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.
A Note on Trader Sharpe Ratios
Coates, John M.; Page, Lionel
2009-01-01
Traders in the financial world are assessed by the amount of money they make and, increasingly, by the amount of money they make per unit of risk taken, a measure known as the Sharpe Ratio. Little is known about the average Sharpe Ratio among traders, but the Efficient Market Hypothesis suggests that traders, like asset managers, should not outperform the broad market. Here we report the findings of a study conducted in the City of London which shows that a population of experienced traders attain Sharpe Ratios significantly higher than the broad market. To explain this anomaly we examine a surrogate marker of prenatal androgen exposure, the second-to-fourth finger length ratio (2D∶4D), which has previously been identified as predicting a trader's long term profitability. We find that it predicts the amount of risk taken by traders but not their Sharpe Ratios. We do, however, find that the traders' Sharpe Ratios increase markedly with the number of years they have traded, a result suggesting that learning plays a role in increasing the returns of traders. Our findings present anomalous data for the Efficient Markets Hypothesis. PMID:19946367
A note on trader Sharpe Ratios.
Coates, John M; Page, Lionel
2009-11-25
Traders in the financial world are assessed by the amount of money they make and, increasingly, by the amount of money they make per unit of risk taken, a measure known as the Sharpe Ratio. Little is known about the average Sharpe Ratio among traders, but the Efficient Market Hypothesis suggests that traders, like asset managers, should not outperform the broad market. Here we report the findings of a study conducted in the City of London which shows that a population of experienced traders attain Sharpe Ratios significantly higher than the broad market. To explain this anomaly we examine a surrogate marker of prenatal androgen exposure, the second-to-fourth finger length ratio (2D:4D), which has previously been identified as predicting a trader's long term profitability. We find that it predicts the amount of risk taken by traders but not their Sharpe Ratios. We do, however, find that the traders' Sharpe Ratios increase markedly with the number of years they have traded, a result suggesting that learning plays a role in increasing the returns of traders. Our findings present anomalous data for the Efficient Markets Hypothesis.
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.
High aspect ratio sharp nanotip for nanocantilever integration at CMOS compatible temperature
NASA Astrophysics Data System (ADS)
Wang, P.; Michael, A.; Kwok, CY
2017-08-01
In this paper, we demonstrate a novel low temperature nanofabrication approach that enables the formation of ultra-sharp high aspect ratio (HAR) and high density nanotip structures and their integration onto nanoscale cantilever beams. The nanotip structure consists of a nanoscale thermally evaporated Cr Spindt tip on top of an amorphous silicon rod. An apex radius of the tip, as small as 2.5 nm, has been achieved, and is significantly smaller than any other Spindt tips reported so far. 100 nm wide tips with aspect ratio of more than 50 and tip density of more than 5 × 109 tips cm-2 have been fabricated. The HAR tips have been integrated onto an array of 460 nm wide cantilever beams with high precision and yield. In comparison with other approaches, this approach allows the integration of HAR sharp nanotips with nano-mechanical structures in a parallel and CMOS compatible fashion for the first time to our knowledge. Potential applications include on-chip high-speed atomic force microscopy and field emission devices.
High aspect ratio sharp nanotip for nanocantilever integration at CMOS compatible temperature.
Wang, P; Michael, A; Kwok, C Y
2017-08-11
In this paper, we demonstrate a novel low temperature nanofabrication approach that enables the formation of ultra-sharp high aspect ratio (HAR) and high density nanotip structures and their integration onto nanoscale cantilever beams. The nanotip structure consists of a nanoscale thermally evaporated Cr Spindt tip on top of an amorphous silicon rod. An apex radius of the tip, as small as 2.5 nm, has been achieved, and is significantly smaller than any other Spindt tips reported so far. 100 nm wide tips with aspect ratio of more than 50 and tip density of more than 5 × 10(9) tips cm(-2) have been fabricated. The HAR tips have been integrated onto an array of 460 nm wide cantilever beams with high precision and yield. In comparison with other approaches, this approach allows the integration of HAR sharp nanotips with nano-mechanical structures in a parallel and CMOS compatible fashion for the first time to our knowledge. Potential applications include on-chip high-speed atomic force microscopy and field emission devices.
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
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.
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.
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.
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.
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.
SHARP - IV. An apparent flux-ratio anomaly resolved by the edge-on disc in B0712+472
NASA Astrophysics Data System (ADS)
Hsueh, J.-W.; Oldham, L.; Spingola, C.; Vegetti, S.; Fassnacht, C. D.; Auger, M. W.; Koopmans, L. V. E.; McKean, J. P.; Lagattuta, D. J.
2017-08-01
Flux-ratio anomalies in quasar lenses can be attributed to dark matter substructure surrounding the lensing galaxy and thus used to constrain the substructure mass fraction. Previous applications of this approach infer a substructure abundance that is potentially in tension with the predictions of Λ cold dark matter cosmology. However, the assumption that all flux-ratio anomalies are due to substructure is a strong one and alternative explanations have not been fully investigated. Here, we use new high-resolution near-IR Keck II adaptive optics imaging for the lens system CLASS B0712+472 to perform pixel-based lens modelling for this system and, in combination with the new Very Long Baseline Array radio observations, show that the inclusion of the disc in the lens model can explain the flux-ratio anomalies without the need for dark matter substructures. The projected disc mass comprises 16 per cent of the total lensing mass within the Einstein radius and the total disc mass is 1.79 × 1010 M⊙. The case of B0712+472 adds to the evidence that not all flux-ratio anomalies are due to dark subhaloes and highlights the importance of taking the effects of baryonic structures more fully into account in order to obtain an accurate measure of the substructure mass fraction.
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.
NASA Astrophysics Data System (ADS)
Wright, James R.
2006-12-01
I present the use of Sherman's Theorem, and a development approach, for optimal solutions to real-time estimation problems that are multidimensional, nonlinear, stochastic, and have random multidimensional forcing function modeling errors that drive the state. Satisfaction of Sherman's Theorem guarantees that the mean-squared state estimate error on each state estimate component is minimized. Sherman's Theorem is not new, but my application of Sherman's Theorem is new. To Malcolm Shuster, who taught me about torque replacement modeling with rate-gyro sensors, and argues fiercely in defense of Maximum Likelihood Estimation (MLE).
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)
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)
... this page: //medlineplus.gov/ency/patientinstructions/000444.htm Handling sharps and needles To use the sharing features ... Health Administration. OSHA fact sheet: protecting yourself when handling contaminated sharps. Updated January 2011. Available at: www. ...
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.
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
2014-03-26
NASA Terra spacecraft views central South Dakota, where the Missouri River forms a meander bend, creating Lake Sharpe. Eventually, the Missouri River will cut through the skinny peninsula, creating a shorter path.
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.
Cartland, H.; Fiske, P.; Greenwood, R.; Hargiss, D.; Heston, P.; Hinsey, N.; Hunter, J.; Massey, W.
1995-01-10
The worlds largest light gas gun at SHARP (Super High Altitude Research Project) is completed and in the past year has launched 9 scramjets. Typical masses and velocities are 5.9 kg at 2.8 km/sec.and 4.4 kg at 3.1 km/sec. In so doing SHARP launched the first fully functioning, hydrogen burning scramjet at mach 8. The SHARP launcher is unique in having a 4 inch diameter and 155 foot-long barrel. This enables lower acceleration launches than any other system. In addition the facility can deliver high energy projectiles to targets in the open air without having to contain the impact fragments. This allows one to track lethality test debris for several thousand feet.
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
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.
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
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.
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.
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…
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…
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…
2014-09-11
This is a map of lower Mount Sharp on Mars, showing the major geologic units identified from orbit. The rocks of the Murray Formation, mapped in green, likely represent the oldest layers of Mount Sharp that NASA Curiosity rover will explore.
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)
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,…
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,…
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.
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.
Topological interpretation of the Luttinger theorem
NASA Astrophysics Data System (ADS)
Seki, Kazuhiro; Yunoki, Seiji
2017-08-01
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because (i) the Luttinger volume is represented as the winding number of the single-particle Green's function and, thus, (ii) the deviation of the theorem, expressed with a ratio between the interacting and noninteracting single-particle Green's functions, is also represented as the winding number of this ratio. The formulation based on the winding number naturally leads to two types of the generalized Luttinger theorem. Exploring two examples of single-band translationally invariant interacting electrons, i.e., simple metal and Mott insulator, we show that the first type falls into the original statement for Fermi liquids given by Luttinger, where poles of the single-particle Green's function appear at the chemical potential, while the second type corresponds to the extended one for nonmetallic cases with no Fermi surface such as insulators and superconductors generalized by Dzyaloshinskii, where zeros of the single-particle Green's function appear at the chemical potential. This formulation also allows us to derive a sufficient condition for the validity of the Luttinger theorem of the first type by applying the Rouche's theorem in complex analysis as an inequality. Moreover, we can rigorously prove in a nonperturbative manner, without assuming any detail of a microscopic Hamiltonian, that the generalized Luttinger theorem of both types is valid for generic interacting fermions as long as the particle-hole symmetry is preserved. Finally, we show that the winding number of the single-particle Green's function can also be associated with the distribution function of quasiparticles, and therefore the number of quasiparticles is equal to the Luttinger volume. This implies that
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…
ERIC Educational Resources Information Center
Musto, Garrod
2010-01-01
Within his classroom, the author is often confronted by students who fail to see, or accept, the relevance of mathematics both to their lives and the world around them. One topic which is regularly perceived as being disconnected from people's daily lives is that of circle theorems, especially among less motivated students. In this article, the…
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.
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
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
Generalized Kochen-Specker theorem
NASA Astrophysics Data System (ADS)
Aravind, P. K.
2003-11-01
A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)] is extended to all higher dimensions. A set of 18 states in four dimensions is used to give closely related proofs of the generalized Kochen-Specker, Kochen-Specker, and Bell theorems that shed some light on the relationship between these three theorems.
On Leighton's comparison theorem
NASA Astrophysics Data System (ADS)
Ghatasheh, Ahmed; Weikard, Rudi
2017-06-01
We give a simple proof of a fairly flexible comparison theorem for equations of the type -(p (u‧ + su)) ‧ + rp (u‧ + su) + qu = 0 on a finite interval where 1 / p, r, s, and q are real and integrable. Flexibility is provided by two functions which may be chosen freely (within limits) according to the situation at hand. We illustrate this by presenting some examples and special cases which include Schrödinger equations with distributional potentials as well as Jacobi difference equations.
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.
The Non-Signalling theorem in generalizations of Bell's theorem
NASA Astrophysics Data System (ADS)
Walleczek, J.; Grössing, G.
2014-04-01
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational
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.
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.
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.…
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.…
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…
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)
Point and Circle Configurations; A New Theorem.
ERIC Educational Resources Information Center
Dorwart, Harold L.
1988-01-01
Point and circle configurations are not well known, so Clifford's chain of theorems and Miquel's theorem, whose diagrams exhibit such configurations, are discussed. A new theorem similar to Miquel's is then presented. (MNS)
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.
