On the role of sharp chains in the transport theorem
NASA Astrophysics Data System (ADS)
Falach, L.; Segev, R.
2016-03-01
A generalized transport theorem for convecting irregular domains is presented in the setting of Federer's geometric measure theory. A prototypical r-dimensional domain is viewed as a flat r-chain of finite mass in an open set of an n-dimensional Euclidean space. The evolution of such a generalized domain in time is assumed to follow a continuous succession of Lipschitz embedding so that the spatial gradient may be nonexistent in a subset of the domain with zero measure. The induced curve is shown to be continuous with respect to the flat norm and differential with respect to the sharp norm on currents in Rn. A time-dependent property is naturally assigned to the evolving region via the action of an r-cochain on the current associated with the domain. Applying a representation theorem for cochains, the properties are shown to be locally represented by an r-form. Using these notions, a generalized transport theorem is presented.
Ultrasensitivity and sharp threshold theorems for multisite systems
NASA Astrophysics Data System (ADS)
Dougoud, M.; Mazza, C.; Vinckenbosch, L.
2017-02-01
This work studies the ultrasensitivity of multisite binding processes where ligand molecules can bind to several binding sites. It considers more particularly recent models involving complex chemical reactions in allosteric phosphorylation processes and for transcription factors and nucleosomes competing for binding on DNA. New statistics-based formulas for the Hill coefficient and the effective Hill coefficient are provided and necessary conditions for a system to be ultrasensitive are exhibited. It is first shown that the ultrasensitivity of binding processes can be approached using sharp-threshold theorems which have been developed in applied probability theory and statistical mechanics for studying sharp threshold phenomena in reliability theory, random graph theory and percolation theory. Special classes of binding process are then introduced and are described as density dependent birth and death process. New precise large deviation results for the steady state distribution of the process are obtained, which permits to show that switch-like ultrasensitive responses are strongly related to the multi-modality of the steady state distribution. Ultrasensitivity occurs if and only if the entropy of the dynamical system has more than one global minimum for some critical ligand concentration. In this case, the Hill coefficient is proportional to the number of binding sites, and the system is highly ultrasensitive. The classical effective Hill coefficient I is extended to a new cooperativity index I q , for which we recommend the computation of a broad range of values of q instead of just the standard one I = I 0.9 corresponding to the 10%-90% variation in the dose-response. It is shown that this single choice can sometimes mislead the conclusion by not detecting ultrasensitivity. This new approach allows a better understanding of multisite ultrasensitive systems and provides new tools for the design of such systems.
2013-01-01
neutrino factory, ablation of pellets in tokamaks, and processes in hybrid magnetoinertial fusion. Sharp Interface Algorithm for Large Density Rati...for the proposed muon collider / neutrino factory, ablation of pellets in tokamaks, and processes in hybrid magnetoinertial fusion. Keywords: Front
Le Chenadec, Vincent; Pitsch, Heinz
2013-09-15
This paper presents a novel approach for solving the conservative form of the incompressible two-phase Navier–Stokes equations. In order to overcome the numerical instability induced by the potentially large density ratio encountered across the interface, the proposed method includes a Volume-of-Fluid type integration of the convective momentum transport, a monotonicity preserving momentum rescaling, and a consistent and conservative Ghost Fluid projection that includes surface tension effects. The numerical dissipation inherent in the Volume-of-Fluid treatment of the convective transport is localized in the interface vicinity, enabling the use of a kinetic energy conserving discretization away from the singularity. Two- and three-dimensional tests are presented, and the solutions shown to remain accurate at arbitrary density ratios. The proposed method is then successfully used to perform the detailed simulation of a round water jet emerging in quiescent air, therefore suggesting the applicability of the proposed algorithm to the computation of realistic turbulent atomization.
Moons, K G; van Es, G A; Deckers, J W; Habbema, J D; Grobbee, D E
1997-01-01
We evaluated the extent to which the sensitivity, specificity, and likelihood ratio of the exercise test to diagnose coronary artery disease vary across subgroups of a certain patient population. Among 295 patients suspected of coronary artery disease, as independently determined by coronary angiography, we assessed variation in sensitivity and specificity according to patient history, physical examination, exercise test results, and disease severity in 207 patients with and 88 patients without coronary artery disease, respectively. The sensitivity varied substantially according to sex (women 30% and men 64%), systolic blood pressure at baseline (53% to 65%), expected workload (50% to 64%), systolic blood pressure at peak exercise (50% to 67%), relative workload (33% to 68%), and number of diseased vessels (39% to 77%). The specificity varied across subgroups of sex (men 89% and women 97%) and relative workload (85% to 98%). The likelihood ratio varied (3.8 to 17.0) across the same patient subgroups, as did the sensitivity. As each population tends to be heterogeneous with respect to patient characteristics, no single level of these parameters can be given that is adequate for all subgroups. Use of these parameters as a basis for calculating diagnostic probabilities in individual patients using Bayes' theorem has serious limitations.
Li Chao; Lovelace, Geoffrey
2008-03-15
Extreme-mass-ratio inspirals (EMRIs) and intermediate-mass-ratio inspirals (IMRIs) - binaries in which a stellar-mass object spirals into a massive black hole or other massive, compact body - are important sources of gravitational waves for LISA and LIGO, respectively. Thorne has speculated that the waves from EMRIs and IMRIs encode, in principle, all the details of (i) the central body's spacetime geometry (metric), (ii) the tidal coupling (energy and angular momentum exchange) between the central body and orbiting object, and (iii) the evolving orbital elements. Fintan Ryan has given a first partial proof that this speculation is correct: Restricting himself to nearly circular, nearly equatorial orbits and ignoring tidal coupling, Ryan proved that the central body's metric is encoded in the waves. In this paper we generalize Ryan's theorem. Retaining Ryan's restriction to nearly circular and nearly equatorial orbits, and dropping the assumption of no tidal coupling, we prove that Thorne's conjecture is nearly fully correct: the waves encode not only the central body's metric but also the evolving orbital elements and (in a sense slightly different from Thorne's conjecture) the evolving tidal coupling.
Caballero, David; Villanueva, Guillermo; Plaza, Jose Antonio; Mills, Christopher A; Samitier, Josep; Errachid, Abdelhamid
2010-01-01
The shape and dimensions of an atomic force microscope tip are crucial factors to obtain high resolution images at the nanoscale. When measuring samples with narrow trenches, inclined sidewalls near 90 degrees or nanoscaled structures, standard silicon atomic force microscopy (AFM) tips do not provide satisfactory results. We have combined deep reactive ion etching (DRIE) and focused ion beam (FIB) lithography techniques in order to produce probes with sharp rocket-shaped silicon AFM tips for high resolution imaging. The cantilevers were shaped and the bulk micromachining was performed using the same DRIE equipment. To improve the tip aspect ratio we used FIB nanolithography technique. The tips were tested on narrow silicon trenches and over biological samples showing a better resolution when compared with standard AFM tips, which enables nanocharacterization and nanometrology of high-aspect-ratio structures and nanoscaled biological elements to be completed, and provides an alternative to commercial high aspect ratio AFM tips.
NASA Technical Reports Server (NTRS)
Lee, Angelene M. (Inventor)
1992-01-01
This invention relates to a system for use in disposing of potentially hazardous items and more particularly a Sharps receptacle for used hypodermic needles and the like. A Sharps container is constructed from lightweight alodined nonmagnetic metal material with a cup member having an elongated tapered shape and length greater than its transverse dimensions. A magnet in the cup member provides for metal retention in the container. A nonmagnetic lid member has an opening and spring biased closure flap member. The flap member is constructed from stainless steel. A Velcro patch on the container permits selective attachment at desired locations.
Sharp-Tip Silver Nanowires Mounted on Cantilevers for High-Aspect-Ratio High-Resolution Imaging.
Ma, Xuezhi; Zhu, Yangzhi; Kim, Sanggon; Liu, Qiushi; Byrley, Peter; Wei, Yang; Zhang, Jin; Jiang, Kaili; Fan, Shoushan; Yan, Ruoxue; Liu, Ming
2016-11-09
Despite many efforts to fabricate high-aspect-ratio atomic force microscopy (HAR-AFM) probes for high-fidelity, high-resolution topographical imaging of three-dimensional (3D) nanostructured surfaces, current HAR probes still suffer from unsatisfactory performance, low wear-resistivity, and extravagant prices. The primary objective of this work is to demonstrate a novel design of a high-resolution (HR) HAR AFM probe, which is fabricated through a reliable, cost-efficient benchtop process to precisely implant a single ultrasharp metallic nanowire on a standard AFM cantilever probe. The force-displacement curve indicated that the HAR-HR probe is robust against buckling and bending up to 150 nN. The probes were tested on polymer trenches, showing a much better image fidelity when compared with standard silicon tips. The lateral resolution, when scanning a rough metal thin film and single-walled carbon nanotubes (SW-CNTs), was found to be better than 8 nm. Finally, stable imaging quality in tapping mode was demonstrated for at least 15 continuous scans indicating high resistance to wear. These results demonstrate a reliable benchtop fabrication technique toward metallic HAR-HR AFM probes with performance parallel or exceeding that of commercial HAR probes, yet at a fraction of their cost.
INTERPOLATION THEOREMS FOR THE SPACES L_{p,q}
NASA Astrophysics Data System (ADS)
Ovchinnikov, V. I.
1989-02-01
A sharp or optimal interpolation theorem is proved for the Lorentz spaces L_{p,q}, generalizing the Marcinkiewicz theorem and refining the Riesz-Thorin theorem and the Stein-Weiss theorem. This theorem extends to the spaces \\overline{X}_{\\theta,p} of the real method constructed from any Banach pair; thus it extends also to Besov spaces.Bibliography: 12 titles.
ERIC Educational Resources Information Center
Davis, Philip J.
1993-01-01
Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)
Yu, Y. Q.; Shemon, E. R.; Thomas, J. W.; Mahadevan, Vijay S.; Rahaman, Ronald O.; Solberg, Jerome
2016-03-31
SHARP is an advanced modeling and simulation toolkit for the analysis of nuclear reactors. It is comprised of several components including physical modeling tools, tools to integrate the physics codes for multi-physics analyses, and a set of tools to couple the codes within the MOAB framework. Physics modules currently include the neutronics code PROTEUS, the thermal-hydraulics code Nek5000, and the structural mechanics code Diablo. This manual focuses on performing multi-physics calculations with the SHARP ToolKit. Manuals for the three individual physics modules are available with the SHARP distribution to help the user to either carry out the primary multi-physics calculation with basic knowledge or perform further advanced development with in-depth knowledge of these codes. This manual provides step-by-step instructions on employing SHARP, including how to download and install the code, how to build the drivers for a test case, how to perform a calculation and how to visualize the results. Since SHARP has some specific library and environment dependencies, it is highly recommended that the user read this manual prior to installing SHARP. Verification tests cases are included to check proper installation of each module. It is suggested that the new user should first follow the step-by-step instructions provided for a test problem in this manual to understand the basic procedure of using SHARP before using SHARP for his/her own analysis. Both reference output and scripts are provided along with the test cases in order to verify correct installation and execution of the SHARP package. At the end of this manual, detailed instructions are provided on how to create a new test case so that user can perform novel multi-physics calculations with SHARP. Frequently asked questions are listed at the end of this manual to help the user to troubleshoot issues.
Yu, Y. Q.; Shemon, E. R.; Mahadevan, Vijay S.; Rahaman, Ronald O.
2016-02-29
SHARP, developed under the NEAMS Reactor Product Line, is an advanced modeling and simulation toolkit for the analysis of advanced nuclear reactors. SHARP is comprised of three physics modules currently including neutronics, thermal hydraulics, and structural mechanics. SHARP empowers designers to produce accurate results for modeling physical phenomena that have been identified as important for nuclear reactor analysis. SHARP can use existing physics codes and take advantage of existing infrastructure capabilities in the MOAB framework and the coupling driver/solver library, the Coupled Physics Environment (CouPE), which utilizes the widely used, scalable PETSc library. This report aims at identifying the coupled-physics simulation capability of SHARP by introducing the demonstration example called sahex in advance of the SHARP release expected by Mar 2016. sahex consists of 6 fuel pins with cladding, 1 control rod, sodium coolant and an outer duct wall that encloses all the other components. This example is carefully chosen to demonstrate the proof of concept for solving more complex demonstration examples such as EBR II assembly and ABTR full core. The workflow of preparing the input files, running the case and analyzing the results is demonstrated in this report. Moreover, an extension of the sahex model called sahex_core, which adds six homogenized neighboring assemblies to the full heterogeneous sahex model, is presented to test homogenization capabilities in both Nek5000 and PROTEUS. Some primary information on the configuration and build aspects for the SHARP toolkit, which includes capability to auto-download dependencies and configure/install with optimal flags in an architecture-aware fashion, is also covered by this report. A step-by-step instruction is provided to help users to create their cases. Details on these processes will be provided in the SHARP user manual that will accompany the first release.
Sharp Estimates in Ruelle Theorems for Matrix Transfer Operators
NASA Astrophysics Data System (ADS)
Campbell, J.; Latushkin, Y.
A matrix coefficient transfer operator , on the space of -sections of an m-dimensional vector bundle over n-dimensional compact manifold is considered. The spectral radius of is estimated bya; and the essential spectral radius by
Snell, Janet
Pioneering nurse Margarete Sharp worked in one of the country's first clinics for people who misuse drugs. After 45 years in the field, she is convinced that, with the right level of support from nurses, social workers and doctors, drug treatment can work.
NASA Astrophysics Data System (ADS)
Webster, Nathan A. S.; Pownceby, Mark I.; Madsen, Ian C.; Studer, Andrew J.; Manuel, James R.; Kimpton, Justin A.
2014-12-01
Effects of basicity, B (CaO:SiO2 ratio) on the thermal range, concentration, and formation mechanisms of silico-ferrite of calcium and aluminum (SFCA) and SFCA-I iron ore sinter bonding phases have been investigated using an in situ synchrotron X-ray diffraction-based methodology with subsequent Rietveld refinement-based quantitative phase analysis. SFCA and SFCA-I phases are the key bonding materials in iron ore sinter, and improved understanding of the effects of processing parameters such as basicity on their formation and decomposition may assist in improving efficiency of industrial iron ore sintering operations. Increasing basicity significantly increased the thermal range of SFCA-I, from 1363 K to 1533 K (1090 °C to 1260 °C) for a mixture with B = 2.48, to ~1339 K to 1535 K (1066 °C to 1262 °C) for a mixture with B = 3.96, and to ~1323 K to 1593 K (1050 °C to 1320 °C) at B = 4.94. Increasing basicity also increased the amount of SFCA-I formed, from 18 wt pct for the mixture with B = 2.48 to 25 wt pct for the B = 4.94 mixture. Higher basicity of the starting sinter mixture will, therefore, increase the amount of SFCA-I, considered to be more desirable of the two phases. Basicity did not appear to significantly influence the formation mechanism of SFCA-I. It did, however, affect the formation mechanism of SFCA, with the decomposition of SFCA-I coinciding with the formation of a significant amount of additional SFCA in the B = 2.48 and 3.96 mixtures but only a minor amount in the highest basicity mixture. In situ neutron diffraction enabled characterization of the behavior of magnetite after melting of SFCA produced a magnetite plus melt phase assemblage.
Bell's theorem and Bayes' theorem
NASA Astrophysics Data System (ADS)
Garrett, A. J. M.
1990-12-01
Bell's theorem is expounded as an analysis in Bayesian probabilistic inference. Assume that the result of a spin measurement on a spin- 1/2 particle is governed by a variable internal to the particle (local, “hidden”), and examine pairs of particles having zero combined angular momentum so that their internal variables are correlated: knowing something about the internal variable of one tells us something about that of the other. By measuring the spin of one particle, we infer something about its internal variable; through the correlation, about the internal variable of the second particle, which may be arbitrarily distant and is by hypothesis unchanged by this measurement (locality); and make (probabilistic) prediction of spin observations on the second particle. Each link in this chain has a counterpart in the Bayesian analysis of the situation. Irrespective of the details of the internal variable description, such prediction is violated by measurements on many particle pairs, so that locality—effectively the only physics invoked—fails. The time ordering of the two measurements is not Lorentz-invariant, implying acausality. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of the statistics of the results imply it has a nonlocal—acausal interpretation; one such, the “transactional” interpretation, is presented to demonstrable advantage, and some misconceptions about quantum theory are pursued. The “unobservability” loophole in photonic Bell experiments is proven to be closed. It is shown that this mechanism cannot be used for signalling; signalling would become possible only if the hidden variables, which we insist must underlie the statistical character of the observations (the alternative is to give up), are uncovered in deviations from quantum predictions. Their reticence is understood as a consequence of their nonlocality: it is not easy to isolate and measure something nonlocal. Once the hidden variables
Vorticity, Stokes' Theorem and the Gauss's Theorem
NASA Astrophysics Data System (ADS)
Narayanan, M.
2004-12-01
Vorticity is a property of the flow of any fluid and moving fluids acquire properties that allow an engineer to describe that particular flow in greater detail. It is important to recognize that mere motion alone does not guarantee that the air or any fluid has vorticity. Vorticity is one of four important quantities that define the kinematic properties of any fluid flow. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. However, the divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into, or away from the region through its boundary. This is also known as Gauss's Theorem. It should also be noted that there are many useful extensions of Gauss's Theorem, including the extension to include surfaces of discontinuity in V. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. Integral (Surface) [(DEL X V)] . dS = Integral (Contour) [V . dx] In this paper, the author outlines and stresses the importance of studying and teaching these mathematical techniques while developing a course in Hydrology and Fluid Mechanics. References Arfken, G. "Gauss's Theorem." 1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. Morse, P. M. and Feshbach, H. "Gauss's Theorem." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 37-38, 1953. Eric W. Weisstein. "Divergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DivergenceTheorem.html
Courant-Sharp Eigenvalues for the Equilateral Torus, and for the Equilateral Triangle
NASA Astrophysics Data System (ADS)
Bérard, Pierre; Helffer, Bernard
2016-12-01
We address the question of determining the eigenvalues {λn} (listed in nondecreasing order, with multiplicities) for which Courant's nodal domain theorem is sharp i.e., for which there exists an associated eigenfunction with {n} nodal domains (Courant-sharp eigenvalues). Following ideas going back to Pleijel (1956), we prove that the only Courant-sharp eigenvalues of the flat equilateral torus are the first and second, and that the only Courant-sharp Dirichlet eigenvalues of the equilateral triangle are the first, second, and fourth eigenvalues. In the last section we sketch similar results for the right-angled isosceles triangle and for the hemiequilateral triangle.
The NASA Sharp Flight Experiment
NASA Technical Reports Server (NTRS)
Rasky, Daniel J.; Salute, Joan; Kolodziej, Paul; Bull, Jeffrey
1998-01-01
The Slender Hypersonic Aerothermodynamic Research Program (SHARP) was initiated by NASA Ames, and executed in partnership with Sandia National Laboratory and the US Air Force, to demonstrate sharp, passive leading edge designs for hypersonic vehicles, incorporating new ultra-high temperature ceramics (UHTC's). These new ceramic composites have been undergoing development, characterization and ground testing at NASA Ames for the last nine years. This paper will describe the background, flight objectives, design and pertinent flight results of SHARP, and some of the potential implications for future hypersonic vehicle designs.
ERIC Educational Resources Information Center
Parameswaran, Revathy
2009-01-01
This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich…
ERIC Educational Resources Information Center
Smith, Michael D.
2016-01-01
The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages.
Trigonometry, Including Snell's Theorem.
ERIC Educational Resources Information Center
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
ERIC Educational Resources Information Center
Benyi, Arpad; Casu, Ioan
2009-01-01
Pompeiu's theorem states that if ABC is an "equilateral" triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B,…
Sharp Injuries Among Medical Students
Ghasemzadeh, Iman; Kazerooni, Mitra; Davoodian, Parivash; Hamedi, Yaghoob; Sadeghi, Payam
2015-01-01
Introduction: Sharp injuries threaten the health of healthcare employees. They cause the transmission of many diseases such as hepatitis B and C, AIDS, etc., which can increase the associated costs associated with them. The aim of this study was to investigate the frequency of sharp injuries among the students of Hormozgan University of Medical Sciences. Method: This cross-sectional study was conducted during 2012-2013 in Hormozgan University of Medical Sciences, IR Iran. The target population consisted of the medical, nursing, midwifery, operating room technician, and medical laboratory students in the 2012-2013 academic year. Census sampling was conducted, and accordingly, 500 students participated in the study Data was collected using modified questionnaire of the University of San Diego’s injury report form. The collected data were entered into SPSS V.19 and analyzed using descriptive statistical tests. Findings: Finally 377 students (75.4%) returned the questionnaire. Among the studied students, 184 students (39.3%) had had sharp injuries. The frequency of damaging Vein puncture was the most common mechanism of injury Discussion and Conclusion: The prevalence of sharp injuries is high among students which can increase the risk of disease and its subsequent risks, and thus, increase the cost and stress among students. It seems that holding workshops and increasing students’ awareness and skills to face these risks can be effective in mitigating them. PMID:26156935
A generalization of Nekhoroshev's theorem
NASA Astrophysics Data System (ADS)
Bates, Larry; Cushman, Richard
2016-11-01
Nekhoroshev discovered a beautiful theorem in Hamiltonian systems that includes as special cases not only the Poincaré theorem on periodic orbits but also the theorem of Liouville-Arnol'd on completely integrable systems [7]. Sadly, his early death precluded him publishing a full account of his proof. The aim of this paper is twofold: first, to provide a complete proof of his original theorem and second a generalization to the noncommuting case. Our generalization of Nekhoroshev's theorem to the nonabelian case subsumes aspects of the theory of noncommutative complete integrability as found in Mishchenko and Fomenko [5] and is similar to what Nekhoroshev's theorem does in the abelian case.
NASA Astrophysics Data System (ADS)
Pérez-Espigares, Carlos; Redig, Frank; Giardinà, Cristian
2015-08-01
For non-equilibrium systems of interacting particles and for interacting diffusions in d-dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.
Virial Theorem and Scale Transformations.
ERIC Educational Resources Information Center
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
Rediscovering Schreinemakers' Theorem.
ERIC Educational Resources Information Center
Bathurst, Bruce
1983-01-01
Schreinemakers' theorem (arrangement of curves around an invariant point), derived from La Chatelier's principle, can be rediscovered by students asked to use the principle when solving a natural problem such as "How does diluting a mineral/fluid alter shape of a pressure/temperature diagram?" Background information and instructional…
NASA Astrophysics Data System (ADS)
Evans, Denis J.; Searles, Debra J.
2002-11-01
The question of how reversible microscopic equations of motion can lead to irreversible macroscopic behaviour has been one of the central issues in statistical mechanics for more than a century. The basic issues were known to Gibbs. Boltzmann conducted a very public debate with Loschmidt and others without a satisfactory resolution. In recent decades there has been no real change in the situation. In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in thermostatted dissipative non-equilibrium systems. The relation was derived heuristically and applied to the special case of dissipative non-equilibrium systems subject to constant energy 'thermostatting'. These restrictions meant that the full importance of the Theorem was not immediately apparent. Within a few years, derivations of the Theorem were improved but it has only been in the last few of years that the generality of the Theorem has been appreciated. We now know that the Second Law of Thermodynamics can be derived assuming ergodicity at equilibrium, and causality. We take the assumption of causality to be axiomatic. It is causality which ultimately is responsible for breaking time reversal symmetry and which leads to the possibility of irreversible macroscopic behaviour. The Fluctuation Theorem does much more than merely prove that in large systems observed for long periods of time, the Second Law is overwhelmingly likely to be valid. The Fluctuation Theorem quantifies the probability of observing Second Law violations in small systems observed for a short time. Unlike the Boltzmann equation, the FT is completely consistent with Loschmidt's observation that for time reversible dynamics, every dynamical phase space trajectory and its conjugate time reversed 'anti-trajectory', are both solutions of the underlying equations of motion. Indeed the standard proofs of
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.
Non-traditional theorems unfolding
NASA Astrophysics Data System (ADS)
Wares, Arsalan
2015-02-01
The purpose of this paper is to provide examples of 'non-traditional' proof-related activities or theorems that can be explored through paper folding by university and high-school students. These theorems were encountered through playful acts of paper folding by the author. The author used these activities successfully with preservice teachers. The paper contains proof outlines for each theorem.
Generalized no-broadcasting theorem.
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-14
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with "superquantum" correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
Generalized No-Broadcasting Theorem
NASA Astrophysics Data System (ADS)
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-01
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with “superquantum” correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
ERIC Educational Resources Information Center
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
1987-03-20
with standard expressions of spherical trigonometry is sinr)0 = cos0 sini//0 (4.37) which is consistent with the results obtained previously with...theorems for discrete transforms. However, sampling questions inlroduce difficult obstacles in the develop- ment of a discrete theory. First, sampling...additional obstacle to discrete represen- tations of the CT. An example of qualitative predication of the shape of silhouettes with the Silhouette-Slice
The Steep Nekhoroshev's Theorem
NASA Astrophysics Data System (ADS)
Guzzo, M.; Chierchia, L.; Benettin, G.
2016-03-01
Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be {1/(2nα_1\\cdotsα_{n-2}}) ({α_i}'s being Nekhoroshev's steepness indices and {n ≥ 3} the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.
Needlestick and sharps injury prevention.
Wilburn, Susan Q
2004-09-30
Every day while caring for patients, nurses are at risk to exposure to bloodborne pathogens potentially resulting in infections such as HIV or hepatitis B and C. These exposures, while preventable, are often accepted as being a part of the job. In the United States, needlestick injuries have begun to decrease from an estimated one million exposures per year in 1996 to 385,000 per year in 2000. This decline has resulted from the protections afforded by the Occupational Safety and Health Administration's (OSHA) Bloodborne Pathogens Standard. Reasons for the success in decreasing needlestick and sharps injuries may be attributed to the elimination of needle recapping and the use of safer needle devices, sharps collection boxes, gloves and personal protective gear, and universal precautions. The prevention of needlestick injuries has made slow progress over the past 20 years since the HIV epidemic drew attention to the deadly nature of health care work and to protection of health care worker health and safety. In Africa, where the AIDS virus originated and where the prevalence of the human immunodeficiency virus (HIV) among hospitalized patients is highest in the world, attention has been directed only recently at protecting health care workers. Nurses, especially those infected from a preventable exposure, have been at the forefront of advocacy for prevention. This article includes a review about the hazard of exposure to bloodborne pathogens and epidemiology of occupational infection. The author discusses how to apply standard methods of occupational health and industry hygiene using the hierarchy of controls framework to prevent exposure to blood, and discusses evidence-based prevention and efficacy of particular control measures. Legislative progress and implementation of enforceable policy to protect health care workers is outlined.
Fluctuation theorem for Hamiltonian systems: Le Chatelier's principle.
Evans, D J; Searles, D J; Mittag, E
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle
NASA Astrophysics Data System (ADS)
Evans, Denis J.; Searles, Debra J.; Mittag, Emil
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
[Objectivity of BSE symptoms using Bayes theorem].
Hässig, M; Urech Hässig, B; Knubben-Schweizer, G
2011-12-01
In clinical epidemiology the Bayes theorem finds ever more use to render clinical acting more objective. It is shown that unusual examinations of BSE (bovine spongiform encephalopathy) as noise producing with ladle covers may quite objectively be evaluated. With the help of the likelihood ratio computed thereby, also a ranking of importance (clinical utility) of symptoms can be provided. The single most important symptom for BSE is photosensibility.
Courant-sharp eigenvalues of Neumann 2-rep-tiles
NASA Astrophysics Data System (ADS)
Band, Ram; Bersudsky, Michael; Fajman, David
2016-11-01
We find the Courant-sharp Neumann eigenvalues of the Laplacian on some 2-rep-tile domains. In {R}2 , the domains we consider are the isosceles right triangle and the rectangle with edge ratio √{2} (also known as the A4 paper). In {R}n , the domains are boxes which generalize the mentioned planar rectangle. The symmetries of those domains reveal a special structure of their eigenfunctions, which we call folding/unfolding. This structure affects the nodal set of the eigenfunctions, which, in turn, allows to derive necessary conditions for Courant-sharpness. In addition, the eigenvalues of these domains are arranged as a lattice which allows for a comparison between the nodal count and the spectral position. The Courant-sharpness of most eigenvalues is ruled out using those methods. In addition, this analysis allows to estimate the nodal deficiency—the difference between the spectral position and the nodal count.
Bayes' theorem in paleopathological diagnosis.
Byers, Steven N; Roberts, Charlotte A
2003-05-01
The utility of Bayes' theorem in paleopathological diagnoses is explored. Since this theorem has been used heavily by modern clinical medicine, its usefulness in that field is described first. Next, the mechanics of the theorem are discussed, along with methods for deriving the prior probabilities needed for its application. Following this, the sources of these prior probabilities and their accompanying problems in paleopathology are considered. Finally, an application using prehistoric rib lesions is presented to demonstrate the utility of this method to paleopathology.
Recurrence theorems: A unified account
Wallace, David
2015-02-15
I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.
Multidimensional Tauberian theorems for generalized functions
NASA Astrophysics Data System (ADS)
Drozhzhinov, Yu N.
2016-12-01
This is a brief survey of multidimensional Tauberian theorems for generalized functions. Included are theorems of Hardy-Littlewood type, Tauberian and Abelian comparison theorems of Keldysh type, theorems of Wiener type, and Tauberian theorems for generalized functions with values in Banach spaces. Bibliography: 58 titles.
Composite, ordered material having sharp surface features
D'Urso, Brian R.; Simpson, John T.
2006-12-19
A composite material having sharp surface features includes a recessive phase and a protrusive phase, the recessive phase having a higher susceptibility to a preselected etchant than the protrusive phase, the composite material having an etched surface wherein the protrusive phase protrudes from the surface to form a sharp surface feature. The sharp surface features can be coated to make the surface super-hydrophobic.
Don Sharp Home Improvements Information Sheet
Don Sharp Home Improvements (the Company) is located in Bartlett, Tennessee. The settlement involves renovation activities conducted at property constructed prior to 1978, located in Memphis, Tennessee.
Assessing the enhancement of image sharpness
NASA Astrophysics Data System (ADS)
Bouzit, Samira; MacDonald, Lindsay W.
2006-01-01
This study investigated four different image sharpness enhancement methods. Two methods applied standard sharpening filters (Sharpen and Sharpen More) in PhotoShop and the other two were based on adjustment of the image power spectrum using the human visual contrast sensitivity function. A psychophysical experiment was conducted with 25 observers, the results of which are presented and discussed. Five conclusions are drawn from this experiment: (1) Performance of the sharpening methods; (2) Image dependence; (3) Influence of two different colour spaces on sharpness manipulation; (4) Correlation between perceived image sharpness and image preference; and (5) Effect of image sharpness enhancement on the image power spectrum.
Roo: A parallel theorem prover
Lusk, E.L.; McCune, W.W.; Slaney, J.K.
1991-11-01
We describe a parallel theorem prover based on the Argonne theorem-proving system OTTER. The parallel system, called Roo, runs on shared-memory multiprocessors such as the Sequent Symmetry. We explain the parallel algorithm used and give performance results that demonstrate near-linear speedups on large problems.
ERIC Educational Resources Information Center
Lopez-Real, Francis
2008-01-01
While the author was searching the web, he came across an article by Michael Keyton of IMSA (Illinois Mathematics and Science Academy) called "Theorems of mystery". The phrase is Keyton's own, and he defines such a theorem as "a result that has considerable structure with minimal hypotheses." The simplest of his 10 examples is one that many…
The 1965 Penrose singularity theorem
NASA Astrophysics Data System (ADS)
Senovilla, José M. M.; Garfinkle, David
2015-06-01
We review the first modern singularity theorem, published by Penrose in 1965. This is the first genuine post-Einsteinian result in general relativity, where the fundamental and fruitful concept of the closed trapped surface was introduced. We include historical remarks, an appraisal of the theorem's impact, and relevant current and future work that belongs to its legacy.
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Equivalence theorem in effective theories
NASA Astrophysics Data System (ADS)
Chicherin, D.; Gorbenko, V.; Vereshagin, V.
2011-11-01
The famous equivalence theorem is reexamined in order to make it applicable to the case of effective theories. We slightly modify the formulation of this theorem and prove it based on the notion of the generating functional for Green functions. This allows one to trace (directly in terms of graphs) the mutual cancellation of different groups of contributions.
A Decomposition Theorem for Finite Automata.
ERIC Educational Resources Information Center
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
'Sharpe', a clonal plum rootstock for peach
Technology Transfer Automated Retrieval System (TEKTRAN)
Sharpe clonal rootstock for peach is jointly released for grower trial by the U.S. Department of Agriculture, Agricultural Research Service (Byron, GA), and Florida Agricultural Experiment Station. Sharpe, previously tested as FLA1-1, was discovered in the wild and appears to be a hybrid of Chickas...
NASA Astrophysics Data System (ADS)
Guney, Veli Ugur
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible
Overview of the SHARP campaign: Motivation, design, and major outcomes
NASA Astrophysics Data System (ADS)
Olaguer, Eduardo P.; Kolb, Charles E.; Lefer, Barry; Rappenglück, Bernhard; Zhang, Renyi; Pinto, Joseph P.
2014-03-01
The Study of Houston Atmospheric Radical Precursors (SHARP) was a field campaign developed by the Houston Advanced Research Center on behalf of the Texas Environmental Research Consortium. SHARP capitalized on previous research associated with the Second Texas Air Quality Study and the development of the State Implementation Plan (SIP) for the Houston-Galveston-Brazoria (HGB) ozone nonattainment area. These earlier studies pointed to an apparent deficit in ozone production in the SIP attainment demonstration model despite the enhancement of simulated emissions of highly reactive volatile organic compounds in accordance with the findings of the original Texas Air Quality Study in 2000. The scientific hypothesis underlying the SHARP campaign was that there are significant undercounted primary and secondary sources of the radical precursors, formaldehyde, and nitrous acid, in both heavily industrialized and more typical urban areas of Houston. These sources, if properly taken into account, could increase the production of ozone in the SIP model and the simulated efficacy of control strategies designed to bring the HGB area into ozone attainment. This overview summarizes the precursor studies and motivations behind SHARP, as well as the overall experimental design and major findings of the 2009 field campaign. These findings include significant combustion sources of formaldehyde at levels greater than accounted for in current point source emission inventories; the underestimation of formaldehyde and nitrous acid emissions, as well as CO/NOx and NO2/NOx ratios, by mobile source models; and the enhancement of nitrous acid by atmospheric organic aerosol.
A new approach to sharp Moser-Trudinger and Adams type inequalities: A rearrangement-free argument
NASA Astrophysics Data System (ADS)
Lam, Nguyen; Lu, Guozhen
The main purpose of this paper is two-fold. On the one hand, we will develop a new approach to establish sharp singular Moser-Trudinger and Adams type inequalities in unbounded domains of Euclidean spaces without using the standard symmetrization. On the other hand, we will prove the sharp singular Adams type inequality on high order Sobolev spaces W(Rn) of arbitrary integer order m (Theorem 1.1) which improves the results of Ruf and Sani (2013) [48] where sharp Adams inequalities were established for even m and those of the authors (Lam and Lu, 2012 [28,29]) for odd m but with different and more restricted norms. We first establish the sharp local singular Adams inequality on domains Ω in Rn of finite measure (Theorem 1.4). We take a perspective that any function in the high order Sobolev spaces W(Rn) can be represented as a Bessel potential. Thus, we can fully use the tools from harmonic analysis and the kernel properties of the polyharmonic operators (. Once we have established this sharp local Adams inequality, then we can adapt the rearrangement-free method we will develop in this paper to derive a global sharp Adams inequality from a local one. Our argument substantially simplifies those in Ruf and Sani (2013) [48] and Lam and Lu (2012) [28,29] and avoids the use of rather deep and complicated comparison principle of solutions to polyharmonic operators used in Ruf and Sani (2013) [48], Lam and Lu (2012) [28,29]. Moreover, our theorem holds on Sobolev spaces W(Rn) of any positive fractional order α
The Digital Morphological Sampling Theorem
NASA Astrophysics Data System (ADS)
Haralick, Robert M.; Zhuang, Xinhua; Lin, Charlotte; Lee, James
1988-02-01
There are potential industrial applications for any methodology which inherently reduces processing time and cost and yet produces results sufficiently close to the result of full processing. It is for this reason that a morphological sampling theorem is important. The morphological sampling theorem described in this paper states: (1) how a digital image must be morphologically filtered before sampling in order to preserve the relevant information after sampling; (2) to what precision an appropriately morphologically filtered image can be reconstructed after sampling; and (3) the relationship between morphologically operating before sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element. The digital sampling theorem is developed first for the case of binary morphology and then it is extended to gray scale morphology through the use of the umbra homomorphism theorems.
Factor and Remainder Theorems: An Appreciation
ERIC Educational Resources Information Center
Weiss, Michael
2016-01-01
The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…
Knowledge Base Editor (SharpKBE)
NASA Technical Reports Server (NTRS)
Tikidjian, Raffi; James, Mark; Mackey, Ryan
2007-01-01
The SharpKBE software provides a graphical user interface environment for domain experts to build and manage knowledge base systems. Knowledge bases can be exported/translated to various target languages automatically, including customizable target languages.
Summer High School Apprenticeship Research Program (SHARP)
NASA Technical Reports Server (NTRS)
1997-01-01
The summer of 1997 will not only be noted by NASA for the mission to Mars by the Pathfinder but also for the 179 brilliant apprentices that participated in the SHARP Program. Apprentice participation increased 17% over last year's total of 153 participants. As indicated by the End-of-the-Program Evaluations, 96% of the programs' participants rated the summer experience from very good to excellent. The SHARP Management Team began the year by meeting in Cocoa Beach, Florida for the annual SHARP Planning Conference. Participants strengthened their Education Division Computer Aided Tracking System (EDCATS) skills, toured the world-renowned Kennedy Space Center, and took a journey into space during the Alien Encounter Exercise. The participants returned to their Centers with the same goals and objectives in mind. The 1997 SHARP Program goals were: (1) Utilize NASA's mission, unique facilities and specialized workforce to provide exposure, education, and enrichment experiences to expand participants' career horizons and inspire excellence in formal education and lifelong learning. (2) Develop and implement innovative education reform initiatives which support NASA's Education Strategic Plan and national education goals. (3) Utilize established statistical indicators to measure the effectiveness of SHARP's program goals. (4) Explore new recruiting methods which target the student population for which SHARP was specifically designed. (5) Increase the number of participants in the program. All of the SHARP Coordinators reported that the goals and objectives for the overall program as well as their individual program goals were achieved. Some of the goals and objectives for the Centers were: (1) To increase the students' awareness of science, mathematics, engineering, and computer technology; (2) To provide students with the opportunity to broaden their career objectives; and (3) To expose students to a variety of enrichment activities. Most of the Center goals and
A sharp interpolation between the Hölder and Gaussian Young inequalities
NASA Astrophysics Data System (ADS)
da Pelo, Paolo; Lanconelli, Alberto; Stan, Aurel I.
2016-03-01
We prove a very general sharp inequality of the Hölder-Young-type for functions defined on infinite dimensional Gaussian spaces. We begin by considering a family of commutative products for functions which interpolates between the pointwise and Wick products; this family arises naturally in the context of stochastic differential equations, through Wong-Zakai-type approximation theorems, and plays a key role in some generalizations of the Beckner-type Poincaré inequality. We then obtain a crucial integral representation for that family of products which is employed, together with a generalization of the classic Young inequality due to Lieb, to prove our main theorem. We stress that our main inequality contains as particular cases the Hölder inequality and Nelson’s hyper-contractive estimate, thus providing a unified framework for two fundamental results of the Gaussian analysis.
Ferromagnetism beyond Lieb's theorem
NASA Astrophysics Data System (ADS)
Costa, Natanael C.; Mendes-Santos, Tiago; Paiva, Thereza; Santos, Raimundo R. dos; Scalettar, Richard T.
2016-10-01
The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction U is turned on, Lieb proved rigorously that at half-filling (ρ =1 ) the ground state has a nonzero spin. In this paper we consider a "CuO2 lattice" (also known as "Lieb lattice," or as a decorated square lattice), in which "d orbitals" occupy the vertices of the squares, while "p orbitals" lie halfway between two d orbitals; both d and p orbitals can accommodate only up to two electrons. We use exact determinant quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, Ud=Up , originally considered by Lieb, and the inhomogeneous (IH) case, Ud≠Up . For the H case at half-filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all U . For the IH system at half-filling, we argue that the case Up≠Ud falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases Up=0 ,Ud=U and Up=U ,Ud=0 . We found that the different environments of d and p sites lead to a ferromagnetic insulator when Ud=0 ; by contrast, Up=0 leads to to a metal without any magnetic ordering. In addition, we have also established that at density ρ =1 /3 , strong antiferromagnetic correlations set in, caused by the presence of one fermion on each
Nambu-Goldstone theorem and spin-statistics theorem
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
New double soft emission theorems
NASA Astrophysics Data System (ADS)
Cachazo, Freddy; He, Song; Yuan, Ellis Ye
2015-09-01
We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, Dirac-Born-Infeld, Einstein-Maxwell-Scalar, nonlinear sigma model and Yang-Mills-Scalar. We use the recently found Cachazo-He-Yuan representation of these theories in order to give a simple proof of the leading order part of all these theorems.
