the equations of motion for N-coupled flexible bodies and point masses. [spacecraft trajectories

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1975-01-01

The equations of motion for a system of coupled flexible bodies, rigid bodies, point masses, and symmetric wheels were derived. The equations were cast into a partitioned matrix form in which certain partitions became nontrivial when the effects of flexibility were treated. The equations are shown to contract to the coupled rigid body equations or expand to the coupled flexible body equations all within the same basic framework. Furthermore, the coefficient matrix always has the computationally desirable property of symmetry. Making use of the derived equations, a comparison was made between the equations which described a flexible body model and those which described a rigid body model of the same elastic appendage attached to an arbitrary coupled body system. From the comparison, equivalence relations were developed which defined how the two modeling approaches described identical dynamic effects.

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

High-order rogue waves of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Liu, Wei

2017-10-01

High-order rogue wave solutions of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin-Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

THE COSMIC RAY EQUATOR AND THE GEOMAGNETISM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sakurai, K.

1960-01-01

It was formerly thought that the disagreement of the position of geomagnetic dipole equator with that of the cosmic ray equator was caused by 45 deg westward shifting of the latter. Referring to the theory of geomagnetic effect on cosmic rays, it was determined whether such westward shifting could be existent or not. It was found that the deviation of the cosmic ray equator from the geomagnetic dipole equator is negligible even if the magnetic cavity is present around the earth's outer atmosphere. Taking into account such results, the origin of the cosmic ray equator was investigated. It was foundmore » that this equater could be produced by the higher harmonic components combined with the dipole component of geomagnetism. The relation of the origin of the cosmic ray equater to the eccentric dipoles, near the outer pant of the earth's core, contributing to the secular variation of geomagnetism was considered. (auth)« less

Applications of the ETEM for obtaining optical soliton solutions for the Lakshmanan-Porsezian-Daniel model

NASA Astrophysics Data System (ADS)

Manafian, Jalil; Foroutan, Mohammadreza; Guzali, Aref

2017-11-01

This paper examines the effectiveness of an integration scheme which is called the extended trial equation method (ETEM) for solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the Lakshmanan-Porsezian-Daniel (LPD) equation with Kerr and power laws of nonlinearity which describes higher-order dispersion, full nonlinearity and spatiotemporal dispersion is considered, and as an achievement, a series of exact travelling-wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of LPD equation. The movement of obtained solutions is shown graphically, which helps to understand the physical phenomena of this optical soliton equation. Many other such types of nonlinear equations arising in basic fabric of communications network technology and nonlinear optics can also be solved by this method.

Heat Stress Equation Development and Usage for Dryden Flight Research Center (DFRC)

NASA Technical Reports Server (NTRS)

Houtas, Franzeska; Teets, Edward H., Jr.

2012-01-01

Heat Stress Indices are equations that integrate some or all variables (e.g. temperature, relative humidity, wind speed), directly or indirectly, to produce a number for thermal stress on humans for a particular environment. There are a large number of equations that have been developed which range from simple equations that may ignore basic factors (e.g. wind effects on thermal loading, fixed contribution from solar heating) to complex equations that attempt to incorporate all variables. Each equation is evaluated for a particular use, as well as considering the ease of use and reliability of the results. The meteorology group at the Dryden Flight Research Center has utilized and enhanced the American College of Sports Medicine equation to represent the specific environment of the Mojave Desert. The Dryden WBGT Heat Stress equation has been vetted and implemented as an automated notification to the entire facility for the safety of all personnel and visitors.

Inflow performance relationship for perforated wells producing from solution gas drive reservoir

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sukarno, P.; Tobing, E.L.

1995-10-01

The IPR curve equations, which are available today, are developed for open hole wells. In the application of Nodal System Analysis in perforated wells, an accurate calculation of pressure loss in the perforation is very important. Nowadays, the equation which is widely used is Blount, Jones and Glaze equation, to estimate pressure loss across perforation. This equation is derived for single phase flow, either oil or gas, therefore it is not suitable for two-phase production wells. In this paper, an IPR curve equation for perforated wells, producing from solution gas drive reservoir, is introduced. The equation has been developed usingmore » two phase single well simulator combine to two phase flow in perforation equation, derived by Perez and Kelkar. A wide range of reservoir rock and fluid properties and perforation geometry are used to develop the equation statistically.« less

Implementation of Kane's Method for a Spacecraft Composed of Multiple Rigid Bodies

NASA Technical Reports Server (NTRS)

Stoneking, Eric T.

2013-01-01

Equations of motion are derived for a general spacecraft composed of rigid bodies connected via rotary (spherical or gimballed) joints in a tree topology. Several supporting concepts are developed in depth. Basis dyads aid in the transition from basis-free vector equations to component-wise equations. Joint partials allow abstraction of 1-DOF, 2-DOF, 3-DOF gimballed and spherical rotational joints to a common notation. The basic building block consisting of an "inner" body and an "outer" body connected by a joint enables efficient organization of arbitrary tree structures. Kane's equation is recast in a form which facilitates systematic assembly of large systems of equations, and exposes a relationship of Kane's equation to Newton and Euler's equations which is obscured by the usual presentation. The resulting system of dynamic equations is of minimum dimension, and is suitable for numerical solution by computer. Implementation is ·discussed, and illustrative simulation results are presented.

MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model - User Guide to Modularization Concepts and the Ground-Water Flow Process

USGS Publications Warehouse

Harbaugh, Arlen W.; Banta, Edward R.; Hill, Mary C.; McDonald, Michael G.

2000-01-01

MODFLOW is a computer program that numerically solves the three-dimensional ground-water flow equation for a porous medium by using a finite-difference method. Although MODFLOW was designed to be easily enhanced, the design was oriented toward additions to the ground-water flow equation. Frequently there is a need to solve additional equations; for example, transport equations and equations for estimating parameter values that produce the closest match between model-calculated heads and flows and measured values. This report documents a new version of MODFLOW, called MODFLOW-2000, which is designed to accommodate the solution of equations in addition to the ground-water flow equation. This report is a user's manual. It contains an overview of the old and added design concepts, documents one new package, and contains input instructions for using the model to solve the ground-water flow equation.

The three dimensional motion and stability of a rotating space station: Cable-counterweight configuration

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Evans, K. S.

1974-01-01

The three dimensional equations of motion for a cable connected space station--counterweight system are developed using a Lagrangian formulation. The system model employed allows for cable and end body damping and restoring effects. The equations are then linearized about the equilibrium motion and nondimensionalized. To first degree, the out-of-plane equations uncouple from the inplane equations. Therefore, the characteristic polynomials for the in-plane and out-of-plane equations are developed and treated separately. From the general in-plane characteristic equation, necessary conditions for stability are obtained. The Routh-Hurwitz necessary and sufficient conditions for stability are derived for the general out-of-plane characteristic equation. Special cases of the in-plane and out-of-plane equations (such as identical end masses, and when the cable is attached to the centers of mass of the two end bodies) are then examined for stability criteria.

Solving the interval type-2 fuzzy polynomial equation using the ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim

2014-07-01

Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

Theory and modeling of atmospheric turbulence, part 2

NASA Technical Reports Server (NTRS)

Chen, C. M.