Fluctuation theorem: A critical review
NASA Astrophysics Data System (ADS)
Malek Mansour, M.; Baras, F.
2017-10-01
Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.
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
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.
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…
MEASURABLE UTILITY AND THE MEASURABLE CHOICE THEOREM.
Three theorems are proved that are useful in mathematical treatments of economic models with a continuum of economic agents . The first, called the...measurable. Both these theorems generalize known theorems on these subjects. The third theorem treats a situation in which the set of economic agents forms
'Sharpe', a clonal plum rootstock for peach
USDA-ARS?s Scientific Manuscript database
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...
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
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.
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.
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.
Soft theorems in superstring theory
NASA Astrophysics Data System (ADS)
Sen, Ashoke
2017-06-01
We use insights from superstring field theory to prove the subleading soft graviton theorem for tree amplitudes of (compactified) heterotic and type II string theories for arbitrary number of finite energy NS (NSNS) sector external states but only one soft graviton. We also prove the leading soft graviton theorem in these theories for arbitrary number of external soft gravitons. In our analysis there is no restriction on the mass and spin of the finite energy external states. This method can also be used to give a proof of the subleading soft graviton theorem for tree amplitudes in quantum field theories coupled to gravity with generic interactions. We discuss the technical issue involved in extending this analysis to loop amplitudes of superstring theory including Ramond sector external states, and its possible resolution.
The NMR reciprocity theorem for arbitrary probe geometry.
van der Klink JJ
2001-01-01
It is shown that the NMR reciprocity theorem is a variant of a problem considered by Lorentz in 1895. This formulation is quite general and applies to electric-dipole-based as well as coil-based or resonator-based magnetic resonance probes. The reasoning is related to, but different from, the proof of the reciprocity theorem for radiofrequency networks and for transmit/receive antenna systems in telecommunications. The signal-to-noise ratio of the NMR experiment is also discussed in very general terms. Copyright 2001 Academic Press.
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.
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.
Grand Canyon Similar to Mount Sharp
2012-08-27
Before NASA Curiosity rover landed on Mars, the strata exposed in Mount Sharp were compared to those in the Grand Canyon of the western United States, shown here. Scientists are surprised by just how close the similarities are.
First Sampling Hole in Mount Sharp
2014-09-25
This image from the Mars Hand Lens Imager MAHLI camera on NASA Curiosity Mars rover shows the first sample-collection hole drilled in Mount Sharp, the layered mountain that is the science destination of the rover extended mission.
Mount Sharp Panorama in Raw Colors
2013-03-15
This mosaic of images from the Mastcam onboard NASA Mars rover Curiosity shows Mount Sharp in raw color. Raw color shows the scene colors as they would look in a typical smart-phone camera photo, before any adjustment.
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
Mount Sharp Inside Gale Crater, Mars
2012-03-28
Curiosity, the big rover of NASA Mars Science Laboratory mission, will land in August 2012 near the foot of a mountain inside Gale Crater. The mission project science group is calling the mountain Mount Sharp.
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.
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.
No-go theorem for ergodicity and an Einstein relation
NASA Astrophysics Data System (ADS)
Froemberg, D.; Barkai, E.
2013-08-01
We provide a simple no-go theorem for ergodicity and the generalized Einstein relation for anomalous diffusion processes. The theorem states that either ergodicity in the sense of equal time and ensemble averaged mean squared displacements (MSD) is broken, and/or the generalized Einstein relation for time averaged diffusivity and mobility is invalid, which is in complete contrast to normal diffusion processes. We also give a general relation for the time averages of drift and MSD for ergodic (in the MSD sense) anomalous diffusion processes, showing that the ratio of these quantities depends on the measurement time. The Lévy walk model is used to exemplify the no-go theorem.
Pion Electroproduction and Siegert's Theorem
NASA Astrophysics Data System (ADS)
Tiator, Lothar
2016-11-01
Nucleon to Resonance transition form factors are discussed within the MAID model for pion electroproduction on the nucleon. For low Q^2 the consequences of Siegert's theorem are presented and medium to large violations of the Long Wavelength Limit at the pseudo-threshold are observed for the phenomenological parametrizations of the longitudinal transition form factors of different nucleon resonances.
STOCHASTIC POINT PROCESSES: LIMIT THEOREMS.
A stochastic point process in R(n) is a triple (M,B,P) where M is the class of all countable sets in R(n) having no limit points, B is the smallest...converge to a mixture of Poisson processes. These results are established via a generalization of a classical limit theorem for Bernoulli trials. (Author)
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.
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,…
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…
NASA Astrophysics Data System (ADS)
Chambers, Chris M.; Moss, Ian G.
1994-08-01
A generalization of Price's theorem is given for application to inflationary cosmologies. Namely, we show that on a Schwarzschild-de Sitter background there are no static solutions to the wave or gravitational perturbation equations for modes with angular momentum greater than their intrinsic spin.
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.)
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…
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…
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,…
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…
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…
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.
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.
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.
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.
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.
Analysis of sharpness Fano resonance curve based on eye-like resonators
NASA Astrophysics Data System (ADS)
Lou, Xiao-wei; Cui, Jin-jiang; Dong, Ning-ning; Xu, Jian-gen; Tan, Hui-ming
2014-11-01
For given intrinsic losses of a single ring resonator sensor, there exists the maximum sharpness, at the extinction ratio of -6dB. However, the maximum sharpness of a single ring resonator sensor is sensitive for the coupling coefficient. In order to obtain the maximum sharpness, the coupling region of the single rings must have a higher precision of manufacture. To solve this problem, this paper proposed eye-like resonator which is formed by a ring resonator (named inner loop) embedd in the dual-bus-coupled ring resonator (named outer loop). Eye-like resonators can generate the asymmetric Fano-resonance spectra of the drop port, numerical calculation of spectra on the drop port is utilized by the transfer matrix method. As the round trip loss varies, the maximum value of sharpness and the corresponding transmission at the resonant point can be obtained by tuning the phase ratio of the outer loop to the inner loop. The maximum value of sharpness increases with the round trip loss, as the outer loop and inner loop coupling coefficient changing, the maximum value of sharpness of Fano-resonance change slowly in a wide range. As the round trip loss and coupling coefficients of the outer loop and inner loop varies, the corresponding transmission at the resonant point remains almost the same, about -6dB. The sharpness of Fano resonant peak is insensitive for the coupling coefficients, which can reduce the requirements of manufacture of coupling region.
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
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.
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.
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.
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.}
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.
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 and the Jules Verne Launcher
NASA Astrophysics Data System (ADS)
Hunter, John; Cartland, Harry
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% of the best US rocket delivery cost. This technology will enable the next phase of man's exploration of space.
Note: Electrochemical etching of sharp iridium tips
NASA Astrophysics Data System (ADS)
Lalanne, Jean-Benoît; Paul, William; Oliver, David; Grütter, Peter H.
2011-11-01
We describe an etching procedure for the production of sharp iridium tips with apex radii of 15-70 nm, as determined by scanning electron microscopy, field ion microscopy, and field emission measurements. A coarse electrochemical etch followed by zone electropolishing is performed in a relatively harmless calcium chloride solution with high success rate.
Heading for Mount Sharp, Sol 329
2013-07-11
Lower slopes of Mount Sharp appear at the top of this image taken by the right Navigation Camera Navcam of NASA Mars rover Curiosity at the end of a drive of about 135 feet during the 329th Martian day, or sol, of the rover work on Mars.
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.
Edge Sharpness Assessment by Parametric Modeling: Application to Magnetic Resonance Imaging.
Ahmad, R; Ding, Y; Simonetti, O P
2015-05-01
In biomedical imaging, edge sharpness is an important yet often overlooked image quality metric. In this work, a semi-automatic method to quantify edge sharpness in the presence of significant noise is presented with application to magnetic resonance imaging (MRI). The method is based on parametric modeling of image edges. First, an edge map is automatically generated and one or more edges-of-interest (EOI) are manually selected using graphical user interface. Multiple exclusion criteria are then enforced to eliminate edge pixels that are potentially not suitable for sharpness assessment. Second, at each pixel of the EOI, an image intensity profile is read along a small line segment that runs locally normal to the EOI. Third, the profiles corresponding to all EOI pixels are individually fitted with a sigmoid function characterized by four parameters, including one that represents edge sharpness. Last, the distribution of the sharpness parameter is used to quantify edge sharpness. For validation, the method is applied to simulated data as well as MRI data from both phantom imaging and cine imaging experiments. This method allows for fast, quantitative evaluation of edge sharpness even in images with poor signal-to-noise ratio. Although the utility of this method is demonstrated for MRI, it can be adapted for other medical imaging applications.
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.
SHARPS III Update Review--Autumn 1982.
1982-09-14
permit up to 75 system parameter cards, 65 electronic parameter cards (type 21), 12 unique sonar depth codes, and 15 title and 35 message lines in the...for a sonar description file that will drive SHARPS through active sonobuoy predic- tions for three buoys (designated SBA , SBB, and SBC on the type 10...state functions would 4-1 be reinstated following the yanks. A problem arising from reverting to the old code was that all sonar description files
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.
Scattering theorems for dyadic chiral fields
NASA Astrophysics Data System (ADS)
Athanasiadis, Christodoulos; Gotopoulos, Stavros
2004-06-01
A time-harmonic plane dyadic electromagnetic field is scattered by a chiral body in a chiral environment. The body is either a perfect conductor or a dielectric. The incident field is a linear combination of left-circularly polarized and right-circularly polarized dyadic electromagnetic fields, each of which has a different wave number. We prove reciprocity and scattering theorems in dyadic form, which incorporate as special cases the corresponding known theorems for vector electromagnetic waves. Specializing to the same direction of incidence and observation in the general scattering theorems we obtain forward scattering theorems.
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.
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 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.
Chemostratigraphy of Lower Mount Sharp, Gale Crater
NASA Astrophysics Data System (ADS)
Wiens, R. C.; Frydenvang, J.; Watkins, J. A.; Mangold, N.; Le Deit, L.; Blaney, D. L.; Bridges, J.; Forni, O.; Gasda, P. J.; Gasnault, O.; Lanza, N.; Maurice, S.; Milliken, R.; Newsom, H. E.; Ollila, A. M.; Vasavada, A. R.