Mixing rates and limit theorems for random intermittent maps
NASA Astrophysics Data System (ADS)
Bahsoun, Wael; Bose, Christopher
2016-04-01
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps {{T}α} using the full parameter range 0<α <∞ , in general. We derive a number of results around a common theme that illustrates in detail how the constituent map that is fastest mixing (i.e. smallest α) combined with details of the randomizing process, determines the asymptotic properties of the random transformation. Our key result (theorem 1.1) establishes sharp estimates on the position of return time intervals for the quenched dynamics. The main applications of this estimate are to limit laws (in particular, CLT and stable laws, depending on the parameters chosen in the range 0<α <1 ) for the associated skew product; these are detailed in theorem 3.2. Since our estimates in theorem 1.1 also hold for 1≤slant α <∞ we study a second class of random transformations derived from piecewise affine Gaspard-Wang maps, prove existence of an infinite (σ-finite) invariant measure and study the corresponding correlation asymptotics. To the best of our knowledge, this latter kind of result is completely new in the setting of random transformations.
Sharp boundary analysis of electrostatic flute modes
Lemons, D. S.
1989-07-01
A linear, electrostatic, stability analysis of a magnetized cross-fielddrifting plasma with a sharp boundary is presented. The analysis corrects anerror in a previously published sharp boundary theory (Phys. Fluids /bold 19/,882 (1976)) and extends another theory (Geophys. Res. Lett. /bold 14/, 60(1987)) to include finite electron mass and non-neutral perturbations. Theinstability's long wavelength structure is associated with the classical fluteinstability, while the peak of the growth rate curve, at much shorterwavelengths, is a Buneman-like instability.
Quantum cryptography without Bell's theorem
NASA Astrophysics Data System (ADS)
Bennett, Charles H.; Brassard, Gilles; Mermin, N. David
1992-02-01
Ekert has described a cryptographic scheme in which Einstein-Podolsky-Rosen (EPR) pairs of particles are used to generate identical random numbers in remote places, while Bell's theorem certifies that the particles have not been measured in transit by an eavesdropper. We describe a related but simpler EPR scheme and, without invoking Bell's theorem, prove it secure against more general attacks, including substitution of a fake EPR source. Finally we show our scheme is equivalent to the original 1984 key distribution scheme of Bennett and Brassard, which uses single particles instead of EPR pairs.
Forensic Veterinary Pathology: Sharp Injuries in Animals.
de Siqueira, A; Cuevas, S E Campusano; Salvagni, F A; Maiorka, P C
2016-09-01
Sharp-force injuries are injuries caused by a mechanical force using sharp objects against the skin. Sharp-force injuries are mainly classified as stab, incised, chop, and therapeutic wounds and are less frequent than blunt-force injuries in animals. The analysis of the edges of the wound is crucial, especially if more than one type of lesion is involved. It may be difficult to differentiate between sharp trauma and blunt trauma, because lacerations can resemble incised wounds. The accurate documentation and examination of these injuries may indicate the instrument involved, the relationship between the animal and the perpetrator, and the force of the stab. Situations in which this type of trauma occurs may involve social violence, accidents, hunting, veterinary medical management, and religious rituals. The causes of death related to this type of trauma include hypovolemic shock, pneumothorax, or asphyxiation due to aspiration of blood. Necropsy findings should provide objective and unbiased information about the cause and manner of death to aid the investigation and further judgment of a possible crime.
SHARP {Summer High School Apprenticeship Research Program}
NASA Technical Reports Server (NTRS)
Glasco, Deborah (Technical Monitor)
2002-01-01
The Year 2002 was another successful year for SHARP. Even after 22 years of SHARP, the Program continues to grow. There were 12 NASA Field Installations with a total of 210 apprentices who participated in the summer 2002 Program supported by 215 mentors in the fields of science and engineering. The apprentices were chosen from a pool of 1,379 applicants. This was a record year for applications exceeding the previous year by over 60%. For the second consecutive year, the number of female participants exceeded the number of males with 53% female and 47% male participants in the program. The main thrust of our recruiting efforts is still focused on underrepresented populations; especially African American, Hispanic, and Native American. At the conclusion of the summer program, most SHARP Apprentices indicated on the EDCATS that they would be interested in pursuing careers in Aerospace (56.2%) while the second largest career choice was a job at NASA (45.7%). The smallest number (11.9%) were interested in careers in the government. The table of responses is listed in the Appendix. Once again this year we were fortunate in that the SHARP COTR, Ms. Deborah Glasco, gained the support of MURED funding sources at NASA to fully fund additional apprentices and boost the number of apprentices to 210.
Electrostatics experiments with sharp metal points
NASA Astrophysics Data System (ADS)
Ivanov, Dragia; Nikolov, Stefan
2016-11-01
In this paper we examine the phenomena that arise around an electrically charged sharp metal spike and present numerous experiments that can be used in the teaching of electrostatics. The experiments are quite spectacular and attention-grabbing while being relatively simple and easy to perform in any decently supplied physics education laboratory that is equipped with an electrostatic machine (like a Wimshurst machine).
Acoustic streaming of a sharp edge.
Ovchinnikov, Mikhail; Zhou, Jianbo; Yalamanchili, Satish
2014-07-01
Anomalous acoustic streaming is observed emanating from sharp edges of solid bodies that are vibrating in fluids. The streaming velocities can be orders of magnitude higher than expected from the Rayleigh streaming at similar amplitudes of vibration. Acoustic velocity of fluid relative to a solid body diverges at a sharp edge, giving rise to a localized time-independent body force acting on the fluid. This force results in a formation of a localized jet. Two-dimensional numerical simulations are performed to predict acoustic streaming for low amplitude vibration using two methods: (1) Steady-state solution utilizing perturbation theory and (2) direct transient solution of the Navier-Stokes equations. Both analyses agree with each other and correctly predict the streaming of a sharp-edged vibrating blade measured experimentally. The origin of the streaming can be attributed to the centrifugal force of the acoustic fluid flow around a sharp edge. The dependence of this acoustic streaming on frequency and velocity is examined using dimensional analysis. The dependence law is devised and confirmed by numerical simulations.
Sharp and the Jules Verne Launcher
Hunter, J.; Cartland, H.
1996-03-01
Lawrence Livermore National Laboratory (LLNL) has built the worlds largest hydrogen gas gun called SHARP, (Super High Altitude Research Project). Originally designed to launch 5 kg to a 450 km altitude, SHARP is configured horizontally at Site 300 in Tracy, California. SHARP is successfully delivering 5 kg scramjets at Mach 9 in aerophysics tests. Some of the results of the scramjet tests are enlightening and are presented insofar as they are relevant to future launches into space. Using a light gas gun to launch payloads into orbit has been analyzed. We look at LEO (Low Earth Orbit), GEO (Geosynchronous Earth Orbit), and LO (Lunar Orbit). We present a conceptual design for a large light gas gun called the Jules Verne Launcher (JVL). The JVL can deliver 3.3 metric tons to a 500 km low earth orbit. We anticipate one launch per day. We present the history of light gas guns, the SHARP design and performance, and the JVL design. Another section is devoted to the vehicle environment and resultant design. Lastly, we present a cost analysis. Our results indicated that the JVL will be able to deliver 1000 metric tons of payload to LEO yearly. The cost will be 5{percent} of the best US rocket delivery cost. This technology will enable the next phase of man{close_quote}s exploration of space. {copyright} {ital 1996 American Institute of Physics.}
Angle Defect and Descartes' Theorem
ERIC Educational Resources Information Center
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
Discovering the Inscribed Angle Theorem
ERIC Educational Resources Information Center
Roscoe, Matt B.
2012-01-01
Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…
Generalized Pump-restriction Theorem
Sinitsyn, Nikolai A; Chernyak, Vladimir Y
2008-01-01
We formulate conditions under which periodic modulations of parameters on a finite graph with stochastic transitions among its nodes do not lead to overall pump currents through any given link. Our theorem unifies previously known results with the new ones and provides a universal approach to explore futher restrictions on stochastic pump effect in non-adiabatically driven systems with detailed balance.
Illustrating the Central Limit Theorem
ERIC Educational Resources Information Center
Corcoran, Mimi
2016-01-01
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
Expanding the Interaction Equivalency Theorem
ERIC Educational Resources Information Center
Rodriguez, Brenda Cecilia Padilla; Armellini, Alejandro
2015-01-01
Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner) is present at a high level. This…
Arriving at the Pythagorean Theorem.
ERIC Educational Resources Information Center
Jaramillo, James; Brown, Jonathan Caius
This lesson plan uses group activity and manipulative materials to teach English-speaking students (ages 15-16) of diverse ethnic backgrounds an operatonal understanding of the Pythagorean Theorem. It is based on theories of constructivism and holism and includes teacher instructions, discussion questions, a retrospective vision, and an ancillary…
Existence Theorems for Vortices in the Aharony-Bergman-Jaferis-Maldacena Model
NASA Astrophysics Data System (ADS)
Han, Xiaosen; Yang, Yisong
2015-01-01
A series of sharp existence and uniqueness theorems are established for the multiple vortex solutions in the supersymmetric Chern-Simons-Higgs theory formalism of Aharony, Bergman, Jaferis, and Maldacena, for which the Higgs bosons and Dirac fermions lie in the bifundamental representation of the general gauge symmetry group . The governing equations are of the BPS type and derived by Kim, Kim, Kwon, and Nakajima in the mass-deformed framework labeled by a continuous parameter.
Pythagorean Theorem Proofs: Connecting Interactive Websites
ERIC Educational Resources Information Center
Lin, Cheng-Yao
2007-01-01
There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)
A Fundamental Theorem on Particle Acceleration
Xie, Ming
2003-05-01
A fundamental theorem on particle acceleration is derived from the reciprocity principle of electromagnetism and a rigorous proof of the theorem is presented. The theorem establishes a relation between acceleration and radiation, which is particularly useful for insightful understanding of and practical calculation about the first order acceleration in which energy gain of the accelerated particle is linearly proportional to the accelerating field.
A note on generalized Weyl's theorem
NASA Astrophysics Data System (ADS)
Zguitti, H.
2006-04-01
We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.
Generalizations of Ptolemy and Brahmagupta Theorems
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
Khalfin's Theorem and Neutral Mesons Subsystem
NASA Astrophysics Data System (ADS)
Urbanowski, Krzysztof
2009-01-01
The consequences of Khalfin's Theorem are discussed. we find, eg., that diagonal matrix elements of the exact effective Hamiltonian for the neutral meson complex can not be equal if CPT symmetry holds and CP symmetry is violated. Within a given model we examine numerically the Khalfin's Theorem and show in a graphic form how the Khalfin's Theorem works.
The Sharp Lepton Quandary: Reasonable cautions
Griffin, J.J.
1996-02-01
Surprisingly, the new APEX experiment designed to measure a definitive invariant mass distribution of the sharp pairs previously reported in similar heavy ion studies reports null results. Although it asserts no direct conflict with any data reported by EPOS/I, the APEX report nevertheless seems to have encouraged the view that the earlier (EPOS/I) observations were erroneous, and by extrapolation, that the whole (e{sup +}e{sup {minus}}) Puzzle data set can be dismissed as an unfortunate set of physically meaningless statistical fluctuations. We wish here to argue that such sweeping judgments should be postponed, on the grounds that (1) the published APEX analysis of their data is self-inconsistent, and can therefore sustain no valid inference about the EPOS/I data; (2) the data which supports the occurrence of sharp (e{sup +}e{sup {minus}}) pairs is much more extensive than the EPOS/I data, so that the APEX surprise must be considered as one episode in a much longer struggle finally to settle the question of whether these weak signals are significant or not; (3) a qualitative phenomenology exists which can organize the whole range of data of the Sharp Lepton Problem, and which suggests that (4) certain low energy (and low cost) experiments ought to be explored for their creation of sharp pairs; as follows: the study of pairs emitted following scattering of few MeV electron and positron beams from neutral U and Th atoms, and the study of pairs emitted following the resonant absorption of photons of 1.5 to 2.0 MeV on U and Th atoms. We first present a brief data-oriented history of the Sharp Lepton Problem, to show that no single unexpected null result can provide an adequate basis for rejecting the great range and quantity of data which evidences the occurrence of sharp pairs. We then consider the Quadronium Composite Particle Scenario for these processes, and its Quantum Electrodynamical implications, in support of the above recommendations.
Generalized Bloch theorem and chiral transport phenomena
NASA Astrophysics Data System (ADS)
Yamamoto, Naoki
2015-10-01
Bloch theorem states the impossibility of persistent electric currents in the ground state of nonrelativistic fermion systems. We extend this theorem to generic systems based on the gauged particle number symmetry and study its consequences on the example of chiral transport phenomena. We show that the chiral magnetic effect can be understood as a generalization of the Bloch theorem to a nonequilibrium steady state, similarly to the integer quantum Hall effect. On the other hand, persistent axial currents are not prohibited by the Bloch theorem and they can be regarded as Pauli paramagnetism of relativistic matter. An application of the generalized Bloch theorem to quantum time crystals is also discussed.
The de Finetti theorem for test spaces
NASA Astrophysics Data System (ADS)
Barrett, Jonathan; Leifer, Matthew
2009-03-01
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
SHARP/PRONGHORN Interoperability: Mesh Generation
Avery Bingham; Javier Ortensi
2012-09-01
Progress toward collaboration between the SHARP and MOOSE computational frameworks has been demonstrated through sharing of mesh generation and ensuring mesh compatibility of both tools with MeshKit. MeshKit was used to build a three-dimensional, full-core very high temperature reactor (VHTR) reactor geometry with 120-degree symmetry, which was used to solve a neutron diffusion critical eigenvalue problem in PRONGHORN. PRONGHORN is an application of MOOSE that is capable of solving coupled neutron diffusion, heat conduction, and homogenized flow problems. The results were compared to a solution found on a 120-degree, reflected, three-dimensional VHTR mesh geometry generated by PRONGHORN. The ability to exchange compatible mesh geometries between the two codes is instrumental for future collaboration and interoperability. The results were found to be in good agreement between the two meshes, thus demonstrating the compatibility of the SHARP and MOOSE frameworks. This outcome makes future collaboration possible.
Modeling the Geologic History of Mt. Sharp
NASA Technical Reports Server (NTRS)
Pascuzzo, A.; Allen, C.
2015-01-01
Gale is an approximately 155 km diameter crater located on the martian dichotomy boundary (5 deg S 138 deg E). Gale is estimated to have formed 3.8 - 3.5 Gya, in the late Noachian or early Hesperian. Mt. Sharp, at the center of Gale Crater, is a crescent shaped sedimentary mound that rises 5.2 km above the crater floor. Gale is one of the few craters that has a peak reaching higher than the rim of the crater wall. The Curiosity rover is currently fighting to find its way across a dune field at the northwest base of the mound searching for evidence of habitability. This study used orbital images and topographic data to refine models for the geologic history of Mt. Sharp by analyzing its morphological features. In addition, it assessed the possibility of a peak ring in Gale. The presence of a peak ring can offer important information to how Mt. Sharp was formed and eroded early in Gale's history.
The Floquet Adiabatic Theorem revisited
NASA Astrophysics Data System (ADS)
Weinberg, Phillip; Bukov, Marin; D'Alessio, Luca; Kolodrubetz, Michael; Davidson, Shainen; Polkovnikov, Anatoli
2015-03-01
The existance of the adiabatic theorem for Floquet systems has been the subject of an active debate with different articles reaching opposite conclusions over the years. In this talk we clarify the situation by deriving a systematic expansion in the time-derivatives of a slow parameter for the occupation probabilities of the Floque states. Our analysis shows that the in a certain limit the transition between Floquet eigenstates are suppressed and it is possible to define an adiabatic theorem for Floquet systems. Crucially we observe however that the conditions for adiabaticity in ordinary and Floquet systems are different and that this difference can become important when the amplitude of the periodic driving is large. We illustrate our results with specific examples of a periodically driven harmonic oscillator and cold atoms in optical lattices which are relevant in current experiments.
Equivalence theorem of uncertainty relations
NASA Astrophysics Data System (ADS)
Li, Jun-Li; Qiao, Cong-Feng
2017-01-01
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e. the variance-based ones and the entropic forms, showing that the entropy of an operator in a quantum system can be built from the variances of a set of commutative operators. This means that an uncertainty relation in the language of entropy may be mapped onto a variance-based one, and vice versa. Employing the equivalence theorem, alternative formulations of entropic uncertainty relations are obtained for the qubit system that are stronger than the existing ones in the literature, and variance-based uncertainty relations for spin systems are reached from the corresponding entropic uncertainty relations.
Navier Stokes Theorem in Hydrology
NASA Astrophysics Data System (ADS)
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
Current status of sharps waste management in the lower-level health facilities in Tanzania.
Manyele, Samwel V; Mujuni, Churchil M
2010-10-01
Sharps waste is part of infectious medical waste, management of which is a critical problem in Tanzanian health facilities. This study aimed at assessing the current status of sharps waste management in lower level health facilities (LLHFs) in Ilala Municipality in Tanzania. In this study a sample of 135 LLHFs (103 dispensaries, 13 clinics, 11 laboratories, and 8 health centers) was involved. The average number of workers per facility was 10, with positively skewed probability density function (up to 80 workers). The average patient-to-workers ratio was 5.87. About 59% of the LLHFs improvised sharps waste containers (SWCs). Sharps waste was transported by hands in 77% of LLHFs leading to high risks of exposure to needle stick injuries. Boots, aprons and masks were among the personal protective equipment (PPE) missing in most LLHFs, while latex gloves that cannot protect workers from injuries caused by sharps waste were readily available. Most facilities stored sharps waste for about 72 hours (before treatment), which is beyond the recommended maximum storage time of 24 hours. About 39.3% of LLHFs utilized on-site single-chamber incinerators for sharps waste treatment, which are of poor design, have rusted mechanical parts, short and rusted chimneys, and without automatic flame ignition burners. It is concluded that sharps waste management in LLHFs is poor, which puts workers, the public and the environment at risk of exposure to blood-borne pathogens. It is, therefore, important that the municipality should establish a waste processing center which will collect and incinerate all sharps waste.
Uniqueness Theorem for Black Objects
Rogatko, Marek
2010-06-23
We shall review the current status of uniqueness theorem for black objects in higher dimensional spacetime. At the beginning we consider static charged asymptotically flat spacelike hypersurface with compact interior with both degenerate and non-degenerate components of the event horizon in n-dimensional spacetime. We gave some remarks concerning partial results in proving uniqueness of stationary axisymmetric multidimensional solutions and winding numbers which can uniquely characterize the topology and symmetry structure of black objects.
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NASA Technical Reports Server (NTRS)
2004-01-01
This sharp, high-resolution image shows a rock target dubbed 'Robert E,' on a rock called Stone Mountain at Meridiani Planum, Mars. It is one of the highest-resolution images ever taken while looking at a rock on another planet. Scientists are studying this area, which measures 3 centimeters (1.2 inches) across, for clues about how the rock formed. The image was created by merging five separate images taken at varying distances from the target by the microscopic imager, an instrument located on the Mars Exploration Rover Opportunity's instrument deployment device, or 'arm.'
On Liouville's theorem in fluid mechanics
NASA Astrophysics Data System (ADS)
Morrison, P. J.; Bouchet, F.; Thalabard, S.; Zaboronski, O. V.
2011-11-01
Since the early work of Burgers it has been known that discretizations of fluid models possess a version of Liouville's theorem on conservation of phase space volume. In fact, spectral representations of two-dimensional turbulence are known to have a detailed version of this theorem. The existence of such Liouville theorems led many (e.g. Burgers, Lee, Kraichnan and Montgomery) to consider various statistical mechanical approaches to turbulence. We show how this theorem arises naturally from the Hamiltonian structure of inviscid fluid equations.
Cosmological perturbations and the Weinberg theorem
Akhshik, Mohammad; Firouzjahi, Hassan; Jazayeri, Sadra E-mail: firouz@ipm.ir
2015-12-01
The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.
Fluctuation theorem for partially masked nonequilibrium dynamics
NASA Astrophysics Data System (ADS)
Shiraishi, Naoto; Sagawa, Takahiro
2015-01-01
We establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production satisfies the integral fluctuation theorem. Our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines. In particular, our result gives a unified fluctuation theorem for both autonomous and nonautonomous Maxwell's demons, where mutual information plays a crucial role. Furthermore, we derive a fluctuation-dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations.
The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces
NASA Astrophysics Data System (ADS)
Huang, Jianhua
2005-12-01
In this paper we present some new matching theorems with open cover and closed cover by using the generalized R-KKM theorems [L. Deng, X. Xia, Generalized R-KKM theorem in topological space and their applications, J. Math. Anal. Appl. 285 (2003) 679-690] in the topological spaces with property (H). As applications, some coincidence theorems are established in topological spaces. Our results extend and generalize some known results.
Uniqueness theorems in bioluminescence tomography.
Wang, Ge; Li, Yi; Jiang, Ming
2004-08-01
Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case the BLT solution is not unique by constructing the set of all the solutions to this inverse problem. Then, we show the uniqueness of the solution in the case of impulse sources. Finally, we present our main theorem that solid/hollow ball sources can be uniquely determined up to nonradiating sources. For better readability, the exact conditions for and rigorous proofs of the theorems are given in the Appendices. Further research directions are also discussed.
Green's function asymptotics and sharp interpolation inequalities
NASA Astrophysics Data System (ADS)
Zelik, S. V.; Ilyin, A. A.
2014-04-01
A general method is proposed for finding sharp constants for the embeddings of the Sobolev spaces H^m(\\mathscr{M}) on an n-dimensional Riemannian manifold \\mathscr{M} into the space of bounded continuous functions, where m\\gt n/2. The method is based on an analysis of the asymptotics with respect to the spectral parameter of the Green's function of an elliptic operator of order 2m whose square root has domain determining the norm of the corresponding Sobolev space. The cases of the n-dimensional torus {T}^n and the n-dimensional sphere {S}^n are treated in detail, as well as certain manifolds with boundary. In certain cases when \\mathscr{M} is compact, multiplicative inequalities with remainder terms of various types are obtained. Inequalities with correction terms for periodic functions imply an improvement for the well-known Carlson inequalities. Bibliography: 28 titles.
NASA Astrophysics Data System (ADS)
Ruderman, M. S.; Petrukhin, N. S.; Pelinovsky, E.
2016-04-01
We study kink oscillations of thin magnetic tubes. We assume that the density inside and outside the tube (and possibly also the cross-section radius) can vary along the tube. This variation is assumed to be of such a form that the kink speed is symmetric with respect to the tube centre and varies monotonically from the tube ends to the tube centre. Then we prove a theorem stating that the ratio of periods of the fundamental mode and first overtone is a monotonically increasing function of the ratio of the kink speed at the tube centre and the tube ends. In particular, it follows from this theorem that the period ratio is lower than two when the kink speed increases from the tube ends to its centre, while it is higher than two when the kink speed decreases from the tube ends to its centre. The first case is typical for non-expanding coronal magnetic loops, and the second for prominence threads. We apply the general results to particular problems. First we consider kink oscillations of coronal magnetic loops. We prove that, under reasonable assumptions, the ratio of the fundamental period to the first overtone is lower than two and decreases when the loop size increases. The second problem concerns kink oscillations of prominence threads. We consider three internal density profiles: generalised parabolic, Gaussian, and Lorentzian. Each of these profiles contain the parameter α that is responsible for its sharpness. We calculate the dependence of the period ratio on the ratio of the mean to the maximum density. For all considered values of α we find that a formula relating the period ratio and the ratio of the mean and maximum density suggested by Soler, Goossens, and Ballester ( Astron. Astrophys. 575, A123, 2015) gives a sufficiently good approximation to the exact dependence.
Bring the Pythagorean Theorem "Full Circle"
ERIC Educational Resources Information Center
Benson, Christine C.; Malm, Cheryl G.
2011-01-01
Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…
TAUBERIAN THEOREMS FOR MATRIX REGULAR VARIATION
MEERSCHAERT, M. M.; SCHEFFLER, H.-P.
2013-01-01
Karamata’s Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated. PMID:24644367
Visualizing the Central Limit Theorem through Simulation
ERIC Educational Resources Information Center
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
The Pythagorean Theorem: I. The finite case
Kadison, Richard V.
2002-01-01
The Pythagorean Theorem and variants of it are studied. The variations evolve to a formulation in terms of noncommutative, conditional expectations on von Neumann algebras that displays the theorem as the basic result of noncommutative, metric, Euclidean Geometry. The emphasis in the present article is finite dimensionality, both “discrete” and “continuous.” PMID:11929992
A Note on Morley's Triangle Theorem
ERIC Educational Resources Information Center
Mueller, Nancy; Tikoo, Mohan; Wang, Haohao
2012-01-01
In this note, we offer a proof of a variant of Morley's triangle theorem, when the exterior angles of a triangle are trisected. We also offer a generalization of Morley's theorem when angles of an "n"-gon are "n"-sected. (Contains 9 figures.)
The Classical Version of Stokes' Theorem Revisited
ERIC Educational Resources Information Center
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
General Theorems about Homogeneous Ellipsoidal Inclusions
ERIC Educational Resources Information Center
Korringa, J.; And Others
1978-01-01
Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)
Using Pictures to Enhance Students' Understanding of Bayes' Theorem
ERIC Educational Resources Information Center
Trafimow, David
2011-01-01
Students often have difficulty understanding algebraic proofs of statistics theorems. However, it sometimes is possible to prove statistical theorems with pictures in which case students can gain understanding more easily. I provide examples for two versions of Bayes' theorem.
A fluidized granular medium as an instance of the Fluctuation theorem
NASA Astrophysics Data System (ADS)
Menon, Narayanan; Feitosa, Klebert
2003-03-01
Recent theoretical work by Gallavotti and Cohen has led to a theorem on the spectrum of fluctuations in the entropy production rate of a driven nonequilibrium steady state. This fluctuation theorem has been difficult to experimentally illustrate in a macroscopic system because the fluctuations are typically too small to apply strong tests of the results of the theorem. We apply the theorem's result to a particulate system where fluctuations are quite large. The experimental quantities we study are the fluctuations in the flux of power and momentum into a small volume of a 2D vibration-fluidized granular medium. We find that the ratio of the probabilities of a positive and a negative fluctuation of a given amplitude is approximately exponential in that amplitude. We acknowledge support from NSF DMR-9874833.
On the Theorem of Correspondence.
Krøjgaard, Peter
2017-03-01
In a recent paper, Mammen (Integrative Psychological and Behavioral Science, 50, 196-233, 2016a) brought novel arguments into the discussion concerning the importance of being able to single out and track objects through space and time. Mammen offered a formal account of two basic, yet distinct, ways in which we as human beings encounter objects in the real world, that is, sense and choice categories. In this paper I discuss aspects of his theory and in particular the Theorem of Correspondence. I shall attempt to argue that Mammen's formal account is indeed a novel and powerful analytical generic tool allowing us to see the important relevance in different domains of being able to establish choice categories. Meanwhile, I will attempt to show that evidence from the so-called multiple object tracking studies -- even though these use highly artificial stimuli -- provide compelling evidence in support of Mammen's formal account.
Singlet and triplet instability theorems
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Posterior Probability and Fluctuation Theorem in Stochastic Processes
NASA Astrophysics Data System (ADS)
Ohkubo, Jun
2009-12-01
A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via Bayes’ theorem. In conventional fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when suitable assumptions are employed.
Consideration of vision and picture quality: psychological effects induced by picture sharpness
NASA Astrophysics Data System (ADS)
Kusaka, Hideo
1989-08-01
A psychological hierarchy model of human vision(1)(2) suggests that the visual signals are processed in a serial manner from lower to higher stages: that is "sensation" - "perception" - "emotion." For designing a future television system, it is important to find out what kinds of physical factors affect the "emotion" experienced by an observer in front of the display. This paper describes the psychological effects induced by the sharpness of the picture. The subjective picture quality was evaluated for the same pictures with five different levels of sharpness. The experiment was performed on two kinds of printed pictures: (A) a woman's face, and (B) a town corner. From these experiments, it was found that the amount of high-frequency peaking (physical value of the sharpness) which psychologically gives the best picture quality, differs between pictures (A) and (B). That is, the optimum picture sharpness differs depending on the picture content. From these results, we have concluded that the psychophysical sharpness of the picture is not only determined at the stage of "perception" (e.g., resolution or signal to noise ratio, which everyone can judge immediately), but also at the stage of "emotion" (e.g., sensation of reality or beauty).
A computational method for sharp interface advection
Bredmose, Henrik; Jasak, Hrvoje
2016-01-01
We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of arbitrary polyhedral cells. The algorithm is based on the volume of fluid (VOF) idea of calculating the volume of one of the fluids transported across the mesh faces during a time step. The novelty of the isoAdvector concept consists of two parts. First, we exploit an isosurface concept for modelling the interface inside cells in a geometric surface reconstruction step. Second, from the reconstructed surface, we model the motion of the face–interface intersection line for a general polygonal face to obtain the time evolution within a time step of the submerged face area. Integrating this submerged area over the time step leads to an accurate estimate for the total volume of fluid transported across the face. The method was tested on simple two-dimensional and three-dimensional interface advection problems on both structured and unstructured meshes. The results are very satisfactory in terms of volume conservation, boundedness, surface sharpness and efficiency. The isoAdvector method was implemented as an OpenFOAM® extension and is published as open source. PMID:28018619
Sharp Tips on the Atomic Force Microscope
NASA Technical Reports Server (NTRS)
2008-01-01
This image shows the eight sharp tips of the NASA's Phoenix Mars Lander's Atomic Force Microscope, or AFM. The AFM is part of Phoenix's Microscopy, Electrochemistry, and Conductivity Analyzer, or MECA.
The microscope maps the shape of particles in three dimensions by scanning them with one of the tips at the end of a beam. For the AFM image taken, the tip at the end of the upper right beam was used. The tip pointing up in the enlarged image is the size of a smoke particle at its base, or 2 microns. This image was taken with a scanning electron microscope before Phoenix launched on August 4, 2007.
The AFM was developed by a Swiss-led consortium in collaboration with Imperial College London.
The Phoenix Mission is led by the University of Arizona, Tucson, on behalf of NASA. Project management of the mission is by NASA's Jet Propulsion Laboratory, Pasadena, Calif. Spacecraft development is by Lockheed Martin Space Systems, Denver.
The Pythagorean Theorem and the Solid State
NASA Astrophysics Data System (ADS)
Kelly, Brenda S.; Splittgerber, Allen G.
2005-05-01
Solid-state parameters such as radius ratios, packing efficiencies, and crystal densities may be calculated for various crystal structures from basic Euclidean geometry relating to the Pythagorean theorem of right triangles. Because simpler cases are often discussed in the standard inorganic chemistry texts, this article only presents calculations for closest-packed A-type lattices (one type of particle) and several compound AB lattices (A and B particles) including sodium chloride, cesium chloride, zinc blende (sphalerite), wurtzite, and fluorite. For A-type metallic crystals, the use of recommended values of atomic radii results in calculated densities within 1% of observed values. For AB lattices, assuming ionic crystals, the use of recommended values of ionic radii results in density determinations that are usually but not always close to observed values. When there is covalent character to the bonding, the use of covalent radii results in calculated densities that correlate well with observed values. If interionic or interatomic spacings are used, the calculated densities are always close to the observed values. As indicated by a survey of the standard inorganic texts, these calculations are generally not presented. However, as an illustration of the application of simple mathematical principles to the study of chemistry, discussion of the methods presented in this manuscript may be of value in classroom presentations pertaining to the solid state.
Analogues of Chernoff's theorem and the Lie-Trotter theorem
Neklyudov, Alexander Yu
2009-10-31
This paper is concerned with the abstract Cauchy problem .x=Ax, x(0)=x{sub 0} element of D(A), where A is a densely defined linear operator on a Banach space X. It is proved that a solution x( {center_dot} ) of this problem can be represented as the weak limit lim {sub n{yields}}{sub {infinity}}{l_brace}F(t/n){sup n}x{sub 0}{r_brace}, where the function F:[0,{infinity}){yields}L(X) satisfies the equality F'(0)y=Ay, y element of D(A), for a natural class of operators. As distinct from Chernoff's theorem, the existence of a global solution to the Cauchy problem is not assumed. Based on this result, necessary and sufficient conditions are found for the linear operator C to be closable and for its closure to be the generator of a C{sub 0}-semigroup. Also, we obtain new criteria for the sum of two generators of C{sub 0}-semigroups to be the generator of a C{sub 0}-semigroup and for the Lie-Trotter formula to hold. Bibliography: 13 titles.
Kato type operators and Weyl's theorem
NASA Astrophysics Data System (ADS)
Duggal, B. P.; Djordjevic, S. V.; Kubrusly, Carlos
2005-09-01
A Banach space operator T satisfies Weyl's theorem if and only if T or T* has SVEP at all complex numbers [lambda] in the complement of the Weyl spectrum of T and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity. If T* (respectively, T) has SVEP and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity (respectively, T is Kato type at all [lambda][set membership, variant]iso[sigma](T)), then T satisfies a-Weyl's theorem (respectively, T* satisfies a-Weyl's theorem).
The Lax-Onsager regression `theorem' revisited
NASA Astrophysics Data System (ADS)
Lax, Melvin
2000-05-01
It is stated by Ford and O'Connell in this festschrift issue and elsewhere that "there is no quantum regression theorem" although Lax "obtained a formula for correlation in a driven quantum system that has come to be called the quantum regression theorem". This produces a puzzle: "How can it be that a non-existent theorem gives correct results?" Clarification will be provided in this paper by a description of the Lax procedure, with a quantitative estimate of the error for a damped harmonic oscillator based on expressions published in the 1960's.
Enhancements to the SHARP Build System and NEK5000 Coupling
McCaskey, Alex; Bennett, Andrew R.; Billings, Jay Jay
2014-10-01
The SHARP project for the Department of Energy's Nuclear Energy Advanced Modeling and Simulation (NEAMS) program provides a multiphysics framework for coupled simulations of advanced nuclear reactor designs. It provides an overall coupling environment that utilizes custom interfaces to couple existing physics codes through a common spatial decomposition and unique solution transfer component. As of this writing, SHARP couples neutronics, thermal hydraulics, and structural mechanics using PROTEUS, Nek5000, and Diablo respectively. This report details two primary SHARP improvements regarding the Nek5000 and Diablo individual physics codes: (1) an improved Nek5000 coupling interface that lets SHARP achieve a vast increase in overall solution accuracy by manipulating the structure of the internal Nek5000 spatial mesh, and (2) the capability to seamlessly couple structural mechanics calculations into the framework through improvements to the SHARP build system. The Nek5000 coupling interface now uses a barycentric Lagrange interpolation method that takes the vertex-based power and density computed from the PROTEUS neutronics solver and maps it to the user-specified, general-order Nek5000 spectral element mesh. Before this work, SHARP handled this vertex-based solution transfer in an averaging-based manner. SHARP users can now achieve higher levels of accuracy by specifying any arbitrary Nek5000 spectral mesh order. This improvement takes the average percentage error between the PROTEUS power solution and the Nek5000 interpolated result down drastically from over 23 % to just above 2 %, and maintains the correct power profile. We have integrated Diablo into the SHARP build system to facilitate the future coupling of structural mechanics calculations into SHARP. Previously, simulations involving Diablo were done in an iterative manner, requiring a large amount manual work, and left only as a task for advanced users. This report will detail a new Diablo build system that
Hippocampal sharp waves: their origin and significance.
Buzsáki, G
1986-11-29
This study investigated the spatial distribution and cellular-synaptic generation of hippocampal sharp waves (SPW) in the dorsal hippocampus of the awake rat. Depth analyses of SPWs were performed by stepping the recording electrode in 82.5 microns increments. SPWs were present during slow wave sleep, awake immobility, drinking, grooming and eating (0.01-2/s). The largest negative SPWs were recorded from the middle part of the stratum radiatum of CA1, the stratum lucidum of CA3, the inner molecular layer of the dentate gyrus and from layer I of the subiculum, in that order. The polarity of the SPWs was positive in layers II-IV of the subiculum, in stratum oriens and stratum pyramidale of CA1 and CA3, and in the hilus of the dentate gyrus. The electrical gradients across the null zones of the field SPWs were as large as 8-14 mV/mm. SPWs were associated with population bursts of pyramidal cells and increased discharges of interneurons and granule cells. During the SPW the excitability of granule cells and pyramidal cells to afferent volleys increased considerably. Picrotoxin and atropine and aspiration lesion of the fimbria-fornix increased either the amplitude or the frequency of SPWs. Diazepam and Nembutal could completely abolish SPWs. It is suggested that: hippocampal SPWs are triggered by a population burst of CA3 pyramidal cells as a result of temporary disinhibition from afferent control; and field SPWs represent summed extracellular PSPs of CA1 and subicular pyramidal cells, and dentate granular cells induced by the Schaffer collaterals and the associational fibers of hilar cells, respectively. The relevance of the physiological SPWs to epileptic interictal spikes and long-term potentiation is discussed.
Comparison theorems for causal diamonds
NASA Astrophysics Data System (ADS)
Berthiere, Clément; Gibbons, Gary; Solodukhin, Sergey N.
2015-09-01
We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the redshift factor which, as we show explicitly in the spherically symmetric case, is monotonic in the radial direction, and it takes its maximal value at the center. As a by-product of our discussion we rederive Bishop's inequality without assuming the positivity of the spatial Ricci tensor. We then generalize our considerations to arbitrary, static and not necessarily spherically symmetric, asymptotically flat spacetimes. In the case of spacetimes with a horizon our generalization involves the so-called domain of dependence. The respective volume, expressed in terms of the duration measured by a distant observer compared with the volume of the domain in Minkowski spacetime, exhibits behaviors which differ if d =4 or d >4 . This peculiarity of four dimensions is due to the logarithmic subleading term in the asymptotic expansion of the metric near infinity. In terms of the invariant duration measured by a comoving observer associated with the diamond we establish an inequality which is universal for all d . We suggest some possible applications of our results including comparison theorems for entanglement entropy, causal set theory, and fundamental limits on computation.
Duality Theorems in Ergodic Transport
NASA Astrophysics Data System (ADS)
Lopes, Artur O.; Mengue, Jairo K.
2012-11-01
We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose σ is the shift acting on Bernoulli space X={1,2,…, d}ℕ, and, consider a fixed continuous cost function c: X× X→ℝ. Denote by Π the set of all Borel probabilities π on X× X, such that, both its x and y marginals are σ-invariant probabilities. We are interested in the optimal plan π which minimizes ∫ c dπ among the probabilities in Π. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on c. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs c the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan π by convex combinations of plans such that the support projects in periodic orbits.
Structure theorem for Vaisman completely solvable solvmanifolds
NASA Astrophysics Data System (ADS)
Sawai, Hiroshi
2017-04-01
Locally conformal Kähler manifold is said to be a Vaisman manifold if the Lee form is parallel with respect to the Riemannian metric. In this paper, we have the structure theorem for Vaisman completely solvable solvmanifolds.
ALGEBRAIC DEPENDENCE THEOREMS ON COMPLEX PSEUDOCONCAVE SPACES
The notion of pseudoconcave space is introduced and classical theorems on algebraic dependence of meromorphic functions are extended for this new class of spaces and for sections in a coherent sheaf. (Author)
[Count on your beliefs. Bayes' theorem in diagnosis].
Taube, A; Malmquist, J
2001-06-13
Bayesian analysis of data finds increasing use in medical statistics, diagnostic evaluation and decision analysis. The central element in bayesian analysis is a set of mathematical rules for integrated evaluation of prior knowledge and new information. In many situations this approach has superior ability to deliver dependable updated knowledge and to provide an optimal probability basis for decisions. This article (the first of two) presents Bayes' theorem and its application in diagnostic work. It is explained how likelihood ratios of diagnostic tests interact with the outcome of such tests in the conversion of initial information (prior odds) to enhanced information (posterior odds).
Sahoo- and Wayment-Type Integral Mean Value Theorems
ERIC Educational Resources Information Center
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
The Great Emch Closure Theorem and a combinatorial proof of Poncelet's Theorem
NASA Astrophysics Data System (ADS)
Avksentyev, E. A.
2015-11-01
The relations between the classical closure theorems (Poncelet's, Steiner's, Emch's, and the zigzag theorems) and some of their generalizations are discussed. It is known that Emch's Theorem is the most general of these, while the others follow as special cases. A generalization of Emch's Theorem to pencils of circles is proved, which (by analogy with the Great Poncelet Theorem) can be called the Great Emch Theorem. It is shown that the Great Emch and Great Poncelet Theorems are equivalent and can be derived one from the other using elementary geometry, and also that both hold in the Lobachevsky plane as well. A new closure theorem is also obtained, in which the construction of closure is slightly more involved: closure occurs on a variable circle which is tangent to a fixed pair of circles. In conclusion, a combinatorial proof of Poncelet's Theorem is given, which deduces the closure principle for an arbitrary number of steps from the principle for three steps using combinatorics and number theory. Bibliography: 20 titles.