1984-01-01

Two dimensional geostrophic turbulence driven by a random force is investigated. Based on the Liouville equation, which simulates the primitive hydrodynamical equations, a group-kinetic theory of turbulence is developed and the kinetic equation of the scaled singlet distribution is derived. The kinetic equation is transformed into an equation of spectral balance in the equilibrium and non-equilibrium states. Comparison is made between the propagators and the Green's functions in the case of the non-asymptotic quasi-linear equation to prove the equivalence of both kinds of approximations used to describe perturbed trajectories of plasma turbulence. The microdynamical state of fluid turbulence is described by a hydrodynamical system and transformed into a master equation analogous to the Vlasov equation for plasma turbulence. The spectral balance for the velocity fluctuations of individual components shows that the scaled pressure strain correlation and the cascade transfer are two transport functions that play the most important roles.

New Similarity Reductions and Compacton Solutions for Boussinesq-Like Equations with Fully Nonlinear Dispersion

NASA Astrophysics Data System (ADS)

Yan, Zhen-Ya

2001-10-01

In this paper, similarity reductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m,n) equations) utt=(u^n)xx+(u^m)xxxx, which is a generalized model of Boussinesq equation utt=(u^2)xx+uxxxx and modified Bousinesq equation utt=(u^3)xx+uxxxx, are considered by using the direct reduction method. As a result, several new types of similarity reductions are found. Based on the reduction equations and some simple transformations, we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of B(1,n) equations and B(m,m) equations, respectively. The project supported by National Key Basic Research Development Project Program of China under Grant No. G1998030600 and Doctoral Foundation of China under Grant No. 98014119

Extension of Gibbs-Duhem equation including influences of external fields

NASA Astrophysics Data System (ADS)

Guangze, Han; Jianjia, Meng

2018-03-01

Gibbs-Duhem equation is one of the fundamental equations in thermodynamics, which describes the relation among changes in temperature, pressure and chemical potential. Thermodynamic system can be affected by external field, and this effect should be revealed by thermodynamic equations. Based on energy postulate and the first law of thermodynamics, the differential equation of internal energy is extended to include the properties of external fields. Then, with homogeneous function theorem and a redefinition of Gibbs energy, a generalized Gibbs-Duhem equation with influences of external fields is derived. As a demonstration of the application of this generalized equation, the influences of temperature and external electric field on surface tension, surface adsorption controlled by external electric field, and the derivation of a generalized chemical potential expression are discussed, which show that the extended Gibbs-Duhem equation developed in this paper is capable to capture the influences of external fields on a thermodynamic system.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Evolution of basic equations for nearshore wave field

PubMed Central

ISOBE, Masahiko

2013-01-01

In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680

Multi criteria evaluation for universal soil loss equation based on geographic information system

NASA Astrophysics Data System (ADS)

Purwaamijaya, I. M.

2018-05-01

The purpose of this research were to produce(l) a conceptual, functional model designed and implementation for universal soil loss equation (usle), (2) standard operational procedure for multi criteria evaluation of universal soil loss equation (usle) using geographic information system, (3) overlay land cover, slope, soil and rain fall layers to gain universal soil loss equation (usle) using multi criteria evaluation, (4) thematic map of universal soil loss equation (usle) in watershed, (5) attribute table of universal soil loss equation (usle) in watershed. Descriptive and formal correlation methods are used for this research. Cikapundung Watershed, Bandung, West Java, Indonesia was study location. This research was conducted on January 2016 to May 2016. A spatial analysis is used to superimposed land cover, slope, soil and rain layers become universal soil loss equation (usle). Multi criteria evaluation for universal soil loss equation (usle) using geographic information system could be used for conservation program.

Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

NASA Astrophysics Data System (ADS)

Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

2018-06-01

Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

Recursion Operators and Bi-Hamiltonian Structures in Multidimensions II,

DTIC Science & Technology

1986-07-01

a Symmifetry (1.2). For example the Kadomtsev - Petviashvili (KP) equation and the Davey-Stewartson (DS) equation admit two such hierarchies of...Degasperis, Nuovo Cimento, 398, 1 (1977). [16] P. Caudrey, Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation ...these equations possess infinitely many time dependent symmetries and constants of motion. The master symmetries T for these equations are simply derived

Nonlinear Waves.

DTIC Science & Technology

1986-05-27

purposes will be the Korteweg-deVries (KdV) equation u, 6uu, u. , =0 (1) in one spatial dimension, and the Kadomtsev - Petviashvili (KP) equation (u, - 6uu...one temporal dimen- sion: the Modified Kadomtsev - Petviashvili II (MKPII), and Davey-Stewartson I (OSII) equation . The hyperoolic analogs of (1), (2...by introducing ’Ś an intermediate version of the equations associated with (1), an infinite family of conserva- Kadomtsev - Petviashvili equation

A new method of imposing boundary conditions for hyperbolic equations

NASA Technical Reports Server (NTRS)

Funaro, D.; ative.

1987-01-01

A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.

Quasi-Newton methods for parameter estimation in functional differential equations

NASA Technical Reports Server (NTRS)

Brewer, Dennis W.

1988-01-01

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

Loop equations and bootstrap methods in the lattice

DOE PAGES

Anderson, Peter D.; Kruczenski, Martin

2017-06-17

Pure gauge theories can be formulated in terms of Wilson Loops by means of the loop equation. In the large-N limit this equation closes in the expectation value of single loops. In particular, using the lattice as a regulator, it becomes a well defined equation for a discrete set of loops. In this paper we study different numerical approaches to solving this equation.

Variations in the Solution of Linear First-Order Differential Equations. Classroom Notes

ERIC Educational Resources Information Center

Seaman, Brian; Osler, Thomas J.

2004-01-01

A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…

An Evaluation of the Kernel Equating Method: A Special Study with Pseudotests Constructed from Real Test Data. Research Report. ETS RR-06-02

ERIC Educational Resources Information Center

von Davier, Alina A.; Holland, Paul W.; Livingston, Samuel A.; Casabianca, Jodi; Grant, Mary C.; Martin, Kathleen

2006-01-01

This study examines how closely the kernel equating (KE) method (von Davier, Holland, & Thayer, 2004a) approximates the results of other observed-score equating methods--equipercentile and linear equatings. The study used pseudotests constructed of item responses from a real test to simulate three equating designs: an equivalent groups (EG)…

Using the Kernel Method of Test Equating for Estimating the Standard Errors of Population Invariance Measures. Research Report. ETS RR-06-20

ERIC Educational Resources Information Center

Moses, Tim

2006-01-01

Population invariance is an important requirement of test equating. An equating function is said to be population invariant when the choice of (sub)population used to compute the equating function does not matter. In recent studies, the extent to which equating functions are population invariant is typically addressed in terms of practical…

The Equation, the Whole Equation, and Nothing but the Equation! One Approach to the Teaching of Linear Equations.