2016-12-01
The Curiosity rover is ascending Mt. Sharp, a large sedimentary mound at the center of Gale crater, Mars. Over the last two years Curiosity has progressed across the Murray formation, which is the lowermost exposed member of the Mt. Sharp Group, and consists mostly of thinly laminated lacustrine deposits. During this traverse, Curiosity has encountered two additional units: The Stimson unit consists of eolian cross-bedded sandstones that unconformably drape the Murray and are interpreted as remnants of ancient dunes post-dating the lacustrine period. An enigmatic blocky unit has also been encountered in the vicinity of Brandberg (sol 1160) and Bimbe (1398). The geologic nature of this unit is unclear, but Bimbe in particular provides the only conglomerates observed on Mt. Sharp. In contrast to Bradbury rise, Bimbe conglomerates contain angular clasts. These fluvial sediments could source from further up Mt. Sharp. Over 4000 elemental composition observations have been made by ChemCam on > 400 targets on Mt. Sharp. In contrast to the Bradbury group which contains more felsic coarse-grained material than average Mars, initial Murray at Pahrump (sols 750-900) shows a reversal, with coarse-grained interbedded sandstones closer to average Mars and fine-grained material shows more felsic compositions (higher Al, Si). At Marias Pass (sol 1000), finely laminated layers of nearly pure silica (e.g., > 85 wt. % SiO2) were encountered in Murray, and opal and tridymite were observed by CheMin at Buckskin. Bridger Basin (sol 1120) revealed clear fracture-related silica enrichments cross-cutting both Murray and Stimson units, suggesting strong groundwater interaction post-dating both units. Bimbe conglomerates have diverse compositions, while dark-toned blocky floats have high Na2O (> 4.5 wt. %) but low Al2O3 (< 9 wt. %), much lower than Jake_M (sol 45). A significant observation starting in the Murray Unit is the presence of boron and Na enrichments (likely NaCl) in and around
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 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.
SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH ...
SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN vSHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN - Snake River Bridge at Lyons' Ferry, State Route 261 spanning Snake River, Starbuck, Columbia County, WA
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…
A Physical Proof of the Pythagorean Theorem
ERIC Educational Resources Information Center
Treeby, David
2017-01-01
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…
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…
Euler and the Fundamental Theorem of Algebra.
ERIC Educational Resources Information Center
Duham, William
1991-01-01
The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)
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…
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…
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.)
A note on Morley's triangle theorem
NASA Astrophysics Data System (ADS)
Mueller, Nancy; Tikoo, Mohan; Wang, Haohao
2012-06-01
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.
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
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
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)
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…
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.)
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.
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.
The Euler Line and Nine-Point-Circle Theorems.
ERIC Educational Resources Information Center
Eccles, Frank M.
1999-01-01
Introduces the Euler line theorem and the nine-point-circle theorem which emphasize transformations and the power of functions in a geometric concept. Presents definitions and proofs of theorems. (ASK)
Diverse Terrain Types on Mount Sharp, Mars
2015-05-08
A sweeping panorama combining 33 telephoto images into one Martian vista presents details of several types of terrain visible on Mount Sharp from a location along the route of NASA's Curiosity Mars rover. The rover's Mast Camera (Mastcam) recorded the component images with its right-eye camera on April 10, 2015, during the 952nd Martian day, or sol, of Curiosity's work on Mars, before that sol's drive. The panorama spans from south-southeast, at left, to west-southwest. The color has been approximately white-balanced to resemble how the scene would appear under daytime lighting conditions on Earth. Higher elevations on Mount Sharp are visible at left, including the jagged skyline to the right of a 100-meter scale bar overlaid on the image. (One hundred meters is about 328 feet.) The 2-meter (7-foot) scale bar near the center of the scene is on an exposure of pale mudstone within Mount Sharp's basal geological unit, the Murray formation, and nearby darker rocks. The 3-meter (10-foot) scale bar farther to the right is at the base of a rise called "Gray Wolf Peak." "Logan Pass," a science destination for the rover, is at a dip on the horizon near the right edge of the panorama. Malin Space Science Systems, San Diego, built and operates the rover's Mastcam. NASA's Jet Propulsion Laboratory, a division of the California Institute of Technology, Pasadena, manages the Mars Science Laboratory Project for NASA's Science Mission Directorate, Washington. JPL designed and built the project's Curiosity rover. http://photojournal.jpl.nasa.gov/catalog/PIA19397
A sharp-focusing schlieren optical deflectometer
NASA Technical Reports Server (NTRS)
Alvi, F. S.; Settles, G. S.; Weinstein, L. M.
1993-01-01
A new instrument capable of localized, nonintrusive turbulence measurements is developed by combining a focusing schlieren system with an optical deflectometer. This instrument records the fluctuating light intensity at a point in the focused schlieren image. Its capability is verified by making benchmark measurements of Kelvin-Helmholtz vortices produced in a low-speed axisymmetric mixing layer. The sharp-focusing effect is demonstrated both visually and quantitatively. The results show that the instrument is capable of optical turbulence measurements within a 4 mm depth-of-field.
Catastrophe optics of sharp-edge diffraction.
Borghi, Riccardo
2016-07-01
A classical problem of diffraction theory, namely plane wave diffraction by sharp-edge apertures, is here reformulated from the viewpoint of the fairly new subject of catastrophe optics. On using purely geometrical arguments, properly embedded into a wave optics context, uniform analytical estimates of the diffracted wavefield at points close to fold caustics are obtained, within paraxial approximation, in terms of the Airy function and its first derivative. Diffraction from parabolic apertures is proposed to test reliability and accuracy of our theoretical predictions.
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.'
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.
Digital holographic microscopy and focusing methods based on image sharpness.
İlhan, Hazar A; Doğar, Mert; Özcan, Merıç
2014-09-01
Digital holographic microscope allows imaging of opaque and transparent specimens without staining. A digitally recorded hologram must be reconstructed numerically at the actual depth of the object to obtain a focused image. We have developed a high-resolution digital holographic microscope for imaging amplitude and phase objects with autofocusing capability. If the actual depth of an object is not known a priori, it is estimated by comparing the sharpness of several reconstructions at different distances, which is very demanding in means of computational power when the recorded hologram is large. In this paper, we present 11 different sharpness metrics for estimating the actual focus depths of objects. The speed performance of focusing is discussed, and a scaling technique is introduced where the speed of autofocusing increases on the order of square of the scale ratio. We measured the performance of scaling on computer-generated holograms and on recorded holograms of a biological sample. We show that simulations are in good agreement with the experimental results. © 2014 The Authors Journal of Microscopy © 2014 Royal Microscopical Society.
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.
Singlet and triplet instability theorems
NASA Astrophysics Data System (ADS)
Yamada, Tomonori; Hirata, So
2015-09-01
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.
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.
Glimpse of Bagnold Dunes Edging Mount Sharp
2015-11-16
The dark band in the lower portion of this Martian scene is part of the "Bagnold Dunes" dune field lining the northwestern edge of Mount Sharp, inside Gale Crater. The view combines multiple images taken with the Mast Camera (Mastcam) on NASA's Curiosity Mars rover on Sept. 25, 2015, during the 1,115th Martian day, or sol, of Curiosity's work on Mars. The images are from Mastcam's right-eye camera, which has a telephoto lens. The view is toward south-southeast. Curiosity will visit examples of the Bagnold Dunes on the rover's route to higher layers of Mount Sharp. The informal name for the dune field is a tribute to British military engineer Ralph Bagnold (1896-1990), a pioneer in the study of how winds move sand particles of dunes on Earth. The dune field is evident as a dark band in orbital images of the area inside Gale Crater where Curiosity has been active since landing in 2012, such as a traverse map at PIA20162. Dunes are larger than wind-blown ripples of sand or dust that Curiosity and other rovers have visited previously. The scene is presented with a color adjustment that approximates white balancing, to resemble how the rocks and sand would appear under daytime lighting conditions on Earth. http://photojournal.jpl.nasa.gov/catalog/PIA19929
Status report on SHARP coupling framework.
Caceres, A.; Tautges, T. J.; Lottes, J.; Fischer, P.; Rabiti, C.; Smith, M. A.; Siegel, A.; Yang, W. S.; Palmiotti, G.
2008-05-30
This report presents the software engineering effort under way at ANL towards a comprehensive integrated computational framework (SHARP) for high fidelity simulations of sodium cooled fast reactors. The primary objective of this framework is to provide accurate and flexible analysis tools to nuclear reactor designers by simulating multiphysics phenomena happening in complex reactor geometries. Ideally, the coupling among different physics modules (such as neutronics, thermal-hydraulics, and structural mechanics) needs to be tight to preserve the accuracy achieved in each module. However, fast reactor cores in steady state mode represent a special case where weak coupling between neutronics and thermal-hydraulics is usually adequate. Our framework design allows for both options. Another requirement for SHARP framework has been to implement various coupling algorithms that are parallel and scalable to large scale since nuclear reactor core simulations are among the most memory and computationally intensive, requiring the use of leadership-class petascale platforms. This report details our progress toward achieving these goals. Specifically, we demonstrate coupling independently developed parallel codes in a manner that does not compromise performance or portability, while minimizing the impact on individual developers. This year, our focus has been on developing a lightweight and loosely coupled framework targeted at UNIC (our neutronics code) and Nek (our thermal hydraulics code). However, the framework design is not limited to just using these two codes.
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.
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.
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).
Cosmological singularity theorems and black holes
NASA Astrophysics Data System (ADS)
Vilenkin, Alexander; Wall, Aron C.
2014-03-01
An extension of Penrose's singularity theorem is proved for spacetimes where black holes are allowed to form from nonsingular initial data. With standard assumptions about the spacetime, and assuming the existence of a trapped surface which lies outside of black hole horizons and is not completely surrounded by horizons, we show that the spacetime region outside (or on) the horizons must contain singularities. If the trapped surface is surrounded by horizons, we show that the horizons divide spacetime into causally disconnected pieces. Unlike the original Penrose theorem, our theorems provide some information about the location of singularities. We illustrate how they can be used to rule out some cosmological scenarios.
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.
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.
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.
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)
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.
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…
Illustrating the Central Limit Theorem through Microsoft Excel Simulations
ERIC Educational Resources Information Center
Moen, David H.; Powell, John E.
2005-01-01
Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…
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…
Fishman, S.; Soffer, A.
2016-07-15
We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.
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 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.
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 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…
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
Application of KAM Theorem to Earth Orbiting Satellites
2009-03-01
Planar, Three-Body Problem (RCPTBP), specifically the motion of asteroids under the effects of the Sun and Jupiter [5–7]. Celletti and Chierchia [6] showed...that the 7 asteroid 12-Victoria, in a Keplerian orbit about the Sun and perturbed by Jupiter , could be modeled using the KAM theorem; in this case...the perturbation is equal to the Jupiter -Sun mass ratio, ε ≈ 10−3. They were able to show that the results of their analysis agreed well with observed
[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).
The effective field theory of inflation models with sharp features
Bartolo, Nicola; Cannone, Dario; Matarrese, Sabino E-mail: dario.cannone@pd.infn.it
2013-10-01
We describe models of single-field inflation with small and sharp step features in the potential (and sound speed) of the inflaton field, in the context of the Effective Field Theory of Inflation. This approach allows us to study the effects of features in the power-spectrum and in the bispectrum of curvature perturbations, from a model-independent point of view, by parametrizing the features directly with modified ''slow-roll'' parameters. We can obtain a self-consistent power-spectrum, together with enhanced non-Gaussianity, which grows with a quantity β that parametrizes the sharpness of the step. With this treatment it is straightforward to generalize and include features in other coefficients of the effective action of the inflaton field fluctuations. Our conclusion in this case is that, excluding extrinsic curvature terms, the only interesting effects at the level of the bispectrum could arise from features in the first slow-roll parameter ε or in the speed of sound c{sub s}. Finally, we derive an upper bound on the parameter β from the consistency of the perturbative expansion of the action for inflaton perturbations. This constraint can be used for an estimation of the signal-to-noise ratio, to show that the observable which is most sensitive to features is the power-spectrum. This conclusion would change if we consider the contemporary presence of a feature and a speed of sound c{sub s} < 1, as, in such a case, contributions from an oscillating folded configuration can potentially make the bispectrum the leading observable for feature models.