A Converse of Fermat's Little Theorem
ERIC Educational Resources Information Center
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
A Physical Proof of the Pythagorean Theorem
NASA Astrophysics Data System (ADS)
Treeby, David
2017-02-01
What proof of the Pythagorean theorem might appeal to a physics teacher? A proof that involved the notion of mass would surely be of interest. While various proofs of the Pythagorean theorem employ the circumcenter and incenter of a right-angled triangle, we are not aware of any proof that uses the triangle's center of mass. This note details one such proof. Though far from the most elegant approach, we believe it to be novel.
Littlewood-Paley Theorem for Schrodinger Operators
2006-07-26
26 JUL 2006 2. REPORT TYPE 3. DATES COVERED 00-00-2006 to 00-00-2006 4. TITLE AND SUBTITLE Littlewood -Paley theorem for Schrodinger operators...associated with H are well defined. We further give a Littlewood -Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes...unclassified c THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 LITTLEWOOD -PALEY THEOREM FOR SCHRÖDINGER
Reinterpreting the Sharp Edges of Planetary Rings
NASA Astrophysics Data System (ADS)
Rimlinger, Thomas; Hamilton, Douglas P.; Hahn, Joseph M.
2016-10-01
Narrow ringlets are found throughout the Solar System and are typically 1-100 km wide. Angular momentum, L, is the key to understanding how narrow rings remain confined; L2 ∝ a(1 - e2) for semimajor axis a and eccentricity e. In a circular ring, L conservation demands that the ring quickly spread apart when some colliding particles lose energy while others gain it. By contrast, in an eccentric ring, energy loss and the associated decay of the average semi-major axes can be offset by a decrease in the average eccentricity. We argue that a ring's lifetime can be greatly extended if particles arrange themselves in this way (Borderies et al. 1984). The key difference of our model, however, is that rings need not be shepherded and can confine themselves provided they are sufficiently eccentric. Satellites merely extend the rings' lifespans by pumping up their eccentricities.This confinement mechanism can explain the existence and longevity of narrow ringlets in a variety of contexts. Saturn's Titan ringlet, which is quite circular, may nevertheless be able to confine itself indefinitely if its eccentricity decay is balanced by the increase from the resonance with Titan. Preliminary simulations presented by Rimlinger et al. at this year's DDA Conference have verified that this ring can self-confine even in the absence of any satellite; we update these findings with new results that include the effects of Titan. Furthermore, Mimas' resonance with the edge of the B ring may excite its higher order modes to similar effect. We update the findings of Hahn and Spitale (2013), who used artificial forces to confine the B ring's edge, and suggest that with a suitable viscosity and density, no such forces will be needed to keep the edge sharp. Finally, a ring that is "born" with a sufficiently high eccentricity may live for hundreds of millions or even billions of years in isolation if the rate of decay is slow enough. We present simulations exploring such a scenario.
Analysis of sharps injury occurrences at a hospital in Singapore.
Ng, Leng Nee; Lim, Hui Li; Chan, Yiong Huak; Bin Bachok, Dzulazwan
2002-10-01
Relatively little attention has been directed to investigating the risks of sharps injuries in Singapore. This study examines the epidemiology and causes of sharps injuries at a university teaching hospital. The type of instruments, site of injuries and personnel involved in each sharps injury were determined retrospectively by reviewing the Incident Reports forms and Infection Control records between 1997 and 2000. Descriptive information on the forms and records were extracted and collected on standard charts. The data were then analysed using SPSS Windows software. The rates of sharps injuries were 11.0 per 100 medical staff and 6.9 per 100 nursing staff. Medical staff yielded highest proportion of sharps injuries rendering 33 cases (40.2%), followed by 24 cases involving nursing staff (29.3%) and 12 cases of nursing students (14.6%). In total, 62.2% of injuries were caused by hollow bore needles (51 cases). Non-hollow bore needle injuries only accounted for 17.1% of total injuries (14 cases). Hollow bore needles accounted for the highest proportion of sharps injuries in this study, corresponding to findings in other studies. Rates of injuries were similar to the rates found at another local hospital. At the hospital studied, sharps with safety features had effectively produced no reported cases of sharps injuries.
Shahmoradi, Ali; Reinecke, Lisa; Kroos, Christina; Wichert, Sven P.; Oster, Henrik; Wehr, Michael C.; Taneja, Reshma; Hirrlinger, Johannes; Rossner, Moritz J.
2014-01-01
Increasing evidence suggests that clock genes may be implicated in a spectrum of psychiatric diseases, including sleep and mood related disorders as well as schizophrenia. The bHLH transcription factors SHARP1/DEC2/BHLHE41 and SHARP2/DEC1/BHLHE40 are modulators of the circadian system and SHARP1/DEC2/BHLHE40 has been shown to regulate homeostatic sleep drive in humans. In this study, we characterized Sharp1 and Sharp2 double mutant mice (S1/2-/-) using online EEG recordings in living animals, behavioral assays and global gene expression profiling. EEG recordings revealed attenuated sleep/wake amplitudes and alterations of theta oscillations. Increased sleep in the dark phase is paralleled by reduced voluntary activity and cortical gene expression signatures reveal associations with psychiatric diseases. S1/2-/- mice display alterations in novelty induced activity, anxiety and curiosity. Moreover, mutant mice exhibit impaired working memory and deficits in prepulse inhibition resembling symptoms of psychiatric diseases. Network modeling indicates a connection between neural plasticity and clock genes, particularly for SHARP1 and PER1. Our findings support the hypothesis that abnormal sleep and certain (endo)phenotypes of psychiatric diseases may be caused by common mechanisms involving components of the molecular clock including SHARP1 and SHARP2. PMID:25340473
Theoretical performance characteristics of sharp-lip inlets at subsonic speeds
NASA Technical Reports Server (NTRS)
Fradenburgh, Evan A; Demarquis, D Wyatt
1954-01-01
A method is presented for the estimation of the subsonic-flight-speed characteristics of sharp-lip inlets applicable to supersonic aircraft. The analysis, based on a simple momentum balance consideration, permits the computation of inlet-pressure-recovery mass-flow relations and additive-drag coefficients for forward velocities from zero to the speed of sound. The penalties for operation of a sharp-lip inlet at velocity ratios other than 1.0 may be severe; at lower velocity ratios an additive drag is incurred that is not cancelled by lip suction, while at higher velocity ratios, unavoidable losses in inlet total pressure will result. In particular, at the take-off condition, the total pressure and the mass flow for a choked inlet are only 79 percent of the values ideally attainable with a rounded lip. The test specimens were polished and unnotched. The manufacturer of the material, the Aluminum Company of America, has made axial-load tests on 24S-T4 and 75S-T6 rod material. The test techniques used at the three laboratories are described in detail; the test results are presented and are compared with each other and with results obtained on unpolished sheet by the National Bureau of Standards. Experimental data obtained at zero speed with a sharp-lip supersonic inlet model were in substantial agreement with the theoretical results. (author)
S-HARP: A parallel dynamic spectral partitioner
Sohn, A.; Simon, H.
1998-01-01
Computational science problems with adaptive meshes involve dynamic load balancing when implemented on parallel machines. This dynamic load balancing requires fast partitioning of computational meshes at run time. The authors present in this report a fast parallel dynamic partitioner, called S-HARP. The underlying principles of S-HARP are the fast feature of inertial partitioning and the quality feature of spectral partitioning. S-HARP partitions a graph from scratch, requiring no partition information from previous iterations. Two types of parallelism have been exploited in S-HARP, fine grain loop level parallelism and coarse grain recursive parallelism. The parallel partitioner has been implemented in Message Passing Interface on Cray T3E and IBM SP2 for portability. Experimental results indicate that S-HARP can partition a mesh of over 100,000 vertices into 256 partitions in 0.2 seconds on a 64 processor Cray T3E. S-HARP is much more scalable than other dynamic partitioners, giving over 15 fold speedup on 64 processors while ParaMeTiS1.0 gives a few fold speedup. Experimental results demonstrate that S-HARP is three to 10 times faster than the dynamic partitioners ParaMeTiS and Jostle on six computational meshes of size over 100,000 vertices.
Anti-Bell - Refutation of Bell's theorem
NASA Astrophysics Data System (ADS)
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
Ergodic theorem, ergodic theory, and statistical mechanics
Moore, Calvin C.
2015-01-01
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697
Republication of: A theorem on Petrov types
NASA Astrophysics Data System (ADS)
Goldberg, J. N.; Sachs, R. K.
2009-02-01
This is a republication of the paper “A Theorem on Petrov Types” by Goldberg and Sachs, Acta Phys. Pol. 22 (supplement), 13 (1962), in which they proved the Goldberg-Sachs theorem. The article has been selected for publication in the Golden Oldies series of General Relativity and Gravitation. Typographical errors of the original publication were corrected by the editor. The paper is accompanied by a Golden Oldie Editorial containing an editorial note written by Andrzej Krasiński and Maciej Przanowski and Goldberg’s brief autobiography. The editorial note explains some difficult parts of the proof of the theorem and discusses the influence of results of the paper on later research.
Applications of AI for automated monitoring - The SHARP system
NASA Technical Reports Server (NTRS)
Atkinson, David J.; James, Mark L.
1990-01-01
This paper describes a software system which utilizes artificial intelligence technology to automate several real-time mission operations functions. The paper gives an overview of Voyager spacecraft telecommunications operations at the Jet Propulsion Laboratory to highlight requirements for operations automation in the area of real-time monitoring and analysis. A knowledge-based system, called the 'Spacecraft Health Automated Reasoning Prototype' (SHARP), was developed to explore methods for automated ground data system health and status analysis. The prototype system was applied to Voyager spacecraft telecommunications operations, and installed in the Voyager real-time telecommunications operations area during the spacecraft's encounter with the planet Neptune. The paper reviews the design of the fault detection and diagnosis portions of SHARP, and discusses the performance of SHARP during the encounter. Two follow-on systems based on SHARP which are now in development are also discussed.
Sharp tipped plastic hollow microneedle array by microinjection moulding
NASA Astrophysics Data System (ADS)
Yung, K. L.; Xu, Yan; Kang, Chunlei; Liu, H.; Tam, K. F.; Ko, S. M.; Kwan, F. Y.; Lee, Thomas M. H.
2012-01-01
A method of producing sharp tipped plastic hollow microneedle arrays using microinjection moulding is presented in this paper. Unlike traditional approaches, three mould inserts were used to create the sharp tips of the microneedles. Mould inserts with low surface roughness were fabricated using a picosecond laser machine. Sharp tipped plastic hollow microneedles 500 µm in height were fabricated using a microinjection moulding machine developed by the authors’ group. In addition, the strength of the microneedle was studied by simulation and penetration experiments. Results show that the microneedles can penetrate into skin, delivering liquid successfully without any breakage or severe deformation. Techniques presented in this paper can be used to fabricate sharp tipped plastic hollow microneedle arrays massively with low cost.
Eccentric neurosurgical virtuoso: the life and times of William Sharpe.
Rehder, Roberta; Cohen, Alan R
2015-07-01
William Sharpe was an intriguing figure in the history of American neurosurgery. He was an extraordinarily bright and gifted man who led a flamboyant, colorful, and unconventional life. He had an international impact on the field of neurosurgery during the first half of the 20th century, yet few practicing neurosurgeons know his name. In this report, the authors discuss Sharpe's contributions to neurosurgery along with the remarkable quirkiness that came to define his professional and personal life.
The sharp constant in Markov's inequality for the Laguerre weight
Sklyarov, Vyacheslav P
2009-06-30
We prove that the polynomial of degree n that deviates least from zero in the uniformly weighted metric with Laguerre weight is the extremal polynomial in Markov's inequality for the norm of the kth derivative. Moreover, the corresponding sharp constant does not exceed (8{sup k} n {exclamation_point} k {exclamation_point})/((n-k){exclamation_point} (2k){exclamation_point}). For the derivative of a fixed order this bound is asymptotically sharp as n{yields}{infinity}. Bibliography: 20 items.
Atomic layer engineering of perovskite oxides for chemically sharp heterointerfaces.
Choi, Woo Seok; Rouleau, Christopher M; Seo, Sung Seok A; Luo, Zhenlin; Zhou, Hua; Fister, Timothy T; Eastman, Jeffrey A; Fuoss, Paul H; Fong, Dillon D; Tischler, Jonathan Z; Eres, Gyula; Chisholm, Matthew F; Lee, Ho Nyung
2012-12-18
Atomic layer engineering enables fabrication of a chemically sharp oxide heterointerface. The interface formation and strain evolution during the initial growth of LaAlO(3) /SrTiO(3) heterostructures by pulsed laser deposition are investigated in search of a means for controlling the atomic-sharpness of the interface. This study shows that inserting a monolayer of LaAlO(3) grown at high oxygen pressure dramatically enhances interface abruptness.
Method of forming a sharp edge on an optical device
NASA Technical Reports Server (NTRS)
Fleetwood, C. M.; Rice, S. H.
1980-01-01
A sharp edge is formed on an optical device by placing the optical device in a holding mechanism; grinding one surface so that it and a surface of the holding mechanism are co-planar; and polishing both the surface of the optical device and the surface of the holding mechanism with felt until an edge on the surface of the optical device adjacent to the surface of the holding mechanism obtains a desired sharpness.
Effects of registration regularization and atlas sharpness on segmentation accuracy.
Yeo, B T Thomas; Sabuncu, Mert R; Desikan, Rahul; Fischl, Bruce; Golland, Polina
2008-10-01
In non-rigid registration, the tradeoff between warp regularization and image fidelity is typically determined empirically. In atlas-based segmentation, this leads to a probabilistic atlas of arbitrary sharpness: weak regularization results in well-aligned training images and a sharp atlas; strong regularization yields a "blurry" atlas. In this paper, we employ a generative model for the joint registration and segmentation of images. The atlas construction process arises naturally as estimation of the model parameters. This framework allows the computation of unbiased atlases from manually labeled data at various degrees of "sharpness", as well as the joint registration and segmentation of a novel brain in a consistent manner. We study the effects of the tradeoff of atlas sharpness and warp smoothness in the context of cortical surface parcellation. This is an important question because of the increasingly availability of atlases in public databases, and the development of registration algorithms separate from the atlas construction process. We find that the optimal segmentation (parcellation) corresponds to a unique balance of atlas sharpness and warp regularization, yielding statistically significant improvements over the FreeSurfer parcellation algorithm. Furthermore, we conclude that one can simply use a single atlas computed at an optimal sharpness for the registration-segmentation of a new subject with a pre-determined, fixed, optimal warp constraint. The optimal atlas sharpness and warp smoothness can be determined by probing the segmentation performance on available training data. Our experiments also suggest that segmentation accuracy is tolerant up to a small mismatch between atlas sharpness and warp smoothness.
An invariance theorem in acoustic scattering theory
NASA Astrophysics Data System (ADS)
Ha-Duong, T.
1996-10-01
Karp's theorem states that if the far-field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle is invariant under the group of orthogonal transformations in 0266-5611/12/5/007/img1 (rotations in 0266-5611/12/5/007/img2), then the scatterer is a sphere (circle). The theorem is generalized to the case where the invariant group of the far field pattern is only a subgroup of the orthogonal group, and for a class of mixed boundary conditions.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.
Haptic Perception of Edge Sharpness in Real and Virtual Environments.
Park, Jaeyoung; Provancher, William; Tan, Hong Z
2016-09-21
We investigate the accuracy with which the haptic sharpness perception of a virtual edge is matched to that of a real edge and the effect of the virtual surface stiffness on the match. The perceived sharpness of virtual edges was estimated in terms of the point of subjective equality (PSE) when participants matched the sharpness of virtual edges to that of real edges with a radius of 0.5, 2.5 and 12.5 mm over a virtual stiffness range of 0.6 to 3.0 N/mm. The perceived sharpness of a real and a virtual edge of the same radius was significantly different under all but one of the experimental conditions and there was a significant effect of virtual surface stiffness on the accuracy of the match. The results suggest that the latter is presumably due to a constant penetration force employed by the participants that influenced the penetration depth and perceived sharpness of virtual edges at different surface stiffness levels. Our findings provide quantitative relations for appropriately offsetting the radii of virtual edges in order to achieve the desired perceived sharpness of virtual edges.
Note on the theorems of Bjerknes and Crocco
NASA Technical Reports Server (NTRS)
Theodorsen, Theodore
1946-01-01
The theorems of Bjerknes and Crocco are of great interest in the theory of flow around airfoils at Mach numbers near and above unity. A brief note shows how both theorems are developed by short vector transformations.
Student Research Project: Goursat's Other Theorem
ERIC Educational Resources Information Center
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
The Pythagorean Theorem and the Solid State
ERIC Educational Resources Information Center
Kelly, Brenda S.; Splittgerber, Allan G.
2005-01-01
Packing efficiency and crystal density can be calculated from basic geometric principles employing the Pythagorean theorem, if the unit-cell structure is known. The procedures illustrated have applicability in courses such as general chemistry, intermediate and advanced inorganic, materials science, and solid-state physics.
Type Theory, Computation and Interactive Theorem Proving
2015-09-01
Springer, Heidelberg, 61-76, 2014. [9] Jeremy Avigad and John Harrison , “Formally verified mathematics,” Communications of the ACM, 57(4):66-75, 2014. [10...inequalities," in Gerwin Klein and Ruben Gamboa, eds., Interactive Theorem Proving 2014, Springer, Heidelberg, 61-76, 2014. 9) Jeremy Avigad and John Harrison
Generalized Friedland's theorem for C0-semigroups
NASA Astrophysics Data System (ADS)
Cichon, Dariusz; Jung, Il Bong; Stochel, Jan
2008-07-01
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
On Viviani's Theorem and Its Extensions
ERIC Educational Resources Information Center
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
Abel's Theorem Simplifies Reduction of Order
ERIC Educational Resources Information Center
Green, William R.
2011-01-01
We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.
Codimension- p Paley-Wiener theorems
NASA Astrophysics Data System (ADS)
Yang, Yan; Qian, Tao; Sommen, Frank
2007-04-01
We obtain the generalized codimension- p Cauchy-Kovalevsky extension of the exponential function e^{i
An extension theorem for conformal gauge singularities
NASA Astrophysics Data System (ADS)
Lübbe, Christian; Tod, Paul
2009-11-01
We analyze conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem along a congruence of timelike conformal geodesics.
Tennis Rackets and the Parallel Axis Theorem
ERIC Educational Resources Information Center
Christie, Derek
2014-01-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
Fundamental Theorems of Algebra for the Perplexes
ERIC Educational Resources Information Center
Poodiak, Robert; LeClair, Kevin
2009-01-01
The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…
The soft photon theorem for bremsstrahlung
Heller, L.
1990-01-01
We review this theorem and discuss the possible importance of the second term in the expansion of the cross section in powers of the photon momentum, especially for radiation from particle coming from the decay of resonances. 10 refs., 4 figs.
A non-differentiable Noether's theorem
NASA Astrophysics Data System (ADS)
Cresson, Jacky; Greff, Isabelle
2011-02-01
In the framework of the nondifferentiable embedding of Lagrangian systems, defined by Cresson and Greff [non-dierentiable embedding of lagrangian systems and partial dierential equations. Preprint Max-Plank-Institut für Mathematik in den Naturwissenschaften, Leipzig 16, 26 (2010)], we prove a Noether's theorem based on the lifting of one-parameter groups of diffeomorphisms.
Reflection theorem for Lorentz-Minkowski spaces
NASA Astrophysics Data System (ADS)
Lee, Nam-Hoon
2016-07-01
We generalize the reflection theorem of the Lorentz-Minkowski plane to that of the Lorentz-Minkowski spaces of higher dimensions. As a result, we show that an isometry of the Lorentz-Minkowski spacetime is a composition of at most 5 reflections.
Ptolemy's Theorem and Familiar Trigonometric Identities.
ERIC Educational Resources Information Center
Bidwell, James K.
1993-01-01
Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)
"Dealing" with the Central Limit Theorem
ERIC Educational Resources Information Center
Matz, David C.; Hause, Emily L.
2008-01-01
We describe an easy-to-employ, hands-on demonstration using playing cards to illustrate the central limit theorem. This activity allows students to see how a collection of sample means drawn from a nonnormally distributed population will be normally distributed. Students who took part in the demonstration reported it to be helpful in understanding…
The Formation and Erosion History of Mt. Sharp
NASA Technical Reports Server (NTRS)
Allen, Carlton C.; Dapremont, Angela M.
2014-01-01
The Curiosity rover is exploring 155 km diameter Gale crater and Mt. Sharp, Gale's 5 km high central mound (Fig. 1). This study addresses the formation and erosion history of Mt. Sharp. Gale lies on the topographic dichotomy between the southern highlands and the northern plains - a drop of over 2 km [1,2]. Altitude differences between the north and south rim reflect this regional slope, as do altitude differences between the deep annulus north of Mt. Sharp and the southern crater floor. Orbiter and rover images demonstrate that most exposed areas on Mt. Sharp consist of thin, sub-parallel units interpreted as sedimentary layers [3]. Gale is typical of the 50 large martian craters that have been totally or partially filled with such layers [4,5]. In many craters these sediments have been deeply eroded. Central Peak and Peak Ring: The highest point on Mt. Sharp, near the crater's center, is interpreted as a central peak [6]. The peak has a massive lower portion and a thin, smooth capping deposit (Fig. 2). Gale's size is transitional between martian craters with single central peaks and craters with peak rings approximately half the crater's diameter [2,6]. The boundaries of Mt. Sharp, as well as an arc of hills to the southeast of the mountain, closely match a circle approximately 80 km in diameter (Fig. 3). This morphology suggests that the Gale impact may have formed both a central peak and a partial peak ring, which is covered by the sediments of Mt. Sharp in the north and possibly exposed in the arc of eroded hills in the southeast quadrant (Figs. 3,4).
Harmonic admittance and dispersion equations--the theorem.
Plessky, Viktor P; Biryukov, Sergey V; Koskela, Julius
2002-04-01
The harmonic admittance is known as a powerful tool for analyzing the excitation and propagation of surface acoustic waves (SAWs) in periodic electrode arrays. In particular, the dispersion relationships for open- and short-circuited systems are indicated, respectively, by the zeros and poles of the harmonic admittance. Here, we show that a strict reverse relationship also exists: the harmonic admittance of a periodic system of electrodes may always be expressed as the ratio of two determinants, which have been specifically constructed to describe the eigen-modes of the open- and short-circuited systems. There is no need to solve these equations to find the admittance. The existence of a connection between the excitation and propagation problems was recognized within the coupling-of-modes theory by Chen and Haus and was recently used to model surface transverse waves by Koskela et al., but a rigorous mathematical proof was only found later by Biryukov. Here, we reproduce this theorem in detail, give some examples of calculations based on this theorem, and compare the results with measured admittance curves.
Applications of square-related theorems
NASA Astrophysics Data System (ADS)
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
A Simple Geometrical Derivation of the Spatial Averaging Theorem.
ERIC Educational Resources Information Center
Whitaker, Stephen
1985-01-01
The connection between single phase transport phenomena and multiphase transport phenomena is easily accomplished by means of the spatial averaging theorem. Although different routes to the theorem have been used, this paper provides a route to the averaging theorem that can be used in undergraduate classes. (JN)
Extending the Principal Axis Theorem to Fields Other than R.
ERIC Educational Resources Information Center
Friedberg, Stephen H.
1990-01-01
That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)
Using Dynamic Geometry to Explore Non-Traditional Theorems
ERIC Educational Resources Information Center
Wares, Arsalan
2010-01-01
The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…
Precision truing of diamond wheel with sharp edge
NASA Astrophysics Data System (ADS)
Ge, Cheng; Guo, Bing; Zhao, QIngliang; Chen, Bing; Wang, Jinhu
2014-08-01
Diamond wheel with sharp edge has small contour structures, which can lead to fast wear of wheel in the grinding process. Traditional truing methods are hard to apply to this kind of wheels. Therefore, as for the difficulty of precision truing of diamond wheel with sharp edge, the novel methods for resin and metal bonded diamond wheels with sharp edge are presented, respectively. In this experiment, a conditioning procedure with rare metal alloy block Ta was used to true the resin bonded diamond grinding wheel and in the same way Nb alloy block was utilized to complete rough truing of metal bonded diamond grinding wheel. Then a CNC truing technique with rotational green carbide (GC) truing stick was applied to precise truing of metal bonded diamond grinding wheel. Methods mentioned above were measured in order to evaluate the performance of truing. Geometric features of the wheel sharp edge were duplicated on the organic glass (PMMA) in order to measure and calculate the radius of the sharp edge. The edge radius of trued resin bonded wheel and metal bonded wheel is perceived as an important assessment. The experiments results revealed that the edge radius of 12.45μm for the resin bonded wheel and the edge radius of 30.17μm for the metal bonded wheel could be achieved.
NASA-Ames Summer High School Apprenticeship Research Program (SHARP)
NASA Technical Reports Server (NTRS)
Powell, P.
1983-01-01
The function of SHARP is to recognize high school juniors who have demonstrated unusually high promise for sucess in mathemtics and science. Twenty academically talented students who will be seniors in high school in September were chosen to participate in SHARP 83. Mentors were selected to provide students with first-hand experiences in a research and development environment in order that each student might try out his or her tentative professional career choice. Some special features of SHARP included field trips to private industries doing similar and related research, special lectures on topics of research here at ARC, individual and group counseling sessions, written research papers and oral reports, and primarily the opportunity to be exposed to the present frontiers in space exploration and research. The long-range goal of SHARP is to contribute to the future recruitment of needed scientists and engineers. This final report is summary of all the phases of the planning and implemenation of the 1983 Summer High School Apprenticeship Research Program (SHARP).
Investigation of micromixing by acoustically oscillated sharp-edges.
Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco
2016-03-01
Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel.
Investigation of micromixing by acoustically oscillated sharp-edges
Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco
2016-01-01
Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel. PMID:27158292
Internet-based assessment of image sharpness enhancement
NASA Astrophysics Data System (ADS)
MacDonald, Lindsay; Bouzit, Samira
2008-01-01
Two internet-based psychophysical experiments were conducted to investigate the performance of an image sharpness enhancement method, based on adjustment of spatial frequencies in the image according to the contrast sensitivity function and compensation of MTF losses of the display. The method was compared with the widely-used unsharp mask (USM) filter from PhotoShop. The experiment was performed in two locations with different groups of observers: one in the UK, and the second in the USA. Three Apple LCD displays (15" studio, 23" HD cinema and 15" PowerBook) were used at both sites. Observers assessed the sharpness and pleasantness of the displayed images. Analysis of the results led to four major conclusions: (1) Performance of the sharpening methods; (2) Influence of MTF compensation; (3) Image dependency; and (4) Comparison between sharpness perception and preference judgement at both sites.
Deler-Hernández, Albert; Fikáček, Martin
2016-01-01
Abstract In order to understand the identity of the Central American species of the genus Phaenonotum Sharp, 1882, the type specimens of the species described by Sharp (1882) deposited in the David Sharp collection in the Natural History Museum in London have been re-examined. The following species are redescribed: Phaenonotum apicale Sharp, 1882, Phaenonotum collare Sharp, 1882, Phaenonotum dubium Sharp, 1882 (confirmed as junior synonym of Phaenonotum exstriatum (Say, 1835)), Phaenonotum laevicolle Sharp, 1882, Phaenonotum rotundulum Sharp, 1882 and Phaenonotum tarsale Sharp, 1882. Lectotypes are designated for Phaenonotum apicale, Phaenonotum collare, Phaenonotum rotundulum and Phaenonotum tarsale. External diagnostic characters and morphology of male genitalia are illustrated. A table summarizing diagnostic characters allowing the identification of the species is provided. PMID:27110202
Deler-Hernández, Albert; Fikáček, Martin
2016-01-01
In order to understand the identity of the Central American species of the genus Phaenonotum Sharp, 1882, the type specimens of the species described by Sharp (1882) deposited in the David Sharp collection in the Natural History Museum in London have been re-examined. The following species are redescribed: Phaenonotum apicale Sharp, 1882, Phaenonotum collare Sharp, 1882, Phaenonotum dubium Sharp, 1882 (confirmed as junior synonym of Phaenonotum exstriatum (Say, 1835)), Phaenonotum laevicolle Sharp, 1882, Phaenonotum rotundulum Sharp, 1882 and Phaenonotum tarsale Sharp, 1882. Lectotypes are designated for Phaenonotum apicale, Phaenonotum collare, Phaenonotum rotundulum and Phaenonotum tarsale. External diagnostic characters and morphology of male genitalia are illustrated. A table summarizing diagnostic characters allowing the identification of the species is provided.
NASA Astrophysics Data System (ADS)
Yoo, Seung Hoon; Min, Byung Jun; Cho, Sungho; Kim, Eun Ho; Park, Jeong Hoon; Jung, Won-Gyun; Kim, Geun Beom; Kim, Kum Bae; Kim, Jaehoon; Jeong, Hojin; Lee, Kitae; Park, Sung Yong
2017-01-01
In this paper, the effects of the plasma density on laser-accelerated electron beams for radiation therapy with a sharp density transition are investigated. In the sharp density-transition scheme for electron injection, the crucial issue is finding the optimum density conditions under which electrons injected only during the first period of the laser wake wave are accelerated further. In this paper, we report particle-in-cell simulation results for the effects of both the scale length and the densitytransition ratio on the generation of a quasi-mono-energetic electron bunch. The effects of both the transverse parabolic channel and the plasma length on the electron-beam's quality are investigated. Also, we show the experimental results for the feasibility of a sharp density-transition structure. The dosimetric properties of these very high-energy electron beams are calculated using Monte Carlo simulations.
Synthetic-aperture radar autofocus by maximizing sharpness.
Fienup, J R
2000-02-15
To focus a synthetic-aperture radar image that is suffering from phase errors, a phase-error estimate is found that, when it is applied, maximizes the sharpness of the image. Closed-form expressions are derived for the gradients of a sharpness metric with respect to phase-error parameters, including both a point-by-point (nonparametric) phase function and coefficients of a polynomial expansion. Use of these expressions allows for a highly efficient gradient-search algorithm for high-order phase errors. The effectiveness of the algorithm is demonstrated with an example.
Pointing towards colonoscopy: sharp foreign body removal via colonoscopy
Hershman, Melissa; Shamah, Steven; Mudireddy, Prashant; Glick, Michael
2017-01-01
Removal of sharp foreign bodies via upper endoscopy is common; however, management in the setting of distal migration is not well-documented. We report two cases of objects beyond the ligament of Treitz, including successful extraction of a 4.4 cm sewing pin from the cecum using hot biopsy forceps with a protector hood to shield colonic mucosa, and in a separate case, a 3.4 cm glass shard from the ascending colon using a Roth Net retriever. We demonstrate that monitoring with serial radiographs and examination may allow for supervised passage of sharp objects into the colon, where removal can be performed safely via colonoscopy. PMID:28243052
Investigation of acoustic streaming patterns around oscillating sharp edges
Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco
2014-01-01
Oscillating sharp edges have been employed to achieve rapid and homogeneous mixing in microchannels using acoustic streaming. Here we use a perturbation approach to study the flow around oscillating sharp edges in a microchannel. This work extends prior experimental studies to numerically characterize the effect of various parameters on the acoustically induced flow. Our numerical results match well with the experimental results. We investigated multiple device parameters such as the tip angle, oscillation amplitude, and channel dimensions. Our results indicate that, due to the inherent nonlinearity of acoustic streaming, the channel dimensions could significantly impact the flow patterns and device performance. PMID:24903475
A torus bifurcation theorem with symmetry
NASA Technical Reports Server (NTRS)
Vangils, S. A.; Golubitsky, M.
1989-01-01
Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-01-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571
Aging and nonergodicity beyond the Khinchin theorem
Burov, S.; Metzler, R.; Barkai, E.
2010-01-01
The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin’s theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics. PMID:20624984
Generalized Sampling Theorem for Bandpass Signals
NASA Astrophysics Data System (ADS)
Prokes, Ales
2006-12-01
The reconstruction of an unknown continuously defined function[InlineEquation not available: see fulltext.] from the samples of the responses of[InlineEquation not available: see fulltext.] linear time-invariant (LTI) systems sampled by the[InlineEquation not available: see fulltext.]th Nyquist rate is the aim of the generalized sampling. Papoulis (1977) provided an elegant solution for the case where[InlineEquation not available: see fulltext.] is a band-limited function with finite energy and the sampling rate is equal to[InlineEquation not available: see fulltext.] times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST) for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.
Fluctuation theorem for constrained equilibrium systems.
Gilbert, Thomas; Dorfman, J Robert
2006-02-01
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
Fluctuation theorem for constrained equilibrium systems
NASA Astrophysics Data System (ADS)
Gilbert, Thomas; Dorfman, J. Robert
2006-02-01
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
A Geometrical Approach to Bell's Theorem
NASA Technical Reports Server (NTRS)
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
About the Stokes decomposition theorem of waves
NASA Astrophysics Data System (ADS)
Lacaze, B.
2011-06-01
The Stokes decomposition theorem deals with the electrical field E→=X,Y of a light beam. The theorem asserts that a beam can be viewed as the sum of two differently polarized parts. This result was recently discussed for light in the frame of the unified theory of coherence. We study the general case of an electromagnetic wave which can be in radio, radar, communications, or light. We assume stationary components with any power spectrum and finite or infinite bandwidth. We show that an accurate definition of polarization and unpolarization is a key parameter which rules the set of solutions of the problem. When dealing with a "strong definition" of unpolarization, the problem is treated in the frame of stationary processes and linear invariant filters. When dealing with a "weak definition", solutions are given by elementary properties of bidimensional random variables.
Construction of momentum theorem using cross moments
NASA Astrophysics Data System (ADS)
Hahm, T. S.; Wang, Lu; Diamond, P. H.
2009-11-01
Charney-Drazin theorem has been extended to Hasegawa Wakatani system for zonal flow problem in magnetic fusion [P.H. Diamond, et al., Plasma Phys. Control. Fusion 50, 124018 (2008)]. For this model, the guiding center density is the potential vorticity and zonal flow is influenced by the particle flux. In this work we construct momentum theorems in terms of a hierarchy of cross moments
Volume integral theorem for exotic matter
Nandi, Kamal Kanti; Zhang Yuanzhong; Kumar, K.B. Vijaya
2004-12-15
We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well-known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.
Spontaneously broken spacetime symmetries and Goldstone's theorem.
Low, Ian; Manohar, Aneesh V
2002-03-11
Goldstone's theorem states that there is a massless mode for each broken symmetry generator. It has been known for a long time that the naive generalization of this counting fails to give the correct number of massless modes for spontaneously broken spacetime symmetries. We explain how to get the right count of massless modes in the general case, and discuss examples involving spontaneously broken Poincaré and conformal invariance.
Infinite flag varieties and conjugacy theorems
Peterson, Dale H.; Kac, Victor G.
1983-01-01
We study the orbit of a highest-weight vector in an integrable highest-weight module of the group G associated to a Kac-Moody algebra [unk](A). We obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of [unk](A). In particular, we prove conjugacy theorems for Cartan and Borel subalgebras of [unk](A), so that the Cartan matrix A is an invariant of [unk](A). PMID:16593298
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Tests of the lattice index theorem
Jordan, Gerald; Hoellwieser, Roman; Faber, Manfried; Heller, Urs M.
2008-01-01
We investigate the lattice index theorem and the localization of the zero modes for thick classical center vortices. For nonorientable spherical vortices, the index of the overlap Dirac operator differs from the topological charge although the traces of the plaquettes deviate only by a maximum of 1.5% from trivial plaquettes. This may be related to the fact that even in Landau gauge some links of these configuration are close to the nontrivial center elements.
Temporal Distributional Limit Theorems for Dynamical Systems
NASA Astrophysics Data System (ADS)
Dolgopyat, Dmitry; Sarig, Omri
2017-02-01
Suppose {T^t} is a Borel flow on a complete separable metric space X, f:X→ R is Borel, and xin X. A temporal distributional limit theorem is a scaling limit for the distributions of the random variables X_T:=int _0^t f(T^s x)ds, where t is chosen randomly uniformly from [0, T], x is fixed, and T→ ∞. We discuss such laws for irrational rotations, Anosov flows, and horocycle flows.
Asynchronous networks: modularization of dynamics theorem
NASA Astrophysics Data System (ADS)
Bick, Christian; Field, Michael
2017-02-01
Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or dynamical modules. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network: the modularization of dynamics theorem. We give examples to illustrate the main results.
Theorem Proving In Higher Order Logics
NASA Technical Reports Server (NTRS)
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Haag's Theorem and Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Edwin
2017-01-01
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
77 FR 56647 - Lisa Jean Sharp: Debarment Order
Federal Register 2010, 2011, 2012, 2013, 2014
2012-09-13
... Director of Clinical Trials for Lee Research Institute. Schering/ Plough was a pharmaceutical company... Lee Research Institute, Ms. Sharp's employer, to perform a clinical study known as ``A 28-Day Study... study. Before beginning the clinical study, FDA required Schering/Plough to provide the Agency with...
Hardy type inequalities in [Formula: see text] with sharp remainders.
Ioku, Norisuke; Ishiwata, Michinori; Ozawa, Tohru
2017-01-01
Sharp remainder terms are explicitly given on the standard Hardy inequalities in [Formula: see text] with [Formula: see text]. Those remainder terms provide a direct and exact understanding of Hardy type inequalities in the framework of equalities as well as of the nonexistence of nontrivial extremals.
A Validity Scale for the Sharp Consumer Satisfaction Scales.
ERIC Educational Resources Information Center
Tanner, Barry A.; Stacy, Webb, Jr.
1985-01-01
A validity scale for the Sharp Consumer Satisfaction Scale was developed and used in experiments to assess patients' satisfaction with community mental health centers. The scale discriminated between clients who offered suggestions and those who did not. It also improved researcher's ability to predict true scores from obtained scores. (DWH)
8. RHODES DITCH: VIEW TO SOUTHEAST, SHOWING SHARP 'U' CONTOURED ...
8. RHODES DITCH: VIEW TO SOUTHEAST, SHOWING SHARP 'U' CONTOURED ABOVE SWALE. DITCH IS ALSO VISIBLE IN DISTANCE, RUNNING HORIZONTALLY ACROSS PHOTO, ON FAR HILLSIDE. - Natomas Ditch System, Rhodes Ditch, West of Bidwell Street, north of U.S. Highway 50, Folsom, Sacramento County, CA
Ethnically Diverse Older Adults' Beliefs about Staying Mentally Sharp
ERIC Educational Resources Information Center
Friedman, Daniela B.; Laditka, Sarah B.; Laditka, James N.; Wu, Bei; Liu, Rui; Price, Anna E.; Tseng, Winston; Corwin, Sara J.; Ivey, Susan L.; Hunter, Rebecca; Sharkey, Joseph R.
2011-01-01
This study examined diverse older adults' (n = 396, ages 50+) views about how to stay mentally sharp. We conducted 42 focus groups in four languages at nine United States locations using a standardized discussion guide and methods. The groups represented African Americans, American Indians, Chinese Americans, Latinos, Whites other than Latinos,…
Study on electrostatic resonance of nanoprisms with sharp corners
NASA Astrophysics Data System (ADS)
Chan, Wai Soen; Ng, Ka Ki; Yu, Kin Wah
2015-03-01
We have studied the electrostatic resonance of metal nanoprisms with sharp corners numerically. We consider an infinite metal cylinder with polygonal base, e.g. square. The incident electric field lies in the plane of cross-section of the cylinder. Yu and co-workers proposed Green's function formalism (GFF) to numerically calculate the electric potential and field distribution in plasmonic systems. We will adopt the scheme to demonstrate the effect of sharp corners, particularly on the effect of electrostatic resonance spectrum, as in the spectral analysis proposed by Bergman and Milton. Hetherington and Thorpe investigated the conductivity of a sheet containing dilute inclusion with sharp corners, they made use of a conformal mapping approach to calculate the conductivity from circular inclusions. Helsing, McPhedran and Milton also investigated the optical properties of a metamaterial lattice with inclusions having sharp corners. We study the possibility of improving numerical accuracy by combining the conformal mapping approach and GFF. We may extend similar approach to investigate the properties of plasmonic systems, for examples nanoboties and nanostars.
GENERAL VIEW OF SHARP FREEZE ROOM ON LEVEL 2; LOOKING ...
GENERAL VIEW OF SHARP FREEZE ROOM ON LEVEL 2; LOOKING WEST; PIPES ON CEILING CARRIED COMPRESSED AMMONIA; NOTE NONBEARING GLAZED TILE WALLS BETWEEN COLUMNS; FLOORS ARE BRICK - Rath Packing Company, Cooler Building, Sycamore Street between Elm & Eighteenth Streets, Waterloo, Black Hawk County, IA
Stress and Fear of Exposure to Sharps in Nurses
Moayed, Malihe Sadat; Mahmoudi, Hosein; Ebadi, Abbas; Sharif Nia, Hamid
2016-01-01
Background Injuries caused by sharp objects, which involve biological hazards are considered as one of the most important factors that lead to stress among the nursing staff. Contact with sharp objects is a major concern among healthcare workers, especially nurses. Objectives This study was done to determine the amount of stress caused by exposure to sharp medical instruments among nurses. Materials and Methods This was a cross-sectional research on 527 nurses, working at different medical centers across Iran, with a cluster-sampling method. The relevant data was collected with a valid and reliable questionnaire. The Cronbach’s alpha coefficient of internal consistency of this instrument was 0.92 and interclass correlation coefficient was 0.94 Results The results showed that ward satisfaction, having master of science, age, and number of contacts were significantly able to predict variance in stress scores. The adjusted line regression model explained 36% of the overall variance in stress score (R2 = 0.60) Conclusions The results of this study showed that exposure to sharp objects may cause high stress in the nursing staff. Considering higher levels of stress in the area of contact care, the provisions on how to deal with patients and safe care can help reduce stress. PMID:27822279
[Overview of sharps injuries among health-care workers].