ERIC Educational Resources Information Center

Pirie, Susan E. B.; Martin, Lyndon

1997-01-01

Presents the results of a case study which looked at the mathematics classroom of one teacher trying to teach mathematics with meaning to pupils or lower ability at the secondary level. Contrasts methods of teaching linear equations to a variety of ability levels and uses the Pirie-Kieren model to account for the successful growth in understanding…

Quaternion Regularization of the Equations of the Perturbed Spatial Restricted Three-Body Problem: I

NASA Astrophysics Data System (ADS)

Chelnokov, Yu. N.

2017-11-01

We develop a quaternion method for regularizing the differential equations of the perturbed spatial restricted three-body problem by using the Kustaanheimo-Stiefel variables, which is methodologically closely related to the quaternion method for regularizing the differential equations of perturbed spatial two-body problem, which was proposed by the author of the present paper. A survey of papers related to the regularization of the differential equations of the two- and threebody problems is given. The original Newtonian equations of perturbed spatial restricted three-body problem are considered, and the problem of their regularization is posed; the energy relations and the differential equations describing the variations in the energies of the system in the perturbed spatial restricted three-body problem are given, as well as the first integrals of the differential equations of the unperturbed spatial restricted circular three-body problem (Jacobi integrals); the equations of perturbed spatial restricted three-body problem written in terms of rotating coordinate systems whose angular motion is described by the rotation quaternions (Euler (Rodrigues-Hamilton) parameters) are considered; and the differential equations for angular momenta in the restricted three-body problem are given. Local regular quaternion differential equations of perturbed spatial restricted three-body problem in the Kustaanheimo-Stiefel variables, i.e., equations regular in a neighborhood of the first and second body of finite mass, are obtained. The equations are systems of nonlinear nonstationary eleventhorder differential equations. These equations employ, as additional dependent variables, the energy characteristics of motion of the body under study (a body of a negligibly small mass) and the time whose derivative with respect to a new independent variable is equal to the distance from the body of negligibly small mass to the first or second body of finite mass. The equations obtained in the paper permit developing regular methods for determining solutions, in analytical or numerical form, of problems difficult for classicalmethods, such as the motion of a body of negligibly small mass in a neighborhood of the other two bodies of finite masses.

Utility of Equations to Estimate Peak Oxygen Uptake and Work Rate From a 6-Minute Walk Test in Patients With COPD in a Clinical Setting.

PubMed

Kirkham, Amy A; Pauhl, Katherine E; Elliott, Robyn M; Scott, Jen A; Doria, Silvana C; Davidson, Hanan K; Neil-Sztramko, Sarah E; Campbell, Kristin L; Camp, Pat G

2015-01-01

To determine the utility of equations that use the 6-minute walk test (6MWT) results to estimate peak oxygen uptake ((Equation is included in full-text article.)o2) and peak work rate with chronic obstructive pulmonary disease (COPD) patients in a clinical setting. This study included a systematic review to identify published equations estimating peak (Equation is included in full-text article.)o2 and peak work rate in watts in COPD patients and a retrospective chart review of data from a hospital-based pulmonary rehabilitation program. The following variables were abstracted from the records of 42 consecutively enrolled COPD patients: measured peak (Equation is included in full-text article.)o2 and peak work rate achieved during a cycle ergometer cardiopulmonary exercise test, 6MWT distance, age, sex, weight, height, forced expiratory volume in 1 second, forced vital capacity, and lung diffusion capacity. Estimated peak (Equation is included in full-text article.)o2 and peak work rate were estimated from 6MWT distance using published equations. The error associated with using estimated peak (Equation is included in full-text article.)o2 or peak work to prescribe aerobic exercise intensities of 60% and 80% was calculated. Eleven equations from 6 studies were identified. Agreement between estimated and measured values was poor to moderate (intraclass correlation coefficients = 0.11-0.63). The error associated with using estimated peak (Equation is included in full-text article.)o2 or peak work rate to prescribe exercise intensities of 60% and 80% of measured values ranged from mean differences of 12 to 35 and 16 to 47 percentage points, respectively. There is poor to moderate agreement between measured peak (Equation is included in full-text article.)o2 and peak work rate and estimations from equations that use 6MWT distance, and the use of the estimated values for prescription of aerobic exercise intensity would result in large error. Equations estimating peak (Equation is included in full-text article.)o2 and peak work rate are of low utility for prescribing exercise intensity in pulmonary rehabilitation programs.

Performance of Chronic Kidney Disease Epidemiology Collaboration Creatinine-Cystatin C Equation for Estimating Kidney Function in Cirrhosis

PubMed Central

Mindikoglu, Ayse L.; Dowling, Thomas C.; Weir, Matthew R.; Seliger, Stephen L.; Christenson, Robert H.; Magder, Laurence S.

2013-01-01

Conventional creatinine-based glomerular filtration rate (GFR) equations are insufficiently accurate for estimating GFR in cirrhosis. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) recently proposed an equation to estimate GFR in subjects without cirrhosis using both serum creatinine and cystatin C levels. Performance of the new CKD-EPI creatinine-cystatin C equation (2012) was superior to previous creatinine- or cystatin C-based GFR equations. To evaluate the performance of the CKD-EPI creatinine-cystatin C equation in subjects with cirrhosis, we compared it to GFR measured by non-radiolabeled iothalamate plasma clearance (mGFR) in 72 subjects with cirrhosis. We compared the “bias”, “precision” and “accuracy” of the new CKD-EPI creatinine-cystatin C equation to that of 24-hour urinary creatinine clearance (CrCl), Cockcroft-Gault (CG) and previously reported creatinine- and/or cystatin C-based GFR-estimating equations. Accuracy of CKD-EPI creatinine-cystatin C equation as quantified by root mean squared error of difference scores [differences between mGFR and estimated GFR (eGFR) or between mGFR and CrCl, or between mGFR and CG equation for each subject] (RMSE=23.56) was significantly better than that of CrCl (37.69, P=0.001), CG (RMSE=36.12, P=0.002) and GFR-estimating equations based on cystatin C only. Its accuracy as quantified by percentage of eGFRs that differed by greater than 30% with respect to mGFR was significantly better compared to CrCl (P=0.024), CG (P=0.0001), 4-variable MDRD (P=0.027) and CKD-EPI creatinine 2009 (P=0.012) equations. However, for 23.61% of the subjects, GFR estimated by CKD-EPI creatinine-cystatin C equation differed from the mGFR by more than 30%. CONCLUSIONS The diagnostic performance of CKD-EPI creatinine-cystatin C equation (2012) in patients with cirrhosis was superior to conventional equations in clinical practice for estimating GFR. However, its diagnostic performance was substantially worse than reported in subjects without cirrhosis. PMID:23744636

Are cystatin C-based equations superior to creatinine-based equations for estimating GFR in Chinese elderly population?