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.
Janati, A Bruce; AlGhasab, Naif Saad; Alshammari, Raed Ayed; saad AlGhassab, Abdulmohsen; Al-Aslami Yossef Fahad
2016-06-01
There exists a paucity of data in the EEG literature on characteristics of "atypical" interictal epileptiform discharges (IEDs), including sharp slow waves (SSWs). This article aims to address the clinical, neurophysiological, and neuropathological significance of SSW The EEGs of 920 patients at a tertiary-care facility were prospectively reviewed over a period of one year. Thirty-six patients had SSWs in their EEG. Of these, 6 patients were excluded because of inadequate clinical data. The clinical and neuroimaging data of the remaining 30 patients were then retrospectively collected and reviewed, and the findings were correlated. The data revealed that SSWs were rare and age-related EEG events occurring primarily in the first two decades of life. All patients with SSWs had documented epilepsy, presenting clinically with partial or generalized epilepsy. It is notable that one-third of the patients with SSWs had chronic or static central nervous system (CNS) pathology, particularly congenital CNS anomalies. Though more than one mechanism may be involved in the pathogenesis of SSWs, this research indicates that the most compelling theory is a deeply seated cortical generator giving rise to this EEG pattern. The presence of SSWs should alert clinicians to the presence of partial or generalized epilepsy or an underlying chronic or static CNS pathology, in particular congenital CNS anomalies, underscoring the significance of brain magnetic resonance imaging in the work-up of this population.
2015-10-08
A view from the Kimberly formation on Mars taken by NASA Curiosity rover. The strata in the foreground dip towards the base of Mount Sharp, indicating the ancient depression that existed before the larger bulk of the mountain formed. The colors are adjusted so that rocks look approximately as they would if they were on Earth, to help geologists interpret the rocks. This "white balancing" to adjust for the lighting on Mars overly compensates for the absence of blue on Mars, making the sky appear light blue and sometimes giving dark, black rocks a blue cast. This image was taken by the Mast Camera (Mastcam) on Curiosity on the 580th Martian day, or sol, of the mission. Malin Space Science Systems, San Diego, built and operates Curiosity's Mastcam. NASA's Jet Propulsion Laboratory, a division of the California Institute of Technology, Pasadena, built the rover and manages the project for NASA's Science Mission Directorate, Washington. http://photojournal.jpl.nasa.gov/catalog/PIA19839
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.
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
Risk of sharps injuries among home care aides: Results of the Safe Home Care survey.
Brouillette, Natalie M; Quinn, Margaret M; Kriebel, David; Markkanen, Pia K; Galligan, Catherine J; Sama, Susan R; Gore, Rebecca J; Laramie, Angela K; Davis, Letitia
2017-04-01
Home care (HC) aides constitute an essential, rapidly growing workforce. Technology advances are enabling complex medical care at home, including procedures requiring the percutaneous use of sharp medical devices, also known as sharps. Objectives were to quantify risks of sharps injuries (SI) in a large HC aide population, compare risks between major occupational groups, and evaluate SI risk factors. A questionnaire survey was administered to aides hired by HC agencies and directly by clients. One thousand one hundred seventy-eight aides completed questions about SI and potential risk factors occurring in the 12 months before the survey. SI rates were calculated and Poisson regression models identified risk factors. Aides had a 2% annual risk of experiencing at least 1 SI (95% confidence interval [CI], 1.1-2.6). Client-hired aides, men, and immigrants had a higher risk than their counterparts. Risk factors among all HC aides included helping a client use a sharp device (rate ratio [RR], 5.62; 95% CI, 2.75-11.50), observing used sharps lying around the home (RR, 2.68; 95% CI, 1.27-5.67), and caring for physically aggressive clients (RR, 2.82; 95% CI, 1.36-5.85). HC aides experience serious risks of SI. Preventive interventions are needed, including safety training for clients and their families, as well as aides. Copyright © 2017 Association for Professionals in Infection Control and Epidemiology, Inc. Published by Elsevier Inc. All rights reserved.
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).
Almost sharp fronts for the surface quasi-geostrophic equation.
Córdoba, Diego; Fefferman, Charles; Rodrigo, José Luis
2004-03-02
We investigate the evolution of "almost sharp" fronts for the surface quasi-geostrophic equation. This equation was originally introduced in the geophysical context to investigate the formation and evolution of fronts, i.e., discontinuities between masses of hot and cold air. These almost sharp fronts are weak solutions of quasi-geostrophic with large gradient. We relate their evolution to the evolution of sharp fronts.
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.
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
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.
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.
Adiabatic Theorem for Quantum Spin Systems
NASA Astrophysics Data System (ADS)
Bachmann, S.; De Roeck, W.; Fraas, M.
2017-08-01
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
Adiabatic Theorem for Quantum Spin Systems.
Bachmann, S; De Roeck, W; Fraas, M
2017-08-11
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ϵ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
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.
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.
Strong Large Deviation and Local Limit Theorems
1989-08-01
Strong Large Deviation and Local Limit Theorenisi by (D -N araitia Rao Chaganty and Jayaraii Setrhurainari ____Old DoiinUnitnerity and Florida State...deviations, Local Limit Theorems. El L ,CT OCQT23 1989 u2 ’JB 169 Abstract M os t laCd~viaio re11 t ; asym~1O 5 Iptotic expressions to log P( In > ! y...ji(S) < xandl let b",-*x Define q,,(y,; b, S) = V(b,,/p(S)) P(?),(!I, - Y) E S)]. as the pseudo-density futnction of I- . By a local limit theorem
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.
Asymptotic symmetries and subleading soft graviton theorem
NASA Astrophysics Data System (ADS)
Campiglia, Miguel; Laddha, Alok
2014-12-01
Motivated by the equivalence between the soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the Bondi, van der Burg, Metzner and Sachs (BMS) group, we propose a new extension (different from the so-called extended BMS) of the BMS group that is a semidirect product of supertranslations and Diff(S2) . We propose a definition for the canonical generators associated with the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.
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
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.
The Viner-Wong Envelope Theorem.
ERIC Educational Resources Information Center
Silberberg, Eugene
1999-01-01
Observes that the envelope theorem, a fundamental tool in duality analysis, is still a puzzle to many people. Argues that the essence of a solution proposed by Paul Samuelson (1947) is also unclear to many people, but can be communicated with a simple cost diagram. Presents and explains the proposed diagram. (DSK)
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.
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.
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.
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.
Fixed point theorems and dissipative processes.
NASA Technical Reports Server (NTRS)
Hale, J. K.; Lopes, O.
1973-01-01
Operators of the type considered by Hale et al. (1972) are used to show that under certain conditions there is a fixed point in a dissipative map within a Banach space. The conditions required for the existence of this fixed point are discussed in detail. Several fixed point theorems are formulated and proved.
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…
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.
The Binomial Theorem Tastes the Rainbow.
ERIC Educational Resources Information Center
Cuff, Carolyn K.
1998-01-01
Discusses the commercial for Skittles candies and asks the question "How many flavor combinations can you find?" Focuses on the modeling for a Skittles exercise which includes a brief outline of the mathematical modeling process. Guides students in the use of the binomial theorem and Pascal's triangle in this activity. (ASK)
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…
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.
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.
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)
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.
An Ordinary but Surprisingly Powerful Theorem
ERIC Educational Resources Information Center
Sultan, Alan
2009-01-01
Being a mathematician, the author started to wonder if there are any theorems in mathematics that seem very ordinary on the outside, but when applied, have surprisingly far reaching consequences. The author thought about this and came up with the following unlikely candidate which follows immediately from the definition of the area of a rectangle…
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.
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…
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…
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…
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)
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.
Tennis Rackets and the Parallel Axis Theorem
NASA Astrophysics Data System (ADS)
Christie, Derek
2014-04-01
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.
"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…
An Elementary Proof of Pick's Theorem.
ERIC Educational Resources Information Center
Pullman, Howard W.
1979-01-01
Pick's Theorem, a statement of the relationship between the area of a polygonal region on a lattice and its interior and boundary lattice points, is familiar to those whose students have participated in activities and discovery lessons using the geoboard. The proof presented, although rather long, is well within the grasp of the average geometry…
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.
Sharp Vision Reveals Intimacy of Stars
NASA Astrophysics Data System (ADS)
2005-11-01
Sharp Vision Reveals Intimacy of Stars AMBER instrument on VLTI Probes Environment of Stars Using the newly installed AMBER instrument on ESO's Very Large Telescope Interferometer, which combines the light from two or three 8.2-m Unit Telescopes thereby amounting to observe with a telescope of 40 to 90 metres in diameter, two international teams of astronomers observed with unprecedented detail the environment of two stars. One is a young, still-forming star and the new results provide useful information on the conditions leading to the creation of planets. The other is on the contrary a star entering the latest stages of its life. The astronomers found, in both cases, evidence for a surrounding disc. ESO PR Photo 36a/05 ESO PR Photo 36a/05 The Young Stellar Object MWC 297 (Artist's View) [Preview - JPEG: 400 x 502 pix - 50k] [Normal - JPEG: 800 x 1004 pix - 330k] A first group of astronomers [1], led by Fabien Malbet from the Laboratoire d'Astrophysique de Grenoble, France, studied the young 10-solar mass stellar object MWC 297, which is still in the very early stage of its life [2]. "This scientific breakthrough opens the doors to an especially detailed scrutiny of the very close environment of young stars and will bring us invaluable knowledge on how planets form", says Malbet. It is amazing to see the amount of details the astronomers could achieve while observing an object located more than 800 light-years away and hidden by a large amount of gas and dust. They found the object to be surrounded by a proto-planetary disc extending to about the size of our Solar System, but truncated in his inner part until about half the distance between the Earth and the Sun. Moreover, the scientists found the object to be surrounded by an outflowing wind, the velocity of which increased by a factor 9, from about 70 km/s near the disc to 600 km/s in the polar regions [3]. "The reason why the inner part of the disc should be truncated is not clear", adds Malbet. "This raises
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.
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, . 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, , can be approximated by , where is the of the Weibull function that fits best to the cumulative noise distribution, and depends on the transducer. We derive general expressions for and , from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when , . 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 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 for contrast discrimination suggests that, if internal noise is stimulus-independent, it has lower kurtosis than a Gaussian. PMID:24124456
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)
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)
The essence of the generalized Newton binomial theorem
NASA Astrophysics Data System (ADS)
Liu, Cheng-shi
2010-10-01
Under the frame of the homotopy analysis method, Liao gives a generalized Newton binomial theorem and thinks it as a rational base of his theory. In the paper, we prove that the generalized Newton binomial theorem is essentially the usual Newton binomial expansion at another point. Our result uncovers the essence of generalized Newton binomial theorem as a key of the homotopy analysis method.