Gopar-Nieto, Rodrigo; Juárez-Pérez, Cuauhtémoc Arturo; Cabello-López, Alejandro; Haro-García, Luis Cuauhtémoc; Aguilar-Madrid, Guadalupe
2015-01-01
Sharps injuries are one of the most frequent health-care related accidents. It is estimated globally that 35 million workers are at risk; in Mexico there is no data available for this type of injuries. They are associated with lack of training, instrument and procedure risk, fatigue and stress. The occupational distribution is nurses 45 %, technicians 20 %, doctors 20 % and maintenance workers 5 %. The most commonly associated procedures are injection, venipuncture, suture, and insertion and manipulation of IV catheters. Hepatitis B is the most commonly transmitted agent. Emotional distress is huge as well as the cost of prophylaxis and follow-up. More than half of the injuries are not notified. The most common reasons for not reporting are: the belief that the exposure has low risk of infection, the lack of knowledge of reporting systems and the assumption that it is difficult to notify. Many strategies have been created to reduce the incidence of sharps injuries, such as: identifying the risk of blood exposure, the creation of politics to minimize the risk, the education and training to create a safe workplace, the enhancing of the reporting system, the use of double-gloving and using safety-engineered sharps devices. In many countries these politics have reduced the incidence of sharps injuries as well as the economic burden.
Four theorems on the psychometric function.
May, Keith A; Solomon, Joshua A
2013-01-01
In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus
Spatial Bistability Generates hunchback Expression Sharpness in the Drosophila Embryo
Lopes, Francisco J. P.; Vieira, Fernando M. C.; Holloway, David M.; Bisch, Paulo M.; Spirov, Alexander V.
2008-01-01
During embryonic development, the positional information provided by concentration gradients of maternal factors directs pattern formation by providing spatially dependent cues for gene expression. In the fruit fly, Drosophila melanogaster, a classic example of this is the sharp on–off activation of the hunchback (hb) gene at midembryo, in response to local concentrations of the smooth anterior–posterior Bicoid (Bcd) gradient. The regulatory region for hb contains multiple binding sites for the Bcd protein as well as multiple binding sites for the Hb protein. Some previous studies have suggested that Bcd is sufficient for properly sharpened Hb expression, yet other evidence suggests a need for additional regulation. We experimentally quantified the dynamics of hb gene expression in flies that were wild-type, were mutant for hb self-regulation or Bcd binding, or contained an artificial promoter construct consisting of six Bcd and two Hb sites. In addition to these experiments, we developed a reaction–diffusion model of hb transcription, with Bcd cooperative binding and hb self-regulation, and used Zero Eigenvalue Analysis to look for multiple stationary states in the reaction network. Our model reproduces the hb developmental dynamics and correctly predicts the mutant patterns. Analysis of our model indicates that the Hb sharpness can be produced by spatial bistability, in which hb self-regulation produces two stable levels of expression. In the absence of self-regulation, the bistable behavior vanishes and Hb sharpness is disrupted. Bcd cooperative binding affects the position where bistability occurs but is not itself sufficient for a sharp Hb pattern. Our results show that the control of Hb sharpness and positioning, by hb self-regulation and Bcd cooperativity, respectively, are separate processes that can be altered independently. Our model, which matches the changes in Hb position and sharpness observed in different experiments, provides a theoretical
The van Cittert-Zernike theorem for electromagnetic fields.
Ostrovsky, Andrey S; Martínez-Niconoff, Gabriel; Martínez-Vara, Patricia; Olvera-Santamaría, Miguel A
2009-02-02
The van Cittert-Zernike theorem, well known for the scalar optical fields, is generalized for the case of vector electromagnetic fields. The deduced theorem shows that the degree of coherence of the electromagnetic field produced by the completely incoherent vector source increases on propagation whereas the degree of polarization remains unchanged. The possible application of the deduced theorem is illustrated by an example of optical simulation of partially coherent and partially polarized secondary source with the controlled statistical properties.
Borsuk-Ulam theorem in infinite-dimensional Banach spaces
NASA Astrophysics Data System (ADS)
Gel'man, B. D.
2002-02-01
The well-known classical Borsuk-Ulam theorem has a broad range of applications to various problems. Its generalization to infinite-dimensional spaces runs across substantial difficulties because its statement is essentially finite-dimensional. A result established in the paper is a natural generalization of the Borsuk-Ulam theorem to infinite-dimensional Banach spaces. Applications of this theorem to various problems are discussed.
A Converse of the Mean Value Theorem Made Easy
ERIC Educational Resources Information Center
Mortici, Cristinel
2011-01-01
The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…
Wilson loop and magnetic monopole through a non-Abelian Stokes theorem
Kondo, Kei-Ichi
2008-04-15
I show that the Wilson loop operator for the SU(N) Yang-Mills gauge connection is exactly rewritten in terms of conserved gauge-invariant magnetic and electric currents through a non-Abelian Stokes theorem of the Diakonov-Petrov type. Here the magnetic current originates from the magnetic monopole derived in the gauge-invariant way from the pure Yang-Mills theory even in the absence of the Higgs scalar field, in sharp contrast to the 't Hooft-Polyakov magnetic monopole in the Georgi-Glashow gauge-Higgs model. The resulting representation indicates that the Wilson loop operator in fundamental representations can be a probe for a single magnetic monopole irrespective of N in SU(N) Yang-Mills theory, against the conventional wisdom. Moreover, I show that the quantization condition for the magnetic charge follows from the fact that the non-Abelian Stokes theorem does not depend on the surface chosen for writing the surface integral. The obtained geometrical and topological representations of the Wilson loop operator have important implications to understanding quark confinement according to the dual superconductor picture.
Wilson loop and magnetic monopole through a non-Abelian Stokes theorem
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi
2008-04-01
I show that the Wilson loop operator for the SU(N) Yang-Mills gauge connection is exactly rewritten in terms of conserved gauge-invariant magnetic and electric currents through a non-Abelian Stokes theorem of the Diakonov-Petrov type. Here the magnetic current originates from the magnetic monopole derived in the gauge-invariant way from the pure Yang-Mills theory even in the absence of the Higgs scalar field, in sharp contrast to the ’t Hooft Polyakov magnetic monopole in the Georgi-Glashow gauge-Higgs model. The resulting representation indicates that the Wilson loop operator in fundamental representations can be a probe for a single magnetic monopole irrespective of N in SU(N) Yang-Mills theory, against the conventional wisdom. Moreover, I show that the quantization condition for the magnetic charge follows from the fact that the non-Abelian Stokes theorem does not depend on the surface chosen for writing the surface integral. The obtained geometrical and topological representations of the Wilson loop operator have important implications to understanding quark confinement according to the dual superconductor picture.
The Nekhoroshev theorem and the observation of long-term diffusion in Hamiltonian systems
NASA Astrophysics Data System (ADS)
Guzzo, Massimiliano; Lega, Elena
2016-11-01
The long-term diffusion properties of the action variables in real analytic quasiintegrable Hamiltonian systems is a largely open problem. The Nekhoroshev theorem provides bounds to such a diffusion as well as a set of techniques, constituting its proof, which have been used to inspect also the instability of the action variables on times longer than the Nekhoroshev stability time. In particular, the separation of the motions in a superposition of a fast drift oscillation and an extremely slow diffusion along the resonances has been observed in several numerical experiments. Global diffusion, which occurs when the range of the slow diffusion largely exceeds the range of fast drift oscillations, needs times larger than the Nekhoroshev stability times to be observed, and despite the power of modern computers, it has been detected only in a small interval of the perturbation parameter, just below the critical threshold of application of the theorem. In this paper we show through an example how sharp this phenomenon is.
Sharp magnetic structures from dynamos with density stratification
NASA Astrophysics Data System (ADS)
Jabbari, Sarah; Brandenburg, Axel; Kleeorin, Nathan; Rogachevskii, Igor
2017-01-01
Recent direct numerical simulations (DNS) of large-scale turbulent dynamos in strongly stratified layers have resulted in surprisingly sharp bipolar structures at the surface. Here we present new DNS of helically and non-helically forced turbulence with and without rotation and compare with corresponding mean-field simulations (MFS) to show that these structures are a generic outcome of a broader class of dynamos in density-stratified layers. The MFS agree qualitatively with the DNS, but the period of oscillations tends to be longer in the DNS. In both DNS and MFS, the sharp structures are produced by converging flows at the surface and might be driven in nonlinear stage of evolution by the Lorentz force associated with the large-scale dynamo-driven magnetic field if the dynamo number is at least 2.5 times supercritical.
Sharp Refractory Composite Leading Edges on Hypersonic Vehicles
NASA Technical Reports Server (NTRS)
Walker, Sandra P.; Sullivan, Brian J.
2003-01-01
On-going research of advanced sharp refractory composite leading edges for use on hypersonic air-breathing vehicles is presented in this paper. Intense magnitudes of heating and of heating gradients on the leading edge lead to thermal stresses that challenge the survivability of current material systems. A fundamental understanding of the problem is needed to further design development. Methodology for furthering the technology along with the use of advanced fiber architectures to improve the thermal-structural response is explored in the current work. Thermal and structural finite element analyses are conducted for several advanced fiber architectures of interest. A tailored thermal shock parameter for sharp orthotropic leading edges is identified for evaluating composite material systems. The use of the tailored thermal shock parameter has the potential to eliminate the need for detailed thermal-structural finite element analyses for initial screening of material systems being considered for a leading edge component.
A qualitative approach to Bayes' theorem.
Medow, Mitchell A; Lucey, Catherine R
2011-12-01
While decisions made according to Bayes' theorem are the academic normative standard, the theorem is rarely used explicitly in clinical practice. Yet the principles can be followed without intimidating mathematics. To do so, one can first categorise the prior-probability of the disease being tested for as very unlikely (less likely than 10%), unlikely (10-33%), uncertain (34-66%), likely (67-90%) or very likely (more likely than 90%). Usually, for disorders that are very unlikely or very likely, no further testing is needed. If the prior probability is unlikely, uncertain or likely, a test and a Bayesian-inspired update process incorporating the result can help. A positive result of a good test increases the probability of the disorder by one likelihood category (eg, from uncertain to likely) and a negative test decreases the probability by one category. If testing is needed to escape the extremes of likelihood (eg, a very unlikely but particularly dangerous condition or in the circumstance of population screening, or a very likely condition with a particularly noxious treatment), two tests may be needed to achieve. Negative results of tests with sensitivity ≥99% are sufficient to rule-out a diagnosis; positive results of tests with specificity ≥99% are sufficient to rule-in a diagnosis. This method overcomes some common heuristic errors: ignoring the base rate, probability adjustment errors and order effects. The simplicity of the method, while still adhering to the basic principles of Bayes' theorem, has the potential to increase its application in clinical practice.
Stochastic thermodynamics, fluctuation theorems and molecular machines.
Seifert, Udo
2012-12-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Stochastic thermodynamics, fluctuation theorems and molecular machines
NASA Astrophysics Data System (ADS)
Seifert, Udo
2012-12-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Sharp continuity bounds for entropy and conditional entropy
NASA Astrophysics Data System (ADS)
Chen, ZhiHua; Ma, ZhiHao; Nikoufar, Ismail; Fei, Shao-Ming
2017-02-01
The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is derived. This inequality is shown to be tight in the sense that equality can be attained for every prescribed value of the trace norm distance. It includes the sharp Fannes inequality for von Neumann entropy as a special case.
Habitat Suitability Index Models: Plains sharp-tailed grouse
Prose, Bart L.
1987-01-01
A review and synthesis of existing information were used to develop a Habitat Suitability Index (HSI) model for the plains sharp-tailed grouse (Tympanuchus phasianellus jamesi). The model consolidates habitat use information into a framework appropriate for field application, and is scaled to produce an index between 0.0 (unsuitable habitat) to 1.0 (optimum habitat). HSI models are designed to be used with Habitat Evaluation Procedures previously developed by the U.S. Fish and Wildlife Service.
On the Edge: Haptic Discrimination of Edge Sharpness
Skinner, Andy L.; Kent, Christopher; Rossiter, Jonathan M.; Benton, Christopher P.; Groen, Martin G. M.; Noyes, Jan M.
2013-01-01
The increasing ubiquity of haptic displays (e.g., smart phones and tablets) necessitates a better understanding of the perceptual capabilities of the human haptic system. Haptic displays will soon be capable of locally deforming to create simple 3D shapes. This study investigated the sensitivity of our haptic system to a fundamental component of shapes: edges. A novel set of eight high quality shape stimuli with test edges that varied in sharpness were fabricated in a 3D printer. In a two alternative, forced choice task, blindfolded participants were presented with two of these shapes side by side (one the reference, the other selected randomly from the remaining set of seven) and after actively exploring the test edge of each shape with the tip of their index finger, reported which shape had the sharper edge. We used a model selection approach to fit optimal psychometric functions to performance data, and from these obtained just noticeable differences and Weber fractions. In Experiment 1, participants performed the task with four different references. With sharpness defined as the angle at which one surface meets the horizontal plane, the four JNDs closely followed Weber’s Law, giving a Weber fraction of 0.11. Comparisons to previously reported Weber fractions from other haptic manipulations (e.g. amplitude of vibration) suggests we are sufficiently sensitive to changes in edge sharpness for this to be of potential utility in the design of future haptic displays. In Experiment 2, two groups of participants performed the task with a single reference but different exploration strategies; one was limited to a single touch, the other unconstrained and free to explore as they wished. As predicted, the JND in the free exploration condition was lower than that in the single touch condition, indicating exploration strategy affects sensitivity to edge sharpness. PMID:24023852
Generating Test Templates via Automated Theorem Proving
NASA Technical Reports Server (NTRS)
Kancherla, Mani Prasad
1997-01-01
Testing can be used during the software development process to maintain fidelity between evolving specifications, program designs, and code implementations. We use a form of specification-based testing that employs the use of an automated theorem prover to generate test templates. A similar approach was developed using a model checker on state-intensive systems. This method applies to systems with functional rather than state-based behaviors. This approach allows for the use of incomplete specifications to aid in generation of tests for potential failure cases. We illustrate the technique on the cannonical triangle testing problem and discuss its use on analysis of a spacecraft scheduling system.
Penrose's singularity theorem in a Finsler spacetime
NASA Astrophysics Data System (ADS)
Babak Aazami, Amir; Javaloyes, Miguel Angel
2016-01-01
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting. This activity is supported by the programme 'Young leaders in research' 18942/JLI/13 by Fundación Séneca, Regional Agency for Science and Technology from the Region of Murcia, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
Generalizations of Brandl's theorem on Engel length
NASA Astrophysics Data System (ADS)
Quek, S. G.; Wong, K. B.; Wong, P. C.
2013-04-01
Let n < m be positive integers such that [g,nh] = [g,mh] and assume that n and m are chosen minimal with respect to this property. Let gi = [g,n+ih] where i = 1,2,…,m-n. Then π(g,h) = (g1,…,gm-n) is called the Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.
Central limit theorems under special relativity.
McKeague, Ian W
2015-04-01
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
No-cloning theorem on quantum logics
Miyadera, Takayuki; Imai, Hideki
2009-10-15
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
Fluctuation theorem in dynamical systems with quenched disorder
NASA Astrophysics Data System (ADS)
Drocco, Jeffrey; Olson Reichhardt, Cynthia; Reichhardt, Charles
2010-03-01
We demonstrate that the fluctuation theorem of Gallavotti and Cohen can be used to characterize far from equilibrium dynamical nonthermal systems in the presence of quenched disorder where strong fluctuations or crackling noise occur. By observing the frequency of entropy-destroying trajectories, we show that the theorem holds in specific dynamical regimes near the threshold for motion, indicating that these systems might be ideal candidates for understanding what types of nonthermal fluctuations could be used in constructing generalized fluctuation theorems. We also discuss how the theorem could be tested with global or local probes in systems such as superconducting vortices, magnetic domain walls, stripe phases, Coulomb glasses and earthquake models.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
Woolgar, Eric; Wylie, William
2016-02-15
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
Equipartition theorem and the dynamics of liquids
Levashov, Valentin A.; Egami, Takeshi; Aga, Rachel S; Morris, James R
2008-01-01
In liquids, phonons have a very short lifetime and the total potential energy does not depend linearly on temperature. Thus it may appear that atomic vibrations in liquids cannot be described by the harmonic-oscillator model and that the equipartition theorem for the potential energy is not upheld. In this paper we show that the description of the local atomic dynamics in terms of the atomic-level stresses provides such a description, satisfying the equipartition theorem. To prove this point we carried out molecular-dynamics simulations with several pairwise potentials, including the Lennard-Jones potential, the modified Johnson potential, and the repulsive part of the Johnson potential, at various particle number densities. In all cases studied the total self-energy of the atomic-level stresses followed the (3/2)kBT law. From these results we suggest that the concept of local atomic stresses can provide description of thermodynamic properties of glasses and liquids on the basis of harmonic atomistic excitations. An example of application of this approach to the description of the glass transition temperature in metallic glasses is discussed.
On the inversion of Fueter's theorem
NASA Astrophysics Data System (ADS)
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2016-10-01
The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space R n + 1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension n. The present work extends the result to all dimensions n by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function f defined in a suitable open set in R n + 1, where n is a positive integer, we can find a slice hyperholomorphic function f → such that f =Δ (n - 1) / 2 f →. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.
Bell's theorem, inference, and quantum transactions
NASA Astrophysics Data System (ADS)
Garrett, A. J. M.
1990-04-01
Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, “local”) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's new transactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the “delayed choice” experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theorem reinforces arguments in favor of hidden variables.
De Finetti Theorem on the CAR Algebra
NASA Astrophysics Data System (ADS)
Crismale, Vitonofrio; Fidaleo, Francesco
2012-10-01
The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend the De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self-containing interest.
Group Theoretical Interpretation of von Neumann's Theorem on Composite Systems.
ERIC Educational Resources Information Center
Bergia, S.; And Others
1979-01-01
Shows that von Neumann's mathematical theorem on composite systems acquires a transparent physical meaning with reference to a suitable physical example; a composite system in a state of definite angular momentum. Gives an outline of the theorem, and the results are restated in Dirac's notation, thus generalizing von Neumann's results which were…
Generalizations of Karp's theorem to elastic scattering theory
NASA Astrophysics Data System (ADS)
Tuong, Ha-Duong
Karp's theorem states that if the far field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle in R2 is invariant under the group of rotations, then the scatterer is a circle. The theorem is generalized to the elastic scattering problems and the axisymmetric scatterers in R3.
When 95% Accurate Isn't: Exploring Bayes's Theorem
ERIC Educational Resources Information Center
CadwalladerOlsker, Todd D.
2011-01-01
Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…
Unique Factorization and the Fundamental Theorem of Arithmetic
ERIC Educational Resources Information Center
Sprows, David
2017-01-01
The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a…
On Euler's Theorem for Homogeneous Functions and Proofs Thereof.
ERIC Educational Resources Information Center
Tykodi, R. J.
1982-01-01
Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)
Solving boundary-value electrostatics problems using Green's reciprocity theorem
NASA Astrophysics Data System (ADS)
Hu, Ben Yu-Kuang
2001-12-01
Formal solutions to electrostatics boundary-value problems are derived using Green's reciprocity theorem. This method provides a more transparent interpretation of the solutions than the standard Green's function derivation. An energy-based argument for the reciprocity theorem is also presented.
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2009-02-20
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
Leaning on Socrates to Derive the Pythagorean Theorem
ERIC Educational Resources Information Center
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…
On the Weighted Mean Value Theorem for Integrals
ERIC Educational Resources Information Center
Polezzi, M.
2006-01-01
The Mean Value Theorem for Integrals is a powerful tool, which can be used to prove the Fundamental Theorem of Calculus, and to obtain the average value of a function on an interval. On the other hand, its weighted version is very useful for evaluating inequalities for definite integrals. This article shows the solutions on applying the weighted…
Interactive Theorem Finding through Continuous Variation of Geometric Configurations.
ERIC Educational Resources Information Center
Schumann, Heinz
1991-01-01
Described and evaluated are microcomputers as a tool for construction in geometry education and heuristic theorem finding through interactive continuous variation of geometric configurations. Numerous examples of theorem finding processes are provided using the prototype graphics system CABRI-Geometer. (MDH)
Level reduction and the quantum threshold theorem
NASA Astrophysics Data System (ADS)
Aliferis, Panagiotis (Panos)
Computers have led society to the information age revolutionizing central aspects of our lives from production and communication to education and entertainment. There exist, however, important problems which are intractable with the computers available today and, experience teaches us, will remain so even with the more advanced computers we can envision for tomorrow.Quantum computers promise speedups to some of these important but classically intractable problems. Simulating physical systems, a problem of interest in a diverse range of areas from testing physical theories to understanding chemical reactions, and solving number factoring, a problem at the basis of cryptographic protocols that are used widely today on the internet, are examples of applications for which quantum computers, when built, will offer a great advantage over what is possible with classical computer technology.The construction of a quantum computer of sufficient scale to solve interesting problems is, however, especially challenging. The reason for this is that, by its very nature, operating a quantum computer will require the coherent control of the quantum state of a very large number of particles. Fortunately, the theory of quantum error correction and fault-tolerant quantum computation gives us confidence that such quantum states can be created, can be stored in memory and can also be manipulated provided the quantum computer can be isolated to a sufficient degree from sources of noise.One of the central results in the theory of fault-tolerant quantum computation, the quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum accuracy threshold. This thesis provides a simpler and more transparent non-inductive proof of this theorem based on the concept of level reduction. This concept is also used in proving the
Climbing Mt. Sharp: Maximizing Curiosity's Science Over Traversable Terrains
NASA Astrophysics Data System (ADS)
Fraeman, A. A.; Arvidson, R. E.; Bellutta, P.; Sletten, R. S.; Team, M.
2013-12-01
As Curiosity transitions from the plains of Gale Crater to the flanks of Mt. Sharp, the rover will begin to encounter material and terrains that could present greater mobility challenges. These challenges include the presence of significantly steeper slopes and large dunes that have the potential to embed the vehicle. Strategic path planning during this phase of the mission will therefore require carefully selecting a traversable route that is both time-efficient and that will provide access to the most scientifically rewarding targets. We consider possible solutions to this optimization problem by examining multiple orbital data sets in order to locate likely mobility hazards and to select potential science waypoints for future in situ investigation. High resolution HiRISE monochromatic images and digital elevation models show filled craters, rock fields, areas with slopes too steep for the rover to traverse, and other possible mobility obstacles on the northwest flank of Mt. Sharp. Using this context, we review accessibility to scientific targets on Mt. Sharp that have been previously discussed in landing site workshop presentations and peer-reviewed publications. Additionally, we identify new targets using detailed geologic maps combined with oversampled CRISM observations that provide mineralogical information at unprecedented high spatial resolutions (up to 6 m/pixel). For example, the spatially sharpened CRISM spectral data show a localized hematite deposit that is associated with the upper-most stratum of a ridge which is located ~3km from the rover's entry point to Mt. Sharp. This deposit may represent a previously habitable environment and is therefore a high priority target for in situ investigation. In order to study the hematite and also to eventually access the phyllosilicate-bearing trough that is located directly behind the ridge, Curiosity will have to cross this ridge, but the ridge edges are often defined by regions with slopes that are too steep
Metal nanoparticles with sharp corners: Universal properties of plasmon resonances
NASA Astrophysics Data System (ADS)
Sturman, B.; Podivilov, E.; Gorkunov, M.
2013-03-01
We predict the simultaneous occurrence of two fundamental phenomena for metal nanoparticles possessing sharp corners with variable curvature: First, the main dipolar plasmonic mode experiences a strong red shift with increasing corner curvature; for large values of the curvature, the resonant frequency is controlled by the apex angle of the corner. Second, the split-off plasmonic mode experiences a strong localization at the corners. Altogether, this paves the way for the tailoring of metal nanostructures providing a wavelength-selective excitation of localized plasmons and a strong near-field enhancement of linear and nonlinear optical phenomena.
Direct handling of sharp interfacial energy for microstructural evolution
Hernández–Rivera, Efraín; Tikare, Veena; Noirot, Laurence; ...
2014-08-24
In this study, we introduce a simplification to the previously demonstrated hybrid Potts–phase field (hPPF), which relates interfacial energies to microstructural sharp interfaces. The model defines interfacial energy by a Potts-like discrete interface approach of counting unlike neighbors, which we use to compute local curvature. The model is compared to the hPPF by studying interfacial characteristics and grain growth behavior. The models give virtually identical results, while the new model allows the simulator more direct control of interfacial energy.
DSMC Simulations of Shock Interactions About Sharp Double Cones
NASA Technical Reports Server (NTRS)
Moss, James N.
2000-01-01
This paper presents the results of a numerical study of shock interactions resulting from Mach 10 flow about sharp double cones. Computations are made by using the direct simulation Monte Carlo (DSMC) method of Bird. The sensitivity and characteristics of the interactions are examined by varying flow conditions, model size, and configuration. The range of conditions investigated includes those for which experiments have been or will be performed in the ONERA R5Ch low-density wind tunnel and the Calspan-University of Buffalo Research Center (CUBRC) Large Energy National Shock (LENS) tunnel.
HF-stabilization of plasma with sharp boundary
NASA Astrophysics Data System (ADS)
Kotelnikov, I. A.; Yakovchenko, S. G.
The effect of HF natural oscillations of a plasma filament in a conducting cylindrical housing on the flute disturbance stability is investigated. Flute development leads to HF oscillation frequency (omega) variation connected with the energy W variation by the condition of constancy of the adiabatic invariant W/(omega) = const. The last is conserved owing to relative slow variations of flute disturbances. The adiabatic approximation used permits one to obtain simple criteria for flute instability stabilization by a HF field. HF oscillations of a plasma with a sharp boundary are considered.
The virial theorem for the polarizable continuum model
Cammi, R.
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.
Splitting theorem for Z2n -supermanifolds
NASA Astrophysics Data System (ADS)
Covolo, Tiffany; Grabowski, Janusz; Poncin, Norbert
2016-12-01
Smooth Z2n -supermanifolds have been introduced and studied recently. The corresponding sign rule is given by the 'scalar product' of the involved Z2n -degrees. It exhibits interesting changes in comparison with the sign rule using the parity of the total degree. With the new rule, nonzero degree even coordinates are not nilpotent, and even (resp., odd) coordinates do not necessarily commute (resp., anticommute) pairwise. The classical Batchelor-Gawȩdzki theorem says that any smooth supermanifold is diffeomorphic to the 'superization' ΠE of a vector bundle E. It is also known that this result fails in the complex analytic category. Hence, it is natural to ask whether an analogous statement goes through in the category of Z2n -supermanifolds with its local model made of formal power series. We give a positive answer to this question.
Differential diagnosis in immunohistochemistry with Bayes theorem.
Vollmer, Robin T
2009-05-01
When immunohistochemical stains that are specific for specific tumor diagnoses do not yield diagnostic results, we often turn to less specific immunohistochemical stains and consider the resulting lists of possible tumor types. Typically, such lists are ordered according to tumor sensitivities for the stains. In probability terminology, sensitivity is the conditional probability of a positive stain given a specific tumor. Yet, the most useful probability to know is the probability of a specific tumor diagnosis, given a set of staining results. Bayes theorem provides this probability. To illustrate its use for differential diagnosis, I apply it here to the situation of carcinomas of uncertain primary site and use the information provided by stains for cytokeratin 7 and cytokeratin 20.
Elementary theorems regarding blue isocurvature perturbations
NASA Astrophysics Data System (ADS)
Chung, Daniel J. H.; Yoo, Hojin
2015-04-01
Blue CDM-photon isocurvature perturbations are attractive in terms of observability and may be typical from the perspective of generic mass relations in supergravity. We present and apply three theorems useful for blue isocurvature perturbations arising from linear spectator scalar fields. In the process, we give a more precise formula for the blue spectrum associated with the axion model of Kasuya and Kawasaki [Axion Isocurvature Fluctuations with Extremely Blue Spectrum, Phys. Rev. D 80, 023516 (2009).], which can in a parametric corner give a factor of O (10 ) correction. We explain how a conserved current associated with Peccei-Quinn symmetry plays a crucial role and explicitly plot several example spectra including the breaks in the spectra. We also resolve a little puzzle arising from a naive multiplication of isocurvature expression that sheds light on the gravitational imprint of the adiabatic perturbations on the fields responsible for blue isocurvature fluctuations.
A Stochastic Tikhonov Theorem in Infinite Dimensions
Buckdahn, Rainer Guatteri, Giuseppina
2006-03-15
The present paper studies the problem of singular perturbation in the infinite-dimensional framework and gives a Hilbert-space-valued stochastic version of the Tikhonov theorem. We consider a nonlinear system of Hilbert-space-valued equations for a 'slow' and a 'fast' variable; the system is strongly coupled and driven by linear unbounded operators generating a C{sub 0}-semigroup and independent cylindrical Brownian motions. Under well-established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. We avoid differentiability assumptions on the coefficients which would be unnatural in the infinite-dimensional framework.
Walking Through the Impulse-Momentum Theorem
NASA Astrophysics Data System (ADS)
Haugland, Ole Anton
2013-02-01
Modern force platforms are handy tools for investigating forces during human motion. Earlier they were very expensive and were mostly used in research laboratories. But now even platforms that can measure in two directions are quite affordable. In this work we used the PASCO 2-Axis Force Platform. The analysis of the data can serve as a nice illustration of qualitative or quantitative use of the impulse-momentum theorem p - p0 = ∫t0t Fdt = I. The most common use of force platforms is to study the force from the base during the push-off period of a vertical jump. I think this is an activity of great value, and I would recommend it. The use of force platforms in teaching is well documented in research literature.1-4
Extended Ehrenfest theorem with radiative corrections
NASA Astrophysics Data System (ADS)
de la Peña, L.; Cetto, A. M.; Valdés-Hernández, A.
2015-10-01
A set of basic evolution equations for the mean values of dynamical variables is obtained from the Fokker-Planck equation applied to the general problem of a particle subject to a random force. The specific case of stochastic electrodynamics is then considered, in which the random force is due to the zero-point radiation field. Elsewhere it has been shown that when this system reaches a state of energy balance, it becomes controlled by an equation identical to Schrödinger’s, if the radiationless approximation is made. The Fokker-Planck equation was shown to lead to the Ehrenfest theorem under such an approximation. Here we show that when the radiative terms are not neglected, an extended form of the Ehrenfest equation is obtained, from which follow, among others, the correct formulas for the atomic lifetimes and the (nonrelativistic) Lamb shift.
Complex virial theorem and complex scaling
Junker, B.R.
1983-06-01
We present the simple generalization to complex energies of the normal global real scaling used for bound-state calculations to produce a variational energy which satisfies the virial theorem. We show that in two limiting cases, one or the other of which is almost always p satisfied in all calculations, the virially stabilized complex energy is sensitive to only the real part or the imaginary part of the complex virial expression. We then compute the virial expression for a number of wave functions for the 1s2s/sup 2/ /sup 2/S He/sup -/, 1s2s2p /sup 2/P/sup o/ He/sup -/, and 1s/sup 2/2s/sup 2/kp /sup 2/P/sup o/ Be/sup -/ resonances and the corresponding virially stabilized resonance energies. In all calculations one of the limiting cases was applicable.
Quantum violation of fluctuation-dissipation theorem
NASA Astrophysics Data System (ADS)
Shimizu, Akira; Fujikura, Kyota
2017-02-01
We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a ‘squeezed equilibrium state’, which is macroscopically identical to the pre-measurement equilibrium state but is squeezed by the measurement. It is a time-evolving state, in which macrovariables fluctuate and relax. We also explain some of subtle but important points, careless treatments of which often lead to unphysical results, of the linear response theory.
NASA Astrophysics Data System (ADS)
Gong, Zongping; Quan, H. T.
2015-07-01
By taking full advantage of the dynamic property imposed by the detailed balance condition, we derive a new refined unified fluctuation theorem (FT) for general stochastic thermodynamic systems. This FT involves the joint probability distribution functions of the final phase-space point and a thermodynamic variable. Jarzynski equality, Crooks fluctuation theorem, and the FTs of heat as well as the trajectory entropy production can be regarded as special cases of this refined unified FT, and all of them are generalized to arbitrary initial distributions. We also find that the refined unified FT can easily reproduce the FTs for processes with the feedback control, due to its unconventional structure that separates the thermodynamic variable from the choices of initial distributions. Our result is heuristic for further understanding of the relations and distinctions between all kinds of FTs and might be valuable for studying thermodynamic processes with information exchange.
Designing steep, sharp patterns on uniformly ion-bombarded surfaces
Perkinson, Joy C.; Aziz, Michael J.; Brenner, Michael P.; Holmes-Cerfon, Miranda
2016-01-01
We propose and experimentally test a method to fabricate patterns of steep, sharp features on surfaces, by exploiting the nonlinear dynamics of uniformly ion-bombarded surfaces. We show via theory, simulation, and experiment that the steepest parts of the surface evolve as one-dimensional curves that move in the normal direction at constant velocity. The curves are a special solution to the nonlinear equations that arises spontaneously whenever the initial patterning on the surface contains slopes larger than a critical value; mathematically they are traveling waves (shocks) that have the special property of being undercompressive. We derive the evolution equation for the curves by considering long-wavelength perturbations to the one-dimensional traveling wave, using the unusual boundary conditions required for an undercompressive shock, and we show this equation accurately describes the evolution of shapes on surfaces, both in simulations and in experiments. Because evolving a collection of one-dimensional curves is fast, this equation gives a computationally efficient and intuitive method for solving the inverse problem of finding the initial surface so the evolution leads to a desired target pattern. We illustrate this method by solving for the initial surface that will produce a lattice of diamonds connected by steep, sharp ridges, and we experimentally demonstrate the evolution of the initial surface into the target pattern. PMID:27698147
Sharp transitions in nuclear dynamics: Limits to collectivity and stability
NASA Astrophysics Data System (ADS)
Colonna, M.; Di Toro, M.; Latora, V.; Smerzi, A.
Two limiting cases of nuclear dynamics are analysed in details: the disappearing of giant collective motions in hot nuclei and the nuclear disassembly in violent heavy ion collisions. It is shown that sharp transitions occur in the dynamical behaviour of finite nuclei. For collective vibration built on excited states we get a dramatic increase of the widths due to the enhancement of two body collisions with increasing temperature. The case of hot Giant Dipole Resonances (GDR) is discussed. As a consequence of the competition with neutron evaporation we get a sharp quenching of giant photon emission. Pre-equilibrium effects on the GDR formation are also accounted for. Limiting temperatures for the observation of GDR γ-decays are deduced for various nuclei, ranging from 6.0 to 3.5 MeV with increasing mass number. A detailed study of the onset of a new multifragmentation mechanism in violent heavy ion collisions around 50 MeV/u beam energy for symmetric partners is performed. It is shown that the nuclear system enters a dynamical instability region and fragments are directly produced from the growing of fluctuations. An hybrid model is developped just coupling average informations on the system entering the critical region to a statistical multifragmentration decay picture. Some hints towards a fully dynamical description of fragment production are finally discussed.
Consistency relations for sharp features in the primordial spectra
Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris; Soto, Alex E-mail: gpalmaquilod@ing.uchile.cl E-mail: alexsv@ug.uchile.cl
2015-10-01
We study the generation of sharp features in the primordial spectra within the framework of effective field theory of inflation, wherein curvature perturbations are the consequence of the dynamics of a single scalar degree of freedom. We identify two sources in the generation of features: rapid variations of the sound speed c{sub s} (at which curvature fluctuations propagate) and rapid variations of the expansion rate H during inflation. With this in mind, we propose a non-trivial relation linking these two quantities that allows us to study the generation of sharp features in realistic scenarios where features are the result of the simultaneous occurrence of these two sources. This relation depends on a single parameter with a value determined by the particular model (and its numerical input) responsible for the rapidly varying background. As a consequence, we find a one-parameter consistency relation between the shape and size of features in the bispectrum and features in the power spectrum. To substantiate this result, we discuss several examples of models for which this one-parameter relation (between c{sub s} and H) holds, including models in which features in the spectra are both sudden and resonant.
Hybridization between Dusky Grouse and Sharp-tailed Grouse
O'Donnell, Ryan P.
2015-01-01
Cache County, Utah, 7 April 2013: rare hybrid combination of grouse noted. Hybridization between Dusky Grouse (Dendragapus obscurus) and Sharp-tailed Grouse (Tympanuchus phasianellus) has been rarely documented in the wild. The only published record was of one collected from Osoyoos, British Columbia, in 1906 (Brooks 1907, Lincoln 1950). There is also one record of this hybrid in captivity (McCarthy 2006)...Although hybridization within genera is more common than between genera, it is perhaps not all too remarkable that these species would hybridize, given that Dendragapus and Tympanuchus are each other’s closest relatives (Drovetski 2002). The ranges of these two species overlap over a broad area ranging roughly from parts of northern Utah and Colorado to Yukon and the Northwest Territories. Given the close relatedness and extent of overlap of their ranges, it is perhaps surprising that there have not been more reports of this hybrid combination in the over-100 years since Brooks (1907) first described one. The species may be segregated by habitat use, as Sharp-tailed prefer open grassland sites for lekking and shrub areas for nesting, and Dusky are often found in more densely forested conifer stands—although Dusky often use more open habitats in the spring.
Consistency relations for sharp features in the primordial spectra
NASA Astrophysics Data System (ADS)
Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris; Soto, Alex
2015-10-01
We study the generation of sharp features in the primordial spectra within the framework of effective field theory of inflation, wherein curvature perturbations are the consequence of the dynamics of a single scalar degree of freedom. We identify two sources in the generation of features: rapid variations of the sound speed cs (at which curvature fluctuations propagate) and rapid variations of the expansion rate H during inflation. With this in mind, we propose a non-trivial relation linking these two quantities that allows us to study the generation of sharp features in realistic scenarios where features are the result of the simultaneous occurrence of these two sources. This relation depends on a single parameter with a value determined by the particular model (and its numerical input) responsible for the rapidly varying background. As a consequence, we find a one-parameter consistency relation between the shape and size of features in the bispectrum and features in the power spectrum. To substantiate this result, we discuss several examples of models for which this one-parameter relation (between cs and H) holds, including models in which features in the spectra are both sudden and resonant.
Homicidal sharp force injuries inflicted by family members or relatives.
Inoue, Hiromasa; Ikeda, Noriaki; Ito, Takako; Tsuji, Akiko; Kudo, Keiko
2006-04-01
We retrospectively reviewed 35 autopsy cases where death had resulted from homicidal sharp force injuries and compared cases where the injuries had been inflicted by family members or relatives (relative group) with cases where the injuries had been inflicted by an unrelated person (stranger group). We reviewed the age and sex of the victims, the number of stab wounds, the site of the stab wounds, the presence of defence wounds, the detection of alcohol and other drugs and the mental status of the victims and perpetrators. We found the following tendencies: (a) a female victim was more frequently killed by a relative than by a stranger; (b) the percentage of cases receiving a single stab wound and the percentage of cases receiving more than ten stab wounds were both unexpectedly higher in the relative group than in the stranger group, and (c) in the stranger group, when there were no defence wounds, the victim had usually consumed alcohol, whereas when there were neither defence wounds nor alcohol intake, the case usually fell into the relative group. These tendencies will contribute towards our forensic appraisement in autopsy cases resulting from sharp force injuries.
NASA Technical Reports Server (NTRS)
Atkinson, David J.; Doyle, Richard J.; James, Mark L.; Kaufman, Tim; Martin, R. Gaius
1990-01-01
A Spacecraft Health Automated Reasoning Prototype (SHARP) portability study is presented. Some specific progress is described on the portability studies, plans for technology transfer, and potential applications of SHARP and related artificial intelligence technology to telescience operations. The application of SHARP to Voyager telecommunications was a proof-of-capability demonstration of artificial intelligence as applied to the problem of real time monitoring functions in planetary mission operations. An overview of the design and functional description of the SHARP system is also presented as it was applied to Voyager.
Friedmann's equations in all dimensions and Chebyshev's theorem
Chen, Shouxin; Gibbons, Gary W.; Li, Yijun; Yang, Yisong E-mail: gwg1@damtp.cam.ac.uk E-mail: yisongyang@nyu.edu
2014-12-01
This short but systematic work demonstrates a link between Chebyshev's theorem and the explicit integration in cosmological time t and conformal time η of the Friedmann equations in all dimensions and with an arbitrary cosmological constant Λ. More precisely, it is shown that for spatially flat universes an explicit integration in t may always be carried out, and that, in the non-flat situation and when Λ is zero and the ratio w of the pressure and energy density in the barotropic equation of state of the perfect-fluid universe is rational, an explicit integration may be carried out if and only if the dimension n of space and w obey some specific relations among an infinite family. The situation for explicit integration in η is complementary to that in t. More precisely, it is shown in the flat-universe case with Λ ≠ 0 that an explicit integration in η can be carried out if and only if w and n obey similar relations among a well-defined family which we specify, and that, when Λ = 0, an explicit integration can always be carried out whether the space is flat, closed, or open. We also show that our method may be used to study more realistic cosmological situations when the equation of state is nonlinear.