PubMed

Pei, Xiaohua; Liu, Qiao; He, Juan; Bao, Lihua; Yan, Chengjing; Wu, Jianqing; Zhao, Weihong

2012-12-01

Cystatin C has been proposed as a surrogate marker of kidney function. The elderly population accounts for the largest proportion of chronic kidney disease (CKD) patients. The aim of this study was to assess the diagnostic value of serum cystatin C and compare the applicability of cystatin C-based equations with serum creatinine (Scr)-based equations for estimating glomerular filtration rate (GFR). The estimated GFR (eGFR) values from six cystatin C-based equations (Tan, MacIsaac, Ma, Stevens1-3) and three Scr-based equations (CG, MDRD, CKD-EPI) were compared with the reference GFR (rGFR) values from 99mTc-DTPA renal dynamic imaging method. A total of 110 elderly Chinese (60-92 year, 71.05±7.62 year) were enrolled. Cystatin C had better diagnostic value than Scr (relationship coefficient with rGFR: cystatin C -0.847 vs. Scr -0.729, P<0.01; sensitivity: cystatin C 0.90 vs. Scr 0.55, P<0.01; AUCROC: cystatin C 0.857 vs. Scr 0.757, P<0.01). All the equations predicted GFR more accurately for rGFR≥60 ml/min/1.73 m2 than for rGFR<60 ml/min/1.73 m2. Most equations had acceptable accuracy. The cystatin C-based equations deviated from rGFR by -12.78 ml/min/1.73 m2 to -2.12 ml/min/1.73 m2, with accuracy varying from 64.6 to 82.7%. The Scr-based equations deviated from rGFR by -5.37 ml/min/1.73 m2 to -0.68 ml/min/1.73 m2, with accuracy varying from 77.3 to 79.1%. The CKD-EPI, MacIsaac and Ma equations predicted no bias with rGFR (P>0.05), with higher accuracy and lower deviation in the total group. The MacIsaac, CKD-EPI and Stevens3 equations could be optimal for those with normal and mildly impaired kidney function, whereas the Ma equation for those with CKD. Cystatin C is a promising kidney function marker. However, not all cystatin C-based equations could be superior to the Scr-equations.

Soliton structure versus singularity analysis: Third-order completely intergrable nonlinear differential equations in 1 + 1-dimensions

NASA Astrophysics Data System (ADS)

Fuchssteiner, Benno; Carillo, Sandra

1989-01-01

Bäcklund transformations between all known completely integrable third-order differential equations in (1 + 1)-dimensions are established and the corresponding transformations formulas for their hereditary operators and Hamiltonian formulations are exhibited. Some of these Bäcklund transformations are not injective; therefore additional non-commutative symmetry groups are found for some equations. These non-commutative symmetry groups are classified as having a semisimple part isomorphic to the affine algebra A(1)1. New completely integrable third-order integro-differential equations, some depending explicitly on x, are given. These new equations give rise to nonin equation. Connections between the singularity equations (from the Painlevé analysis) and the nonlinear equations for interacting solitons are established. A common approach to singularity analysis and soliton structure is introduced. The Painlevé analysis is modified in such a sense that it carries over directly and without difficulty to the time evolution of singularity manifolds of equations like the sine-Gordon and nonlinear Schrödinger equation. A method to recover the Painlevé series from its constant level term is exhibit. The soliton-singularity transform is recognized to be connected to the Möbius group. This gives rise to a Darboux-like result for the spectral properties of the recursion operator. These connections are used in order to explain why poles of soliton equations move like trajectories of interacting solitons. Furthermore it is explicitly computed how solitons of singularity equations behave under the effect of this soliton-singularity transform. This then leads to the result that only for scaling degrees α = -1 and α = -2 the usual Painlevé analysis can be carried out. A new invariance principle, connected to kernels of differential operators is discovered. This new invariance, for example, connects the explicit solutions of the Liouville equation with the Miura transform. Simple methods are exhibited which allow to compute out of N-soliton solutions of the KdV (Bargman potentials) explicit solutions of equations like the Harry Dym equation. Certain solutions are plotted.

Using Mathematical Algorithms to Modify Glomerular Filtration Rate Estimation Equations

PubMed Central

Zhu, Bei; Wu, Jianqing; Zhu, Jin; Zhao, Weihong

2013-01-01

Background The equations provide a rapid and low-cost method of evaluating glomerular filtration rate (GFR). Previous studies indicated that the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease-Epidemiology (CKD-EPI) and MacIsaac equations need further modification for application in Chinese population. Thus, this study was designed to modify the three equations, and compare the diagnostic accuracy of the equations modified before and after. Methodology With the use of 99 mTc-DTPA renal dynamic imaging as the reference GFR (rGFR), the MDRD, CKD-EPI and MacIsaac equations were modified by two mathematical algorithms: the hill-climbing and the simulated-annealing algorithms. Results A total of 703 Chinese subjects were recruited, with the average rGFR 77.14±25.93 ml/min. The entire modification process was based on a random sample of 80% of subjects in each GFR level as a training sample set, the rest of 20% of subjects as a validation sample set. After modification, the three equations performed significant improvement in slop, intercept, correlated coefficient, root mean square error (RMSE), total deviation index (TDI), and the proportion of estimated GFR (eGFR) within 10% and 30% deviation of rGFR (P10 and P30). Of the three modified equations, the modified CKD-EPI equation showed the best accuracy. Conclusions Mathematical algorithms could be a considerable tool to modify the GFR equations. Accuracy of all the three modified equations was significantly improved in which the modified CKD-EPI equation could be the optimal one. PMID:23472113

Governing equations for electro-conjugate fluid flow

NASA Astrophysics Data System (ADS)

Hosoda, K.; Takemura, K.; Fukagata, K.; Yokota, S.; Edamura, K.

2013-12-01

An electro-conjugation fluid (ECF) is a kind of dielectric liquid, which generates a powerful flow when high DC voltage is applied with tiny electrodes. This study deals with the derivation of the governing equations for electro-conjugate fluid flow based on the Korteweg-Helmholtz (KH) equation which represents the force in dielectric liquid subjected to high DC voltage. The governing equations consist of the Gauss's law, charge conservation with charge recombination, the KH equation, the continuity equation and the incompressible Navier-Stokes equations. The KH equation consists of coulomb force, dielectric constant gradient force and electrostriction force. The governing equation gives the distribution of electric field, charge density and flow velocity. In this study, direct numerical simulation (DNS) is used in order to get these distribution at arbitrary time. Successive over-relaxation (SOR) method is used in analyzing Gauss's law and constrained interpolation pseudo-particle (CIP) method is used in analyzing charge conservation with charge recombination. The third order Runge-Kutta method and conservative second-order-accurate finite difference method is used in analyzing the Navier-Stokes equations with the KH equation. This study also deals with the measurement of ECF ow generated with a symmetrical pole electrodes pair which are made of 0.3 mm diameter piano wire. Working fluid is FF-1EHA2 which is an ECF family. The flow is observed from the both electrodes, i.e., the flow collides in between the electrodes. The governing equation successfully calculates mean flow velocity in between the collector pole electrode and the colliding region by the numerical simulation.