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…
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.
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.
Confidence Hills -- The First Mount Sharp Drilling Site
2014-11-04
This image shows the first holes drilled by NASA Mars rover Curiosity at Mount Sharp. The loose material near the drill holes is drill tailings and an accumulation of dust that slid down the rock during drilling.
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.
Mal`tsev, G.N.
1995-11-01
Methods of the theory of statistical solutions are used to synthesize optimum sharpness functions for adaptation of imaging optical systems. Optimum sharpness functions mean that their extreme values give adequate estimates of the maximum likelihood of virtual phase distortions. It is shown that the synthesized optimum sharpness functions with an analysis in the image plane are rather sensitive to the amount of a priori data and may be used to observe spatially bounded objects on the condition that their shape is known. 10 refs., 1 fig.
Almost sharp fronts for the surface quasi-geostrophic equation
Córdoba, Diego; Fefferman, Charles; Rodrigo, José Luis
2004-01-01
We investigate the evolution of “almost sharp” fronts for the surface quasi-geostrophic equation. This equation was originally introduced in the geophysical context to investigate the formation and evolution of fronts, i.e., discontinuities between masses of hot and cold air. These almost sharp fronts are weak solutions of quasi-geostrophic with large gradient. We relate their evolution to the evolution of sharp fronts. PMID:14978276
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.
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.
[Death caused by sharp injury. Criminologic and criminalistic aspects].
Bajanowski, T; Varro, A; Sepulchre, M A
1991-01-01
From 3497 obductions during the ten years between 1979 and 1988 100 homicides and 18 suicides were caused by sharp trauma. Homicide by sharp trauma is the most frequent method for killing. These 100 homicides were analysed in relation to the age and nationality of victims and perpetrators, place of action, number and localisation of wounds, cause of death. The main results are discussed, particularly those which vary from the results of other authors.
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.
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.
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.
Generalized reciprocity theorem for semiconductor devices
NASA Technical Reports Server (NTRS)
Misiakos, K.; Lindholm, F. A.
1985-01-01
A reciprocity theorem is presented that relates the short-circuit current of a device, induced by a carrier generation source, to the minority-carrier Fermi level in the dark. The basic relation is general under low injection. It holds for three-dimensional devices with position dependent parameters (energy gap, electron affinity, mobility, etc.), and for transient or steady-state conditions. This theorem allows calculation of the internal quantum efficiency of a solar cell by using the analysis of the device in the dark. Other applications could involve measurements of various device parameters, interfacial surface recombination velocity at a polcrystalline silicon emitter contact, for rexample, by using steady-state or transient photon or mass-particle radiation.
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.
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.
Thermodynamics of biochemical networks and duality theorems.
De Martino, Daniele
2013-05-01
One interesting yet difficult computational issue has recently been posed in biophysics in regard to the implementation of thermodynamic constraints to complex networks. Biochemical networks of enzymes inside cells are among the most efficient, robust, differentiated, and flexible free-energy transducers in nature. How is the second law of thermodynamics encoded for these complex networks? In this article it is demonstrated that for chemical reaction networks in the steady state the exclusion (presence) of closed reaction cycles makes possible (impossible) the definition of a chemical potential vector. Interestingly, this statement is encoded in one of the key results in combinatorial optimization, i.e., the Gordan theorem of the alternatives. From a computational viewpoint, the theorem reveals that calculating a reaction's free energy and identifying infeasible loops in flux states are dual problems whose solutions are mutually exclusive, and this opens the way for efficient and scalable methods to perform the energy balance analysis of large-scale biochemical networks.
NASA Astrophysics Data System (ADS)
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-09-01
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.
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. Lastly, we further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
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
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.
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.; ...
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. Lastly, we further demonstrate that the typicalmore » evolution of energy-isolated quantum systems occurs with non-diminishing entropy.« less
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.
Lanford's Theorem and the Emergence of Irreversibility
NASA Astrophysics Data System (ADS)
Uffink, Jos; Valente, Giovanni
2015-04-01
It has been a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A result by Lanford (Dynamical systems, theory and applications, 1975, Asterisque 40:117-137, 1976, Physica 106A:70-76, 1981) shows that, under certain conditions, the famous Boltzmann equation, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. Here, we examine how and in what sense Lanford's theorem succeeds in deriving this remarkable result. Many authors have expressed different views on the question which of the ingredients in Lanford's theorem is responsible for the emergence of irreversibility. We claim that these interpretations miss the target. In fact, we argue that there is no time-asymmetric ingredient at all.
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.
Luttinger theorem and imbalanced Fermi systems
NASA Astrophysics Data System (ADS)
Pieri, Pierbiagio; Strinati, Giancarlo Calvanese
2017-04-01
The proof of the Luttinger theorem, which was originally given for a normal Fermi liquid with equal spin populations formally described by the exact many-body theory at zero temperature, is here extended to an approximate theory given in terms of a "conserving" approximation also with spin imbalanced populations. The need for this extended proof, whose underlying assumptions are here spelled out in detail, stems from the recent interest in superfluid trapped Fermi atoms with attractive inter-particle interaction, for which the difference between two spin populations can be made large enough that superfluidity is destroyed and the system remains normal even at zero temperature. In this context, we will demonstrate the validity of the Luttinger theorem separately for the two spin populations for any "Φ-derivable" approximation, and illustrate it in particular for the self-consistent t-matrix approximation.
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
Fluctuation-Dissipation Theorem for Metastable Systems
NASA Astrophysics Data System (ADS)
Báez, G.; Larralde, H.; Leyvraz, F.; Méndez-Sánchez, R. A.
2003-04-01
We show that an appropriately defined fluctuation-dissipation theorem, connecting generalized susceptibilities and time correlation functions, is valid for times shorter than the nucleation time of the metastable state of Markovian systems satisfying detailed balance. This is done by assuming that such systems can be described by a superposition of the ground and first excited states of the master equation. We corroborate our results numerically for the metastable states of a two-dimensional Ising model.
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.
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
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.
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.
New electromagnetic memories and soft photon theorems
NASA Astrophysics Data System (ADS)
Mao, Pujian; Ouyang, Hao; Wu, Jun-Bao; Wu, Xiaoning
2017-06-01
In this paper, we present a new type of electromagnetic memory. It is a "magnetic" type, or B mode, radiation memory effect. Rather than a residual velocity, we find a position displacement of a charged particle induced by the B mode radiation with memory. We find two types of electromagnetic displacement (ordinary and null). We also show that the null electromagnetic memory formulas are nothing but a Fourier transformation of soft photon theorems.
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.
First Integrals, Liouville Theorem, and Dirac Brackets
NASA Astrophysics Data System (ADS)
Gleria, Iram; Filho, Tarcísio M. Rocha; Figueiredo Neto, Annibal D.; Vianna, José David M.
2017-08-01
In this paper, we discuss the conditions for the existence of first integrals of movement and the Liouville theorem on integrable systems. We revise the core results of the Hamilton-Jacobi theory and discuss the extension of the formalism to encompass constrained systems using Dirac brackets, originally developed in the context of the canonical quantization of constrained systems. As an application, we analyze a Hamiltonian that represents the classical limit of a Fermionic system of oscillators.
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.
Study of hydrodynamic characteristics of a Sharp Eagle wave energy converter
NASA Astrophysics Data System (ADS)
Zhang, Ya-qun; Sheng, Song-wei; You, Ya-ge; Huang, Zhen-xin; Wang, Wen-sheng
2017-06-01
According to Newton's Second Law and the microwave theory, mechanical analysis of multiple buoys which form Sharp Eagle wave energy converter (WEC) is carried out. The movements of every buoy in three modes couple each other when they are affected with incident waves. Based on the above, mechanical models of the WEC are established, which are concerned with fluid forces, damping forces, hinge forces, and so on. Hydrodynamic parameters of one buoy are obtained by taking the other moving buoy as boundary conditions. Then, by taking those hydrodynamic parameters into the mechanical models, the optimum external damping and optimal capture width ratio are calculated out. Under the condition of the optimum external damping, a plenty of data are obtained, such as the displacements amplitude of each buoy in three modes (sway, heave, pitch), damping forces, hinge forces, and speed of the hydraulic cylinder. Research results provide theoretical references and basis for Sharp Eagle WECs in the design and manufacture.
Using Bayes' theorem for free energy calculations
NASA Astrophysics Data System (ADS)
Rogers, David M.
Statistical mechanics is fundamentally based on calculating the probabilities of molecular-scale events. Although Bayes' theorem has generally been recognized as providing key guiding principals for setup and analysis of statistical experiments [83], classical frequentist models still predominate in the world of computational experimentation. As a starting point for widespread application of Bayesian methods in statistical mechanics, we investigate the central quantity of free energies from this perspective. This dissertation thus reviews the basics of Bayes' view of probability theory, and the maximum entropy formulation of statistical mechanics before providing examples of its application to several advanced research areas. We first apply Bayes' theorem to a multinomial counting problem in order to determine inner shell and hard sphere solvation free energy components of Quasi-Chemical Theory [140]. We proceed to consider the general problem of free energy calculations from samples of interaction energy distributions. From there, we turn to spline-based estimation of the potential of mean force [142], and empirical modeling of observed dynamics using integrator matching. The results of this research are expected to advance the state of the art in coarse-graining methods, as they allow a systematic connection from high-resolution (atomic) to low-resolution (coarse) structure and dynamics. In total, our work on these problems constitutes a critical starting point for further application of Bayes' theorem in all areas of statistical mechanics. It is hoped that the understanding so gained will allow for improvements in comparisons between theory and experiment.
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.
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.
The universality of the Carnot theorem
NASA Astrophysics Data System (ADS)
Gonzalez-Ayala, Julian; Angulo-Brown, F.
2013-03-01
It is common in many thermodynamics textbooks to illustrate the Carnot theorem through the use of diverse state equations for gases, paramagnets, and other simple thermodynamic systems. As is well known, the universality of the Carnot efficiency is easily demonstrated in a temperature-entropy diagram, which means that ηC is independent of the working substance. In this paper we remark that the universality of the Carnot theorem goes beyond conventional state equations, and is fulfilled by gas state equations that do not correspond to an ideal gas in the dilution limit, namely V → ∞. Some of these unconventional state equations have certain thermodynamic ‘anomalies’ that nonetheless do not forbid them from obeying the Carnot theorem. We discuss how this very general behaviour arises from Maxwell relations, which are connected with a geometrical property expressed through preserving area transformations. A rule is proposed to calculate the Maxwell relations associated with a thermodynamic system by using the preserving area relationships. In this way it is possible to calculate the number of possible preserving area mappings by giving the number of possible Jacobian identities between all pairs of thermodynamic variables included in the corresponding Gibbs equation. This paper is intended for undergraduates and specialists in thermodynamics and related areas.
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).
Effects of Registration Regularization and Atlas Sharpness on Segmentation Accuracy
Sabuncu, Mert R.; Desikan, Rahul; Fischl, Bruce; Golland, Polina
2008-01-01
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. PMID:18667352
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
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.
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.