This report presents the results of the verification test of the Sharpe Platinum 2013 high-volume, low-pressure gravity-feed spray gun, hereafter referred to as the Sharpe Platinum, which is designed for use in automotive refinishing. The test coating chosen by Sharpe Manufacturi...
Generalized Optical Theorem Detection in Random and Complex Media
NASA Astrophysics Data System (ADS)
Tu, Jing
The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar
Whitney, Richard
2004-01-01
Columbian Sharp-Tailed Grouse (Tympanuchus phasianellus columbianus) (CSTG) are an important traditional and cultural species to the Colville Confederated Tribes (CCT), Spokane Tribe of Indians (STOI), and other Tribes in the Region. They were once the most abundant upland bird in the Region. Currently, the largest remaining population in Washington State occurs on the CCT Reservation in Okanogan County. Increasing agricultural practices and other land uses has contributed to the decline of sharp-tail habitat and populations putting this species at risk. The decline of this species is not new (Yokum, 1952, Buss and Dziedzic, 1955, Zeigler, 1979, Meints 1991, and Crawford and Snyder 1994). The Tribes (CCT and STOI) are determined to protect, enhance and restore habitat for this species continued existence. When Grand Coulee and Chief Joseph Hydro-projects were constructed, inundated habitat used by this species was lost forever adding to overall decline. To compensate and prevent further habitat loss, the CCT proposed a project with Bonneville Power Administration (BPA) funding to address this species and their habitat requirements. The projects main focus is to address habitat utilized by the current CSTG population and determine ways to protect, restore, and enhance habitats for the conservation of this species over time. The project went through the NPPC Review Process and was funded through FY03 by BPA. This report addresses part of the current CCT effort to address the conservation of this species on the Colville Reservation.
Uniqueness theorem for charged dipole rings in five-dimensional minimal supergravity
Tomizawa, Shinya; Ishibashi, Akihiro; Yasui, Yukinori
2010-04-15
We show a uniqueness theorem for charged dipole rotating black rings in the bosonic sector of five-dimensional minimal supergravity, generalizing our previous work [arXiv:0901.4724] on the uniqueness of charged rotating black holes with topologically spherical horizon in the same theory. More precisely, assuming the existence of two commuting axial Killing vector fields and the same rod structure as the known solutions, we prove that an asymptotically flat, stationary charged rotating black hole with nondegenerate connected event horizon of cross-section topology S{sup 1}xS{sup 2} in the five-dimensional Einstein-Maxwell-Chern-Simons theory - if exists - is characterized by the mass, charge, two independent angular momenta, dipole charge, and the ratio of the S{sup 2} radius to the S{sup 1} radius. As anticipated, the necessity of specifying dipole charge - which is not a conserved charge - is the new, distinguished ingredient that highlights difference between the present theorem and the corresponding theorem for vacuum case, as well as difference from the case of topologically spherical horizon within the same minimal supergravity. We also consider a similar boundary value problem for other topologically nontrivial black holes within the same theory, and in particular, discuss some nontrivial issues that arise when attempting to generalize the present uniqueness results to include black lenses--provided there exists such a solution in the theory.
Theorems on positive data: on the uniqueness of NMF.
Laurberg, Hans; Christensen, Mads Graesbøll; Plumbley, Mark D; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
NASA Astrophysics Data System (ADS)
Stenlund, Mikko
2016-09-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff's ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
Theorems on Positive Data: On the Uniqueness of NMF
Laurberg, Hans; Christensen, Mads Græsbøll; Plumbley, Mark D.; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors. PMID:18497868
Evaluation of postoperative sharp waveforms through EEG and magnetoencephalography.
Lee, Jong Woo; Tanaka, Naoaki; Shiraishi, Hideaki; Milligan, Tracey A; Dworetzky, Barbara A; Khoshbin, Shahram; Stufflebeam, Steven M; Bromfield, Edward B
2010-02-01
EEGs obtained after craniotomy are difficult to read because of a breach rhythm consisting of unfiltered sharply contoured physiologic waveforms that can mimic interictal epileptiform discharges. Magnetoencephalography (MEG) is less affected by the skull breach. The postcraniotomy EEG and MEG scans of 20 patients were reviewed by two experienced electroencephalographers. Larger interrater variability was found for EEG as compared with MEG. Review of patients who had postoperative seizures suggested that EEG was more sensitive but less specific than MEG in detecting interictal epileptiform discharges. Furthermore, several instances of sharp waveforms that were difficult to evaluate on EEG were found to be more easily interpretable on MEG. MEG may also help determine whether asymmetries in physiologic rhythms on EEG result from the skull defect or are pathologic. MEG should be considered as an adjunctive study in patients with a breach rhythm for evaluation of interictal epileptiform discharges and cerebral dysfunction.
Diagenetic Crystal Clusters and Dendrites, Lower Mount Sharp, Gale Crater
NASA Technical Reports Server (NTRS)
Kah, L. C.; Kronyak, R.; Van Beek, J.; Nachon, M.; Mangold, N.; Thompson, L.; Wiens, R.; Grotzinger, J.; Farmer, J.; Minitti, M.; Shieber, J.; Oehler, D.
2015-01-01
Since approximately Sol 753 (to sol 840+) the Mars Science Laboratory Curiosity rover has been investigating the Pahrump locality. Mapping of HiRise images suggests that the Pahrup locality represents the first occurrence of strata associated with basal Mount Sharp. Considerable efforts have been made to document the Pahrump locality in detail, in order to constrain both depositional and diagenetic facies. The Pahrump succession consists of approximately 13 meters of recessive-weathering mudstone interbedded with thin (decimeter-scale) intervals of more erosionally resistant mudstone, and crossbedded sandstone in the upper stratigraphic levels. Mudstone textures vary from massive, to poorly laminated, to well-laminated. Here we investigate the distribution and structure of unusual diagenetic features that occur in the lowermost portion of the Pahrump section. These diagenetic features consist of three dimensional crystal clusters and dendrites that are erosionally resistant with respect to the host rock.
The Multi-Stage History of Mt. Sharp
NASA Astrophysics Data System (ADS)
Allen, C.; Dapremont, A.
2013-12-01
The Curiosity rover is exploring Gale crater and Mt. Sharp, Gale's 5-km high central mound. We are investigating the history of alteration and erosion of Mt. Sharp using orbital imagery, spectroscopy and rover observations. Our results suggest a significant time gap between emplacement of the upper and lower sections of the mound. Crater counts show that the lower mound was formed soon after Gale itself, and that it contains distinct units ranging in altitude from approximately -4,500 to -1,800 m. Spectral data suggest that many units contain phyllosilicates. We found that these clay-bearing rocks occur in distinct layers concentrated below -2,900 m. Parts of the lower mound exhibit a transition from clays to sulfates with increasing altitude. The lower mound shows evidence of flowing water, including canyons and inverted channels. Wind erosion produced km-scale yardangs and scalloped cliffs. Our mapping shows that many yardangs in the lower mound are clay-bearing, with a predominant orientation of around N-S. Curiosity's ground-level images show myriad fine-scale, mainly horizontal layers in the lower mound. The rover has found stream beds and conglomerates, indicating that water once flowed on the crater floor. Drilling near the deepest point in Gale produced abundant clay, providing additional evidence of aqueous alteration. Upper mound units range in altitude from -2,100 m to +500 m, and mantle the lower mound above an angular unconformity. Most upper mound units are composed of layers. The formation age of the upper mound is unknown, since few craters are preserved. Clay-bearing layers are detectable in several locations, mainly at altitudes near -2,000 m. There is no evidence of water flow, but wind erosion has scalloped the surfaces and edges of layers, and fine-scale yardangs are common. Correlations between yardangs and clay spectra are apparent only in the lowermost units of the upper mound. Yardang orientations vary, and include N-S, NW-SE, and NE
Subsonic loads on wings having sharp leading edges and tips
NASA Technical Reports Server (NTRS)
Kandil, O. A.; Mook, D. T.; Nayfeh, A. H.
1976-01-01
A vortex-lattice method for predicting the aerodynamics of wings having separation at the sharp edges in incompressible flows is extended to compressible subsonic flows using a modified Prandtl-Glauert transformation. Numerical results showing the effect of freestream Mach number on the aerodynamic coefficients are compared with available experimental data for several planforms. It is shown that the proposed method is suitable for predicting the aerodynamic loads on low-aspect wings at moderate angles of attack for high subsonic freestream Mach number. The method is limited to angles of attack up to 12 deg for high subsonic freestream Mach number and to angles of attack up to 20 deg for Mach number not exceeding 0.5.
A sharp upper bound for departure from normality
Lee, S.L.
1993-08-01
The departure from normality of a matrix is a real scalar that is impractical to compute if a matrix is large and its eigenvalues are unknown. A simple formula is presented for computing an upper bound for departure from normality in the Frobenius norm. This new upper bound is cheaper to compute than the upper bound derived by Henrici. Moreover, the new bound is sharp for Hermitian matrices, skew-Hermitian matrices and, in general, any matrix with eigenvalues that are horizontally or vertically aligned in the complex plane. In terms of applications, the new bound can be used in computing bounds for the spectral norm of matrix functions or bounds for the sensitivity of eigenvalues to matrix perturbations.
Sharp parameter bounds for certain maximal point lenses
NASA Astrophysics Data System (ADS)
Luce, Robert; Sète, Olivier; Liesen, Jörg
2014-05-01
Starting from an -point circular gravitational lens having images, Rhie (ArXiv Astrophysics e-prints,
Space charge limited current emission for a sharp tip
NASA Astrophysics Data System (ADS)
Zhu, Y. B.; Ang, L. K.
2015-05-01
In this paper, we formulate a self-consistent model to study the space charge limited current emission from a sharp tip in a dc gap. The tip is assumed to have a radius in the order of 10s nanometer. The electrons are emitted from the tip due to field emission process. It is found that the localized current density J at the apex of the tip can be much higher than the classical Child Langmuir law (flat surface). A scaling of J ∝ Vg3/2/Dm, where Vg is the gap bias, D is the gap size, and m = 1.1-1.2 (depending on the emission area or radius) is proposed. The effects of non-uniform emission and the spatial dependence of work function are presented.
Sharp intense line in the bioluminescence emission of the firefly.
Barua, A Gohain; Sharma, U; Phukan, M; Hazarika, S
2014-06-01
Numerous investigations have been carried out on the spectral distribution of the light of different species of fireflies. Here we record the emission spectrum of the Indian species of the firefly Luciola praeusta Kiesenwetter 1874 (Coleoptera : Lampyridae : Luciolinae) on a color film. Green and red color-sectors, with an intense yellow one in between, appear in this spectrum. Intensity profile of this spectrum reveals a hitherto undetected strong narrow yellow line, which lies within the full-width-at-half maximum (FWHM) of the intensity profile. The spectrum recorded in a high-resolution spectrometer confirms the presence of this sharp intense line. This finding lends support to an earlier drawn analogy between the in vivo emission of the firefly and laser light.
Sharp bounds for singular values of fractional integral operators
NASA Astrophysics Data System (ADS)
Burman, Prabir
2007-03-01
From the results of Dostanic [M.R. Dostanic, Asymptotic behavior of the singular values of fractional integral operators, J. Math. Anal. Appl. 175 (1993) 380-391] and Vu and Gorenflo [Kim Tuan Vu, R. Gorenflo, Singular values of fractional and Volterra integral operators, in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Minh City, 1995, Ho Chi Minh City Math. Soc., Ho Chi Minh City, 1995, pp. 174-185] it is known that the jth singular value of the fractional integral operator of order [alpha]>0 is approximately ([pi]j)-[alpha] for all large j. In this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is ([pi]j)-[alpha][1+O(j-1)].
Optimization of sharp and viewing-angle-independent structural color
NASA Astrophysics Data System (ADS)
Hsu, Chia Wei; Miller, Owen D.; Johnson, Steven G.; Soljačić, Marin
2015-04-01
Structural coloration produces some of the most brilliant colors in nature and has many applications. However, the two competing properties of narrow bandwidth and broad viewing angle have not been achieved simultaneously in previous studies. Here, we use numerical optimization to discover geometries where a sharp 7% bandwidth in scattering is achieved, yet the peak wavelength varies less than 1%, and the peak height and peak width vary less than 6% over broad viewing angles (0--90$^\\circ$) under a directional illumination. Our model system consists of dipole scatterers arranged into several rings; interference among the scattered waves is optimized to yield the wavelength-selective and angle-insensitive response. Such designs can be useful for the recently proposed transparent displays that are based on wavelength-selective scattering.
Optimization of sharp and viewing-angle-independent structural color.
Hsu, Chia Wei; Miller, Owen D; Johnson, Steven G; Soljačić, Marin
2015-04-06
Structural coloration produces some of the most brilliant colors in nature and has many applications. Motivated by the recently proposed transparent displays that are based on wavelength-selective scattering, here we consider the new problem of transparent structural color, where objects are transparent under omnidirectional broad-band illumination but scatter strongly with a directional narrow-band light source. Transparent structural color requires two competing properties, narrow bandwidth and broad viewing angle, that have not been demonstrated simultaneously previously. Here, we use numerical optimization to discover geometries where a sharp 7% bandwidth in scattering is achieved, yet the peak wavelength varies less than 1%, and the peak height and peak width vary less than 6% over broad viewing angles (0-90°) under a directional illumination. Our model system consists of dipole scatterers arranged into several rings; interference among the scattered waves is optimized to yield the wavelength-selective and angle-insensitive response.
Space charge limited current emission for a sharp tip
Zhu, Y. B. Ang, L. K.
2015-05-15
In this paper, we formulate a self-consistent model to study the space charge limited current emission from a sharp tip in a dc gap. The tip is assumed to have a radius in the order of 10s nanometer. The electrons are emitted from the tip due to field emission process. It is found that the localized current density J at the apex of the tip can be much higher than the classical Child Langmuir law (flat surface). A scaling of J ∝ V{sub g}{sup 3/2}/D{sup m}, where V{sub g} is the gap bias, D is the gap size, and m = 1.1–1.2 (depending on the emission area or radius) is proposed. The effects of non-uniform emission and the spatial dependence of work function are presented.
Fabrication of metallic nano-slit waveguides with sharp bends.
Lu, M.; Ocola, L. E.; Gray, S. K.; Wiederrecht, G.; Center for Nanoscale Materials
2008-01-01
Metallic nanoslit waveguides are promising candidates for ultrahigh-density optical interconnections. A variety of devices based on metallic nanoslit waveguides have already been proposed that show a great superiority over conventional photonic devices for compactness. However very few two-dimensional devices have been experimentally demonstrated with in-plane geometries due to fabrication difficulties. In this article, a feasible process is presented using traditional semiconductor fabrication technologies such as mix-and-match lithography and electroplating, which is capable of fabricating complicated 100 nm wide, 800 nm deep gold slit waveguides with multiple sharp right-angle corners. The process can be extended to volume production manufacturing with minor modifications, thus enabling the fabrication of nanoslit photonic circuits and networks.
The inviscid stability of supersonic flow past a sharp cone
NASA Technical Reports Server (NTRS)
Duck, Peter W.; Shaw, Stephen J.
1990-01-01
The effects of lateral curvature on the development of supersonic laminar inviscid boundary-layer flow on a sharp cone with adiabatic wall conditions are investigated analytically, with a focus on the linear temporal inviscid stability properties. The derivation of the governing equations and of a 'triply generalized' inflexion condition is outlined, and numerical results for freestream Mach number 3.8 are presented in extensive graphs and characterized in detail. A third instability mode related to the viscous mode observed by Duck and Hall (1990) using triple-deck theory is detected and shown to be more unstable and to have larger growth rates than the second mode in some cases. It is found that the 'sonic' neutral mode is affected by the lateral curvature and becomes a supersonic neutral mode.
SHARP: Automated monitoring of spacecraft health and status
NASA Technical Reports Server (NTRS)
Atkinson, David J.; James, Mark L.; Martin, R. Gaius
1991-01-01
Briefly discussed here are the spacecraft and ground systems monitoring process at the Jet Propulsion Laboratory (JPL). Some of the difficulties associated with the existing technology used in mission operations are highlighted. A new automated system based on artificial intelligence technology is described which seeks to overcome many of these limitations. The system, called the Spacecraft Health Automated Reasoning Prototype (SHARP), is designed to automate health and status analysis for multi-mission spacecraft and ground data systems operations. The system has proved to be effective for detecting and analyzing potential spacecraft and ground systems problems by performing real-time analysis of spacecraft and ground data systems engineering telemetry. Telecommunications link analysis of the Voyager 2 spacecraft was the initial focus for evaluation of the system in real-time operations during the Voyager spacecraft encounter with Neptune in August 1989.
The Multi-Stage History of Mt. Sharp
NASA Technical Reports Server (NTRS)
Allen, C.; Dapremont, A.
2013-01-01
The Curiosity rover is exploring Gale crater and Mt. Sharp, Gale's 5-km high central mound. We are investigating the history of alteration and erosion of Mt. Sharp using orbital imagery, spectroscopy and rover observations. Our results suggest a significant time gap between emplacement of the upper and lower sections of the mound. Crater counts show that the lower mound was formed soon after Gale itself, and that it contains distinct units ranging in altitude from approximately -4,500 to -1,800 m. Spectral data suggest that many units contain phyllosilicates. We found that these clay-bearing rocks occur in distinct layers concentrated below -2,900 m. Parts of the lower mound exhibit a transition from clays to sulfates with increasing altitude. The lower mound shows evidence of flowing water, including canyons and inverted channels. Wind erosion produced km-scale yardangs and scalloped cliffs. Our mapping shows that many yardangs in the lower mound are clay-bearing, with a predominant orientation of around N-S. Curiosity's ground-level images show myriad fine-scale, mainly horizontal layers in the lower mound. The rover has found stream beds and conglomerates, indicating that water once flowed on the crater floor. Drilling near the deepest point in Gale produced abundant clay, providing additional evidence of aqueous alteration. Upper mound units range in altitude from -2,100 m to +500 m, and mantle the lower mound above an angular unconformity. Most upper mound units are composed of layers. The formation age of the upper mound is unknown, since few craters are preserved. Clay-bearing layers are detectable in several locations, mainly at altitudes near -2,000 m. There is no evidence of water flow, but wind erosion has scalloped the surfaces and edges of layers, and fine-scale yardangs are common. Correlations between yardangs and clay spectra are apparent only in the lowermost units of the upper mound. Yardang orientations vary, and include N-S, NW-SE, and NE
Hypersonic Flows About a 25 degree Sharp Cone
NASA Technical Reports Server (NTRS)
Moss, James N.
2001-01-01
This paper presents the results of a numerical study that examines the surface heating discrepancies observed between computed and measured values along a sharp cone. With Mach numbers of an order of 10 and the freestream length Reynolds number of an order of 10 000, the present computations have been made with the direct simulation Monte Carlo (DSMC) method by using the G2 code of Bird. The flow conditions are those specified for two experiments conducted in the Veridian 48-inch Hypersonic Shock Tunnel. Axisymmetric simulations are made since the test model was assumed to be at zero incidence. Details of the current calculations are presented, along with comparisons between the experimental data, for surface heating and pressure distributions. Results of the comparisons show major differences in measured and calculated results for heating distributions, with differences in excess of 25 percent for the two cases examined.
Numerical investigation of shedding partial cavities over a sharp wedge
NASA Astrophysics Data System (ADS)
Budich, B.; Neuner, S.; Schmidt, S. J.; Adams, N. A.
2015-12-01
In this contribution, we examine transient dynamics and cavitation patterns of periodically shedding partial cavities by numerical simulations. The investigation reproduces reference experiments of the cavitating flow over a sharp wedge. Utilizing a homogeneous mixture model, full compressibility of the two-phase flow of water and water vapor is taken into account by the numerical method. We focus on inertia-dominated mechanisms, thus modeling the flow as inviscid. Based on the assumptions of thermodynamic equilibrium and barotropic flow, the thermodynamic properties are computed from closed-form analytical relations. Emphasis is put on a validation of the employed numerical approach. We demonstrate that computed shedding dynamics are in agreement with the references. Complex flow features observed in the experiments, including cavitating hairpin and horse-shoe vortices, are also predicted by the simulations. Furthermore, a condensation discontinuity occurring during the collapse phase at the trailing portion of the partial cavity is equally obtained.
Sharp Interface Tracking in Rotating Microflows of Solvent Extraction
Glimm, James; Almeida, Valmor de; Jiao, Xiangmin; Sims, Brett; Li, Xaiolin
2013-01-08
The objective of this project is to develop a specialized sharp interface tracking simulation capability for predicting interaction of micron-sized drops and bubbles in rotating flows relevant to optimized design of contactor devices used in solvent extraction processes of spent nuclear fuel reprocessing. The primary outcomes of this project include the capability to resolve drops and bubbles micro-hydrodynamics in solvent extraction contactors, determining from first principles continuum fluid mechanics how micro-drops and bubbles interact with each other and the surrounding shearing fluid for realistic flows. In the near term, this effort will play a central role in providing parameters and insight into the flow dynamics of models that average over coarser scales, say at the millimeter unit length. In the longer term, it will prove to be the platform to conduct full-device, detailed simulations as parallel computing power reaches the exaflop level. The team will develop an accurate simulation tool for flows containing interacting droplets and bubbles with sharp interfaces under conditions that mimic those found in realistic contactor operations. The main objective is to create an off-line simulation capability to model drop and bubble interactions in a domain representative of the averaged length scale. The technical approach is to combine robust interface tracking software, subgrid modeling, validation quality experiments, powerful computational hardware, and a team with simulation modeling, physical modeling and technology integration experience. Simulations will then fully resolve the microflow of drops and bubbles at the microsecond time scale. This approach is computationally intensive but very accurate in treating important coupled physical phenomena in the vicinity of interfaces. The method makes it possible to resolve spatial scales smaller than the typical distance between bubbles and to model some non-equilibrium thermodynamic features such as finite
NASA Technical Reports Server (NTRS)
Rubin, Alan E.; Pernicka, Ernst
1989-01-01
Bulk compositions of 19 chondrules and one matrix-rich sample from H3.4 Sharps were determined by instrumental neutron activation analysis. Samples were characterized petrographically, and mineral compositions were determined by electron microprobe analysis. There is constancy among ordinary chondrite (OC) groups in the compositional interrelationships of different chondrule types; e.g., in H3 as well as L3 and LL3 chondrites, porphyritic chondrules are more refractory than nonporphyritic chondrules. Precursor components of H3 chondrules are closely related to those of LL3 chondrules. The mean Ir/Ni, Ir/Co, and Ir/Au ratios of H3 chondrules differ from the corresponding ratios of LL3 chondrules at the 99, 90, and 79 percent confidence levels, respectively. The ratios in H3 chondrules exceed those in LL3 chondrules by amounts similar to those by which H whole-rocks exceed LL whole-rocks. These data suggest that there are primary systematic differences in bulk composition between H and LL chondrules. These differences support the inference that chondrule formation occurred after major nebular fractionation events had established the observed bulk compositional differences among OC groups.
Scaling and scale invariance of conservation laws in Reynolds transport theorem framework.
Haltas, Ismail; Ulusoy, Suleyman
2015-07-01
Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.
Polyatomic ions, branching ratios and hot molecules
NASA Astrophysics Data System (ADS)
Mitchell, J. Brian A.
2015-01-01
A discussion is given of the reason for the sharp fall-off observed in Dissociative Recombination (DR) cross sections above about 0.1 eV and of the need for accurate branching ratios being used in complex models of molecular ion chemistry. New measurements from TSR have shown that stored ions are not as cold as they were once thought to be and a new experiment facility is presented.
Digital superresolution and the generalized sampling theorem
NASA Astrophysics Data System (ADS)
Prasad, Sudhakar
2007-02-01
The technique of reconstructing a higher-resolution (HR) image of size ML×ML by digitally processing L×L subpixel-shifted lower-resolution (LR) copies of it, each of size M×M, has now become well established. This particular digital superresolution problem is analyzed from the standpoint of the generalized sampling theorem. It is shown both theoretically and by computer simulation that the choice of regularly spaced subpixel shifts for the LR images tends to maximize the robustness and minimize the error of reconstruction of the HR image. In practice, since subpixel-level control of LR image shifts may be nearly impossible to achieve, however, a more likely scenario, which is also discussed, is one involving random subpixel shifts. It is shown that without reasonably tight bounds on the range of random shifts, the reconstruction is likely to fail in the presence of even small amounts of noise unless either reliable prior information or additional data are available.
On the Spin-Statistics Theorem
NASA Astrophysics Data System (ADS)
Peshkin, Murray
2002-05-01
M.V. Berry and J.M. Robbins* (B) have explained the spin-statistics theorem (SST) within nonrelativistic quantum mechanics (QM), without using relativity or field theory. For two identical spinless particles, their starting point is a coordinate space which consists of unordered pairs r,r' where r and r' represent two points in space, not particle labels. The point r,r' is the point r',r\\. That has topological consequences for the 6D configuration space and for the wave functions |r,r'>. More generally, spin variables are appended and there are N vectors. B gave a beautiful mathematical analysis to go from there to the usual SST under stated assumptions of QM. They also explored alternative assumptions that give unusual results but that may not be physical. I seek additional insight by recasting B's analysis into a form that emphasizes the relative orbital angular momenta of pairs of particles. I report here on the spinless case, where boson statistics emerges in a transparent way. This approach appears to exclude unusual possibilities. Work supported by U.S. DOE contract W-31-109-ENG-38. *Proc. R. Soc. Lond. A 453, 1771 (1997).
Nonequilibrium fluctuation theorems in the presence of local heating
NASA Astrophysics Data System (ADS)
Pradhan, Punyabrata; Kafri, Yariv; Levine, Dov
2008-04-01
We study two nonequilibrium work fluctuation theorems, the Crooks theorem and the Jarzynski equality, for a test system coupled to a spatially extended heat reservoir whose degrees of freedom are explicitly modeled. The sufficient conditions for the validity of the theorems are discussed in detail and compared to the case of classical Hamiltonian dynamics. When the conditions are met the fluctuation theorems are shown to hold despite the fact that the immediate vicinity of the test system goes out of equilibrium during an irreversible process. We also study the effect of the coupling to the heat reservoir on the convergence of ⟨exp(-βW)⟩ to its theoretical mean value, where W is the work done on the test system and β is the inverse temperature. It is shown that the larger the local heating, the slower the convergence.
Generalized Browder's and Weyl's theorems for Banach space operators
NASA Astrophysics Data System (ADS)
Curto, Raúl E.; Han, Young Min
2007-12-01
We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of [sigma](T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f[set membership, variant]H((T)), the space of functions analytic on an open neighborhood of [sigma](T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f[set membership, variant]H([sigma](T)).
Gibbs Paradox Revisited from the Fluctuation Theorem with Absolute Irreversibility
NASA Astrophysics Data System (ADS)
Murashita, Yûto; Ueda, Masahito
2017-02-01
The inclusion of the factor ln (1 /N !) in the thermodynamic entropy proposed by Gibbs is shown to be equivalent to the validity of the fluctuation theorem with absolute irreversibility for gas mixing.
The Pythagorean Theorem: II. The infinite discrete case
Kadison, Richard V.
2002-01-01
The study of the Pythagorean Theorem and variants of it as the basic result of noncommutative, metric, Euclidean Geometry is continued. The emphasis in the present article is the case of infinite discrete dimensionality. PMID:16578869
Wigner-Araki-Yanase theorem beyond conservation laws
NASA Astrophysics Data System (ADS)
Tukiainen, Mikko
2017-01-01
The ability to measure every quantum observable is ensured by a fundamental result in quantum measurement theory. Nevertheless, additive conservation laws associated with physical symmetries, such as the angular momentum conservation, may lead to restrictions on the measurability of the observables. Such limitations are imposed by the theorem of Wigner, Araki, and Yanase (WAY). In this paper a formulation of the WAY theorem is presented rephrasing the measurability limitations in terms of quantum incompatibility. This broader mathematical basis enables us to both capture and generalize the WAY theorem by allowing us to drop the assumptions of additivity and even conservation of the involved quantities. Moreover, we extend the WAY theorem to the general level of positive operator-valued measures.
Comparison theorems for neutral stochastic functional differential equations
NASA Astrophysics Data System (ADS)
Bai, Xiaoming; Jiang, Jifa
2016-05-01
The comparison theorems under Wu and Freedman's order are proved for neutral stochastic functional differential equations with finite or infinite delay whose drift terms satisfy the quasimonotone condition and diffusion term is the same.
Forest Carbon Uptake and the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Zobitz, John
2013-01-01
Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.
Fluctuation theorem in driven nonthermal systems with quenched disorder
Reichhardt, Charles; Reichhardt, C J; Drocco, J A
2009-01-01
We demonstrate that the fluctuation theorem of Evans and Searles can be used to characterize the class of dynamics that arises in nonthermal systems of collectively interacting particles driven over random quenched disorder. By observing the frequency of entropy-destroying trajectories, we show that there are specific dynamical regimes near depinning in which this theorem holds. Hence the fluctuation theorem can be used to characterize a significantly wider class of non-equilibrium systems than previously considered. We discuss how the fluctuation theorem could be tested in specific systems where noisy dynamics appear at the transition from a pinned to a moving phase such as in vortices in type-II superconductors, magnetic domain walls, and dislocation dynamics.
A Computer Science Version of Goedel’s Theorem.
1983-08-01
The author presents a simplified proof of Godel’s theorem by appealing to well-known programming concepts. The significance of Goedel’s result to computer science , mathematics and logic is discussed. (Author)
Two time physics and Hamiltonian Noether theorem for gauge systems
Nieto, J. A.; Ruiz, L.; Silvas, J.; Villanueva, V. M.
2006-09-25
Motivated by two time physics theory we revisited the Noether theorem for Hamiltonian constrained systems. Our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints.
Amplitude estimation of a sine function based on confidence intervals and Bayes' theorem
NASA Astrophysics Data System (ADS)
Eversmann, D.; Pretz, J.; Rosenthal, M.
2016-05-01
This paper discusses the amplitude estimation using data originating from a sine-like function as probability density function. If a simple least squares fit is used, a significant bias is observed if the amplitude is small compared to its error. It is shown that a proper treatment using the Feldman-Cousins algorithm of likelihood ratios allows one to construct improved confidence intervals. Using Bayes' theorem a probability density function is derived for the amplitude. It is used in an application to show that it leads to better estimates compared to a simple least squares fit.
Test of the steady-state fluctuation theorem in turbulent Rayleigh-B'enard convection
NASA Astrophysics Data System (ADS)
Tong, Penger; Shang, Xiaodong
2005-03-01
Local convective heat flux in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in an aspect-ratio-one cell filled with water. It is found that large positive fluctuations of the vertical heat flux occurs more often in the plume-dominated sidewall region and their histograms are highly asymmetric. The statistical properties of the time-averaged local flux fluctuations are analyzed and the results are compared with the predictions of the steady state fluctuation theorem of Gallavotti and Cohen. Work supported by the Research Grants Council of Hong Kong SAR under Grant Nos. HKUST603003 (P.T.) and CUHK403003 (K.Q.X.).
Test of steady-state fluctuation theorem in turbulent Rayleigh-Bénard convection
NASA Astrophysics Data System (ADS)
Shang, X.-D.; Tong, P.; Xia, K.-Q.
2005-07-01
The local entropy production rate σ(r,t) in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in an aspect-ratio-one cell filled with water. The statistical properties of the time-averaged σ(r,t) are analyzed and the results are compared with the predictions of the steady-state fluctuation theorem (SSFT) of Gallavotti and Cohen. The experiment reveals that the SSFT can indeed be extended to the local variables, but further development is needed in order to incorporate the common dynamic complexities of far-from-equilibrium systems into the theory.
Test of steady-state fluctuation theorem in turbulent Rayleigh-Bénard convection.
Shang, X-D; Tong, P; Xia, K-Q
2005-07-01
The local entropy production rate sigma (r,t) in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in an aspect-ratio-one cell filled with water. The statistical properties of the time-averaged sigma (r,t) are analyzed and the results are compared with the predictions of the steady-state fluctuation theorem (SSFT) of Gallavotti and Cohen. The experiment reveals that the SSFT can indeed be extended to the local variables, but further development is needed in order to incorporate the common dynamic complexities of far-from-equilibrium systems into the theory.
Conformal frames and the validity of Birkhoff's theorem
NASA Astrophysics Data System (ADS)
Capozziello, S.; Sáez-Gómez, D.
2012-07-01
Birkhoff's theorem is one of the most important statements of Einstein's general relativity, which generally can not be extended to modified theories of gravity. Here we study the validity of the theorem in scalar-tensor theories using a perturbative approach, and compare the results in the so-called Einstein and Jordan frames. The implications of the results question the physical equivalence between both frames, at least in perturbations.
No-broadcasting theorem and its classical counterpart.
Kalev, Amir; Hen, Itay
2008-05-30
Although it is widely accepted that "no-broadcasting"-the nonclonability of quantum information-is a fundamental principle of quantum mechanics, an impossibility theorem for the broadcasting of general density matrices has not yet been formulated. In this Letter, we present a general proof for the no-broadcasting theorem, which applies to arbitrary density matrices. The proof relies on entropic considerations, and as such can also be directly linked to its classical counterpart, which applies to probabilistic distributions of statistical ensembles.
Levinson theorem for Aharonov-Bohm scattering in two dimensions
Sheka, Denis D.; Mertens, Franz G.
2006-11-15
We apply the recently generalized Levinson theorem for potentials with inverse-square singularities [Sheka et al., Phys. Rev. A 68, 012707 (2003)] to Aharonov-Bohm systems in two dimensions (2D). By this theorem, the number of bound states in a given mth partial wave is related to the phase shift and the magnetic flux. The results are applied to 2D soliton-magnon scattering.
The PBR theorem: Whose side is it on?
NASA Astrophysics Data System (ADS)
Ben-Menahem, Yemima
2017-02-01
This paper examines the implications of the PBR theorem for the debate on the reality of the quantum state. The theorem seeks to undermine epistemic interpretations of the quantum state and support realist interpretations thereof, but there remains ambiguity about the precise nature of epistemic interpretations, and thus ambiguity about the implications of the theorem. The aim of this paper is to examine a radical epistemic interpretation that is not undermined by the theorem and is, arguably, strengthened by it. It is this radical interpretation, rather than the one assumed by the PBR theorem, that many epistemic theorists subscribe to. In order to distinguish the radical epistemic interpretation from alternative interpretations of quantum states-in particular, to distinguish it from instrumentalism-a historical comparison of different approaches to the meaning of quantum probabilities is provided. The comparison highlights, in particular, Schrödinger's work on the nature of quantum probabilities as distinct from probabilities in statistical mechanics, and the implications of this distinction for an epistemic interpretation of probability in the two areas. Schrödinger's work also helps to identify the difficulties in the PBR definition of an epistemic interpretation and is shown to anticipate the radical alternative that is not undermined by the theorem.
Ji, Laixi; Wang, Haijun; Cao, Yuxia; Yan, Ping; Jin, Xiaofei; Nie, Peirui; Wang, Chaojian; Li, Rangqian; Zhang, Chunlong; Yang, Mingxiao; Yang, Jie
2015-01-01
The Feng Gou Zhen (sharp-hook acupuncture) as a traditional form of ancient acupuncture is said to be particularly effective for managing periarthritis of shoulder. We conducted this randomized controlled trial to evaluate the effectiveness of Feng Gou Zhen as an add-on compared to conventional analgesics for patients with PAS. 132 patients were randomly assigned in a 1 : 1 ratio to either a acupuncture group receiving sharp-hook acupuncture plus acupoint injection with conventional analgesics or a control group. Patients from both groups were evaluated at week 0 (baseline), week 1, and week 4. The primary outcome measure was the change from baseline shoulder pain, measured by Visual Analogue Scale at 7 days after treatment. Secondary outcome measures include the (i) function of shoulder joint and (ii) McGill pain questionnaire. The results showed that patients in acupuncture group had better pain relief and function recovery compared with control group (P < 0.05) at 1 week after treatment. Moreover, there were statistical differences between two groups in VAS and shoulder joint function and McGill pain questionnaire at 4 weeks after treatment (P < 0.05). Therefore, the sharp-hook acupuncture helps to relieve the pain and restore the shoulder function for patients with periarthritis of shoulder. PMID:26640496
Moldovan, N.; Divan, R.; Zeng, H.; Carlisle, J. A.; Advanced Diamond Tech.
2009-12-07
Ultrasharp diamond tips make excellent atomic force microscopy probes, field emitters, and abrasive articles due to diamond's outstanding physical properties, i.e., hardness, low friction coefficient, low work function, and toughness. Sharp diamond tips are currently fabricated as individual tips or arrays by three principal methods: (1) focused ion beam milling and gluing onto a cantilever of individual diamond tips, (2) coating silicon tips with diamond films, or (3) molding diamond into grooves etched in a sacrificial substrate, bonding the sacrificial substrate to another substrate or electrodepositing of a handling chip, followed by dissolution of the sacrificial substrate. The first method is tedious and serial in nature but does produce very sharp tips, the second method results in tips whose radius is limited by the thickness of the diamond coating, while the third method involves a costly bonding and release process and difficulties in thoroughly filling the high aspect ratio apex of molding grooves with diamond at the nanoscale. To overcome the difficulties with these existing methods, this article reports on the feasibility of the fabrication of sharp diamond tips by direct etching of ultrananocrystalline diamond (UNCD{reg_sign}) as a starting and structural material. The UNCD is reactive ion etched using a cap-precursor-mask scheme. An optimized etching recipe demonstrates the formation of ultrasharp diamond tips ({approx} 10 nm tip radius) with etch rates of 650 nm/min.
Overview and Major Findings of the Study of Houston Atmospheric Radical Precursors (SHARP) Campaign
NASA Astrophysics Data System (ADS)
Lefer, B. L.; Brune, W. H.; Collins, D. R.; Dibb, J. E.; Griffin, R. J.; Herndon, S. C.; Huey, L. G.; Jobson, B. T.; Luke, W. T.; Mellqvist, J.; Morris, G. A.; Mount, G. H.; North, S. W.; Olaguer, E. P.; Rappenglueck, B.; Ren, X.; Stutz, J.; Yu, X.; Zhang, R.
2010-12-01
Despite recent improvements in Houston’s air quality, particularly in the reduction of the number of days with ozone mixing ratios with a 1-hr average of 125 ppbv or greater, the Houston-Galveston-Brazoria (HGB) metropolitan area still has approximately 30 days where 8-hr ozone levels exceed the 75 ppbv standard. More than a third of these high ozone episodes typically occur during the Springtime. Based on the 2006 TexAQS-II and TRAMP findings highlighting the importance of HONO, HCHO, and potentially ClNO2 as radical sources in the Houston atmosphere, the Study of Houston Atmospheric Radical Precursors (SHARP) 2009 project was designed to address the following goals: (1) determine the contribution of direct emissions of OH radical precursors HCHO and HONO from flares and other point and mobile sources; (2) detect the important urban formation pathways of HONO (day/night, surface, heterogeneous, homogeneous); (3) quantify the impact of soot (fresh and coated) on chemistry and radiation, (4) measure the ambient levels of ClNO2 in Houston and determine its’ potential as a radical source; (5) perform an intercomparison of ambient HONO measurement techniques in a urban environment; (6) identify the relative importance of springtime ozone formation mechanisms in Houston. The overall purpose of pursuing these objectives was to reduce the uncertainties surrounding these processes with the aim of improve our ability to model radicals and ozone formation in Houston and other coastal cities with petrochemical operations. The majority of the time the meteorological and chemical conditions during the 2009 SHARP campaign resulted in clean southerly flow from the Gulf of Mexico. This southerly flow was interrupted at least 4 times by cold front passages during the campaign. Each frontal passage resulted in an 8-hr ozone exceedance one to three days later. Significant findings from the SHARP project from 15 April to 30 May 2009 include: (a) measurements of HCHO emitted
An investigation into a micro-sized droplet impinging on a surface with sharp wettability contrast
NASA Astrophysics Data System (ADS)
Lim, C. Y.; Lam, Y. C.
2014-10-01
An experimental investigation was conducted into a micro-sized droplet jetted onto a surface with sharp wettability contrast. The dynamics of micro-sized droplet impingement on a sharp wettability contrast surface, which is critical in inkjet printing technology, has not been investigated in the literature. Hydrophilic lines with line widths ranging from 27 to 53 µm, and contact angle ranging from 17° to 77°, were patterned on a hydrophobic surface with a contact angle of 107°. Water droplets with a diameter of 81 µm were impinged at various offset distances from the centre of the hydrophilic line. The evolution of the droplet upon impingement can be divided into three distinct phases, namely the kinematic phase, the translating phase where the droplet moves towards the centre of the hydrophilic line, and the conforming phase where the droplet spreads along the line. The key parameters affecting the conformability of the droplet to the hydrophilic line pattern are the ratio of the line width to the initial droplet diameter and the contact angle of the hydrophilic line. The droplet will only conform completely to the hydrophilic pattern if the line width is not overly small relative to the droplet and the contact angle of the hydrophilic line is sufficiently low. The impact offset distance does not affect the final shape and final location of the droplet, as long as part of the droplet touches the hydrophilic line upon impingement. This process has a significant impact on inkjet printing technology as high accuracy of inkjet droplet deposition and shape control can be achieved through wettability patterning.