Some Remarks on Similarity and Soliton Solutions of Nonlinear Klein-Gordon Equation

NASA Astrophysics Data System (ADS)

Tajiri, Masayoshi

1984-11-01

The three-dimensional nonlinear Klein-Gordon [, Higgs field and Yang-Milles] (3D-KG [, H and YM]) equation is first reduced to the 2D nonlinear Schrödinger (2D-NLS) and 2D-KG [, H and YM] equations, and secondly to the 1D-NLS and 1D-KG [, H and YM] equations by similarity transformations. It is shown that similar type soliton solutions of the 3D-KG, H and YM equations, which have singularity on a plane in (x, y, z, t) space, are obtained by substituting the soliton solutions of the 1D-NLS or 1D-KG (or H) equation into the similarity transformations. The soliton solutions of the YM equation are also investigated.

A more fundamental approach to the derivation of nonlinear acoustic wave equations with fractional loss operators (L).

PubMed

Prieur, Fabrice; Vilenskiy, Gregory; Holm, Sverre

2012-10-01

A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["Nonlinear acoustic wave equations with fractional loss operators," J. Acoust. Soc. Am. 130(3), 1125-1132 (2011)]. The loss operator of the obtained nonlinear wave equations differs from the previous derivations as well as the dispersion equation, but when approximating for low frequencies the expressions for the frequency dependent attenuation and velocity dispersion remain unchanged.

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Sasa-Satsuma higher-order nonlinear Schrödinger equation and its bilinearization and multisoliton solutions.

PubMed

Gilson, C; Hietarinta, J; Nimmo, J; Ohta, Y

2003-07-01

Higher-order and multicomponent generalizations of the nonlinear Schrödinger equation are important in various applications, e.g., in optics. One of these equations, the integrable Sasa-Satsuma equation, has particularly interesting soliton solutions. Unfortunately, the construction of multisoliton solutions to this equation presents difficulties due to its complicated bilinearization. We discuss briefly some previous attempts and then give the correct bilinearization based on the interpretation of the Sasa-Satsuma equation as a reduction of the three-component Kadomtsev-Petviashvili hierarchy. In the process, we also get bilinearizations and multisoliton formulas for a two-component generalization of the Sasa-Satsuma equation (the Yajima-Oikawa-Tasgal-Potasek model), and for a (2+1)-dimensional generalization.

Duality Quantum Simulation of the Yang-Baxter Equation

NASA Astrophysics Data System (ADS)

Zheng, Chao; Wei, Shijie

2018-04-01

The Yang-Baxter equation has become a significant theoretical tool in a variety of areas of physics. It is desirable to investigate the quantum simulation of the Yang-Baxter equation itself, exploring the connections between quantum integrability and quantum information processing, in which the unity of both the Yang-Baxter equation system and its quantum entanglement should be kept as a whole. In this work, we propose a duality quantum simulation algorithm of the Yang-Baxter equation, which contains the Yang-Baxter system and an ancillary qubit. Contrasting to conventional methods in which the two hand sides of the equation are simulated separately, they are simulated simultaneously in this proposal. Consequently, it opens up a way to further investigate entanglements in a Yang-Baxter equation.

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

Stability analysis solutions and optical solitons in extended nonlinear Schrödinger equation with higher-order odd and even terms

NASA Astrophysics Data System (ADS)

Peng, Wei-Qi; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

2018-01-01

In this paper, the extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms is investigated, whose particular cases are the Hirota equation, the Sasa-Satsuma equation and Lakshmanan-Porsezian-Daniel equation by selecting some specific values on the parameters of higher-order terms. We first study the stability analysis of the equation. Then, using the ansatz method, we derive its bright, dark solitons and some constraint conditions which can guarantee the existence of solitons. Moreover, the Ricatti equation extension method is employed to derive some exact singular solutions. The outstanding characteristics of these solitons are analyzed via several diverting graphics.

Duality Quantum Simulation of the Yang-Baxter Equation

NASA Astrophysics Data System (ADS)

Zheng, Chao; Wei, Shijie

2018-07-01

The Yang-Baxter equation has become a significant theoretical tool in a variety of areas of physics. It is desirable to investigate the quantum simulation of the Yang-Baxter equation itself, exploring the connections between quantum integrability and quantum information processing, in which the unity of both the Yang-Baxter equation system and its quantum entanglement should be kept as a whole. In this work, we propose a duality quantum simulation algorithm of the Yang-Baxter equation, which contains the Yang-Baxter system and an ancillary qubit. Contrasting to conventional methods in which the two hand sides of the equation are simulated separately, they are simulated simultaneously in this proposal. Consequently, it opens up a way to further investigate entanglements in a Yang-Baxter equation.

Field equations from Killing spinors

NASA Astrophysics Data System (ADS)

Açık, Özgür

2018-02-01

From the Killing spinor equation and the equations satisfied by their bilinears, we deduce some well-known bosonic and fermionic field equations of mathematical physics. Aside from the trivially satisfied Dirac equation, these relativistic wave equations in curved spacetimes, respectively, are Klein-Gordon, Maxwell, Proca, Duffin-Kemmer-Petiau, Kähler, twistor, and Rarita-Schwinger equations. This result shows that, besides being special kinds of Dirac fermions, Killing fermions can be regarded as physically fundamental. For the Maxwell case, the problem of motion is analysed in a reverse manner with respect to the studies of Einstein-Groemer-Infeld-Hoffmann and Jean Marie Souriau. In the analysis of the gravitino field, a generalised 3-ψ rule is found which is termed the vanishing trace constraint.

A Method for the Construction of Hereditary Constitutive Equations of Laminates Bases on a Hereditary Constitutive Equation for a Layer

NASA Astrophysics Data System (ADS)

Dumansky, Alexander M.; Tairova, Lyudmila P.

2008-09-01

A method for the construction of hereditary constitutive equation is proposed for the laminate on the basis of hereditary constitutive equations of a layer. The method is developed from the assumption that in the directions of axes of orthotropy the layer follows elastic behavior, and obeys hereditary constitutive equations under shear. The constitutive equations of the laminate are constructed on the basis of classical laminate theory and algebra of resolvent operators. Effective matrix algorithm and relationships of operator algebra are used to derive visco-elastic stiffness and compliance of the laminate. The example of construction of hereditary constitutive equations of cross-ply carbon fiber-reinforced plastic is presented.

Infinite Conservation Laws, Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Zhang, Xiang-Zhi; Dong, Huan-He

2017-12-01

Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and (1+1)-dimensional and (2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally, we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the (1+1) and (2+1)-dimensional Toda-type equations. Supported by the Fundamental Research Funds for the Central University under Grant No. 2017XKZD11

On Reductions of the Hirota-Miwa Equation

NASA Astrophysics Data System (ADS)

Hone, Andrew N. W.; Kouloukas, Theodoros E.; Ward, Chloe

2017-07-01

The Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota-Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge transformation), defined by a triple of integers or half-integers, which produce bilinear ordinary difference equations of Somos/Gale-Robinson type. Here it is explained how to obtain Lax pairs and presymplectic structures for these reductions, in order to demonstrate Liouville integrability of some associated maps, certain of which are related to reductions of discrete Toda and discrete KdV equations.

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

DOE PAGES

Larios, Adam; Petersen, Mark R.; Titi, Edriss S.; ...