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.
A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian
NASA Astrophysics Data System (ADS)
Rösler, Margit; Voit, Michael
2015-02-01
We consider compact Grassmann manifolds G/K over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type BC. From an explicit integral representation of these polynomials we deduce a sharp Mehler-Heine formula, that is an approximation of the Heckman-Opdam polynomials in terms of Bessel functions, with a precise estimate on the error term. This result is used to derive a central limit theorem for random walks on the semi-lattice parametrizing the dual of G/K, which are constructed by successive decompositions of tensor powers of spherical representations of G. The limit is the distribution of a Laguerre ensemble in random matrix theory. Most results of this paper are established for a larger continuous set of multiplicity parameters beyond the group cases.
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.
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
Sample skewness as a statistical measurement of neuronal tuning sharpness.
Samonds, Jason M; Potetz, Brian R; Lee, Tai Sing
2014-05-01
We propose using the statistical measurement of the sample skewness of the distribution of mean firing rates of a tuning curve to quantify sharpness of tuning. For some features, like binocular disparity, tuning curves are best described by relatively complex and sometimes diverse functions, making it difficult to quantify sharpness with a single function and parameter. Skewness provides a robust nonparametric measure of tuning curve sharpness that is invariant with respect to the mean and variance of the tuning curve and is straightforward to apply to a wide range of tuning, including simple orientation tuning curves and complex object tuning curves that often cannot even be described parametrically. Because skewness does not depend on a specific model or function of tuning, it is especially appealing to cases of sharpening where recurrent interactions among neurons produce sharper tuning curves that deviate in a complex manner from the feedforward function of tuning. Since tuning curves for all neurons are not typically well described by a single parametric function, this model independence additionally allows skewness to be applied to all recorded neurons, maximizing the statistical power of a set of data. We also compare skewness with other nonparametric measures of tuning curve sharpness and selectivity. Compared to these other nonparametric measures tested, skewness is best used for capturing the sharpness of multimodal tuning curves defined by narrow peaks (maximum) and broad valleys (minima). Finally, we provide a more formal definition of sharpness using a shape-based information gain measure and derive and show that skewness is correlated with this definition.
Sample Skewness as a Statistical Measurement of Neuronal Tuning Sharpness
Samonds, Jason M.; Potetz, Brian R.; Lee, Tai Sing
2014-01-01
We propose using the statistical measurement of the sample skewness of the distribution of mean firing rates of a tuning curve to quantify sharpness of tuning. For some features, like binocular disparity, tuning curves are best described by relatively complex and sometimes diverse functions, making it difficult to quantify sharpness with a single function and parameter. Skewness provides a robust nonparametric measure of tuning curve sharpness that is invariant with respect to the mean and variance of the tuning curve and is straightforward to apply to a wide range of tuning, including simple orientation tuning curves and complex object tuning curves that often cannot even be described parametrically. Because skewness does not depend on a specific model or function of tuning, it is especially appealing to cases of sharpening where recurrent interactions among neurons produce sharper tuning curves that deviate in a complex manner from the feedforward function of tuning. Since tuning curves for all neurons are not typically well described by a single parametric function, this model independence additionally allows skewness to be applied to all recorded neurons, maximizing the statistical power of a set of data. We also compare skewness with other nonparametric measures of tuning curve sharpness and selectivity. Compared to these other nonparametric measures tested, skewness is best used for capturing the sharpness of multimodal tuning curves defined by narrow peaks (maximum) and broad valleys (minima). Finally, we provide a more formal definition of sharpness using a shape-based information gain measure and derive and show that skewness is correlated with this definition. PMID:24555451
Heterogeneous sharpness for cross-spectral face recognition
NASA Astrophysics Data System (ADS)
Cao, Zhicheng; Schmid, Natalia A.
2017-05-01
Matching images acquired in different electromagnetic bands remains a challenging problem. An example of this type of comparison is matching active or passive infrared (IR) against a gallery of visible face images, known as cross-spectral face recognition. Among many unsolved issues is the one of quality disparity of the heterogeneous images. Images acquired in different spectral bands are of unequal image quality due to distinct imaging mechanism, standoff distances, or imaging environment, etc. To reduce the effect of quality disparity on the recognition performance, one can manipulate images to either improve the quality of poor-quality images or to degrade the high-quality images to the level of the quality of their heterogeneous counterparts. To estimate the level of discrepancy in quality of two heterogeneous images a quality metric such as image sharpness is needed. It provides a guidance in how much quality improvement or degradation is appropriate. In this work we consider sharpness as a relative measure of heterogeneous image quality. We propose a generalized definition of sharpness by first achieving image quality parity and then finding and building a relationship between the image quality of two heterogeneous images. Therefore, the new sharpness metric is named heterogeneous sharpness. Image quality parity is achieved by experimentally finding the optimal cross-spectral face recognition performance where quality of the heterogeneous images is varied using a Gaussian smoothing function with different standard deviation. This relationship is established using two models; one of them involves a regression model and the other involves a neural network. To train, test and validate the model, we use composite operators developed in our lab to extract features from heterogeneous face images and use the sharpness metric to evaluate the face image quality within each band. Images from three different spectral bands visible light, near infrared, and short
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
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
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.
Phase-field lattice Boltzmann modeling of boiling using a sharp-interface energy solver
NASA Astrophysics Data System (ADS)
Mohammadi-Shad, Mahmood; Lee, Taehun
2017-07-01
The main objective of this paper is to extend an isothermal incompressible two-phase lattice Boltzmann equation method to model liquid-vapor phase change problems using a sharp-interface energy solver. Two discrete particle distribution functions, one for the continuity equation and the other for the pressure evolution and momentum equations, are considered in the current model. The sharp-interface macroscopic internal energy equation is discretized with an isotropic finite difference method to find temperature distribution in the system. The mass flow generated at liquid-vapor phase interface is embedded in the pressure evolution equation. The sharp-interface treatment of internal energy equation helps to find the interfacial mass flow rate accurately where no free parameter is needed in the calculations. The proposed model is verified against available theoretical solutions of the two-phase Stefan problem and the two-phase sucking interface problem, with which our simulation results are in good agreement. The liquid droplet evaporation in a superheated vapor, the vapor bubble growth in a superheated liquid, and the vapor bubble rising in a superheated liquid are analyzed and underlying physical characteristics are discussed in detail. The model is successfully tested for the liquid-vapor phase change with large density ratio up to 1000.
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)…
On a Limit Theorem and Invariance Principle for Symmetric Statistics.
1986-07-01
A177 292 ON A LIMIT THEOREM AND INVARIANCE PRINCIPLE FOR / SYMMETRIC STATISTICS .(U) NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROC...TI TLE (Include SeCUPntY Claaftceaon, .12F20 "On a limit theorem and invariance princinle ior symmetricls- j 12. PERSONAL AUTHI4O( M.andrekar, V. 13...University of North Carolina Chapel Hill, North Carolina ON A LIMIT THEOREM AND INVARIANCE PRINCIPLE FOR SYMMIETRIC STATISTICS Approved for public release
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.
Extending Bell's Theorem: Ruling out Paramater Independent Hidden Variable Theories
NASA Astrophysics Data System (ADS)
Leegwater, G. J.
2016-03-01
Bell's Theorem may well be the best known result in the foundations of quantum mechanics. Here, it is presented as stating that for any hidden variable theory the combination of the conditions Parameter Independence, Outcome Independence, Source Independence and Compatibility with Quantum Theory leads to a contradiction. Based on work by Roger Colbeck and Renato Renner, an extension of Bell's Theorem is considered. In this extension the theorem is strengthened by replacing Outcome Independence by a strictly weaker condition.
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)…
Geometric fluctuation theorem for a spin-boson system
NASA Astrophysics Data System (ADS)
Watanabe, Kota L.; Hayakawa, Hisao
2017-08-01
We derive an extended fluctuation theorem for geometric pumping of a spin-boson system under periodic control of environmental temperatures by using a Markovian quantum master equation. We obtain the current distribution, the average current, and the fluctuation in terms of the Monte Carlo simulation. To explain the results of our simulation we derive an extended fluctuation theorem. This fluctuation theorem leads to the fluctuation dissipation relations but the absence of the conventional reciprocal relation.
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.
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
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.
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.
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.
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.
Central limit theorems under special relativity
McKeague, Ian W.
2015-01-01
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. PMID:25798020
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.
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.
Reciprocity theorem for smith-purcell configurations
NASA Astrophysics Data System (ADS)
Scarlat, Florea; Facina, M.
2001-06-01
The reciprocity theorem is referred to the equivalence of the obtained relations for the Smith-Purcell radiation, in both cases when the electron beam is propagating forward and backward with respect to the metal grating, respectively. The results of the radiation factor for the Smith-Purcell radiation in the ((theta) , (phi) ) direction generated by relativistic electron beams with energy up to 100 MeV and rectangular perfectly conducting gratings are presented. The results obtained prove the equivalence of the Smith-Purcell radiation field in both cases of propagation for the electron beam.
Nekhoroshev theorem for the periodic Toda lattice.
Henrici, Andreas; Kappeler, Thomas
2009-09-01
The periodic Toda lattice with N sites is globally symplectomorphic to a two parameter family of N-1 coupled harmonic oscillators. The action variables fill out the whole positive quadrant of R(N-1). We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space (2000 Mathematics Subject Classification: 37J35, 37J40, 70H06).
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.
NASA Astrophysics Data System (ADS)
Lampart, Jonas; Lewin, Mathieu
2015-12-01
We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with {0 ≤slant n ≤slant N} particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.
The Poincaré-Hopf Theorem for line fields revisited
NASA Astrophysics Data System (ADS)
Crowley, Diarmuid; Grant, Mark
2017-07-01
A Poincaré-Hopf Theorem for line fields with point singularities on orientable surfaces can be found in Hopf's 1956 Lecture Notes on Differential Geometry. In 1955 Markus presented such a theorem in all dimensions, but Markus' statement only holds in even dimensions 2 k ≥ 4. In 1984 Jänich presented a Poincaré-Hopf theorem for line fields with more complicated singularities and focussed on the complexities arising in the generalized setting. In this expository note we review the Poincaré-Hopf Theorem for line fields with point singularities, presenting a careful proof which is valid in all dimensions.
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.
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.
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.
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.
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
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,…
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
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.
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
Mount Sharp Buttes and Layers From Near Darwin
2014-12-11
This view from the Mastcam on NASA Curiosity Mars rover shows dramatic buttes and layers on the lower flank of Mount Sharp. It was taken on Sept. 7, 2013, from near the waypoint called Darwin on the route toward an entry point to the mountain.
Sharp Crater Rim with Dark Material and Boulders
2012-03-02
This image from NASA Dawn spacecraft shows part of the sharp, fresh rim of a large crater on asteroid Vesta. There is some bright material slumping towards the center of this crater but this is mostly overshadowed by the dark material.
Ripples Beside Pahrump Hills Outcrop at Base of Mount Sharp
2014-11-18
This northeast-facing view from the lower edge of the pale Pahrump Hills outcrop at the base of Mount Sharp includes wind-sculpted ripples of sand and dust in the middle ground. It was taken by Curiosity Navcam on Nov. 13, 2014.