Sharp bounds on causal effects using a surrogate endpoint.
Kuroki, Manabu
2013-11-10
This paper considers a problem of evaluating the causal effect of a treatment X on a true endpoint Y using a surrogate endpoint S, in the presence of unmeasured confounders between S and Y. Such confounders render the causal effect of X on Y unidentifiable from the causal effect of X on S and the joint probability of S and Y. To evaluate the causal effect of X on Y in such a situation, this paper derives closed-form formulas for the sharp bounds on the causal effect of X on Y based on both the causal effect of X on S and the joint probability of S and Y under various assumptions. In addition, we show that it is not always necessary to observe Y to test the null causal effect of X on Y under the monotonicity assumption between X and S. These bounds enable clinical practitioners and researchers to assess the causal effect of a treatment on a true endpoint using a surrogate endpoint with minimum computational effort.
Sharp knee phenomenon of primary cosmic ray energy spectrum
NASA Astrophysics Data System (ADS)
Ter-Antonyan, Samvel
2014-06-01
Primary energy spectral models are tested in the energy range of 1-200 PeV using standardized extensive air shower responses from BASJE-MAS, Tibet, GAMMA and KASCADE scintillation shower arrays. Results point toward the two-component origin of observed cosmic ray energy spectra in the knee region consisting of a pulsar component superimposed upon rigidity-dependent power law diffuse Galactic flux. The two-component energy spectral model accounts for both the sharp knee shower spectral phenomenon and observed irregularity of all-particle energy spectrum in the region of 50-100 PeV. Alternatively, tested multipopulation primary energy spectra predicted by nonlinear diffusive shock acceleration models describe observed shower spectra in the knee region provided that the cutoff magnetic rigidities of accelerating particles are 6±0.3 and 45±2 PV for the first two populations, respectively. Both tested spectral models confirm the predominant H-He primary nuclei origin of observed shower spectral knee. The parameters of tested energy spectra are evaluated using solutions of the inverse problem on the basis of the corresponding parameterizations of energy spectra for primary H, He, O-like and Fe-like nuclei, standardized shower size spectral responses in the 550-1085 g/cm2 atmospheric slant depth range and near vertical muon truncated size spectra detected by the GAMMA array.
Sharp wave ripples during learning stabilize the hippocampal spatial map.
Roux, Lisa; Hu, Bo; Eichler, Ronny; Stark, Eran; Buzsáki, György
2017-04-10
Cognitive representation of the environment requires a stable hippocampal map, but the mechanisms maintaining a given map are unknown. Because sharp wave-ripples (SPW-R) orchestrate both retrospective and prospective spatial information, we hypothesized that disrupting neuronal activity during SPW-Rs affects spatial representation. Mice learned new sets of three goal locations daily in a multiwell maze. We used closed-loop SPW-R detection at goal locations to trigger optogenetic silencing of a subset of CA1 pyramidal neurons. Control place cells (nonsilenced or silenced outside SPW-Rs) largely maintained the location of their place fields after learning and showed increased spatial information content. In contrast, the place fields of SPW-R-silenced place cells remapped, and their spatial information remained unaltered. SPW-R silencing did not impact the firing rates or proportions of place cells. These results suggest that interference with SPW-R-associated activity during learning prevents stabilization and refinement of hippocampal maps.
The inviscid stability of supersonic flow past a sharp cone
NASA Technical Reports Server (NTRS)
Duck, Peter W.; Shaw, Stephen J.
1990-01-01
The laminar boundary layer which forms on a sharp cone in a supersonic freestream, where lateral curvature plays a key role in the physics of the problem is considered. This flow is then analyzed from the point of view of linear, temporal, inviscid stability. The basic, non-axisymmetric disturbance equations are derived for general flows of this class, and a so called triply generalized inflexion condition is found for the existence of subsonic neutral modes of instability. This condition is analogous to the well-known generalized inflexion condition found in planar flows, although in the present case the condition depends on both axial and aximuthal wavenumbers. Extensive numerical results are presented for the stability problem at a freestream Mach number of 3.8, for a range of streamwise locations. These results reveal that a new mode of instability may occur, peculiar to flows of this type involving curvature. Additionally, asymptotic analyses valid close to the tip of the cone, far downstream of the cone are presented, and these give a partial (asymptotic) description of this additional mode of instability.
A sharp interface immersed boundary method for compressible viscous flows
NASA Astrophysics Data System (ADS)
Ghias, R.; Mittal, R.; Dong, H.
2007-07-01
An immersed boundary method for computing viscous, subsonic compressible flows with complex shaped stationary immersed boundaries is presented. The method employs a ghost-cell technique for imposing the boundary conditions on the immersed boundaries. The current approach leads to a sharp representation of the immersed boundaries, a property that is especially useful for flow simulations at high Reynolds numbers. Another unique feature of the method is that it can be applied on Cartesian as well as generalized body non-conformal curvilinear meshes. A mixed second-order central difference-QUICK scheme is used which allows a high degree of control over the numerical damping. A bilinear interpolation scheme used in conjunction with the ghost-cell approach results in second-order global as well as local spatial accuracy. The solver is parallelized for distributed memory platforms using domain decomposition and message passing interface (MPI) and salient features of the parallel algorithm are presented. The accuracy, fidelity and efficiency of the solver are examined by simulating flow past circular cylinders and airfoils and comparing against experimental data and other established results. Finally, we present results from a simulation of wing-tip flow at a relatively high Reynolds number in order to demonstrate the ability of the solver to model complex, non-canonical three-dimensional flows.
Residue theorem and summing over Kaluza-Klein excitations
Feng Taifu; Chen Jianbin; Gao Tiejun; Sun Kesheng
2011-11-01
Applying the equations of motion together with corresponding boundary conditions of bulk profiles at infrared and ultraviolet branes, we verify some lemmas on the eigenvalues of Kaluza-Klein modes in extension of the standard model with a warped extra dimension and the custodial symmetry SU(3){sub c}xSU(2){sub L}xSU(2){sub R}xU(1){sub X}xP{sub LR}. Using the lemmas and performing properly analytic extensions of bulk profiles, we present the sufficient condition for a convergent series of Kaluza-Klein excitations and sum over the series through the residue theorem. The method can also be applied to sum over the infinite series of Kaluza-Klein excitations in a universal extra dimension. Furthermore, we analyze the possible connection between the propagators in five-dimensional full theory and the product of bulk profiles with corresponding propagators of exciting Kaluza-Klein modes in four-dimensional effective theory, and recover some relations presented in the literature for warped and universal extra dimensions, respectively. As an example, we present the correction from new physics to the branching ratio of B{yields}X{sub s{gamma}} to the order O({mu}{sub EW}{sup 2}/{Lambda}{sub KK}{sup 2}) in extension of the standard model with a warped extra dimension and the custodial symmetry, where {Lambda}{sub KK} denotes the energy scale of low-lying Kaluza-Klein excitations and {mu}{sub EW} denotes the electroweak energy scale.
Mechanisms of sharp wave initiation and ripple generation.
Schlingloff, Dániel; Káli, Szabolcs; Freund, Tamás F; Hájos, Norbert; Gulyás, Attila I
2014-08-20
Replay of neuronal activity during hippocampal sharp wave-ripples (SWRs) is essential in memory formation. To understand the mechanisms underlying the initiation of irregularly occurring SWRs and the generation of periodic ripples, we selectively manipulated different components of the CA3 network in mouse hippocampal slices. We recorded EPSCs and IPSCs to examine the buildup of neuronal activity preceding SWRs and analyzed the distribution of time intervals between subsequent SWR events. Our results suggest that SWRs are initiated through a combined refractory and stochastic mechanism. SWRs initiate when firing in a set of spontaneously active pyramidal cells triggers a gradual, exponential buildup of activity in the recurrent CA3 network. We showed that this tonic excitatory envelope drives reciprocally connected parvalbumin-positive basket cells, which start ripple-frequency spiking that is phase-locked through reciprocal inhibition. The synchronized GABA(A) receptor-mediated currents give rise to a major component of the ripple-frequency oscillation in the local field potential and organize the phase-locked spiking of pyramidal cells. Optogenetic stimulation of parvalbumin-positive cells evoked full SWRs and EPSC sequences in pyramidal cells. Even with excitation blocked, tonic driving of parvalbumin-positive cells evoked ripple oscillations. Conversely, optogenetic silencing of parvalbumin-positive cells interrupted the SWRs or inhibited their occurrence. Local drug applications and modeling experiments confirmed that the activity of parvalbumin-positive perisomatic inhibitory neurons is both necessary and sufficient for ripple-frequency current and rhythm generation. These interneurons are thus essential in organizing pyramidal cell activity not only during gamma oscillation, but, in a different configuration, during SWRs.
A Sharp Edge of the Cratonic Lithosphere of North America
NASA Astrophysics Data System (ADS)
Harper, T. B.; Skryzalin, P. A.; Menke, W. H.; Levin, V. L.; Darbyshire, F. A.
2015-12-01
Using teleseismic travel time delays, we develop a tomographic model of the lithosphere beneath northeastern North America, from the shore of James Bay in Quebec to the Atlantic coast of New England and to a depth of 300 km. Three major terranes lie within this cratonic margin: the 2.7 Ga Superior province, the 1 Ga Grenville orogenic belt and the 0.3-0.4 Ga Appalachian terranes, which are bounded by the Grenville Front (GF) and Appalachian Front (AF), respectively. Additionally, the 0.8 Ga Avalon terrain was accreted to coastal New England by strike-skip faulting during the Appalachian orogeny. Our tomographic model uses earthquake seismograms recorded by permanent US and Canadian stations, the Transportable Array and the temporary QMIII deployment. All data were corrected for instrument response and record sections were examined visually to identify gross errors in response and timing. Differential arrival times of P and PKP waves were determined by cross-correlation and have a maximum amplitude of about ±1 second. In our model, lithospheric boundaries do not correlate well with geological boundaries, nor do they strike parallel to them. The seismically-fast (by 5% relative to AK135) cratonic lithosphere of North America is much thicker than that of the younger terranes, extending to 200 km or more depth but with a sharp east-dipping eastern edge located (at Moho depths) 100-250 km northwest of the GF. The lithosphere beneath the Grenville and Appalachian terranes, which were affected by subduction during the Grenville and Appalachian orogenies, is slower (by 4%). A sliver of seismically-fast lithosphere, extending to ~150 km depth, occurs along the Atlantic coast and is interpreted as the Avalonian lithosphere.
Keeping the Edges Sharp II: Honing Simulations of Narrow Rings
NASA Astrophysics Data System (ADS)
Rimlinger, Thomas; Hamilton, Douglas; Hahn, Joseph M.
2016-05-01
It has long been believed that shepherd satellites are necessary to keep narrow rings confined. While a pair of nearby satellites brackets Saturn’s F ring and Uranus’ Epsilon ring, dozens of other ringlets observed around the outer three planets seem to be unattended. Hamilton et al. (this meeting) have argued analytically that eccentric or inclined rings can maintain their sharp edges for millions or even billions of years despite continually dissipating energy. Here, we present numerical integrations showing isolated eccentric ringlets that do not spread; our model includes only the gravity from an oblate planet, ring self-gravity, and viscosity. We use the symplectic integrator epi_int written by Hahn & Spitale (2013).For narrow rings, the weak perturbation forces that we study act on secular rather than orbital timescales. Therefore, we find that we can use an unusually long timestep, in which these weak forces are applied once every ~30 orbits, with good energy and angular momentum conservation. Long timesteps allow us to run simulations that might otherwise take hours or even days in a matter of minutes. We present comparisons between simulations with identical initial conditions but varying timesteps to show that our approach is appropriate for this class of problems. This technique of speeding up numerical integrations works for any symplectic integrator, requiring only that the forces be weak and that the timescale of interest be long. Problems well suited to this approach (those with only secular and drag forces) include tidally-damped exoplanets and dust grains subject to radiation pressure and Poynting-Robertson drag.
Serotonin dependent masking of hippocampal sharp wave ripples.
ul Haq, Rizwan; Anderson, Marlene L; Hollnagel, Jan-Oliver; Worschech, Franziska; Sherkheli, Muhammad Azahr; Behrens, Christoph J; Heinemann, Uwe
2016-02-01
Sharp wave ripples (SPW-Rs) are thought to play an important role in memory consolidation. By rapid replay of previously stored information during slow wave sleep and consummatory behavior, they result from the formation of neural ensembles during a learning period. Serotonin (5-HT), suggested to be able to modify SPW-Rs, can affect many neurons simultaneously by volume transmission and alter network functions in an orchestrated fashion. In acute slices from dorsal hippocampus, SPW-Rs can be induced by repeated high frequency stimulation that induces long-lasting LTP. We used this model to study SPW-R appearance and modulation by 5-HT. Although stimulation in presence of 5-HT permitted LTP induction, SPW-Rs were "masked"--but appeared after 5-HT wash-out. This SPW-R masking was dose dependent with 100 nM 5-HT being sufficient--if the 5-HT re-uptake inhibitor citalopram was present. Fenfluramine, a serotonin releaser, could also mask SPW-Rs. Masking was due to 5-HT1A and 5-HT2A/C receptor activation. Neither membrane potential nor membrane conductance changes in pyramidal cells caused SPW-R blockade since both remained unaffected by combining 5-HT and citalopram. Moreover, 10 and 30 μM 5-HT mediated SPW-R masking preceded neuronal hyperpolarization and involved reduced presynaptic transmitter release. 5-HT, as well as a 5-HT1A agonist, augmented paired pulse facilitation and affected the coefficient of variance. Spontaneous SPW-Rs in mice hippocampal slices were also masked by 5-HT and fenfluramine. While neuronal ensembles can acquire long lasting LTP during higher 5-HT levels, lower 5-HT levels enable neural ensembles to replay previously stored information and thereby permit memory consolidation memory.
Central limit theorem: the cornerstone of modern statistics
2017-01-01
According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, σ2n. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding. PMID:28367284
Formalization of the Integral Calculus in the PVS Theorem Prover
NASA Technical Reports Server (NTRS)
Butler, Ricky W.
2004-01-01
The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is
On local-hidden-variable no-go theorems
NASA Astrophysics Data System (ADS)
Methot, A. A.
2006-06-01
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow.
Towards a novel no-hair theorem for black holes
Hertog, Thomas
2006-10-15
We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four-dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.
Remarks on asymptotic symmetries and the subleading soft photon theorem
NASA Astrophysics Data System (ADS)
Conde, Eduardo; Mao, Pujian
2017-01-01
A deep connection has been recently established between soft theorems and symmetries at null infinity in gravity and gauge theories, recasting the former as Ward identities of the latter. In particular, different orders (in the frequency of the soft particle) in the soft theorems are believed to be controlled by different asymptotic symmetries. In this paper we argue that this need not be the case by focusing on the soft photon theorem. We argue that the subleading soft factor follows from the same symmetry responsible for the leading one, namely certain residual (large) gauge transformations of the gauge theory. In particular, expanding the associated charge in inverse powers of the radial coordinate, the (sub)leading charge yields the (sub)leading soft factor.
Saoithín: A Theorem Prover for UTP
NASA Astrophysics Data System (ADS)
Butterfield, Andrew
Saoithín is a theorem prover developed to support the Unifying Theories of Programming (UTP) framework. Its primary design goal was to support the higher-order logic, alphabets, equational reasoning and "programs as predicates" style that is prevalent in much of the UTP literature, from the seminal work by Hoare & He [HH98] onwards. This paper describes the key features of the theorem prover, with an emphasis on the underlying foundations, and how these affect the design and implementation choices. These key features include: a formalisation of a UTP Theory; support for common proof strategies; sophisticated goal/law matching ; and user-defined language constructs. A simple theory of designs with some proof extracts is used to illustrate the above features. The theorem prover has been used with undergraduate students and we discuss some of those experiences. The paper then concludes with a discussion of current limitations and planned improvements to the tool.
Noncommutative topology and the world’s simplest index theorem
van Erp, Erik
2010-01-01
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool for proving results in classical analysis and geometry. PMID:20418506
Time dependent electromagnetic fields and 4-dimensional Stokes' theorem
NASA Astrophysics Data System (ADS)
Andosca, Ryan; Singleton, Douglas
2016-11-01
Stokes' theorem is central to many aspects of physics—electromagnetism, the Aharonov-Bohm effect, and Wilson loops to name a few. However, the pedagogical examples and research work almost exclusively focus on situations where the fields are time-independent so that one need only deal with purely spatial line integrals (e.g., ∮ A . d x ) and purely spatial area integrals (e.g., ∫ ( ∇ × A ) . d a = ∫ B . d a ). Here, we address this gap by giving some explicit examples of how Stokes' theorem plays out with time-dependent fields in a full 4-dimensional spacetime context. We also discuss some unusual features of Stokes' theorem with time-dependent fields related to gauge transformations and non-simply connected topology.
Generalized Bezout's Theorem and its applications in coding theory
NASA Technical Reports Server (NTRS)
Berg, Gene A.; Feng, Gui-Liang; Rao, T. R. N.
1996-01-01
This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.
Formulation of Liouville's theorem for grand ensemble molecular simulations
NASA Astrophysics Data System (ADS)
Delle Site, Luigi
2016-02-01
Liouville's theorem in a grand ensemble, that is for situations where a system is in equilibrium with a reservoir of energy and particles, is a subject that, to our knowledge, has not been explicitly treated in literature related to molecular simulation. Instead, Liouville's theorem, a central concept for the correct employment of molecular simulation techniques, is implicitly considered only within the framework of systems where the total number of particles is fixed. However, the pressing demand of applied science in treating open systems leads to the question of the existence and possible exact formulation of Liouville's theorem when the number of particles changes during the dynamical evolution of the system. The intention of this paper is to stimulate a debate about this crucial issue for molecular simulation.
Quantum de Finetti theorem in phase-space representation
NASA Astrophysics Data System (ADS)
Leverrier, Anthony; Cerf, Nicolas J.
2009-07-01
The quantum versions of de Finetti’s theorem derived so far express the convergence of n -partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ⊗n . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n -mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
Strong Kochen-Specker theorem and incomputability of quantum randomness
NASA Astrophysics Data System (ADS)
Abbott, Alastair A.; Calude, Cristian S.; Conder, Jonathan; Svozil, Karl
2012-12-01
The Kochen-Specker theorem shows the impossibility for a hidden variable theory to consistently assign values to certain (finite) sets of observables in a way that is noncontextual and consistent with quantum mechanics. If we require noncontextuality, the consequence is that many observables must not have pre-existing definite values. However, the Kochen-Specker theorem does not allow one to determine which observables must be value indefinite. In this paper we present an improvement on the Kochen-Specker theorem which allows one to actually locate observables which are provably value indefinite. Various technical and subtle aspects relating to this formal proof and its connection to quantum mechanics are discussed. This result is then utilized for the proposal and certification of a dichotomic quantum random number generator operating in a three-dimensional Hilbert space.
Model Checking Failed Conjectures in Theorem Proving: A Case Study
NASA Technical Reports Server (NTRS)
Pike, Lee; Miner, Paul; Torres-Pomales, Wilfredo
2004-01-01
Interactive mechanical theorem proving can provide high assurance of correct design, but it can also be a slow iterative process. Much time is spent determining why a proof of a conjecture is not forthcoming. In some cases, the conjecture is false and in others, the attempted proof is insufficient. In this case study, we use the SAL family of model checkers to generate a concrete counterexample to an unproven conjecture specified in the mechanical theorem prover, PVS. The focus of our case study is the ROBUS Interactive Consistency Protocol. We combine the use of a mechanical theorem prover and a model checker to expose a subtle flaw in the protocol that occurs under a particular scenario of faults and processor states. Uncovering the flaw allows us to mend the protocol and complete its general verification in PVS.
Strength of Butt and Sharp-Cornered Joints
REEDY JR.,EARL DAVID
2000-08-21
There has been considerable progress in recent years towards developing a stress intensity factor-based method for predicting crack initiation at a sharp, bimaterial comer. There is now a comprehensive understanding of the nature of multi-material, two-dimensional, linear-elastic, wedge-tip stress fields. In general, the asymptotic stress state at the apex of dissimilar bonded elastic wedges (i.e. at an interface comer) can have one or more power-law singularities of differing strength and with exponents that can be real or complex. There are, however; many configurations of practical importance, (e.g. adhesively bonded butt joints, hi-material beams, etc.) where interface-comer stresses are described by one, real-valued power-law singularity. In such cases, one can reasonably hypothesize that failure occurs at a critical value of the stress intensity factor: when K{sub a}=K{sub ac}.This approach is completely analogous to LEFM except that the critical stress intensity factor is associated with a discontinuity other than a crack. To apply the K{sub ac} criterion, one must be able to accurately calculate K{sub a} for arbitrary geometries. There are several well-established methods for calculating K{sub a}. These include matching asymptotic and detailed finite element results, evaluation of a path-independent contour integral, and general finite element methods for calculating K. for complex geometries. A rapidly expanding catalog of K{sub a} calibrations is now available for a number of geometries of practical interest. These calibrations provide convenient formulas that can be used in a failure analysis without recourse to a detailed numerical analysis. The K{sub ac} criterion has been applied with some notable successes. For example, the variation in strength of adhesively bonded butt joints with bond thickness and the dependence of this relationship on adhered stiffness is readily explained. No other one-parameter fracture criterion is able to make this sort of
Granular flow behavior at sharp changes in slope
NASA Astrophysics Data System (ADS)
Crosta, Giovanni; De Blasio, Fabio; Locatelli, Michele
2015-04-01
This study extends some recent experiments and analyses performed by the authors to examine the behavior of granular flows along path characterised by sharp changes in slope. In particular, various series of experiments along a bi-linear broken slope (an inclined initial sector followed by a horizontal one) have been completed using a uniform (Hostun, 0.32 mm) sand and a uniform fine gravel (2 mm grains). 60 new have been performed by releasing different volumes (1.5, 2.1 and 5.1 L) on surfaces characterized by different slope angles (35-60°), type of materials (wood and plexiglass), with or without an erodible layer (sand), or in presence of a shallow water pond (0.5 cm). These geometrical features are typical of many large rock and snow avalanches, rock falls and of chalk flows. The latter are usually typical of coastal cliffs where a shallow water environment is typical. The evolution of the flow has been monitored through a laser profilometer at 120 Hz sampling frequency and high speed camera, and in this way it has been possible to follow the evolution of the flow and deposition, and to analyse the change in deposition mode at varying the slope angle, the material and the basal friction. This is an extremely interesting development in the study of the evolution of the deposition and of the final morphology typical of such phenomena, and can support the testing of numerical models. Propagation and deposition occur forward or backward accordingly to the slope angle and the basal friction. Forward movement and deposition occur at high slope angles and with low basal friction. The opposite is true for the backward deposition. The internal "layering" within the deposit is also strongly controlled by the combination of such parameters. The time evolution of the flow allowed to determine the velocity of flow and the mode of deposition through the analysis of the change in thickness, position of the front and of the flow tail. Presence of water reduces the runout of
ERIC Educational Resources Information Center
Barrett, Scott M.; Bolding, M. Chad; Munsell, John F.
2012-01-01
Virginia's SHARP logger program is a Cooperative Extension program currently providing training to over 1,500 loggers, foresters, and others. We conducted a mail survey of SHARP loggers to characterize program participants, assess programming needs, and evaluate program effectiveness. Results indicate a diverse group of participants in terms of…
Im, Hyungsoon; Oh, Sang-Hyun
2014-02-26
Ultra-sharp metallic pyramids and wedges with tunable tip angles and 5-nm tip radii are replicated from oxidation-sharpened silicon templates with high throughput (80 million pyramids per wafer). Atomic layer deposition of Al2 O3 shells can protect these sharp pyramidal tips for subsequent usage in near-field imaging.
Federal Register 2010, 2011, 2012, 2013, 2014
2013-04-30
... of the Secretary Notice of Availability (NOA) for Sharpe Permit Relinquishment Project Environmental Assessment AGENCY: Defense Logistics Agency, DoD. ACTION: Notice of Availability (NOA) for Sharpe Permit... end 30 days after publication of this NOA in the Federal Register. Comments received by the end of...
Reasoning by analogy as an aid to heuristic theorem proving.
NASA Technical Reports Server (NTRS)
Kling, R. E.
1972-01-01
When heuristic problem-solving programs are faced with large data bases that contain numbers of facts far in excess of those needed to solve any particular problem, their performance rapidly deteriorates. In this paper, the correspondence between a new unsolved problem and a previously solved analogous problem is computed and invoked to tailor large data bases to manageable sizes. This paper outlines the design of an algorithm for generating and exploiting analogies between theorems posed to a resolution-logic system. These algorithms are believed to be the first computationally feasible development of reasoning by analogy to be applied to heuristic theorem proving.
Nonlinear Dynamic Maximum Power Theorem, with Numerical Method
1983-09-01
Desoer , "The Maximum Power Transfer Theorem for n-Ports," IEEE Trans. Circuit Theory , vol. CT-20, no. 3, pp. 328-330, May 1973. [2] J.L.Wyatt, Jr. and L.O...327-330, May 1974. [10] H. Flanders, "On the Maximal Power Transfer Theorem for n-Ports," Int. J. Circuit Theory and Applications, vol. 4, pp. 319-344...conditions in section 3.1), then the (noncausal) matched load has the form shown in Fig. 2. 3.3) Circuit Example Suppose the source takes the specific
Quantum Theory of Jaynes' Principle, Bayes' Theorem, and Information
NASA Astrophysics Data System (ADS)
Haken, Hermann
2014-12-01
After a reminder of Jaynes' maximum entropy principle and of my quantum theoretical extension, I consider two coupled quantum systems A,B and formulate a quantum version of Bayes' theorem. The application of Feynman's disentangling theorem allows me to calculate the conditional density matrix ρ (A|B) , if system A is an oscillator (or a set of them), linearly coupled to an arbitrary quantum system B. Expectation values can simply be calculated by means of the normalization factor of ρ (A|B) that is derived.
Fluidized Granular Medium as an Instance of the Fluctuation Theorem
NASA Astrophysics Data System (ADS)
Feitosa, Klebert; Menon, Narayanan
2004-04-01
We study the statistics of the power flux into a collection of inelastic beads maintained in a fluidized steady state by external mechanical driving. The power shows large fluctuations, including frequent large negative fluctuations, about its average value. The relative probabilities of positive and negative fluctuations in the power flux are in close accord with the fluctuation theorem of Gallavotti and Cohen, even at time scales shorter than those required by the theorem. We also compare an effective temperature that emerges from this analysis to the kinetic granular temperature.
Fluidized granular medium as an instance of the fluctuation theorem.
Feitosa, Klebert; Menon, Narayanan
2004-04-23
We study the statistics of the power flux into a collection of inelastic beads maintained in a fluidized steady state by external mechanical driving. The power shows large fluctuations, including frequent large negative fluctuations, about its average value. The relative probabilities of positive and negative fluctuations in the power flux are in close accord with the fluctuation theorem of Gallavotti and Cohen, even at time scales shorter than those required by the theorem. We also compare an effective temperature that emerges from this analysis to the kinetic granular temperature.
Fluctuation theorems for total entropy production in generalized Langevin systems
NASA Astrophysics Data System (ADS)
Ghosh, Bappa; Chaudhury, Srabanti
2017-01-01
The validity of the fluctuation theorems for total entropy production of a colloidal particle embedded in a non-Markovian heat bath driven by a time-dependent force in a harmonic potential is probed here. The dynamics of the system is modeled by the generalized Langevin equation with colored noise. The distribution function of the total entropy production is calculated and the detailed fluctuation theorem contains a renormalized temperature term which arises due to the non-Markovian characteristics of the thermal bath.
Extensions of the Feynman-Hellman theorem and applications
NASA Astrophysics Data System (ADS)
Singh, S. Brajamani; Singh, C. A.
1989-10-01
Epstein's [Am. J. Phys. 22, 613 (1954)] off-diagonal and higher-order extensions of the Feynman-Hellmann theorem, obtained by using the basic technique of parameter differentiation under the integral sign, are further pursued. Epstein's rederivation of the Rayleigh-Schrödinger perturbation expansion is also extended to include the degenerate case. The same approach is also used to obtain the Lennard-Jones-Brillouin-Wigner perturbation theory. The quantum virial theorem and its off-diagonal generalization is deduced and its application is illustrated by taking the example of the linear harmonic oscillator. The semiclassical expression for the kinetic energy is obtained directly from the quantization condition.
Generalization of Carey's equality and a theorem on stationary population.
Srinivasa Rao, Arni S R; Carey, James R
2015-09-01
Carey's Equality pertaining to stationary models is well known. In this paper, we have stated and proved a fundamental theorem related to the formation of this Equality. This theorem will provide an in-depth understanding of the role of each captive subject, and their corresponding follow-up duration in a stationary population. We have demonstrated a numerical example of a captive cohort and the survival pattern of medfly populations. These results can be adopted to understand age-structure and aging process in stationary and non-stationary population models.
General self-tuning solutions and no-go theorem
Förste, Stefan; Kim, Jihn E.; Lee, Hyun Min E-mail: jihnekim@gmail.com
2013-03-01
We consider brane world models with one extra dimension. In the bulk there is in addition to gravity a three form gauge potential or equivalently a scalar (by generalisation of electric magnetic duality). We find classical solutions for which the 4d effective cosmological constant is adjusted by choice of integration constants. No go theorems for such self-tuning mechanism are circumvented by unorthodox Lagrangians for the three form respectively the scalar. It is argued that the corresponding effective 4d theory always includes tachyonic Kaluza-Klein excitations or ghosts. Known no go theorems are extended to a general class of models with unorthodox Lagrangians.
Finite de Finetti theorem for infinite-dimensional systems.
D'Cruz, Christian; Osborne, Tobias J; Schack, Rüdiger
2007-04-20
We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state |Psi/Psi| chosen from a family of subsets {Cn} of the full symmetric subspace for n subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give a second equivalent characterization of the family {Cn}.
Distributed Online Judge System for Interactive Theorem Provers
NASA Astrophysics Data System (ADS)
Mizuno, Takahisa; Nishizaki, Shin-ya
2014-03-01
In this paper, we propose a new software design of an online judge system for interactive theorem proving. The distinctive feature of this architecture is that our online judge system is distributed on the network and especially involves volunteer computing. In volunteers' computers, network bots (software robots) are executed and donate computational resources to the central host of the online judge system. Our proposed design improves fault tolerance and security. We gave an implementation to two different styles of interactive theorem prover, Coq and ACL2, and evaluated our proposed architecture. From the experiment on the implementation, we concluded that our architecture is efficient enough to be used practically.
Maintaining knife sharpness in industrial meat cutting: A matter of knife or meat cutter ability.
Karltun, J; Vogel, K; Bergstrand, M; Eklund, J
2016-09-01
Knife sharpness is imperative in meat cutting. The aim of this study was to compare the impact of knife blade steel quality with meat cutters' individual ability to maintain the cutting edge sharp in an industrial production setting. Twelve meat cutters in two different companies using three different knives during normal production were studied in this quasi-experimental study. Methods included were measuring knife cutting force before and after knife use, time knives were used, ratings of sharpness and discomfort and interviews. Results showed that the meat cutters' skill of maintaining sharpness during work had a much larger effect on knife sharpness during work than the knife steel differences. The ability was also related to feelings of discomfort and to physical exertion. It was found that meat cutters using more knives were more likely to suffer from discomfort in the upper limbs, which is a risk for developing MSD.
Hammering versus drilling of sharp and obtuse trocar-point k-wires.
Franssen, B B G M; Schuurman, A H; Mink Van Der Molen, A B; Kon, M
2009-04-01
Kirschner wire characteristics affect the heating of bone during insertion and the subsequent strength of fixation. We inserted 90 sharp and 90 obtuse trocar-tip K-wires into 90 fresh frozen human cadaver metacarpals using either a drill or a pneumatic hammer. The temperature elevation, insertion time and extraction force were measured for four K-wire insertion combinations: drilling sharp; drilling obtuse; hammering sharp; hammering obtuse. Hammering resulted in significantly lower temperature elevations than drilling. Hammering sharp K-wires resulted in the highest extraction forces. The first and fifth metacarpals showed significantly lower temperature elevations than the other metacarpals, while the insertion time was significantly higher in the second and third metacarpal than in the other metacarpals. Hammering sharp trocar-tip K-wires minimises thermal damage to bone and gives the strongest fixation.
Measurements of system sharpness for two digital breast tomosynthesis systems
NASA Astrophysics Data System (ADS)
Marshall, N. W.; Bosmans, H.
2012-11-01
The aim of this work was to propose system sharpness parameters for digital breast tomosynthesis (DBT) systems that include the influence of focus size and focus motion for use in quality assurance protocols. X-ray focus size was measured using a multiple pinhole test object, while detector presampling modulation transfer function (MTF) was measured from projection images of a 10 cm × 10 cm, 1 mm thick steel edge, for the Siemens Inspiration and Hologic Selenia Dimensions DBT systems. The height of the edge above the table was then varied from 1 to 78 mm. The MTF expected from theory for the projection images was calculated from the measured detector MTF, focus size MTF and focus motion MTF and was compared against measured curves. Two methods were used to measure the in-plane MTF in the DBT volume: a tungsten wire of diameter 25 µm and an Al edge 0.2 mm thick, both imaged with a 15 mm thick poly(methyl methacrylate) (PMMA) plate. The in-depth point spread function (PSF) was measured using an angled tungsten wire. The full 3D MTF was estimated with a 0.5 mm diameter aluminium bead held in a 45 mm thick PMMA phantom, with the bead 15 and 65 mm above the table. Inspiration DBT projection images are saved at native detector resolution (85 µm), while the Dimensions re-bins projections to 140 µm pixels (2 × 2 binning); both systems used 2 × 2 binning of projection data before reconstruction. The 50% point for the MTF (MTF0.50) measured in the DBT projection images for the tube-travel direction fell as a function of height above the table from 3.60 to 0.90 mm-1 for the Inspiration system and from 2.50 to 1.20 mm-1 for the Dimensions unit. The maximum deviation of measured MTF0.50 from the calculated value was 13%. MTF0.50 measured in-plane (tube-travel direction) fell as a function of height above the table from 1.66 to 0.97 mm-1 for the Inspiration system and from 2.21 to 1.31 mm-1 for the Dimensions system. The full-width half-maximum for the in-depth PSF was 3
Measurements of system sharpness for two digital breast tomosynthesis systems.
Marshall, N W; Bosmans, H
2012-11-21
The aim of this work was to propose system sharpness parameters for digital breast tomosynthesis (DBT) systems that include the influence of focus size and focus motion for use in quality assurance protocols. X-ray focus size was measured using a multiple pinhole test object, while detector presampling modulation transfer function (MTF) was measured from projection images of a 10 cm × 10 cm, 1 mm thick steel edge, for the Siemens Inspiration and Hologic Selenia Dimensions DBT systems. The height of the edge above the table was then varied from 1 to 78 mm. The MTF expected from theory for the projection images was calculated from the measured detector MTF, focus size MTF and focus motion MTF and was compared against measured curves. Two methods were used to measure the in-plane MTF in the DBT volume: a tungsten wire of diameter 25 µm and an Al edge 0.2 mm thick, both imaged with a 15 mm thick poly(methyl methacrylate) (PMMA) plate. The in-depth point spread function (PSF) was measured using an angled tungsten wire. The full 3D MTF was estimated with a 0.5 mm diameter aluminium bead held in a 45 mm thick PMMA phantom, with the bead 15 and 65 mm above the table. Inspiration DBT projection images are saved at native detector resolution (85 µm), while the Dimensions re-bins projections to 140 µm pixels (2 × 2 binning); both systems used 2 × 2 binning of projection data before reconstruction. The 50% point for the MTF (MTF(0.50)) measured in the DBT projection images for the tube-travel direction fell as a function of height above the table from 3.60 to 0.90 mm(-1) for the Inspiration system and from 2.50 to 1.20 mm(-1) for the Dimensions unit. The maximum deviation of measured MTF(0.50) from the calculated value was 13%. MTF(0.50) measured in-plane (tube-travel direction) fell as a function of height above the table from 1.66 to 0.97 mm(-1) for the Inspiration system and from 2.21 to 1.31 mm(-1) for the Dimensions system. The full-width half-maximum for the in
Elliptical billiard systems and the full Poncelet's theorem in n dimensions
NASA Astrophysics Data System (ADS)
Chang, Shau-Jin; Crespi, Bruno; Shi, Kang-Jie
1993-06-01
In this work is presented a generalization of Poncelet's theorem to n dimensions which is refered to as the full Poncelet's theorem. The theorem states that if the reflections of a trajectory by a sequence of confocal quadrics lead to a closed skew polygon, then there exists an (n-1)-parameter family of polygons having the same property. A physical realization and a projective geometrical proof of this theorem are given. If all the reflecting quadrics coincide, the above theorem reduces to the n-dimensional Poncelet's theorem presented by Chang and Friedberg. The geometrical proof is a finite construction based on a preliminary theorem which extends Hart's lemma. The full Poncelet's theorem may thus be extended to projective geometries over most fields, including discrete ones.
Chemical Composition of lower Mount Sharp at Gale Crater, Mars, as measured by the APXS
NASA Astrophysics Data System (ADS)
Gellert, R.; Boyd, N.; Campbell, J. L.; VanBommel, S.; Perrett, G. M.; Desouza, E.; Thompson, L. M.; Yen, A. S.; Berger, J. A.
2015-12-01
From sol 810 through to 950 the MSL Curiosity Rover carried out detailed investigations at Pahrump, which likely represents the lowest strata of Mount Sharp. The bulk chemistry is very different compared to previously encountered formations like Sheepbed at Yellowknifebay, which resembled an average Mars composition. The bedrock is significantly depleted in Mg and Ca, elevated in Al and Si and enriched in Zn (~2000 ppm), Se (~50 ppm) and Pb(~100 ppm). The composition varies only slightly over the ~10 meter elevation explored at Pahrump and is chemically homogenous on a 10 cm scale. However, some clear trends uphill are present. Zn and Se decrease with elevation, the Fe/Mn ratio, a possible indicator for the Fe3+ content, increases from 50 to 100. Elevated 2.5% P2O5 were encountered at higher elevations. SO3 ranges from 5 to 8% in the drill samples, higher abundances were found in Ca-sulfate veins and diagenetic features that contain ~15% (Mg,Ni)-sulfates. The Pahrump bedrock may be traced ~500m to the north and south. Bonanza King (sol 755, Hidden Valley) and Spokane (sol 989) share the same major chemistry, including similar trends in minor and trace elements. Most recently the rover approached a contact between Pahrump-like bedrock and an overlying, more resistant unit identified from orbit at Marias Pass. High SiO2, ranging from 63 to 72%, was found close to the contact, above which the sandstone composition changes abruptly to that of average Mars. Increased Si is correlated with elevated P and Ti, lower Al and Fe, and a dramatic decrease in Zn, Ni and Cr to very low values of a few 100 ppm and less. The elevated silica and associated elemental trends observed at Marias Pass share characteristics with the high silica bedrock examined at HomePlate in Gusev Crater, where acidic leaching or silica mobilization has been proposed. The stratigraphy together with data from 4 drill samples for SAM and Chemin might shed light on the formation history of this extensive
Direct detection of sharp upper-mantle features with waveform complexity
NASA Astrophysics Data System (ADS)
Sun, D.; Helmberger, D. V.
2009-12-01
A recent technique for processing array data searching for multipathing has been applied to USArray data [Sun and Helmberger, 2009]. A record can be decomposed by S(t) + A×S(t+ΔLR), where S(t) is the synthetics for a reference model. Time separation ΔLR and amplitude ratio A are needed to obtain best cross-correlation between a simulated waveform and data. The travel time of the composite waveform relative to the reference model synthetics is defined as ΔT. A simulated annealing algorithm is used to inverse the parameters of ΔLR, ΔT, and A. Whereas the conventional tomography yields a travel time correction (ΔT), our analysis yields an extra parameter of ΔLR which describe the waveform complexity. With the array, we can construct a mapping of the gradient of ΔLR with complexity patterns. A horizontal structure will introduce the waveform complexity along the distance profile (in-plane multipathing). A azimuthally orientation ΔLR pattern indicates a vertical structure with out-of-plane multipathing. Using such maps generated from artificial data we can easily recognize features produced by downwelling (DW) vs. upwelling (UW) and address their scale lengths. In particular, we find a line of DW's along the Rock Mountain Front which have anomalies similar to those found along the La Ristra line. These ΔLR anomalies are up to 8s, which corresponds to features extending down to the 410 discontinuity with a 6% shear velocity increase. Such features appear to be produced by delamination caused by the sharp lateral temperature gradient [Song and Helmberger, 2007]. The ΔLR patters for the Western US indicates a number of UW's, in which the Yellowstone is particular obvious. The records for events from southwestern and southeastern directions show generally simple waveform across the Yellowstone -Snake River Plain (SRP). For the event from the northeast, the stations along the western edge of SRP show strong waveform distortions, which indicate azimuthally
No-scalar-hair theorem for spherically symmetric reflecting stars
NASA Astrophysics Data System (ADS)
Hod, Shahar
2016-11-01
It is proved that spherically symmetric compact reflecting objects cannot support static bound-state configurations made of scalar fields whose self-interaction potential V (ψ2) is a monotonically increasing function of its argument. Our theorem rules out, in particular, the existence of massive scalar hair outside the surface of a spherically symmetric compact reflecting star.