2017-04-29

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blow-up criteria allow one to gain information about possible singularity formationmore » in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be suficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.« less

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

PubMed

Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

2013-01-01

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

First integrals of the axisymmetric shape equation of lipid membranes

NASA Astrophysics Data System (ADS)

Zhang, Yi-Heng; McDargh, Zachary; Tu, Zhan-Chun

2018-03-01

The shape equation of lipid membranes is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu (Phys. Rev. E 48 2856 (1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler–Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor. Project supported by the National Natural Science Foundation of China (Grant No. 11274046) and the National Science Foundation of the United States (Grant No. 1515007).

Consistent three-equation model for thin films

NASA Astrophysics Data System (ADS)

Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

2017-11-01

Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

The effect of magnetohydrodynamic nano fluid flow through porous cylinder

NASA Astrophysics Data System (ADS)

Widodo, Basuki; Arif, Didik Khusnul; Aryany, Deviana; Asiyah, Nur; Widjajati, Farida Agustini; Kamiran

2017-08-01

This paper concerns about the analysis of the effect of magnetohydrodynamic nano fluid flow through horizontal porous cylinder on steady and incompressible condition. Fluid flow is assumed opposite gravity and induced by magnet field. Porous cylinder is assumed had the same depth of porous and was not absorptive. The First thing to do in this research is to build the model of fluid flow to obtain dimentional governing equations. The dimentional governing equations are consist of continuity equation, momentum equation, and energy equation. Furthermore, the dimensional governing equations are converted to non-dimensional governing equation by using non-dimensional parameters and variables. Then, the non-dimensional governing equations are transformed into similarity equations using stream function and solved using Keller-Box method. The result of numerical solution further is obtained by taking variation of magnetic parameter, Prandtl number, porosity parameter, and volume fraction. The numerical results show that velocity profiles increase and temperature profiles decrease when both of the magnetic and the porosity parameter increase. However, the velocity profiles decrease and the temperature profiles increase when both of the magnetic and the porosity parameter increase.

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Larios, Adam; Petersen, Mark R.; Titi, Edriss S.

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blow-up criteria allow one to gain information about possible singularity formationmore » in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be suficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.« less

Ince's limits for confluent and double-confluent Heun equations

NASA Astrophysics Data System (ADS)

Bonorino Figueiredo, B. D.

2005-11-01

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable z, while the other is given by a series of modified Bessel functions and converges for ∣z∣>∣z0∣, where z0 denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when z0 tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schrödinger equation for inverse fourth- and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.

The Markov process admits a consistent steady-state thermodynamic formalism

NASA Astrophysics Data System (ADS)

Peng, Liangrong; Zhu, Yi; Hong, Liu

2018-01-01

The search for a unified formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for the master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that (1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; (2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; (3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that general Markov processes admit a unified and self-consistent non-equilibrium steady-state thermodynamic formalism, regardless of underlying detailed models.

Lie Symmetry Analysis, Conservation Laws and Exact Power Series Solutions for Time-Fractional Fordy-Gibbons Equation

NASA Astrophysics Data System (ADS)

Feng, Lian-Li; Tian, Shou-Fu; Wang, Xiu-Bin; Zhang, Tian-Tian

2016-09-01

In this paper, the time fractional Fordy-Gibbons equation is investigated with Riemann-Liouville derivative. The equation can be reduced to the Caudrey-Dodd-Gibbon equation, Savada-Kotera equation and the Kaup-Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method. Supported by the Fundamental Research Funds for Key Discipline Construction under Grant No. XZD201602, the Fundamental Research Funds for the Central Universities under Grant Nos. 2015QNA53 and 2015XKQY14, the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Mines, the General Financial Grant from the China Postdoctoral Science Foundation under Grant No. 2015M570498, and Natural Sciences Foundation of China under Grant No. 11301527

Extension of lattice Boltzmann flux solver for simulation of compressible multi-component flows

NASA Astrophysics Data System (ADS)

Yang, Li-Ming; Shu, Chang; Yang, Wen-Ming; Wang, Yan

2018-05-01

The lattice Boltzmann flux solver (LBFS), which was presented by Shu and his coworkers for solving compressible fluid flow problems, is extended to simulate compressible multi-component flows in this work. To solve the two-phase gas-liquid problems, the model equations with stiffened gas equation of state are adopted. In this model, two additional non-conservative equations are introduced to represent the material interfaces, apart from the classical Euler equations. We first convert the interface equations into the full conservative form by applying the mass equation. After that, we calculate the numerical fluxes of the classical Euler equations by the existing LBFS and the numerical fluxes of the interface equations by the passive scalar approach. Once all the numerical fluxes at the cell interface are obtained, the conservative variables at cell centers can be updated by marching the equations in time and the material interfaces can be identified via the distributions of the additional variables. The numerical accuracy and stability of present scheme are validated by its application to several compressible multi-component fluid flow problems.

A Riemann-Hilbert Approach for the Novikov Equation

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Anne; Shepelsky, Dmitry; Zielinski, Lech

2016-09-01

We develop the inverse scattering transform method for the Novikov equation u_t-u_{txx}+4u^2u_x=3u u_xu_{xx}+u^2u_{xxx} considered on the line xin(-∞,∞) in the case of non-zero constant background. The approach is based on the analysis of an associated Riemann-Hilbert (RH) problem, which in this case is a 3× 3 matrix problem. The structure of this RH problem shares many common features with the case of the Degasperis-Procesi (DP) equation having quadratic nonlinear terms (see [Boutet de Monvel A., Shepelsky D., Nonlinearity 26 (2013), 2081-2107, arXiv:1107.5995]) and thus the Novikov equation can be viewed as a ''modified DP equation'', in analogy with the relationship between the Korteweg-de Vries (KdV) equation and the modified Korteweg-de Vries (mKdV) equation. We present parametric formulas giving the solution of the Cauchy problem for the Novikov equation in terms of the solution of the RH problem and discuss the possibilities to use the developed formalism for further studying of the Novikov equation.

Algorithmic framework for group analysis of differential equations and its application to generalized Zakharov-Kuznetsov equations

NASA Astrophysics Data System (ADS)

Huang, Ding-jiang; Ivanova, Nataliya M.

2016-02-01

In this paper, we explain in more details the modern treatment of the problem of group classification of (systems of) partial differential equations (PDEs) from the algorithmic point of view. More precisely, we revise the classical Lie algorithm of construction of symmetries of differential equations, describe the group classification algorithm and discuss the process of reduction of (systems of) PDEs to (systems of) equations with smaller number of independent variables in order to construct invariant solutions. The group classification algorithm and reduction process are illustrated by the example of the generalized Zakharov-Kuznetsov (GZK) equations of form ut +(F (u)) xxx +(G (u)) xyy +(H (u)) x = 0. As a result, a complete group classification of the GZK equations is performed and a number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Lie symmetry reductions and exact solutions for two important invariant models, i.e., the classical and modified Zakharov-Kuznetsov equations, are constructed. The algorithmic framework for group analysis of differential equations presented in this paper can also be applied to other nonlinear PDEs.