[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.
Mount Sharp Panorama in White-Balanced Colors
2013-03-15
This mosaic of images from the Mast Camera Mastcam on NASA Mars rover Curiosity shows Mount Sharp in a white-balanced color adjustment that makes the sky look overly blue but shows the terrain as if under Earth-like lighting.
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.
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.
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.
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…
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.
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…
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…
Systematic Approaches to Experimentation: The Case of Pick's Theorem
ERIC Educational Resources Information Center
Papadopoulos, Ioannis; Iatridou, Maria
2010-01-01
In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…
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)
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.
Three Lectures on Theorem-proving and Program Verification
NASA Technical Reports Server (NTRS)
Moore, J. S.
1983-01-01
Topics concerning theorem proving and program verification are discussed with particlar emphasis on the Boyer/Moore theorem prover, and approaches to program verification such as the functional and interpreter methods and the inductive assertion approach. A history of the discipline and specific program examples are included.
Discovering Theorems in Abstract Algebra Using the Software "GAP"
ERIC Educational Resources Information Center
Blyth, Russell D.; Rainbolt, Julianne G.
2010-01-01
A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…
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…
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…
A new generalized Wick theorem in conformal field theory
NASA Astrophysics Data System (ADS)
Takagi, T.
2017-08-01
We describe a new generalized Wick theorem for interacting fields in two-dimensional conformal field theory and briefly discuss its relation to the Borcherds identity and its derivation by an analytic method. We give examples of calculating operator product expansions using the generalized Wick theorem including fermionic fields.
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)
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 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…
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
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
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.
Theorem Proving in Intel Hardware Design
NASA Technical Reports Server (NTRS)
O'Leary, John
2009-01-01
For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.
The Birkhoff theorem and string clouds
NASA Astrophysics Data System (ADS)
Bronnikov, K. A.; Kim, S.-W.; Skvortsova, M. V.
2016-10-01
We consider spherically symmetric space-times in GR under the unconventional assumptions that the spherical radius r is either a constant or has a null gradient in the (t, x) subspace orthogonal to the symmetry spheres (i.e., {(\\partial r)}2 = 0). It is shown that solutions to the Einstein equations with r={const} contain an extra (fourth) spatial or temporal Killing vector and thus satisfy the Birkhoff theorem under an additional physically motivated condition that the tangential pressure is functionally related to the energy density. This leads to solutions that directly generalize the Bertotti-Robinson, Nariai and Plebanski-Hacyan solutions. Under similar conditions, solutions with {(\\partial r)}2 = 0 but r\
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.
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
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.
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.
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.
On the decoupling theorem for vacuum metastability
NASA Astrophysics Data System (ADS)
Patel, Hiren H.; Radovčić, Branimir
2017-10-01
In this paper, we numerically study the impact heavy field degrees of freedom have on vacuum metastability in a toy model, with the aim of better understanding how the decoupling theorem extends to semiclassical processes. We observe that decoupling applies to partial amplitudes associated with fixed final state field configurations emerging from the tunneling processes, characterized by a scale such as the inverse radius of a spherically symmetric bubble, and not directly on the total lifetime (as determined by the ;bounce;). More specifically, tunneling amplitudes for bubbles with inverse radii smaller than the scale of the heavier fields are largely insensitive to their presence, while those for bubbles with inverse radii larger than that scale may be significantly modified.
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.
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.
A Fubini Theorem for Iterated Stochastic Integrals.
1978-02-01
part icular , for 0 < t1 < t 2 , ( 2 . 2 ) f(t 1 .t2) E f(t1 ,t 2) + J ~ (t 1 ,t ,t2)d~~(T) where ~Gt 1 , i ,t ) is 3(t 1 ,T)—measurable , a.e. I...formally exists and is given by f0(t1,t2 )dt 1 — f(t 1 ,t2 )dB (t1) So that f~ is simply the negative of the diffusion part of it. We now make the following...and the functions {~ p :n = 1,2,...) are as in Theorem 2.A. And g is defined analogously.a,n b In part icular , t t II (t 1,t2) 2 = F
Robbing the Bank with a Theorem Prover
NASA Astrophysics Data System (ADS)
Youn, Paul; Adida, Ben; Bond, Mike; Clulow, Jolyon; Herzog, Jonathan; Lin, Amerson; Rivest, Ronald L.; Anderson, Ross
In this work, we present the first automated analysis of security application programming interfaces (security APIs). In particular, we analyze the API of the IBM 4758 CCA, a hardware security module for banking networks. Adapting techniques from formal analyses of security protocols, we model the API purely according its specification and assuming ideal encryption primitives. We then use the automated theorem-prover Otter to analyze this model, combining its standard reasoning strategies with novel techniques of our own (also presented here). In this way, we derive not only all published API-level attacks against the 4758 CCA, but an extension to these attacks as well. Thus, this work represents the first step toward fully-automated, rigorous analyses of security APIs.
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.
On the Lehmann-Filhés theorem as a consequence of one theorem of Ostrogradsky.
NASA Astrophysics Data System (ADS)
Shirmin, G. I.
It is shown that the so-called Lehmann-Filh´es theorem playing the role of a groundwork in the "method of incomplete integral" of dynamical problems solving is a simple consequence of one theorem of Russian academician M. V. Ostrogradsky. The appropriate proof of that is contained in his famous paper "The Memoir on Differential Equations of the isoperimetric Problem" having been reported to the Russian Academy of Sciences on the 29-th of November 1848. So it is prooved that on the basis of the above mentioned method the priority belongs to M. V. Ostrogradsky who published his results more than half a century earlier than the same was made by Lehmann-Filhés (1904).
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.
Sharp magnetic structures from dynamos with density stratification
NASA Astrophysics Data System (ADS)
Jabbari, Sarah; Brandenburg, Axel; Kleeorin, Nathan; Rogachevskii, Igor
2017-05-01
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 non-linear 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 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.
A shallow convolutional neural network for blind image sharpness assessment.
Yu, Shaode; Wu, Shibin; Wang, Lei; Jiang, Fan; Xie, Yaoqin; Li, Leida
2017-01-01
Blind image quality assessment can be modeled as feature extraction followed by score prediction. It necessitates considerable expertise and efforts to handcraft features for optimal representation of perceptual image quality. This paper addresses blind image sharpness assessment by using a shallow convolutional neural network (CNN). The network takes single feature layer to unearth intrinsic features for image sharpness representation and utilizes multilayer perceptron (MLP) to rate image quality. Different from traditional methods, CNN integrates feature extraction and score prediction into an optimization procedure and retrieves features automatically from raw images. Moreover, its prediction performance can be enhanced by replacing MLP with general regression neural network (GRNN) and support vector regression (SVR). Experiments on Gaussian blur images from LIVE-II, CSIQ, TID2008 and TID2013 demonstrate that CNN features with SVR achieves the best overall performance, indicating high correlation with human subjective judgment.
Sharpness for C1 linearization of planar hyperbolic diffeomorphisms
NASA Astrophysics Data System (ADS)
Zhang, Wenmeng; Zhang, Weinian
2014-12-01
C1 linearization preserves smooth dynamical behaviors and distinguishes qualitative properties in characteristic directions. Planar hyperbolic diffeomorphisms are the most elementary ones of representatively technical difficulties in the study of C1 linearization. In the Poincaré domain (both eigenvalues inside the unit circle S1) a lower bound α0 was given such that C smoothness with α0<α≤1 admits C1 linearization. Our first purpose of this paper is to prove the sharpness of α0 and give a weaker linearization for α≤α0. In the Siegel domain (one eigenvalue inside S1 but the other outside S1) it is known that C smoothness admits C1 linearization for all α∈(0,1]. The second purpose is to prove that the C1 linearization is actually a C linearization and give sharp estimates for β.
An extension of Newton's apsidal precession theorem
NASA Astrophysics Data System (ADS)
Valluri, S. R.; Yu, P.; Smith, G. E.; Wiegert, P. A.
2005-04-01
Newton's apsidal precession theorem in Proposition 45 of Book I of the `Principia' has great mathematical, physical, astronomical and historical interest. The lunar theory and the precession of the perihelion of the planet Mercury are but two examples of the applications of this theorem. We have examined the precession of orbits under varying force laws as measured by the apsidal angle θ(N, e), where N is the index for the centripetal force law, for varying eccentricity e. The paper derives a general function for the apsidal angle, dependent only on e and N as the potential is spherically symmetric. Further, we explore approximate ways of the solution of this equation, in the neighbourhood of N= 2 which happens to be the case of greatest historical interest. Exact solutions are derived where they are possible. The first derivatives ∂θ/∂N and ∂θ/∂h[where h(N, e) is the angular momentum] are analytically expressed in the neighbourhood of N= 2 (case of the inverse square law). The value of ∂θ/∂N is computed numerically as well for 1 <=N < 3. The resulting integrals are interesting improper integrals with singularities at both limits. Some of the integrals, especially for N= 2, can be given in closed form in terms of generalized hypergeometric functions which are reducible in terms of algebraic and logarithmic functions. No evidence was found for isolated cases of zero precession as e was increased. The N= 1 case of the logarithmic potential is also briefly discussed in view of its interest for the dynamics of eccentric orbits and its relevance to realistic galaxy models. The possibility of apsidal precession was also examined for a few cases of high-eccentricity asteroids and extrasolar planets. We find that these systems may provide interesting new laboratories for studies of gravity.
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.
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.
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
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
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.
Convolution theorems: partitioning the space of integral transforms
NASA Astrophysics Data System (ADS)
Lindsey, Alan R.; Suter, Bruce W.
1999-03-01
Investigating a number of different integral transforms uncovers distinct patterns in the type of translation convolution theorems afforded by each. It is shown that transforms based on separable kernels (aka Fourier, Laplace and their relatives) have a form of the convolution theorem providing for a transform domain product of the convolved functions. However, transforms based on kernels not separable in the function and transform variables mandate a convolution theorem of a different type; namely in the transform domain the convolution becomes another convolution--one function with the transform of the other.
Quantum voting and violation of Arrow's impossibility theorem
NASA Astrophysics Data System (ADS)
Bao, Ning; Yunger Halpern, Nicole
2017-06-01
We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.
Area theorem and energy quantization for dissipative optical solitons
Renninger, William H.; Chong, Andy; Wise, Frank W.
2011-01-01
Soliton area theorems express the pulse energy as a function of the pulse shape and the system parameters. From an analytical solution to the cubic-quintic Ginzbug-Landau equation, we derive an area theorem for dissipative optical solitons. In contrast to area theorems for conservative optical solitons, the energy does not scale inversely with the pulse duration, and in addition there is an upper limit to the energy. Energy quantization explains the existence of, and conditions for, multiple-pulse solutions. The theoretical predictions are confirmed with numerical simulations and experiments in the context of dissipative soliton fiber lasers. PMID:21765589
Criterium for the index theorem on the lattice
NASA Astrophysics Data System (ADS)
Bicudo, Pedro
2003-04-01
We study how far the Index Theorem can be extrapolated from the continuum to finite lattices with finite topological charge densities. To examine how the Wilson action approximates the Index theorem, we specialize in the lattice version of the Schwinger model. We propose a new criterion for solutions of the Ginsparg-Wilson Relation constructed with the Wilson action. We conclude that the Neuberger action is the simplest one that maximally complies with the Index Theorem, and that its best parameter in d = 2 is m0 = 1.1 ± 0.1.