An Elementary Proof of a Converse Mean-Value Theorem
ERIC Educational Resources Information Center
Almeida, Ricardo
2008-01-01
We present a new converse mean value theorem, with a rather elementary proof. [The work was supported by Centre for Research on Optimization and Control (CEOC) from the "Fundacaopara a Ciencia e a Tecnologia" FCT, co-financed by the European Community Fund FEDER/POCTI.
Kochen-Specker Theorem as a Precondition for Quantum Computing
NASA Astrophysics Data System (ADS)
Nagata, Koji; Nakamura, Tadao
2016-12-01
We study the relation between the Kochen-Specker theorem (the KS theorem) and quantum computing. The KS theorem rules out a realistic theory of the KS type. We consider the realistic theory of the KS type that the results of measurements are either +1 or -1. We discuss an inconsistency between the realistic theory of the KS type and the controllability of quantum computing. We have to give up the controllability if we accept the realistic theory of the KS type. We discuss an inconsistency between the realistic theory of the KS type and the observability of quantum computing. We discuss the inconsistency by using the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be for an easy detector to a Pauli observable. We cannot accept the realistic theory of the KS type to simulate the double-slit experiment in a significant specific case. The realistic theory of the KS type can not depicture quantum detector. In short, we have to give up both the observability and the controllability if we accept the realistic theory of the KS type. Therefore, the KS theorem is a precondition for quantum computing, i.e., the realistic theory of the KS type should be ruled out.
Fermat's Last Theorem for Factional and Irrational Exponents
ERIC Educational Resources Information Center
Morgan, Frank
2010-01-01
Fermat's Last Theorem says that for integers n greater than 2, there are no solutions to x[superscript n] + y[superscript n] = z[superscript n] among positive integers. What about rational exponents? Irrational n? Negative n? See what an undergraduate senior seminar discovered.
An Experiment on a Physical Pendulum and Steiner's Theorem
ERIC Educational Resources Information Center
Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.
2010-01-01
Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…
Improving Conceptions in Analytical Chemistry: The Central Limit Theorem
ERIC Educational Resources Information Center
Rodriguez-Lopez, Margarita; Carrasquillo, Arnaldo, Jr.
2006-01-01
This article describes the central limit theorem (CLT) and its relation to analytical chemistry. The pedagogic rational, which argues for teaching the CLT in the analytical chemistry classroom, is discussed. Some analytical chemistry concepts that could be improved through an understanding of the CLT are also described. (Contains 2 figures.)
A categorical account of the Hofmann-Mislove theorem
NASA Astrophysics Data System (ADS)
Townsend, Christopher F.
2005-11-01
A categorical account is given of the Hofmann-Mislove theorem, describing the Scott open filters on a frame. The account is stable under an order duality and so is shown to also cover Bunge and Funk's constructive description of the points of the lower power locale.
Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos
ERIC Educational Resources Information Center
Boozer, A. D.
2011-01-01
We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…
LETTERS AND COMMENTS: Reply to 'Noether's theorem once again'
NASA Astrophysics Data System (ADS)
Marinho, Rubens M., Jr.
2009-09-01
This reply answers the issues raised in the comment on my paper (Marinho Jr 2007 Eur. J. Phys. 28 37-43), obtains the Laplace-Runge-Lenz vector (Goldstein 2002 Classical Mechanics 3rd edn (Reading, MA: Addison-Wesley)) using Noether's theorem and includes a Maple program used to derive the results.
Establishing Appropriate Conditions: Students Learning to Apply a Theorem
ERIC Educational Resources Information Center
Scataglini-Belghitar, Giovanna; Mason, John
2012-01-01
During a sequence of tutorials conducted by the first author, it became evident that students were not seeing how to apply the theorem concerning a continuous function on a closed and bounded interval attaining its extreme values in situations in which it is necessary first to construct the closed and bounded interval by reasoning about properties…
An Extension of the Mean Value Theorem for Integrals
ERIC Educational Resources Information Center
Khalili, Parviz; Vasiliu, Daniel
2010-01-01
In this note we present an extension of the mean value theorem for integrals. The extension we consider is motivated by an older result (here referred as Corollary 2), which is quite classical for the literature of Mathematical Analysis or Calculus. We also show an interesting application for computing the sum of a harmonic series.
Null conformal Killing-Yano tensors and Birkhoff theorem
NASA Astrophysics Data System (ADS)
Ferrando, Joan Josep; Sáez, Juan Antonio
2016-04-01
We study the space-times admitting a null conformal Killing-Yano tensor whose divergence defines a Killing vector. We analyze the similarities and differences with the recently studied non null case (Ferrando and Sáez in Gen Relativ Gravit 47:1911, 2015). The results by Barnes concerning the Birkhoff theorem for the case of null orbits are analyzed and generalized.
Rotationally invariant proof of Bell's theorem without inequalities
Cabello, Adan
2003-03-01
The singlet state of two spin-(3/2) particles allows a proof of Bell's theorem without inequalities with two distinguishing features: any local observable can be regarded as an Einstein-Podolsky-Rosen element of reality, and the contradiction with local realism occurs not only for some specific local observables but for any rotation whereof.
The Unforgettable Experience of a Workshop on Pythagoras Theorem
ERIC Educational Resources Information Center
Arwani, Salima Shahzad
2011-01-01
The author conducted a workshop with colleagues in which awareness of Pythagoras' theorem was raised. This workshop was an unforgettable event in the author's life because it was the first time that she had interacted with teachers from a different school system, and it allowed her to develop presentation skills and confidence in her own…
Hamiltonian Noether theorem for gauge systems and two time physics
NASA Astrophysics Data System (ADS)
Villanueva, V. M.; Nieto, J. A.; Ruiz, L.; Silvas, J.
2005-08-01
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al model and, with special emphasis, to two time physics.
Geometric Demonstration of the Fundamental Theorems of the Calculus
ERIC Educational Resources Information Center
Sauerheber, Richard D.
2010-01-01
After the monumental discovery of the fundamental theorems of the calculus nearly 350 years ago, it became possible to answer extremely complex questions regarding the natural world. Here, a straightforward yet profound demonstration, employing geometrically symmetric functions, describes the validity of the general power rules for integration and…
Weak convergence theorems for a countable family of Lipschitzian mappings
NASA Astrophysics Data System (ADS)
Nilsrakoo, Weerayuth; Saejung, Satit
2009-08-01
This paper is concerned with convergence of an approximating common fixed point sequence of countable Lipschitzian mappings in a uniformly convex Banach space. We also establish weak convergence theorems for finding a common element of the set of fixed points, the set of solutions of an equilibrium problem, and the set of solutions of a variational inequality. With an appropriate setting, we obtain and improve the corresponding results recently proved by Moudafi [A. Moudafi, Weak convergence theorems for nonexpansive mappings and equilibrium problems. J. Nonlinear Convex Anal. 9 (2008) 37-43], Tada-Takahashi [A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem. J. Optim. Theory Appl. 133 (2007) 359-370], and Plubtieng-Kumam [S. Plubtieng and P. Kumam, Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings. J. Comput. Appl. Math. (2008) doi:10.1016/j.cam.2008.05.045]. Some of our results are established with weaker assumptions.
A fixed point theorem for certain operator valued maps
NASA Technical Reports Server (NTRS)
Brown, D. R.; Omalley, M. J.
1978-01-01
In this paper, we develop a family of Neuberger-like results to find points z epsilon H satisfying L(z)z = z and P(z) = z. This family includes Neuberger's theorem and has the additional property that most of the sequences q sub n converge to idempotent elements of B sub 1(H).
Thermodynamic laws and equipartition theorem in relativistic Brownian motion.
Koide, T; Kodama, T
2011-06-01
We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.
A Computer Algorithm from DeMoivre's Theorem.
ERIC Educational Resources Information Center
Boyd, James N.
1982-01-01
Details are given of a simple computer program written in BASIC which calculates the sine of an angle through an application of DeMoivre's Theorem. The program is included in the material, and the program's success is discussed in terms of why the approximation works. (MP)
On Feynman's Triangle Problem and the Routh Theorem
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2009-01-01
In this article, we give a brief history of the Feynman's Triangle problem and describe a simple method to solve a general version of this problem, which is called the Routh Theorem. This method could be found useful to school teachers, instructors or lecturers who are involved in teaching geometry.
A shape theorem for Riemannian first-passage percolation
NASA Astrophysics Data System (ADS)
LaGatta, T.; Wehr, J.
2010-05-01
Riemannian first-passage percolation is a continuum model, with a distance function arising from a random Riemannian metric in Rd. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability of 1.
Four Proofs of the Converse of the Chinese Remainder Theorem
ERIC Educational Resources Information Center
Dobbs, D. E.
2008-01-01
Four proofs, designed for classroom use in varying levels of courses on abstract algebra, are given for the converse of the classical Chinese Remainder Theorem over the integers. In other words, it is proved that if m and n are integers greater than 1 such that the abelian groups [double-struck z][subscript m] [direct sum] [double-struck…
Two Theorems on Dissipative Energy Losses in Capacitor Systems
ERIC Educational Resources Information Center
Newburgh, Ronald
2005-01-01
This article examines energy losses in charge motion in two capacitor systems. In the first charge is transferred from a charged capacitor to an uncharged one through a resistor. In the second a battery charges an originally uncharged capacitor through a resistance. Analysis leads to two surprising general theorems. In the first case the fraction…
A Theorem and its Application to Finite Tampers
DOE R&D Accomplishments Database
Feynman, R. P.
1946-08-15
A theorem is derived which is useful in the analysis of neutron problems in which all neutrons have the same velocity. It is applied to determine extrapolated end-points, the asymptotic amplitude from a point source, and the neutron density at the surface of a medium. Formulas fro the effect of finite tampers are derived by its aid, and their accuracy discussed.
Understanding the Sampling Distribution and the Central Limit Theorem.
ERIC Educational Resources Information Center
Lewis, Charla P.
The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…
Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED.
Fodor, Z; Hoelbling, C; Krieg, S; Lellouch, L; Lippert, Th; Portelli, A; Sastre, A; Szabo, K K; Varnhorst, L
2016-08-19
In a previous Letter [Borsanyi et al., Phys. Rev. Lett. 111, 252001 (2013)] we determined the isospin mass splittings of the baryon octet from a lattice calculation based on N_{f}=2+1 QCD simulations to which QED effects have been added in a partially quenched setup. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. Our ensembles include 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. For the parameter which quantifies violations to Dashen's theorem, we obtain ϵ=0.73(2)(5)(17), where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, m_{u}=2.27(6)(5)(4) and m_{d}=4.67(6)(5)(4) MeV in the modified minimal subtraction scheme at 2 GeV and the isospin breaking ratios m_{u}/m_{d}=0.485(11)(8)(14), R=38.2(1.1)(0.8)(1.4), and Q=23.4(0.4)(0.3)(0.4). Our results exclude the m_{u}=0 solution to the strong CP problem by more than 24 standard deviations.
SHARP1/DEC2 inhibits adipogenic differentiation by regulating the activity of C/EBP.
Gulbagci, Neriman Tuba; Li, Li; Ling, Belinda; Gopinadhan, Suma; Walsh, Martin; Rossner, Moritz; Nave, Klaus-Armin; Taneja, Reshma
2009-01-01
SHARP1, a basic helix-loop-helix transcription factor, is expressed in many cell types; however, the mechanisms by which it regulates cellular differentiation remain largely unknown. Here, we show that SHARP1 negatively regulates adipogenesis. Although expression of the early marker CCAAT/enhancer binding protein beta (C/EBPbeta) is not altered, its crucial downstream targets C/EBPalpha and peroxisome proliferator-activated receptor gamma (PPARgamma) are downregulated by SHARP1. Protein interaction studies confirm that SHARP1 interacts with and inhibits the transcriptional activity of both C/EBPbeta and C/EBPalpha, and enhances the association of C/EBPbeta with histone deacetylase 1 (HDAC1). Consistently, in SHARP1-expressing cells, HDAC1 and the histone methyltransferase G9a are retained at the C/EBP regulatory sites on the C/EBPalpha and PPARgamma2 promoters during differentiation, resulting in inhibition of their expression. Interestingly, treatment with troglitazone results in displacement of HDAC1 and G9a, and rescues the differentiation defect of SHARP1-overexpressing cells. Our data indicate that SHARP1 inhibits adipogenesis through the regulation of C/EBP activity, which is essential for PPARgamma-ligand-dependent displacement of co-repressors from adipogenic promoters.
Sharpness-induced energy shifts of quantum well states in Pb islands on Cu(111)
NASA Astrophysics Data System (ADS)
Chan, Wen-Yuan; Lu, Shin-Ming; Su, Wei-Bin; Liao, Chun-Chieh; Hoffmann, Germar; Tsai, Tsong-Ru; Chang, Chia-Seng
2017-03-01
We elucidate that the tip sharpness in scanning tunneling microscopy (STM) can be characterized through the number of field-emission (FE) resonances. A higher number of FE resonances indicates higher sharpness. We observe empty quantum well (QW) states in Pb islands on Cu(111) under different tip sharpness levels. We found that QW states observed by sharper tips always had lower energies, revealing negative energy shifts. This sharpness-induced energy shift originates from an inhomogeneous electric field in the STM gap. An increase in sharpness increases the electric field inhomogeneity, that is, enhances the electric field near the tip apex, but weakens the electric field near the sample. As a result, higher sharpness can increase the electronic phase in vacuum, causing the lowering of QW state energies. Moreover, the behaviors of negative energy shift as a function of state energy are entirely different for Pb islands with a thickness of two and nine atomic layers. This thickness-dependent behavior results from the electrostatic force in the STM gap decreasing with increasing tip sharpness. The variation of the phase contributed from the expansion deformation induced by the electrostatic force in a nine-layer Pb island is significantly greater, sufficient to effectively negate the increase of electronic phase in vacuum.
Sharpness-induced energy shifts of quantum well states in Pb islands on Cu(111).
Chan, Wen-Yuan; Lu, Shin-Ming; Su, Wei-Bin; Liao, Chun-Chieh; Hoffmann, Germar; Tsai, Tsong-Ru; Chang, Chia-Seng
2017-03-03
We elucidate that the tip sharpness in scanning tunneling microscopy (STM) can be characterized through the number of field-emission (FE) resonances. A higher number of FE resonances indicates higher sharpness. We observe empty quantum well (QW) states in Pb islands on Cu(111) under different tip sharpness levels. We found that QW states observed by sharper tips always had lower energies, revealing negative energy shifts. This sharpness-induced energy shift originates from an inhomogeneous electric field in the STM gap. An increase in sharpness increases the electric field inhomogeneity, that is, enhances the electric field near the tip apex, but weakens the electric field near the sample. As a result, higher sharpness can increase the electronic phase in vacuum, causing the lowering of QW state energies. Moreover, the behaviors of negative energy shift as a function of state energy are entirely different for Pb islands with a thickness of two and nine atomic layers. This thickness-dependent behavior results from the electrostatic force in the STM gap decreasing with increasing tip sharpness. The variation of the phase contributed from the expansion deformation induced by the electrostatic force in a nine-layer Pb island is significantly greater, sufficient to effectively negate the increase of electronic phase in vacuum.
Fixed point theorems for generalized contractions in ordered metric spaces
NASA Astrophysics Data System (ADS)
O'Regan, Donal; Petrusel, Adrian
2008-05-01
The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, MEC. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petrusel, I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.
ERIC Educational Resources Information Center
Young, Anne Ludington
1996-01-01
Error estimates for tangent line approximations and for numerical integration are found using special cases of the error formulas for Taylor's Theorem and the Trapezoidal Rule, respectively. Proofs of these theorems rely on a modification of Rolle's Theorem. (Author/MKR)
A variational theorem for creep with applications to plates and columns
NASA Technical Reports Server (NTRS)
Sanders, J Lyell, Jr; Mccomb, Harvey G , Jr; Schlechte, Floyd R
1958-01-01
A variational theorem is presented for a body undergoing creep. Solutions to problems of the creep behavior of plates, columns, beams, and shells can be obtained by means of the direct methods of the calculus of variations in conjunction with the stated theorem. The application of the theorem is illustrated for plates and columns by the solution of two sample problems.
Using Computers To Teach the Concepts of the Central Limit Theorem.
ERIC Educational Resources Information Center
Mittag, Kathleen Cage
A pivotal theorem which is of critical importance to statistical inference in probability and statistics is the Central Limit Theorem (CLT). The theorem concerns the sampling distribution of random samples taken from a population, including population distributions that do not have to be normal distributions. This paper contains a brief history of…
NASA Astrophysics Data System (ADS)
Vermeulen, B.; Hoitink, A. J. F.; Berkum, S. W.; Hidayat, H.
2014-07-01
Autogenic scouring in sharp river bends has received ample attention in laboratory and modeling studies. These studies have significantly advanced our understanding of how flow processes are influenced by strong curvature and how they affect the bathymetry. Here we present a 300 km reach of the Mahakam River in Indonesia, which features several sharp bends (W/R > 0.5), providing a unique field data set to validate existing knowledge on sharp bends. Scour depths were found to strongly exceed what can be expected based on existing understanding of sharp bends and are highly correlated with curvature. A comprehensive stream reconnaissance was carried out to compare the occurrence of sharp bends and deep scours with lateral bank migration. Histograms of the occurrence of erosive, stable, advancing, and bar-type banks as a function of curvature quantify the switch from a mildly curved bend regime to a sharp bend regime. In mild bends, outer banks erode and inner banks advance. In sharp bends the erosion pattern inverts. Outer banks stabilize or advance, while inner banks erode. In sharply curved river bends, bars occur near the outer banks that become less erosive for higher curvatures. Inner banks become more erosive for higher curvatures but nevertheless accommodate the larger portion of exposed bars. No relation was found between the land cover adjacent to the river and the occurrence of sharp bends. Soil processes may play a crucial role in the formation of sharp bends, which is inferred from iron and manganese concretions observed in the riverbanks, indicating ferric horizons and early stages of the formation of plinthic horizons. Historical topographic maps show the planform activity of the river is low, which may relate to the scour holes slowing down planimetric development.
Super-Sharp Radio "Vision" Measures Galaxy's Motion in Space
NASA Astrophysics Data System (ADS)
2005-03-01
Astronomers using the National Science Foundation's Very Long Baseline Array (VLBA) have measured the motion across the sky of a galaxy nearly 2.4 million light-years from Earth. While scientists have been measuring the motion of galaxies directly toward or away from Earth for decades, this is the first time that the transverse motion (called proper motion by astronomers) has been measured for a galaxy that is not a satellite of our own Milky Way Galaxy. M33 Radio/Optical Image of M33 CREDIT: NRAO/AUI/NSF, NOAO/AURA/NSF (Click on image for more files) An international scientific team analyzed VLBA observations made over two and a half years to detect minuscule shifts in the sky position of the spiral galaxy M33. Combined with previous measurements of the galaxy's motion toward Earth, the new data allowed the astronomers to calculate M33's movement in three dimensions for the first time. "A snail crawling on Mars would appear to be moving across the surface more than 100 times faster than the motion we measured for this galaxy," said Mark Reid, of the Harvard-Smithsonian Center for Astrophysics in Cambridge, MA. M33 is a satellite of the larger galaxy M31, the well-known Andromeda Galaxy that is the most distant object visible to the naked eye. Both are part of the Local Group of galaxies that includes the Milky Way. In addition to measuring the motion of M33 as a whole, the astronomers also were able to make a direct measurement of the spiral galaxy's rotation. Both measurements were made by observing the changes in position of giant clouds of molecules inside the galaxy. The water vapor in these clouds acts as a natural maser, strengthening, or amplifying, radio emission the same way that lasers amplify light emission. The natural masers acted as bright radio beacons whose movement could be tracked by the ultra-sharp radio "vision" of the VLBA. Reid and his colleagues plan to continue measuring M33's motion and also to make similar measurements of M31's motion
Super-Sharp Radio 'Eye' Remeasuring the Universe
NASA Astrophysics Data System (ADS)
2011-02-01
Using the super-sharp radio "vision" of astronomy's most precise telescope, scientists have extended a directly-measured "yardstick" three times farther into the cosmos than ever before, an achievement with important implications for numerous areas of astrophysics, including determining the nature of Dark Energy, which constitutes 70 percent of the Universe. The continent-wide Very Long Baseline Array (VLBA) also is redrawing the map of our home Galaxy and is poised to yield tantalizing new information about extrasolar planets, among many other cutting-edge research projects. The VLBA provides the greatest ability to see fine detail, called resolving power, of any telescope in the world. It can produce images hundreds of times more detailed than those from the Hubble Space Telescope -- power equivalent to sitting in New York and reading a newspaper in Los Angeles. This power allows astronomers to make precise cosmic measurements with far-ranging implications for research within our own Galaxy and far beyond. New measurements with the VLBA have placed a galaxy called NGC 6264 at a distance of 450 million light-years from Earth, with an uncertainty of no more than 9 percent. This is the farthest distance ever directly measured, surpassing a measurement of 160 million light-years to another galaxy in 2009. Previously, distances beyond our own Galaxy have been estimated through indirect methods. "Our direct, geometric measurements are independent of the assumptions and complications inherent in other techniques," said James Braatz, of the National Radio Astronomy Observatory (NRAO), who worked with Cheng-Yu Kuo, of the University of Virginia and NRAO. Fine-tuning the measurement of ever-greater distances is vital to determining the expansion rate of the Universe, which helps theorists narrow down possible explanations for the nature of Dark Energy. Different models of Dark Energy predict different values for the expansion rate, known as the Hubble Constant. "Solving
Unsteady flow past wings having sharp-edge separation
NASA Technical Reports Server (NTRS)
Atta, E. H.; Kandil, O. A.; Mook, D. T.; Nayfeh, A. H.
1976-01-01
A vortex-lattice technique is developed to model unsteady, incompressible flow past thin wings. This technique predicts the shape of the wake as a function of time; thus, it is not restricted by planform, aspect ratio, or angle of attack as long as vortex bursting does not occur and the flow does not separate from the wing surface. Moreover, the technique can be applied to wings of arbitrary curvature undergoing general motion; thus, it can treat rigid-body motion, arbitrary wing deformation, gusts in the freestream, and periodic motions. Numerical results are presented for low-aspect rectangular wings undergoing a constant-rate, rigid-body rotation about the trailing edge. The results for the unsteady motion are compared with those predicted by assuming quasi-steady motion. The present results exhibit hysteretic behavior.
Slimani, S; Sahraoui, M; Bennadji, A; Ladjouze-Rezig, A
2014-08-01
Paraneoplastic syndromes commonly occur in malignancies and often precede the first symptoms of the tumor. By definition, paraneoplastic syndromes are only associated with malignancies although some exceptions have been reported, occurring with benign tumors. We report a patient presenting with a clinical and serological Sharp syndrome, followed a few months later by a cervical schwannoma. Curative surgical resection of the mass resulted in a clinical and serological healing from the Sharp syndrome. To our knowledge, this is the first report of a benign schwannoma complicated by a possible paraneoplastic Sharp syndrome.
Vehicular Slip Ratio Control Using Nonlinear Control Theory
NASA Astrophysics Data System (ADS)
Ikeda, Yuichi; Nakajima, Takashi; Chida, Yuichi
In this paper, we discuss integrated vehicle slip ratio control under both deceleration and acceleration without the need for controller switching, and also propose a design method for such an integrated slip ratio controller based on the slip ratio dynamics. When a vehicle switches from acceleration to deceleration and vice versa, the slip ratio varies discontinuously. Here, the slip ratio is approximated to a continuous function by using a sigmoid function. And a controller is then designed by using feedback linearization based on the approximated slip ratio. The stability of the designed control system is proven by Lyapunov stability theorem. Furthermore, we propose a robust control method based on a disturbance observer and sliding mode control theory. Finally, the effectiveness of the proposed control method is verified through numerical simulation.
NASA Technical Reports Server (NTRS)
Mateer, G. G.
1972-01-01
Tests were conducted on 5 deg and 15 deg half-angle sharp cones at wall-to-total-temperature ratios of 0.08 to 0.4, and angles of attack from 0 deg to 20 deg. The results indicate that (1) transition Reynolds numbers decrease with decreasing temperature ratio, (2) local transition Reynolds numbers decrease from the windward to the leeward side of the model, and (3) transition data on the windward ray of cones can be correlated in terms of the crossflow velocity gradient, momentum thickness Reynolds number, local Mach number, and cone half-angle.
Sharp Eccentric Rings in Planetless Hydrodynamical Models of Debris Disks
NASA Technical Reports Server (NTRS)
Lyra, W.; Kuchner, M. J.
2013-01-01
Exoplanets are often associated with disks of dust and debris, analogs of the Kuiper Belt in our solar system. These "debris disks" show a variety of non-trivial structures attributed to planetary perturbations and utilized to constrain the properties of the planets. However, analyses of these systems have largely ignored the fact that, increasingly, debris disks are found to contain small quantities of gas, a component all debris disks should contain at some level. Several debris disks have been measured with a dust-to-gas ratio around unity where the effect of hydrodynamics on the structure of the disk cannot be ignored. Here we report that dust-gas interactions can produce some of the key patterns seen in debris disks that were previously attributed to planets. Through linear and nonlinear modeling of the hydrodynamical problem, we find that a robust clumping instability exists in this configuration, organizing the dust into narrow, eccentric rings, similar to the Fomalhaut debris disk. The hypothesis that these disks might contain planets, though thrilling, is not necessarily required to explain these systems.
VISIT TO DR SHARP - BEN PINKEL - ABE SILVERSTEIN - OSCAR SCHEY - JESSE HALL - JOHN COLLINS BY CONGRE
NASA Technical Reports Server (NTRS)
1949-01-01
VISIT TO DR SHARP - BEN PINKEL - ABE SILVERSTEIN - OSCAR SCHEY - JESSE HALL - JOHN COLLINS BY CONGRESSMAN CARL HENSHAW FROM CALIFORNIA - NORWICK ROSS DEPARTMENT OF COMMERCE - SENOR BUCH DE PERADA REPRESENTATIVE FROM MEXICO -
Improper sharp disposal practices among diabetes patients in home care settings: Need for concern?
Majumdar, Anindo; Sahoo, Jayaprakash; Roy, Gautam; Kamalanathan, Sadishkumar
2015-01-01
In the recent years, outbreaks of blood-borne infections have been reported from assisted living facilities, which were traced back to improper blood glucose monitoring practices. Needle-stick injuries have been implicated in many such cases. This directly raises concerns over sharp disposal practices of diabetic patients self-managing their condition in home care settings. With India being home to a huge diabetic population, this issue, if neglected, can cause substantial damage to the health of the population and a marked economic loss. This article discusses the sharp disposal practices prevalent among diabetes patients, the importance of proper sharp disposal, barriers to safe disposal of sharps, and the options available for doing the same. For adopting an environmentally safe wholesome approach, disposal of plastics generated as a result of diabetes self-care at home is important as well. The article also looks at the possible long-term solutions to these issues that are sustainable in an Indian context.
SharpViSu: integrated analysis and segmentation of super-resolution microscopy data
Andronov, Leonid; Lutz, Yves; Vonesch, Jean-Luc; Klaholz, Bruno P.
2016-01-01
Summary: We introduce SharpViSu, an interactive open-source software with a graphical user interface, which allows performing processing steps for localization data in an integrated manner. This includes common features and new tools such as correction of chromatic aberrations, drift correction based on iterative cross-correlation calculations, selection of localization events, reconstruction of 2D and 3D datasets in different representations, estimation of resolution by Fourier ring correlation, clustering analysis based on Voronoi diagrams and Ripley’s functions. SharpViSu is optimized to work with eventlist tables exported from most popular localization software. We show applications of these on single and double-labelled super-resolution data. Availability and implementation: SharpViSu is available as open source code and as compiled stand-alone application under https://github.com/andronovl/SharpViSu. Contact: klaholz@igbmc.fr Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27153691
LLNL contributions to ANL Report ANL/NE-16/6 "Sharp User Manual"
Solberg, J. M.
2016-05-06
Diablo is a Multiphysics implicit finite element code with an emphasis on coupled structural/thermal analysis. In the SHARP framework, it is used as the structural solver, and may also be used as the mesh smoother.
Needles and Other Sharps (Safe Disposal Outside of Health Care Settings)
... are generally available through pharmacies, medical supply companies, health care providers and online. These containers are made of ... proper disposal methods for sharps used outside of health care settings visit this website or call (800) 643- ...
Print image sharpness analysis based on gray-level co-occurrence matrices
NASA Astrophysics Data System (ADS)
Zhang, Lin; Zhang, Meiyun; Wu, Yangyu
2010-08-01
A novel measure is presented to quantify print image sharpness. Nine texture features of gray level co-occurrence matrices (GLCM) were calculated from the print images respectively which were blurred by Gaussian blurs filter with different radius ranging from 0 to 8 pixels in steps of 2. Experiments were performed on these images with different GLCM distance d (2, 4, 6, 8,10 pixels) and orientation θ (0°, 45°, 90°, 135°) under the constant window size (64 pixels). Furthermore, the correlation matrix of texture features was calculated to judge which texture features can be chosen to assess sharpness most. The test results show contrast and energy provide the most unique information of print image sharpness. And the distance d of GLCM can be determined to be 6 pixels and the different orientation θ has little effect on the trends. The method is reliable and extends GLCM with the sharpness evaluation of variable size, oriented print image.
Flow-field in a vortex with breakdown above sharp edged delta wings
NASA Technical Reports Server (NTRS)
Hayashi, Y.; Nakaya, T.
1978-01-01
The behavior of vortex-flow, accompanied with breakdown, formed above sharp-edged delta wings, was studied experimentally as well as theoretically. Emphasis is placed particularly on the criterion for the breakdown at sufficiently large Reynolds numbers
On the origin of sharp peaks in the X-ray diffraction patterns of xanthan powders.
Lad, M; Todd, T; Morris, G A; MacNaughtan, W; Sworn, G; Foster, T J
2013-08-15
A series of xanthans containing different levels of the charged group pyruvate has been examined. The X-ray diffraction patterns of the powders of these materials had different levels of a sharp pattern superimposed on an amorphous background. As the moisture content increased so the intensity of the sharp pattern increased up to a level between 20% and 40% moisture content where the sharp pattern disappeared. X-ray diffraction pattern identification software and an inorganic X-ray diffraction database showed the origin of the sharp peaks to be due to sodium sulphate polymorphs. The behaviour of the xanthans was thought to be due to the differences in charge on the molecule; however, the increase in the crystalline component observed with increased amounts of water was unexpected. The possibility of the drying of samples was considered but the interplay between ions, the charged polymer and the water present was considered necessary to more closely describe the results.
Parameter Estimation of a Ground Moving Target Using Image Sharpness Optimization.
Yu, Jing; Li, Yaan
2016-06-30
Motion parameter estimation of a ground moving target is an important issue in synthetic aperture radar ground moving target indication (SAR-GMTI) which has significant applications for civilian and military. The SAR image of a moving target may be displaced and defocused due to the radial and along-track velocity components, respectively. The sharpness cost function presents a measure of the degree of focus of the image. In this work, a new ground moving target parameter estimation algorithm based on the sharpness optimization criterion is proposed. The relationships between the quadratic phase errors and the target's velocity components are derived. Using two-dimensional searching of the sharpness cost function, we can obtain the velocity components of the target and the focused target image simultaneously. The proposed moving target parameter estimation method and image sharpness metrics are analyzed in detail. Finally, numerical results illustrate the effective and superior velocity estimation performance of the proposed method when compared to existing algorithms.
Mean Atomic Weight of Chondrules and Matrices in Semarkona, Allende and Sharps Meteorites
NASA Astrophysics Data System (ADS)
Szurgot, M.
2017-02-01
Mean atomic weight Amean of chondrules and matrices of Semarkona, Allende and Sharps meteorites was determined using chemical composition and Amean(Fe/Si) dependence. Amean values of matrices are higher than chondrules and meteorites.
Federal Register 2010, 2011, 2012, 2013, 2014
2013-07-19
... Availability (NOA) for Sharpe Permit Relinquishment Project Environmental Assessment (EA) Finding of No Significant Impact (FONSI). SUMMARY: On April 30, 2013, Defense Logistics Agency (DLA) published a NOA in...
Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning
2016-10-01
An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.
Multidimensional Yamada-Watanabe theorem and its applications to particle systems
NASA Astrophysics Data System (ADS)
Graczyk, Piotr; Małecki, Jacek
2013-02-01
We prove a multidimensional version of the Yamada-Watanabe theorem, i.e., a theorem giving conditions on coefficients of a stochastic differential equation for existence and pathwise uniqueness of strong solutions. It implies an existence and uniqueness theorem for the eigenvalue and eigenvector processes of matrix-valued stochastic processes, called a "spectral" matrix Yamada-Watanabe theorem. The multidimensional Yamada-Watanabe theorem is also applied to particle systems of squared Bessel processes, corresponding to matrix analogues of squared Bessel processes, Wishart and Jacobi matrix processes. The β-versions of these particle systems are also considered.
Bisquert, Juan
2005-11-01
We investigate from basic principles of nonequilibrium statistical mechanics the general reasons why electron transfer across an interface is associated with irreversible elements (resistances) in equivalent circuit modeling. We apply the detailed fluctuation theorem [C. Jarzynski, J. Stat. Phys. 98, 77 (2000)] to a simple model of an interface between two different materials. The elementary transition rates are interpreted in terms of the evolution of a microstate, and obey a ratio that is related to the heat absorbed from the phonon bath while promoting an electron to a higher energy level. The amount of irreversibility (the entropy production), and also the macroscopic current density, can be both obtained with the additional constraint that the system belongs in a particular mesostate, determined by the distribution of chemical and electrostatic potential.
Test of the steady-state fluctuation theorem in turbulent Rayleigh-B'enard convection
NASA Astrophysics Data System (ADS)
Tong, Penger; Shang, Xiaodong
2005-11-01
Local entropy production rate σ(r,t) in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in an aspect-ratio-one cell filled with water. The statistical properties of the time-averaged σ(r,t) are analyzed and the results are compared with the predictions of the steady state fluctuation theorem (SSFT) of Gallavotti and Cohen. The experiment reveals that the SSFT can indeed be extended to the local variables, but further development is needed in order to incorporate the common dynamic complexities of far-from-equilibrium systems into the theory. *Work supported by the Research Grants Council of Hong Kong SAR under Grant Nos. HKUST603504 (P.T.) and CUHK403003 (K.Q.X.).
Examples of probabilistic semantics of the basic coding theorem for uncertainty spaces
Diduk, N.N.
1995-03-01
The basic coding theorem for discrete uncertainty spaces is so far the central result of the developing uncertainty theory. The theorem was first published in and its proof in. A refinement of the basic coding theorem with a new proof was subsequently published. The theoretical value of the basic coding theorem is in that it essentially made possible the development of a general theoretical apparatus covering various types of uncertainty. But this theorem should not be regarded as a purely theoretical result, because it also has a clear applied meaning. Indeed, the theorem deals with what can and cannot be accomplished by encoding elements of uncertainty spaces. Such questions are of considerable practical importance, because problems of finding good information encoding techniques are encountered in many spheres of human activity. Moreover, possible applications of the theorem are not restricted to coding problems: we know that prefix coding is analogous to construction of successful search strategies. Search problems therefore constitute another potential application of the proposed theorem. It is thus useful to consider the practical aspects of the basic coding theorem. The basis for the application of the theorem is its semantics, i.e., the system of possible meaningful interpretations. The present paper examines examples of particular cases of the basic coding theorem which admit a probabilistic interpretation. The choice of the topic is motivated by the fact that uncertainty situations that have a probabilistic meaning are undoubtedly of exceptional interest from both theoretical and applied considerations.
NASA Astrophysics Data System (ADS)
Fraeman, A. A.; Ehlmann, B. L.; Arvidson, R. E.; Edwards, C. S.; Grotzinger, J. P.; Milliken, R. E.; Quinn, D. P.; Rice, M. S.
2016-09-01
We have developed a refined geologic map and stratigraphy for lower Mount Sharp using coordinated analyses of new spectral, thermophysical, and morphologic orbital data products. The Mount Sharp group consists of seven relatively planar units delineated by differences in texture, mineralogy, and thermophysical properties. These units are (1-3) three spatially adjacent units in the Murray formation which contain a variety of secondary phases and are distinguishable by thermal inertia and albedo differences, (4) a phyllosilicate-bearing unit, (5) a hematite-capped ridge unit, (6) a unit associated with material having a strongly sloped spectral signature at visible near-infrared wavelengths, and (7) a layered sulfate unit. The Siccar Point group consists of the Stimson formation and two additional units that unconformably overlie the Mount Sharp group. All Siccar Point group units are distinguished by higher thermal inertia values and record a period of substantial deposition and exhumation that followed the deposition and exhumation of the Mount Sharp group. Several spatially extensive silica deposits associated with veins and fractures show that late-stage silica enrichment within lower Mount Sharp was pervasive. At least two laterally extensive hematitic deposits are present at different stratigraphic intervals, and both are geometrically conformable with lower Mount Sharp strata. The occurrence of hematite at multiple stratigraphic horizons suggests redox interfaces were widespread in space and/or in time, and future measurements by the Mars Science Laboratory Curiosity rover will provide further insights into the depositional settings of these and other mineral phases.
Ehlmann, B. L.; Arvidson, R. E.; Edwards, C. S.; Grotzinger, J. P.; Milliken, R. E.; Quinn, D. P.; Rice, M. S.
2016-01-01
Abstract We have developed a refined geologic map and stratigraphy for lower Mount Sharp using coordinated analyses of new spectral, thermophysical, and morphologic orbital data products. The Mount Sharp group consists of seven relatively planar units delineated by differences in texture, mineralogy, and thermophysical properties. These units are (1–3) three spatially adjacent units in the Murray formation which contain a variety of secondary phases and are distinguishable by thermal inertia and albedo differences, (4) a phyllosilicate‐bearing unit, (5) a hematite‐capped ridge unit, (6) a unit associated with material having a strongly sloped spectral signature at visible near‐infrared wavelengths, and (7) a layered sulfate unit. The Siccar Point group consists of the Stimson formation and two additional units that unconformably overlie the Mount Sharp group. All Siccar Point group units are distinguished by higher thermal inertia values and record a period of substantial deposition and exhumation that followed the deposition and exhumation of the Mount Sharp group. Several spatially extensive silica deposits associated with veins and fractures show that late‐stage silica enrichment within lower Mount Sharp was pervasive. At least two laterally extensive hematitic deposits are present at different stratigraphic intervals, and both are geometrically conformable with lower Mount Sharp strata. The occurrence of hematite at multiple stratigraphic horizons suggests redox interfaces were widespread in space and/or in time, and future measurements by the Mars Science Laboratory Curiosity rover will provide further insights into the depositional settings of these and other mineral phases. PMID:27867788
NASA Technical Reports Server (NTRS)
Martin, R. G. (Editor); Atkinson, D. J.; James, M. L.; Lawson, D. L.; Porta, H. J.
1990-01-01
The development and application of the Spacecraft Health Automated Reasoning Prototype (SHARP) for the operations of the telecommunications systems and link analysis functions in Voyager mission operations are presented. An overview is provided of the design and functional description of the SHARP system as it was applied to Voyager. Some of the current problems and motivations for automation in real-time mission operations are discussed, as are the specific solutions that SHARP provides. The application of SHARP to Voyager telecommunications had the goal of being a proof-of-capability demonstration of artificial intelligence as applied to the problem of real-time monitoring functions in planetary mission operations. AS part of achieving this central goal, the SHARP application effort was also required to address the issue of the design of an appropriate software system architecture for a ground-based, highly automated spacecraft monitoring system for mission operations, including methods for: (1) embedding a knowledge-based expert system for fault detection, isolation, and recovery within this architecture; (2) acquiring, managing, and fusing the multiple sources of information used by operations personnel; and (3) providing information-rich displays to human operators who need to exercise the capabilities of the automated system. In this regard, SHARP has provided an excellent example of how advanced artificial intelligence techniques can be smoothly integrated with a variety of conventionally programmed software modules, as well as guidance and solutions for many questions about automation in mission operations.
Misner-Sharp mass in n-dimensional f(R) gravity
NASA Astrophysics Data System (ADS)
Zhang, Hongsheng; Hu, Yapeng; Li, Xin-Zhou
2014-07-01
We study the Misner-Sharp mass for the f(R) gravity in an n-dimensional (n≥3) spacetime which permits three-type (n-2)-dimensional maximally symmetric subspace. We obtain the Misner-Sharp mass via two approaches. One is the inverse unified first law method and the other is the conserved charge method, which uses a generalized Kodama vector. In the first approach, we assume the unified first law still holds in n-dimensional f(R) gravity, which requires a quasilocal mass form (we define it as the generalized Misner-Sharp mass). In the second approach, the conserved charge corresponding to the generalized local Kodama vector is the generalized Misner-Sharp mass. The two approaches, which are bridged by a constraint, are equivalent. This constraint determines the existence of a well-defined Misner-Sharp mass. In an important special case, we present the explicit form for the static space, and we calculate the Misner-Sharp mass for the Clifton-Barrow solution as an example.