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1983-01-01

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Non-classical and potential symmetry analysis of Richard's equation for moisture flow in soil

NASA Astrophysics Data System (ADS)

Wiltshire, Ron; El-Kafri, Manal

2004-01-01

This paper focuses upon the derivation of the non-classical symmetries of Bluman and Cole as they apply to Richard's equation for water flow in an unsaturated uniform soil. It is shown that the determining equations for the non-classical case lead to four highly non-linear equations which have been solved in five particular cases. In each case the corresponding similarity ansatz has been derived and Richard's equation is reduced to an ordinary differential equation. Explicit solutions are produced when possible. Richard's equation is also expressed as a potential system and in reviewing the classical Lie solutions a new symmetry is derived together with its similarity ansatz. Determining equations are then produced for the potential system using the non-classical algorithm. This results in an under-determined set of equations and an example symmetry that reveals a missing classical case is presented. An example of a classical and a non-classical symmetry reduction applied to the infiltration of moisture in soil is presented. The condition for surface invariance is used to demonstrate the equivalence of a classical Lie and a potential symmetry.

Considering ethics, aesthetics and the dignity of the individual.

PubMed

Strebler, Aline; Valentin, Claude

2014-03-01

There are variations on vulnerability that are often based on opposing authorities. In his book Parcours de la reconnaissance, Paul Ricœur offers a reflection grounded in a survey from Aristotle to Levinas, with way stations in phenomenology, from Hegel to Husserl. He sketches the silhouette of capable man. In a reversal of thinking and positioning, weakness, which could be considered the hallmark of disability in all its forms, becomes a source of mutual wealth and an argument in favour of reciprocity and dialogue. Relying on clinical examples, we propose art as a mediator of the doctor-patient relationship, which in its present unique form forces us to question the dynamics of empathy. A. Strebler A FEW GRAMS OF GOLD IN AN INSECURE WORLD: Vulnerability has long gone hand in hand with precarity. It is disturbing in a world where all is 'comfort and beauty, calm and bliss.' Additionally, vulnerability is a type of wound and wounds are what knit the relationship between patient and care provider. Similarly disturbing is poverty: the pauper is "without": without work, without a home, without a legal residency permit, without money… Poverty is also a wound, and yet it may serve as a path to "truth," according to the philosopher Simone Weil. These two concepts, equally vulnerable, question man's finite nature, and may serve as an introduction to the art of living together. In the midst of this ambiguity, the word "art" stands out. It is a counter-power, a challenge to established authority and politico-economic forms of government; it is inessential, unclassifiable, ungraspable, unthinkable and cannot be evaluated. Art avenges the abyss of ambiguity. C. Valentin COMMON SUMMARY: This article, composed of two core pieces, was written for a common project leading to the creation of a university degree at Paris 5 University (chaired by Pr. Hervé): Ethics, Aesthetics and the Dignity of the Individual. Together, they serve as a forum for reflection and dialogue in which scientists, artists, care workers, teachers, legal professionals interact… It is from this apparent melting pot that a true art of living together emerges.

Impact of Early Intervention on Psychopathology, Crime, and Weil-Being at Age 25

PubMed Central

2015-01-01

Objective This randomized controlled trial tested the efficacy of early intervention to prevent adult psychopathology and improve well-being in early-starting conduct-problem children. Method Kindergarteners (N=9,594) in three cohorts (1991–1993) at 55 schools in four communities were screened for conduct problems, yielding 979 early starters. A total of 891 (91%) consented (51% African American, 47% European American; 69% boys). Children were randomly assigned by school cluster to a 10-year intervention or control. The intervention goal was to develop social competencies in children that would carry them throughout life, through social skills training, parent behavior-management training with home visiting, peer coaching, reading tutoring, and classroom social-emotional curricula. Manualization and supervision ensured program fidelity. Ninety-eight percent participated during grade 1, and 80% continued through grade 10. At age 25, arrest records were reviewed (N=817,92%), and condition-blinded adults psychiatrically interviewed participants (N=702; 81% of living participants) and a peer (N=535) knowledgeable about the participant. Results Intent-to-treat logistic regression analyses indicated that 69% of participants in the control arm displayed at least one externalizing, internalizing, or substance abuse psychiatric problem (based on self- or peer interview) at age 25, in contrast with 59% of those assigned to intervention (odds ratio=0.59, CI=0.43–0.81; number needed to treat=8). This pattern also held for self-interviews, peer interviews, scores using an “and” rule for self- and peer reports, and separate tests for externalizing problems, internalizing problems, and substance abuse problems, as well as for each of three cohorts, four sites, male participants, female participants, African Americans, European Americans, moderate-risk, and high-risk subgroups. Intervention participants also received lower severity-weighted violent (standardized estimate=-0.37) and drug (standardized estimate=-0.43) crime conviction scores, lower risky sexual behavior scores (standardized estimate=-0.24), and higher well-being scores (standardized estimate=0.19). Conclusions This study provides evidence for the efficacy of early intervention in preventing adult psychopathology among high-risk early-starting conduct-problem children. PMID:25219348

Tiered evidence for three kinds of overwash in the past 1.000 years at Anegada, British Virgin Islands

NASA Astrophysics Data System (ADS)

Spiske, M.

2016-12-01

Three kinds of extreme waves are evidenced geologically on Anegada, a low-lying island 120 km south of the Puerto Rico Trench: (1) Modern and historical storms: A coral-rubble ridge lining the island's north shore was refreshed by modern storms and was probably emplaced by historical hurricanes. A category 4 storm in 2010 aggraded sandy fans within 50 m of the south shore and stirred up microbial debris in interior salt ponds. (2) Unusual flooding between 1650 and 1800 CE which may resemble the 1755 Lisbon tsunami: A sand-and-shell sheet extends as much as 1.5 km inland. Its shells were derived from an interior marine pond, not from the reef flat. (3) Catastrophic overwash before 1500 CE: Coral clasts, limestone boulders, and carbonate sand were deposited hundreds of meters inland from the north shore. Many of the coral clasts are complete colonies of the brain coral Diploria strigosa on the order of at least 1 m in diameter. The limestone clasts were derived from cemented Pleistocene deposits. Some form elongate fields pendant to likely sources to their north, and others are imbricated slabs that dip to the north. The carbonate sand locally contains articulated valves of the lucine Codakia orbicularis and the conch Lobatus gigas, which today inhabit the sandy shallows between the island's north shore and the fringing reef. All the dated coral clasts, lucines, and conches are older than 1500 CE, and most are in the range 1200-1480 CE. The extreme waves of type (3) were previously ascribed to a tsunami from faulting along the Puerto Rico Trench. We are also evaluating an alternative explanation - a tsunami-like bore from infragravity waves similar to those produced in the Philippines by 2013 Typhoon Haiyan. This abstract was adapted, with permission, from a journal manuscript by B.F. Atwater, U.S. ten Brink, A.L. Cescon, N. Feuillet, Z. Fuentes, R.B., Halley, C. Nuñez, E.G. Reinhardt, J.H. Roger, Y. Sawai, M. Spiske, M.P., Tuttle, Y. Wei, and J. Weil Accardo.

Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.

PubMed

Frankenfield, David; Roth-Yousey, Lori; Compher, Charlene

2005-05-01

An assessment of energy needs is a necessary component in the development and evaluation of a nutrition care plan. The metabolic rate can be measured or estimated by equations, but estimation is by far the more common method. However, predictive equations might generate errors large enough to impact outcome. Therefore, a systematic review of the literature was undertaken to document the accuracy of predictive equations preliminary to deciding on the imperative to measure metabolic rate. As part of a larger project to determine the role of indirect calorimetry in clinical practice, an evidence team identified published articles that examined the validity of various predictive equations for resting metabolic rate (RMR) in nonobese and obese people and also in individuals of various ethnic and age groups. Articles were accepted based on defined criteria and abstracted using evidence analysis tools developed by the American Dietetic Association. Because these equations are applied by dietetics practitioners to individuals, a key inclusion criterion was research reports of individual data. The evidence was systematically evaluated, and a conclusion statement and grade were developed. Four prediction equations were identified as the most commonly used in clinical practice (Harris-Benedict, Mifflin-St Jeor, Owen, and World Health Organization/Food and Agriculture Organization/United Nations University [WHO/FAO/UNU]). Of these equations, the Mifflin-St Jeor equation was the most reliable, predicting RMR within 10% of measured in more nonobese and obese individuals than any other equation, and it also had the narrowest error range. No validation work concentrating on individual errors was found for the WHO/FAO/UNU equation. Older adults and US-residing ethnic minorities were underrepresented both in the development of predictive equations and in validation studies. The Mifflin-St Jeor equation is more likely than the other equations tested to estimate RMR to within 10% of that measured, but noteworthy errors and limitations exist when it is applied to individuals and possibly when it is generalized to certain age and ethnic groups. RMR estimation errors would be eliminated by valid measurement of RMR with indirect calorimetry, using an evidence-based protocol to minimize measurement error. The Expert Panel advises clinical judgment regarding when to accept estimated RMR using predictive equations in any given individual. Indirect calorimetry may be an important tool when, in the judgment of the clinician, the predictive methods fail an individual in a clinically relevant way. For members of groups that are greatly underrepresented by existing validation studies of predictive equations, a high level of suspicion regarding the accuracy of the equations is warranted.

Northeastern forest survey revised cubic-foot volume equations

Treesearch

Charles T. Scott

1981-01-01

Cubic-foot volume equations are presented for the 17 species groups used in the forest survey of the 14 northeastern states. The previous cubic- foot volume equations were simple linear in form; the revised cubic-foot volume equations are nonlinear.

Solution of differential equations by application of transformation groups

NASA Technical Reports Server (NTRS)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

Similarity solutions of some two-space-dimensional nonlinear wave evolution equations

NASA Technical Reports Server (NTRS)

Redekopp, L. G.

1980-01-01

Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.

Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

NASA Astrophysics Data System (ADS)

Zhou, Xin

1990-03-01

For the direct-inverse scattering transform of the time dependent Schrödinger equation, rigorous results are obtained based on an opertor-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution.

Schwarz maps of algebraic linear ordinary differential equations

NASA Astrophysics Data System (ADS)

Sanabria Malagón, Camilo

2017-12-01

A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

The Missing Data Assumptions of the Nonequivalent Groups with Anchor Test (NEAT) Design and Their Implications for Test Equating. Research Report. ETS RR-09-16

ERIC Educational Resources Information Center

Sinharay, Sandip; Holland, Paul W.

2008-01-01

The nonequivalent groups with anchor test (NEAT) design involves missing data that are missing by design. Three popular equating methods that can be used with a NEAT design are the poststratification equating method, the chain equipercentile equating method, and the item-response-theory observed-score-equating method. These three methods each…

Cauchy-Jost function and hierarchy of integrable equations

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2015-11-01

We describe the properties of the Cauchy-Jost (also known as Cauchy-Baker-Akhiezer) function of the Kadomtsev-Petviashvili-II equation. Using the bar partial -method, we show that for this function, all equations of the Kadomtsev-Petviashvili-II hierarchy are given in a compact and explicit form, including equations for the Cauchy-Jost function itself, time evolutions of the Jost solutions, and evolutions of the potential of the heat equation.

Dynamically orthogonal field equations for stochastic flows and particle dynamics

DTIC Science & Technology

2011-02-01

where uncertainty ‘lives’ as well as a system of Stochastic Di erential Equations that de nes how the uncertainty evolves in the time varying stochastic ... stochastic dynamical component that are both time and space dependent, we derive a system of field equations consisting of a Partial Differential Equation...a system of Stochastic Differential Equations that defines how the stochasticity evolves in the time varying stochastic subspace. These new

The Ffowcs Williams-Hawkings equation - Fifteen years of research

NASA Technical Reports Server (NTRS)

Farassat, F.

1986-01-01

The Ffowcs Williams-Hawkings equation governs the generation of sound in fluids in the presence of solid boundaries in motion. This equation is reviewed for situations where the linearization of the governing equations is allowed. In addition, research on the application of this equation to problems of aeroacoustic is briefly surveyed. Particular attention is given to the formulation of supersonic sources moving in uniform propeller-like motion.

Reply to comment by Claude Michel on "A general power equation for predicting bed load transport rates in gravel bed rivers"

Treesearch

Jeffrey J. Barry; John M. Buffington; John G. King

2005-01-01

We thank Michel [2005] for the opportunity to improve our bed load transport equation [Barry et al., 2004, equation (6)] and to resolve the dimensional complexity that he identified. However, we do not believe that the alternative bed load transport equation proposed by Michel [2005] provides either the mechanistic insight or predictive power of our transport equation...

High Frequency Acoustic Propagation using Level Set Methods

DTIC Science & Technology

2007-01-01

solution of the high frequency approximation to the wave equation. Traditional solutions to the Eikonal equation in high frequency acoustics are...the Eikonal equation derived from the high frequency approximation to the wave equation, ucuH ∇±=∇ )(),( xx , with the nonnegative function c(x...For simplicity, we only consider the case ucuH ∇+=∇ )(),( xx . Two difficulties must be addressed when solving the Eikonal equation in a fixed

An integrable semi-discrete Degasperis-Procesi equation

NASA Astrophysics Data System (ADS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-06-01

Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota’s bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

Residual-based Methods for Controlling Discretization Error in CFD

DTIC Science & Technology

2015-08-24

discrete equations uh into Equation (3), then subtracting the original (continuous) governing equation 0)~( uL gives 0)()~()(  hhh uuLuL  . If...error from Equation (1) results in )()( hhh uL   (4) which for Burgers’ equation becomes  4 2 4 42 3 3 2 2 126 xO x dx udx dx ud u dx d dx d u...GTEE given in Equation (3) gives the continuous residual )()( hhh uuL  (8) which is analogous to the finite element residual (Ainsworth and

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Whitham modulation theory for the two-dimensional Benjamin-Ono equation.

PubMed

Ablowitz, Mark; Biondini, Gino; Wang, Qiao

2017-09-01

Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.

Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation

PubMed Central

Wang, Gang wei; Xu, Tian zhou; Feng, Tao

2014-01-01

In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last, by virtue of the sub-equation method, some exact solutions to the fractional fifth-order KdV equation are provided. PMID:24523885