Fraeman, A A; Ehlmann, B L; Arvidson, R E; Edwards, C S; Grotzinger, J P; Milliken, R E; Quinn, D P; Rice, M S
2016-09-01
We have developed a refined geologic map and stratigraphy for lower Mount Sharp using coordinated analyses of new spectral, thermophysical, and morphologic orbital data products. The Mount Sharp group consists of seven relatively planar units delineated by differences in texture, mineralogy, and thermophysical properties. These units are (1-3) three spatially adjacent units in the Murray formation which contain a variety of secondary phases and are distinguishable by thermal inertia and albedo differences, (4) a phyllosilicate-bearing unit, (5) a hematite-capped ridge unit, (6) a unit associated with material having a strongly sloped spectral signature at visible near-infrared wavelengths, and (7) a layered sulfate unit. The Siccar Point group consists of the Stimson formation and two additional units that unconformably overlie the Mount Sharp group. All Siccar Point group units are distinguished by higher thermal inertia values and record a period of substantial deposition and exhumation that followed the deposition and exhumation of the Mount Sharp group. Several spatially extensive silica deposits associated with veins and fractures show that late-stage silica enrichment within lower Mount Sharp was pervasive. At least two laterally extensive hematitic deposits are present at different stratigraphic intervals, and both are geometrically conformable with lower Mount Sharp strata. The occurrence of hematite at multiple stratigraphic horizons suggests redox interfaces were widespread in space and/or in time, and future measurements by the Mars Science Laboratory Curiosity rover will provide further insights into the depositional settings of these and other mineral phases.
k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy
Esmann, Martin; Becker, Simon F; da Cunha, Bernard B; Brauer, Jens H; Vogelgesang, Ralf; Groß, Petra
2013-01-01
Summary We investigate the radiation patterns of sharp conical gold tapers, which were designed as adiabatic nanofocusing probes for scanning near-field optical microscopy (SNOM). Field calculations show that only the lowest order eigenmode of such a taper can reach the very apex and thus induce the generation of strongly enhanced near-field signals. Higher-order modes are coupled into the far field at finite distances from the apex. Here, we demonstrate experimentally how to distinguish and separate between the lowest and higher-order eigenmodes of such a metallic taper by filtering in the spatial frequency domain. Our approach has the potential to considerably improve the signal-to-background ratio in spectroscopic experiments at the nanoscale. PMID:24205454
The g-theorem and quantum information theory
NASA Astrophysics Data System (ADS)
Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo
2016-10-01
We study boundary renormalization group flows between boundary conformal field theories in 1 + 1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.
Fluctuation theorem for a deterministic one-particle system
NASA Astrophysics Data System (ADS)
Schmick, Malte; Markus, Mario
2004-12-01
A Duffing oscillator is driven by a sum of N chaotic time series. These time series are solutions of the undriven Duffing equation. It is shown that N=1 is sufficient to render the fluctuation theorem [Gallavotti and Cohen, Phys. Rev. Lett. 74, 2694 (1995); Gallavotti, J. Math. Phys. 41, 4061 (2000); Evans and Searles, Adv. Phys. 51, 1529 (2002)] for the power Jτ averaged within intervals of length τ . In particular, the probabilities p(Jτ) follow a nearly Gaussian distribution. Also, ln[p(Jτ)/p(-Jτ)] versus Jτ can be fitted by strikingly linear functions, the slopes being proportional to τ for large τ . These results indicate that validity of the fluctuation theorem requires neither a many-particle system nor a stochastic process, which are requirements used in previous works.
A double commutant theorem for Murray–von Neumann algebras
Liu, Zhe
2012-01-01
Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double commutant theorem characterizes von Neumann algebras as those for which , where , the commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double commutant theorem for Murray–von Neumann algebras. PMID:22543165
Learning-assisted theorem proving with millions of lemmas☆
Kaliszyk, Cezary; Urban, Josef
2015-01-01
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck. PMID:26525678
Entropy Inequalities for Stable Densities and Strengthened Central Limit Theorems
NASA Astrophysics Data System (ADS)
Toscani, Giuseppe
2016-10-01
We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy functionals along the sequence we prove convergence with explicit rate in various norms to a Lévy centered density of parameter λ >1 . This introduces a new information-theoretic approach to the central limit theorem for stable laws, in which the main argument is shown to be the relative fractional Fisher information, recently introduced in Toscani (Ricerche Mat 65(1):71-91, 2016). In particular, it is proven that, with respect to the relative fractional Fisher information, the Lévy density satisfies an analogous of the logarithmic Sobolev inequality, which allows to pass from the monotonicity and decay to zero of the relative fractional Fisher information in the standardized sum to the decay to zero in relative entropy with an explicit decay rate.
Learning in neural networks based on a generalized fluctuation theorem
NASA Astrophysics Data System (ADS)
Hayakawa, Takashi; Aoyagi, Toshio
2015-11-01
Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.
Learning in neural networks based on a generalized fluctuation theorem.
Hayakawa, Takashi; Aoyagi, Toshio
2015-01-01
Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.
Virial theorem in quasi-coordinates and Lie algebroid formalism
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Gheorghiu, Irina; Martínez, Eduardo; Santos, Patrícia
2014-04-01
In this paper, the geometric approach to the virial theorem (VT) developed in [J. F. Cariñena, F. Falceto and M. F. Rañada, A geometric approach to a generalized virial theorem, J. Phys. A: Math. Theor. 45 (2012) 395210, 19 pp.] is written in terms of quasi-velocities (see [J. F. Cariñena, J. Nunes da Costa and P. Santos, Quasi-coordinates from the point of view of Lie algebroid structures, J. Phys. A: Math. Theor. 40 (2007) 10031-10048]). A generalization of the VT for mechanical systems on Lie algebroids is also given, using the geometric tools of Lagrangian and Hamiltonian mechanics on the prolongation of the Lie algebroid.
Bell's Theorem and the Issue of Determinism and Indeterminism
NASA Astrophysics Data System (ADS)
Esfeld, Michael
2015-05-01
The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell's theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for the derivation of Bell's theorem. Determinism as such does not undermine that independence (unless there are particular initial conditions of the universe that would amount to conspiracy). Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave-function can go together with effective wave-functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave-functions are sufficient for the mentioned independence premise to hold.
Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper
NASA Technical Reports Server (NTRS)
Schumann, Johann; Koga, Dennis (Technical Monitor)
1999-01-01
In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).
A uniqueness theorem for the anti-de Sitter soliton.
Galloway, G J; Surya, S; Woolgar, E
2002-03-11
The stability of physical systems depends on the existence of a state of least energy. In gravity, this is guaranteed by the positive energy theorem. For topological reasons, this fails for nonsupersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. For related reasons, this also fails for the anti-de Sitter (AdS) soliton, a globally static, asymptotically toroidal Lambda<0 spacetime with negative mass. Nonetheless, arguing from the AdS conformal field theory (AdS/CFT) correspondence, Horowitz and Myers proposed a new positive energy conjecture, which asserts that the AdS soliton is the unique state of least energy in its asymptotic class. We give a new structure theorem for static Lambda<0 spacetimes and use it to prove uniqueness of the AdS soliton. Our results offer significant support for the new positive energy conjecture and add to the body of rigorous results inspired by the AdS/CFT correspondence.
77 FR 52061 - Notice of Proposed Exemption Involving Sharp HealthCare Located in San Diego, CA
Federal Register 2010, 2011, 2012, 2013, 2014
2012-08-28
... Benefits Security Administration Notice of Proposed Exemption Involving Sharp HealthCare Located in San... involve the Sharp HealthCare Health and Dental Plan (the Plan). The proposed exemption, if granted, would... does not reflect the views of the Department. 1. Background Sharp is an integrated health care...
Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces.
Kim, Jong Kyu; Pathak, Ramesh Prasad; Dashputre, Samir; Diwan, Shailesh Dhar; Gupta, Rajlaxmi
2016-01-01
In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditions. Our results are the extension and improvements of the recent well-known results announced in the current literature.
Implementing Metamathematics as an Approach to Automatic Theorem Proving
1989-01-01
set theory the disjoint union is usually defined from the ordinary union by providing a scheme for tagging elements (see [3]). For any type A, another...in preparing this document. 31 References (1] P. Aczel. The type theoretic interpretation of constructive set theory . In Logic Coo- quium ...Amsterdam:North-Holland, 1978. [2] W. Bledsoe and D. Loveland. Automated Theorem Proving: After 25 Years. American Math Soc., 1984. [3] N. Bourbaki . Theory
Bimeasures and Sampling Theorems for Weakly Harmonizable Processes.
1982-09-27
representation theorem and then such a measure has a unique extension of being a Radon measure by the standard theory of Bourbaki (1], one refers to each such...nontrivial, and this approach has other drawbacks. We therefore do not consider this set in the general format of the sampling theory of random processes...for a more general Cramer class. To carry out this analysis, it is neces- sary to use the properties of bimeasures. Some aspects of the bimeasure theory
Fan beam image reconstruction with generalized Fourier slice theorem.
Zhao, Shuangren; Yang, Kang; Yang, Kevin
2014-01-01
For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N
Applications of Noether conservation theorem to Hamiltonian systems
NASA Astrophysics Data System (ADS)
Mouchet, Amaury
2016-09-01
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether's approach is illustrated on several examples, including classical field theory and quantum dynamics.
Noether's Theorem of Relativistic-Electromagnetic Ideal Hydrodynamics
NASA Astrophysics Data System (ADS)
Gaspar Elsas, J. H.; Koide, T.; Kodama, T.
2015-06-01
We present a variational approach for relativistic ideal hydrodynamics interacting with electromagnetic fields. The momentum of fluid is introduced as the canonical conjugate variable of the position of a fluid element, which coincides with the conserved quantity derived from Noether's theorem. We further show that our formulation can reproduce the usual electromagnetic hydrodynamics which is obtained so as to satisfy the conservation of the inertia of fluid motion.
Noether theorem for Birkhoffian systems on time scales
NASA Astrophysics Data System (ADS)
Song, Chuan-Jing; Zhang, Yi
2015-10-01
Birkhoff equations on time scales and Noether theorem for Birkhoffian system on time scales are studied. First, some necessary knowledge of calculus on time scales are reviewed. Second, Birkhoff equations on time scales are obtained. Third, the conditions for invariance of Pfaff action and conserved quantities are presented under the special infinitesimal transformations and general infinitesimal transformations, respectively. Fourth, some special cases are given. And finally, an example is given to illustrate the method and results.
A notion of graph likelihood and an infinite monkey theorem
NASA Astrophysics Data System (ADS)
Banerji, Christopher R. S.; Mansour, Toufik; Severini, Simone
2014-01-01
We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.
A Quantitative Gibbard-Satterthwaite Theorem Without Neutrality
2014-05-02
circumventing the negative results. One approach, introduced by Bartholdi, Tovey and Trick [3], suggests computational complexity as a barrier against...A quantitative Gibbard-Satterthwaite theorem without neutrality Elchanan Mossel Miklos Racz Electrical Engineering and Computer Sciences University...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) University of California at Berkeley,Electrical Engineering and Computer Sciences,Berkeley,CA,94720 8
Rowlands' Duality Principle: A Generalization of Noether's Theorem?
NASA Astrophysics Data System (ADS)
Karam, Sabah E.
This paper will examine a physical principle that has been used in making valid predictions and generalizes established conservation laws. In a previous paper it was shown how Rowlands' zero-totality condition could be viewed as a generalization of Newton's third law of motion. In this paper it will be argued that Rowlands' Duality Principle is a generalization of Noether's Theorem and that the two principles taken together are truly foundational principles that have tamed Metaphysics.
Normal coderivative for multifunctions and implicit function theorems
NASA Astrophysics Data System (ADS)
Lee, G. M.; Tam, N. N.; Yen, N. D.
2008-02-01
In the framework of the theory of normal coderivative for multifunctions, new implicit function theorems are obtained. The main tools of the proofs are the Ekeland variational principle, a nonsmooth version of Fermat's rule, a sum rule, and the differential estimate for marginal functions established by B.S. Mordukhovich and Y. Shao [B.S. Mordukhovich, Y. Shao, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996) 1235-1280].
Interpretation of the quantum formalism and Bell's theorem
Santos, E. )
1991-02-01
It is argued that quantum mechanics must be interpreted according to the Copenhagen interpretation. Consequently the formalism must be used in a purely operational way. The relation between realism, hidden variables, and the Bell inequalities is discussed. The proof of impossibility of local hidden-variables theories (Bell theorem) is criticized on the basis that the quantum mechanical states violating local realism are not physically realizable states.
Analytical proof of Gisin's theorem for three qubits
Choudhary, Sujit K.; Ghosh, Sibasish; Kar, Guruprasad; Rahaman, Ramij
2010-04-15
Gisin's theorem assures that for any pure bipartite entangled state, there is violation of the inequality of Bell and of Clauser, Horne, Shimony, and Holt, revealing its contradiction with local realistic model. Whether a similar result holds for three-qubit pure entangled states remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy's nonlocality argument.
Diffusional creep and sintering -- The application of bounding theorems
Cocks, A.C.F.; Aparicio, N.D.
1995-02-01
In this paper upper and lower bound theorems for the creep and sintering response of bodies which deform by grain-boundary diffusion controlled mechanisms are presented. The utility of the bounds is demonstrated by using them to analyze the classical problem of Hull-Rimmer void growth. Further insight into the material response when diffusion mechanisms dominate is provided by analyzing the response of two contacting spheres, which represents a fundamental problem for the analysis of stage 1 sintering.
Black holes, information, and the universal coefficient theorem
NASA Astrophysics Data System (ADS)
Patrascu, Andrei T.
2016-07-01
General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article, I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by the demanding invariance of the laws of physics to the change of coefficient structures in cohomology.
Optical theorem for multipole sources in wave diffraction theory
NASA Astrophysics Data System (ADS)
Eremin, Yu. A.; Sveshnikov, A. G.
2016-05-01
The optical theorem is generalized to the case of local body excitation by multipole sources. It is found that, to calculate the extinction cross section, it is sufficient to calculate the scattered field derivatives at a single point. It is shown that the Purcell factor, which is a rather important parameter, can be represented in analytic form. The result is generalized to the case of a local scatterer incorporated in a homogeneous halfspace.
A rigidity theorem for complete noncompact Bach-flat manifolds
NASA Astrophysics Data System (ADS)
Chu, Yawei
2011-02-01
Let (M4,g) be a four-dimensional complete noncompact Bach-flat Riemannian manifold with positive Yamabe constant. In this paper, we show that (M4,g) has a constant curvature if it has a nonnegative constant scalar curvature and sufficiently small L2-norm of trace-free Riemannian curvature tensor. Moreover, we get a gap theorem for (M4,g) with positive scalar curvature.
Klein's theorem and the proof of E0 = mc2
NASA Astrophysics Data System (ADS)
Ohanian, Hans C.
2012-12-01
Despite repeated attempts, Einstein failed to give us a general and rigorous proof of his E0=mc2 relation. A completely general proof emerged in 1918 from a theorem on the four-vector character of energy-momentum of extended systems by the mathematician Felix Klein, but this proof is not well known, rarely seen in textbooks, and sometimes misunderstood. A simple version of this proof is presented here, with discussion of the crucial role of the energy-momentum tensor.
Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields
Pan, Xiao-Yin; Sahni, Viraht
2015-11-07
The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momenta. The proofs differ from the original HK proof and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function. A Percus-Levy-Lieb constrained-search proof expanding the domain of validity to N-representable functions, and to degenerate states, again for fixed electron number and angular momentum, is also provided.
Projection-slice theorem based 2D-3D registration
NASA Astrophysics Data System (ADS)
van der Bom, M. J.; Pluim, J. P. W.; Homan, R.; Timmer, J.; Bartels, L. W.
2007-03-01
In X-ray guided procedures, the surgeon or interventionalist is dependent on his or her knowledge of the patient's specific anatomy and the projection images acquired during the procedure by a rotational X-ray source. Unfortunately, these X-ray projections fail to give information on the patient's anatomy in the dimension along the projection axis. It would be very profitable to provide the surgeon or interventionalist with a 3D insight of the patient's anatomy that is directly linked to the X-ray images acquired during the procedure. In this paper we present a new robust 2D-3D registration method based on the Projection-Slice Theorem. This theorem gives us a relation between the pre-operative 3D data set and the interventional projection images. Registration is performed by minimizing a translation invariant similarity measure that is applied to the Fourier transforms of the images. The method was tested by performing multiple exhaustive searches on phantom data of the Circle of Willis and on a post-mortem human skull. Validation was performed visually by comparing the test projections to the ones that corresponded to the minimal value of the similarity measure. The Projection-Slice Theorem Based method was shown to be very effective and robust, and provides capture ranges up to 62 degrees. Experiments have shown that the method is capable of retrieving similar results when translations are applied to the projection images.
Generalized F-theorem and the ɛ expansion
NASA Astrophysics Data System (ADS)
Fei, Lin; Giombi, Simone; Klebanov, Igor R.; Tarnopolsky, Grigory
2015-12-01
Some known constraints on Renormalization Group flow take the form of inequalities: in even dimensions they refer to the coefficient a of the Weyl anomaly, while in odd dimensions to the sphere free energy F. In recent work [1] it was suggested that the a- and F-theorems may be viewed as special cases of a Generalized F -Theorem valid in continuous dimension. This conjecture states that, for any RG flow from one conformal fixed point to another, {tilde{F}}_{UV}>{tilde{F}}_{IR} , where tilde{F}= sin (π d/2) log {Z}_{S^d} . Here we provide additional evidence in favor of the Generalized F-Theorem. We show that it holds in conformal perturbation theory, i.e. for RG flows produced by weakly relevant operators. We also study a specific example of the Wilson-Fisher O( N) model and define this CFT on the sphere S 4- ɛ , paying careful attention to the beta functions for the coefficients of curvature terms. This allows us to develop the ɛ expansion of tilde{F} up to order ɛ 5. Padé extrapolation of this series to d = 3 gives results that are around 2-3% below the free field values for small N. We also study RG flows which include an anisotropic perturbation breaking the O( N) symmetry; we again find that the results are consistent with {tilde{F}}_{UV}>{tilde{F}}_{IR}.
An analogue of Wagner's theorem for decompositions of matrix algebras
NASA Astrophysics Data System (ADS)
Ivanov, D. N.
2004-12-01
Wagner's celebrated theorem states that a finite affine plane whose collineation group is transitive on lines is a translation plane. The notion of an orthogonal decomposition (OD) of a classically semisimple associative algebra introduced by the author allows one to draw an analogy between finite affine planes of order n and ODs of the matrix algebra M_n(\\mathbb C) into a sum of subalgebras conjugate to the diagonal subalgebra. These ODs are called WP-decompositions and are equivalent to the well-known ODs of simple Lie algebras of type A_{n-1} into a sum of Cartan subalgebras. In this paper we give a detailed and improved proof of the analogue of Wagner's theorem for WP-decompositions of the matrix algebra of odd non-square order an outline of which was earlier published in a short note in "Russian Math. Surveys" in 1994. In addition, in the framework of the theory of ODs of associative algebras, based on the method of idempotent bases, we obtain an elementary proof of the well-known Kostrikin-Tiep theorem on irreducible ODs of Lie algebras of type A_{n-1} in the case where n is a prime-power.
Quantum regression theorem and non-Markovianity of quantum dynamics
NASA Astrophysics Data System (ADS)
Guarnieri, Giacomo; Smirne, Andrea; Vacchini, Bassano
2014-08-01
We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.
Representations of the language recognition problem for a theorem prover
NASA Technical Reports Server (NTRS)
Minker, J.; Vanderbrug, G. J.
1972-01-01
Two representations of the language recognition problem for a theorem prover in first order logic are presented and contrasted. One of the representations is based on the familiar method of generating sentential forms of the language, and the other is based on the Cocke parsing algorithm. An augmented theorem prover is described which permits recognition of recursive languages. The state-transformation method developed by Cordell Green to construct problem solutions in resolution-based systems can be used to obtain the parse tree. In particular, the end-order traversal of the parse tree is derived in one of the representations. An inference system, termed the cycle inference system, is defined which makes it possible for the theorem prover to model the method on which the representation is based. The general applicability of the cycle inference system to state space problems is discussed. Given an unsatisfiable set S, where each clause has at most one positive literal, it is shown that there exists an input proof. The clauses for the two representations satisfy these conditions, as do many state space problems.
Sharp Contradiction for Local-Hidden-State Model in Quantum Steering
NASA Astrophysics Data System (ADS)
Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar
2016-08-01
In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell’s nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR’s original scenario is “steering”, i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox.
Sharp Contradiction for Local-Hidden-State Model in Quantum Steering
Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar
2016-01-01
In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell’s nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR’s original scenario is “steering”, i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox. PMID:27562658
A comprehensive numerical analysis of background phase correction with V-SHARP.
Özbay, Pinar Senay; Deistung, Andreas; Feng, Xiang; Nanz, Daniel; Reichenbach, Jürgen Rainer; Schweser, Ferdinand
2017-04-01
Sophisticated harmonic artifact reduction for phase data (SHARP) is a method to remove background field contributions in MRI phase images, which is an essential processing step for quantitative susceptibility mapping (QSM). To perform SHARP, a spherical kernel radius and a regularization parameter need to be defined. In this study, we carried out an extensive analysis of the effect of these two parameters on the corrected phase images and on the reconstructed susceptibility maps. As a result of the dependence of the parameters on acquisition and processing characteristics, we propose a new SHARP scheme with generalized parameters. The new SHARP scheme uses a high-pass filtering approach to define the regularization parameter. We employed the variable-kernel SHARP (V-SHARP) approach, using different maximum radii (Rm ) between 1 and 15 mm and varying regularization parameters (f) in a numerical brain model. The local root-mean-square error (RMSE) between the ground-truth, background-corrected field map and the results from SHARP decreased towards the center of the brain. RMSE of susceptibility maps calculated with a spatial domain algorithm was smallest for Rm between 6 and 10 mm and f between 0 and 0.01 mm(-1) , and for maps calculated with a Fourier domain algorithm for Rm between 10 and 15 mm and f between 0 and 0.0091 mm(-1) . We demonstrated and confirmed the new parameter scheme in vivo. The novel regularization scheme allows the use of the same regularization parameter irrespective of other imaging parameters, such as image resolution. Copyright © 2016 John Wiley & Sons, Ltd.
Determinants of different deep and superficial CA1 pyramidal cell dynamics during sharp-wave ripples
Aguilar, Juan; Sanchez-Aguilera, Alberto; Viney, Tim J; Gomez-Dominguez, Daniel; Bellistri, Elisa; de la Prida, Liset Menendez
2016-01-01
Sharp-wave ripples represent a prominent synchronous activity pattern in the mammalian hippocampus during sleep and immobility. GABAergic interneuronal types are silenced or fire during these events, but the mechanism of pyramidal cell (PC) participation remains elusive. We found opposite membrane polarization of deep (closer to stratum oriens) and superficial (closer to stratum radiatum) rat CA1 PCs during sharp-wave ripples. Using sharp and multi-site recordings in combination with neurochemical profiling, we observed a predominant inhibitory drive of deep calbindin (CB)-immunonegative PCs that contrasts with a prominent depolarization of superficial CB-immunopositive PCs. Biased contribution of perisomatic GABAergic inputs, together with suppression of CA2 PCs, may explain the selection of CA1 PCs during sharp-wave ripples. A deep-superficial gradient interacted with behavioral and spatial effects to determine cell participation during sleep and awake sharp-wave ripples in freely moving rats. Thus, the firing dynamics of hippocampal PCs are exquisitely controlled at subcellular and microcircuit levels in a cell type–selective manner. PMID:26214372
SHARP: A multi-mission AI system for spacecraft telemetry monitoring and diagnosis
NASA Technical Reports Server (NTRS)
Lawson, Denise L.; James, Mark L.
1989-01-01
The Spacecraft Health Automated Reasoning Prototype (SHARP) is a system designed to demonstrate automated health and status analysis for multi-mission spacecraft and ground data systems operations. Telecommunications link analysis of the Voyager II spacecraft is the initial focus for the SHARP system demonstration which will occur during Voyager's encounter with the planet Neptune in August, 1989, in parallel with real-time Voyager operations. The SHARP system combines conventional computer science methodologies with artificial intelligence techniques to produce an effective method for detecting and analyzing potential spacecraft and ground systems problems. The system performs real-time analysis of spacecraft and other related telemetry, and is also capable of examining data in historical context. A brief introduction is given to the spacecraft and ground systems monitoring process at the Jet Propulsion Laboratory. The current method of operation for monitoring the Voyager Telecommunications subsystem is described, and the difficulties associated with the existing technology are highlighted. The approach taken in the SHARP system to overcome the current limitations is also described, as well as both the conventional and artificial intelligence solutions developed in SHARP.
SHARP - A multi-mission AI system for spacecraft telemetry monitoring and diagnosis
NASA Technical Reports Server (NTRS)
Lawson, Denise L.; James, Mark L.
1989-01-01
The Spacecraft Health Automated Reasoning Prototype (SHARP) is a system designed to demonstrate automated health and status analysis for multi-mission spacecraft and ground data systems operations. Telecommunications link analysis of the Voyager II spacecraft is the initial focus for the SHARP system demonstration which will occur during Voyager's encounter with the planet Neptune in August, 1989, in parallel with real-time Voyager operations. The SHARP system combines conventional computer science methodologies with artificial intelligence techniques to produce an effective method for detecting and analyzing potential spacecraft and ground systems problems. The system performs real-time analysis of spacecraft and other related telemetry, and is also capable of examining data in historical context. A brief introduction is given to the spacecraft and ground systems monitoring process at the Jet Propulsion Laboratory. The current method of operation for monitoring the Voyager Telecommunications subsystem is described, and the difficulties associated with the existing technology are highlighted. The approach taken in the SHARP system to overcome the current limitations is also described, as well as both the conventional and artificial intelligence solutions developed in SHARP.
SHARP: A multi-mission AI system for spacecraft telemetry monitoring and diagnosis
NASA Astrophysics Data System (ADS)
Lawson, Denise L.; James, Mark L.
1989-04-01
The Spacecraft Health Automated Reasoning Prototype (SHARP) is a system designed to demonstrate automated health and status analysis for multi-mission spacecraft and ground data systems operations. Telecommunications link analysis of the Voyager II spacecraft is the initial focus for the SHARP system demonstration which will occur during Voyager's encounter with the planet Neptune in August, 1989, in parallel with real-time Voyager operations. The SHARP system combines conventional computer science methodologies with artificial intelligence techniques to produce an effective method for detecting and analyzing potential spacecraft and ground systems problems. The system performs real-time analysis of spacecraft and other related telemetry, and is also capable of examining data in historical context. A brief introduction is given to the spacecraft and ground systems monitoring process at the Jet Propulsion Laboratory. The current method of operation for monitoring the Voyager Telecommunications subsystem is described, and the difficulties associated with the existing technology are highlighted. The approach taken in the SHARP system to overcome the current limitations is also described, as well as both the conventional and artificial intelligence solutions developed in SHARP.
SHARP - A multi-mission AI system for spacecraft telemetry monitoring and diagnosis
NASA Astrophysics Data System (ADS)
Lawson, Denise L.; James, Mark L.
The Spacecraft Health Automated Reasoning Prototype (SHARP) is a system designed to demonstrate automated health and status analysis for multi-mission spacecraft and ground data systems operations. Telecommunications link analysis of the Voyager II spacecraft is the initial focus for the SHARP system demonstration which will occur during Voyager's encounter with the planet Neptune in August, 1989, in parallel with real-time Voyager operations. The SHARP system combines conventional computer science methodologies with artificial intelligence techniques to produce an effective method for detecting and analyzing potential spacecraft and ground systems problems. The system performs real-time analysis of spacecraft and other related telemetry, and is also capable of examining data in historical context. A brief introduction is given to the spacecraft and ground systems monitoring process at the Jet Propulsion Laboratory. The current method of operation for monitoring the Voyager Telecommunications subsystem is described, and the difficulties associated with the existing technology are highlighted. The approach taken in the SHARP system to overcome the current limitations is also described, as well as both the conventional and artificial intelligence solutions developed in SHARP.
NASA Astrophysics Data System (ADS)
Lawson, Denise L.; James, Mark L.
1989-05-01
The Spacecraft Health Automated Reasoning Prototype (SHARP) is a system designed to demonstrate automated health and status analysis for multi-mission spacecraft and ground data systems operations. Telecommunications link analysis of the Voyager 2 spacecraft is the initial focus for the SHARP system demonstration which will occur during Voyager's encounter with the planet Neptune in August, 1989, in parallel with real time Voyager operations. The SHARP system combines conventional computer science methodologies with artificial intelligence techniques to produce an effective method for detecting and analyzing potential spacecraft and ground systems problems. The system performs real time analysis of spacecraft and other related telemetry, and is also capable of examining data in historical context. A brief introduction is given to the spacecraft and ground systems monitoring process at the Jet Propulsion Laboratory. The current method of operation for monitoring the Voyager Telecommunications subsystem is described, and the difficulties associated with the existing technology are highlighted. The approach taken in the SHARP system to overcome the current limitations is also described, as well as both the conventional and artificial intelligence solutions developed in SHARP.
Valero, Manuel; Cid, Elena; Averkin, Robert G; Aguilar, Juan; Sanchez-Aguilera, Alberto; Viney, Tim J; Gomez-Dominguez, Daniel; Bellistri, Elisa; de la Prida, Liset Menendez
2015-09-01
Sharp-wave ripples represent a prominent synchronous activity pattern in the mammalian hippocampus during sleep and immobility. GABAergic interneuronal types are silenced or fire during these events, but the mechanism of pyramidal cell (PC) participation remains elusive. We found opposite membrane polarization of deep (closer to stratum oriens) and superficial (closer to stratum radiatum) rat CA1 PCs during sharp-wave ripples. Using sharp and multi-site recordings in combination with neurochemical profiling, we observed a predominant inhibitory drive of deep calbindin (CB)-immunonegative PCs that contrasts with a prominent depolarization of superficial CB-immunopositive PCs. Biased contribution of perisomatic GABAergic inputs, together with suppression of CA2 PCs, may explain the selection of CA1 PCs during sharp-wave ripples. A deep-superficial gradient interacted with behavioral and spatial effects to determine cell participation during sleep and awake sharp-wave ripples in freely moving rats. Thus, the firing dynamics of hippocampal PCs are exquisitely controlled at subcellular and microcircuit levels in a cell type-selective manner.
NASA Technical Reports Server (NTRS)
Lawson, Denise L.; James, Mark L.
1989-01-01
The Spacecraft Health Automated Reasoning Prototype (SHARP) is a system designed to demonstrate automated health and status analysis for multi-mission spacecraft and ground data systems operations. Telecommunications link analysis of the Voyager 2 spacecraft is the initial focus for the SHARP system demonstration which will occur during Voyager's encounter with the planet Neptune in August, 1989, in parallel with real time Voyager operations. The SHARP system combines conventional computer science methodologies with artificial intelligence techniques to produce an effective method for detecting and analyzing potential spacecraft and ground systems problems. The system performs real time analysis of spacecraft and other related telemetry, and is also capable of examining data in historical context. A brief introduction is given to the spacecraft and ground systems monitoring process at the Jet Propulsion Laboratory. The current method of operation for monitoring the Voyager Telecommunications subsystem is described, and the difficulties associated with the existing technology are highlighted. The approach taken in the SHARP system to overcome the current limitations is also described, as well as both the conventional and artificial intelligence solutions developed in SHARP.
Empirical and biophysical estimations of human cochlea's psychophysical tuning curve sharpness
NASA Astrophysics Data System (ADS)
Chan, Wei Xuan; Kim, Namkeun; Yoon, Yong-Jin
2016-01-01
Despite the advances in cochlear research, the estimation of auditory nerve fiber frequency tuning of human cochlea is mostly based on psychophysical measurements. Although efforts had been made to estimate human frequency tuning sharpness from various physiological measurements which are less species dependent such as the compound action potential and stimulus-frequency otoacoustic emission delay, conclusions on the relative frequency tuning sharpness compared with that of other mammals vary. We simulated the biophysical human cochlea's tuning curve based on physiological measurements of human cochlea and compared the human frequency tuning sharpness with results from empirical methods as well as experimental data of other mammalian cochleae. The compound action potential are more accurate at frequencies below 3 kHz while the stimulus frequency-otoacoustic emission delay are more accurate at frequencies above 1 kHz regions. The results from mechanical cochlear models, with support from conclusions of the other two empirical methodologies, suggest that the human frequency tuning sharpness at frequencies below 1 kHz is similar to common laboratory mammals but is exceptionally sharp at higher frequencies.
Mishra, Srikanta K; Dinger, Zoë
2016-08-01
The present study objectively quantified the efferent-induced changes in the sharpness of cochlear tuning estimates and compared these alterations in cochlear tuning between adults and children. Click evoked otoacoustic emissions with and without contralateral broadband noise were recorded from 15 young adults and 14 children aged between 5 and 10 yrs. Time-frequency distributions of click evoked otoacoustic emissions were obtained via the S-transform, and the otoacoustic emission latencies were used to estimate the sharpness of cochlear tuning. Contralateral acoustic stimulation caused a significant reduction in the sharpness of cochlear tuning estimates in the low to mid frequency region, but had no effect in the higher frequencies (3175 and 4000 Hz). The magnitude of efferent-induced changes in cochlear tuning estimates was similar between adults and children. The current evidence suggests that the stimulation of the medial olivocochlear efferent neurons causes similar alterations in cochlear frequency selectivity in adults and children.
NASA Astrophysics Data System (ADS)
Yang, Rui; Hu, Bowei; Zhang, Aofang; Gao, Dongxing; Wang, Hui; Shi, Ayuan; Lei, Zhenya; Yang, Pei
2017-03-01
Transmission properties through sharp rectangular waveguide bends are investigated to determine the cut-off bending angles of the wave propagation. We show that a simple metallic diaphragm at the bending corner with properly devised sub-wavelength defect apertures of C-slits would be readily to turn on the transmissions with scarce reflections of the propagating modes, while preserving the integrity of the transmitting fields soon after the bends. In particularly, our design also demonstrates the capability of eliminating all the unwanted cavity resonant transmissions that exist in the three-dimensional cascade sharp waveguide bends, and solely let the desired signals travel along the whole passage of the waveguide. The present approach, using C-slit diaphragms to support the sharp bending behaviors of the guided waves with greatly enhanced transmissions, would be especially effective in constructing novel waveguides and pave the way for the development of more compact and miniaturized electromagnetic systems that exploit these waveguide bends.
NASA Technical Reports Server (NTRS)
1984-01-01
A total of 125 talented high school students had the opportunity to gain first hand experience about science and engineering careers by working directly with a NASA scientist or engineer during the summer. This marked the fifth year of operation for NASA's Summer High School Apprenticehsip Research Program (SHARP). Ferguson Bryan served as the SHARP contractor and worked closely with NASA staff at Headquarters and the eight participating sites to plan, implement, and evaluate the Program. The main objectives were to strengthen SHARP and expand the number of students in the Program. These eight sites participated in the Program: Ames Research Center North, Ames' Dryden Flight Research Facility, Goddard Space Flight Center, Goddard's Wallops Flight Facility, Kennedy Space Center, Langley Research Center, Lewis Research Center, and Marshall Space Flight Center.
Yang, Rui; Hu, Bowei; Zhang, Aofang; Gao, Dongxing; Wang, Hui; Shi, Ayuan; Lei, Zhenya; Yang, Pei
2017-03-21
Transmission properties through sharp rectangular waveguide bends are investigated to determine the cut-off bending angles of the wave propagation. We show that a simple metallic diaphragm at the bending corner with properly devised sub-wavelength defect apertures of C-slits would be readily to turn on the transmissions with scarce reflections of the propagating modes, while preserving the integrity of the transmitting fields soon after the bends. In particularly, our design also demonstrates the capability of eliminating all the unwanted cavity resonant transmissions that exist in the three-dimensional cascade sharp waveguide bends, and solely let the desired signals travel along the whole passage of the waveguide. The present approach, using C-slit diaphragms to support the sharp bending behaviors of the guided waves with greatly enhanced transmissions, would be especially effective in constructing novel waveguides and pave the way for the development of more compact and miniaturized electromagnetic systems that exploit these waveguide bends.
Yang, Rui; Hu, Bowei; Zhang, Aofang; Gao, Dongxing; Wang, Hui; Shi, Ayuan; Lei, Zhenya; Yang, Pei
2017-01-01
Transmission properties through sharp rectangular waveguide bends are investigated to determine the cut-off bending angles of the wave propagation. We show that a simple metallic diaphragm at the bending corner with properly devised sub-wavelength defect apertures of C-slits would be readily to turn on the transmissions with scarce reflections of the propagating modes, while preserving the integrity of the transmitting fields soon after the bends. In particularly, our design also demonstrates the capability of eliminating all the unwanted cavity resonant transmissions that exist in the three-dimensional cascade sharp waveguide bends, and solely let the desired signals travel along the whole passage of the waveguide. The present approach, using C-slit diaphragms to support the sharp bending behaviors of the guided waves with greatly enhanced transmissions, would be especially effective in constructing novel waveguides and pave the way for the development of more compact and miniaturized electromagnetic systems that exploit these waveguide bends. PMID:28322344
NASA Technical Reports Server (NTRS)
Kitts, Christopher
2001-01-01
The NASA Ames Research Center (Thermal Protection Materials and Systems Branch) is investigating new ceramic materials for the thermal protection of atmospheric entry vehicles. An incremental approach to proving the capabilities of these materials calls for a lifting entry flight test of a sharp leading edge component on the proposed SHARP (Slender Hypervelocity Aerothermodynamic Research Probe) vehicle. This flight test will establish the aerothermal performance constraint under real lifting entry conditions. NASA Ames has been developing the SHARP test flight with SSDL (responsible for the SHARP S I vehicle avionics), Montana State University (responsible for the SHARP S I vehicle airframe), the Wickman Spacecraft and Propulsion Company (responsible for the sounding rocket and launch operations), and with the SCU Intelligent Robotics Program, The SCU team was added well after the rest of the development team had formed. The SCU role was to assist with the development of a real-time video broadcast system which would relay onboard flight video to a communication groundstation. The SCU team would also assist with general vehicle preparation as well as flight operations. At the time of the submission of the original SCU proposal, a test flight in Wyoming was originally targeted for September 2000. This date was moved several times into the Fall of 2000. It was then postponed until the Spring of 2001, and later pushed into late Summer 2001. To date, the flight has still not taken place. These project delays resulted in SCU requesting several no-cost extensions to the project. Based on the most recent conversations with the project technical lead, Paul Kolodjiez, the current plan is for the overall SHARP team to assemble what exists of the vehicle, to document the system, and to 'mothball' the vehicle in anticipation of future flight and funding opportunities.
Quantum crooks fluctuation theorem and quantum Jarzynski equality in the presence of a reservoir
Quan, H T; Dong, H
2008-01-01
We consider the quantum mechanical generalization of Crooks Fluctuation and Jarzynski Equality Theorem for an open quantum system. The explicit expression for microscopic work for an arbitrary prescribed protocol is obtained, and the relation between quantum Crooks Fluctuation Theorem, quantum Jarzynski Equality and their classical counterparts are clarified. Numerical simulations based on a two-level toy model are used to demonstrate the validity of the quantum version of the two theorems beyond linear response theory regime.
A Polarimetric Extension of the van Cittert-Zernike Theorem for Use with Microwave Interferometers
NASA Technical Reports Server (NTRS)
Piepmeier, J. R.; Simon, N. K.
2004-01-01
The van Cittert-Zernike theorem describes the Fourier-transform relationship between an extended source and its visibility function. Developments in classical optics texts use scalar field formulations for the theorem. Here, we develop a polarimetric extension to the van Cittert-Zernike theorem with applications to passive microwave Earth remote sensing. The development provides insight into the mechanics of two-dimensional interferometric imaging, particularly the effects of polarization basis differences between the scene and the observer.
Altürk, Ahmet
2016-01-01
Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.
Bajpai, Minu
2016-01-01
Sharp foreign bodies in the oesophagus may present as an entirely asymptomatic child with only radiological evidence but require emergent surgical management. Safety pins, razor blades and needles are a few of the commonly ingested sharp objects in developing countries. The open safety pin is a particularly interesting clinical problem, as the management depends on its location and orientation. Many methods and instruments have been used over the years to remove them from the upper digestive tract. We present a novel method using the rigid paediatric bronchoscope and alligator forceps for the extraction of this unusual foreign body from the oesophagus of a 6 year old girl. PMID:26851436
Kim, Pilkyu; Kim, Jun Ho; Jeong, Mun Seok; Ko, Do-Kyeong; Lee, Jongmin; Jeong, Sungho
2006-10-15
A new technique based on electrochemical etching for the fabrication of sharp metallic tips for scanning probe microscopes is introduced. In the proposed method, a small Teflon mass is attached to the end of an immersed tungsten wire using an aluminum tape, which leads to a significant enhancement of yield rate of sharp tungsten tips with an apex size below 100 nm to over 60%. The functionality of the tungsten tips fabricated by the proposed method is verified by measuring the topography of a standard sample using a shear-force scanning probe microscope.