Criterium for the Index Theorem on the Lattice
NASA Astrophysics Data System (ADS)
Bicudo, Pedro
2003-08-01
We study how far the Index Theorem can be extrapolated from the continuum to finite lattices with finite topological charge densities. To examine how the Wilson action approximates the Index theorem, we specialize in the lattice version of the Schwinger model. We propose a new criterion for solutions of the Ginsparg-Wilson Relation constructed with the Wilson action. We conclude that the Neuberger action is the simplest one that maximally complies with the Index Theorem, and that its best parameter in d = 2 is m0 = 1.1 ± 0.1.
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 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.
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
Kohn's theorem, Larmor's equivalence principle and the Newton-Hooke group
Gibbons, G.W.; Pope, C.N.
2011-07-15
Highlights: > We show that non-relativistic electrons moving in a magnetic field with trapping potential admits as relativity group the Newton-Hooke group. > We use this fact to give a group theoretic interpretation of Kohn's theorem and to obtain the spectrum. > We obtain the lightlike lift of the system exhibiting showing it coincides with the Nappi-Witten spacetime. - Abstract: We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a 'relativity group' which is a one-parameter family of deformations of the standard Galilei group to the Newton-Hooke group which is a Wigner-Inoenue contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn's theorem and related results. Larmor's theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the 'Eisenhart' or 'lightlike' lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdicka-Eardley-Nappi-Witten pp-wave solution of Einstein-Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi-Jackiw group.
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.
Curiosity Rover on Mount Sharp, Seen from Mars Orbit
2017-06-20
The feature that appears bright blue at the center of this scene is NASA's Curiosity Mars rover on the northwestern flank of Mount Sharp, viewed by NASA's Mars Reconnaissance Orbiter. Curiosity is approximately 10 feet long and 9 feet wide (3.0 meters by 2.8 meters). The view is a cutout from observation ESP_050897_1750 taken by the High Resolution Imaging Science Experiment (HiRISE) camera on the orbiter on June 5, 2017. HiRISE has been imaging Curiosity about every three months, to monitor the surrounding features for changes such as dune migration or erosion. When the image was taken, Curiosity was partway between its investigation of active sand dunes lower on Mount Sharp, and "Vera Rubin Ridge," a destination uphill where the rover team intends to examine outcrops where hematite has been identified from Mars orbit. The rover's surroundings include tan rocks and patches of dark sand. As in previous HiRISE color images of Curiosity since the rover was at its landing site, the rover appears bluer than it really is. HiRISE color observations are recorded in a red band, a blue-green band and an infrared band, and displayed in red, green and blue. This helps make differences in Mars surface materials apparent, but does not show natural color as seen by the human eye. Lower Mount Sharp was chosen as a destination for the Curiosity mission because the layers of the mountain offer exposures of rocks that record environmental conditions from different times in the early history of the Red Planet. Curiosity has found evidence for ancient wet environments that offered conditions favorable for microbial life, if Mars has ever hosted life. https://photojournal.jpl.nasa.gov/catalog/PIA21710
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.
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; Wang, Lumin
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.
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.
Color Variations on Mount Sharp, Mars White Balanced
2016-12-13
The foreground of this scene from the Mast Camera (Mastcam) on NASA's Curiosity Mars rover shows purple-hued rocks near the rover's late-2016 location on lower Mount Sharp. The scene's middle distance includes higher layers that are future destinations for the mission. Variations in color of the rocks hint at the diversity of their composition on lower Mount Sharp. The purple tone of the foreground rocks has been seen in other rocks where Curiosity's Chemical and Mineralogy (CheMin) instrument has detected hematite. Winds and windblown sand in this part of Curiosity's traverse and in this season tend to keep rocks relatively free of dust, which otherwise can cloak rocks' color. The three frames combined into this mosaic were acquired by the Mastcam's right-eye camera on Nov. 10, 2016, during the 1,516th Martian day, or sol, of Curiosity's work on Mars. The scene is presented with a color adjustment that approximates white balancing, to resemble how the rocks and sand would appear under daytime lighting conditions on Earth. Sunlight on Mars is tinged by the dusty atmosphere and this adjustment helps geologists recognize color patterns they are familiar with on Earth. The view spans about 15 compass degrees, with the left edge toward southeast. The rover's planned direction of travel from its location when this scene was recorded is generally southeastward. The orange-looking rocks just above the purplish foreground ones are in the upper portion of the Murray formation, which is the basal section of Mount Sharp, extending up to a ridge-forming layer called the Hematite Unit. Beyond that is the Clay Unit, which is relatively flat and hard to see from this viewpoint. The next rounded hills are the Sulfate Unit, Curiosity's highest planned destination. The most distant slopes in the scene are higher levels of Mount Sharp, beyond where Curiosity will drive. Figure 1 is a version of the same scene with annotations added as reference points for distance, size and relative
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.
Luttinger's theorem, superfluid vortices and holography
NASA Astrophysics Data System (ADS)
Iqbal, Nabil; Liu, Hong
2012-10-01
Strongly coupled field theories with gravity duals can be placed at finite density in two ways: electric field flux emanating from behind a horizon, or bulk charged fields outside of the horizon that explicitly source the density. We discuss field-theoretical observables that are sensitive to this distinction. If the charged fields are fermionic, we discuss a modified Luttinger's theorem that holds for holographic systems, in which the sum of boundary theory Fermi surfaces counts only the charge outside of the horizon. If the charged fields are bosonic, we show that the resulting superfluid phase may be characterized by the coefficient of the transverse Magnus force on a moving superfluid vortex, which again is sensitive only to the charge outside of the horizon. For holographic systems, these observables provide a field-theoretical way to distinguish how much charge is held by a dual horizon, but they may be useful in more general contexts as measures of deconfined (i.e. ‘fractionalized’) charge degrees of freedom.
c-Theorem for disordered systems
NASA Astrophysics Data System (ADS)
Gurarie, V.
1999-05-01
We find an analog of Zamolodchikov's c-theorem for disordered two-dimensional non-interacting systems in their supersymmetric field theory representation. We show that the energy momentum tensor of such field theories must be a part of a supermultiplet, and that a new parameter b can be introduced with the help of that multiplet. b flows along the renormalization group trajectories much like the central charge for unitary two-dimensional field theories. While it has not been established if this flow is irreversible, that is, if b always flows down to lower values, it does so for all the cases worked out so far. b gives a new way to label different conformal field theories for disordered systems whose central charge is always 0. b turns out to be related to the central extension of a certain algebra, a generalization of the Virasoro algebra, which we show may be present at the critical points of these theories. b is also related to the finite size corrections of the physical free energy of disordered systems. We discuss possible applications by computing b for two-dimensional Dirac fermions with random gauge potential, in other words, for U(1∣1) Kac-Moody algebra.
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).
Negative probabilities, Fine's theorem, and linear positivity
NASA Astrophysics Data System (ADS)
Halliwell, J. J.; Yearsley, J. M.
2013-02-01
Many situations in quantum theory and other areas of physics lead to quasiprobabilities which seem to be physically useful but can be negative. The interpretation of such objects is not at all clear. In this paper, we show that quasiprobabilities naturally fall into two qualitatively different types, according to whether their non-negative marginals can or cannot be matched to a non-negative probability. The former type of quasiprobabilities, which we call viable, are qualitatively similar to true probabilities, but the latter type, which we call nonviable, may not have a sensible interpretation. Determining the existence of a probability matching given marginals is a nontrivial question in general. In simple examples, Fine's theorem indicates that inequalities of the Bell and Clauser-Horne-Shimony-Holt (CHSH) types provide criteria for its existence, and these examples are considered in detail. Our results have consequences for the linear positivity condition of Goldstein and Page in the context of the histories approach to quantum theory. Although it is a very weak condition for the assignment of probabilities, it fails in some important cases where our results indicate that probabilities clearly exist. We speculate that our method, of matching probabilities to a given set of marginals, provides a general method of assigning probabilities to histories and we show that it passes the Diósi test for the statistical independence of subsystems.
Fatal Injuries of Law Enforcement/Correctional Officers Attacked with Sharp-Edged Weapons().
Chenpanas, Patsy; Bir, Cynthia
2017-05-01
According to the National Law Enforcement Memorial Fund, there were 117 law enforcement fatalities in the United States in 2015. Assaults with sharp-edged weapons have resulted in a total of over 400 fatalities in the United States. The goal of the current research was to examine sharp-edged weapon assaults against law enforcement and correctional agents that resulted in a fatal outcome. A total of twelve autopsy reports were reviewed from across the United States. Four cases involved law enforcement officers, seven involved correctional officers, and one was an off-duty border officer. The male-to-female ratio was 11:1. A total of 70.2% of the wounds analyzed were stab wounds (n = 85), and 29.8% of the wounds were slash wounds (n = 36). Based on this review, the neck, shoulder, and chest regions were the most vulnerable to single fatal stab/slash wounds. Multiple stab/slash wounds often resulted in exsanguination. The use of body armor was only noted in one case. © 2016 American Academy of Forensic Sciences.
NASA Astrophysics Data System (ADS)
Pal, Prem; Sato, Kazuo; Gosalvez, Miguel A.; Shikida, Mitsuhiro
2007-11-01
In this paper, we have studied the undercutting at rounded concave and sharp convex corners in (1 0 0)-silicon wafers using a complementary metal-oxide semiconductor (CMOS) compatible tetramethyl ammonium hydroxide (TMAH) solution with and without surfactant. In order to minimize the undercutting at both corner types while keeping reasonable etch rates, smooth etched-surfaces and CMOS compatibility, the non-ionic surfactant NC-200 that contains 100% polyoxyethylene-alkyl-phenyl-ether is considered. The effect of concentration and etching temperature is studied using 10, 20 and 25 wt% TMAH solutions at 60, 70 and 80 °C. When NC-200 at 0.1% of the total volume of the etchant is used, the undercutting ratio at both rounded concave and sharp convex corners is beneficially reduced as the etchant concentration is increased while, simultaneously, the etch rate increases. This is the opposite trend to the etch characteristics of pure TMAH. In addition, the rough etched surface morphology at low concentration is also improved by using NC-200.
Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem
Gallavotti, G.
1996-09-01
It is shown that the chaoticity hypothesis recently introduced in statistical mechanics, which is analogous to Ruelle`s principle for turbulence, implies the Onsager reciprocity and the fluctuation-dissipation theorem in various reversible models for coexisting transport phenomena.
Floquet theorem with open systems and its applications
NASA Astrophysics Data System (ADS)
Dai, C. M.; Shi, Z. C.; Yi, X. X.
2016-03-01
For a closed quantum system described by a time-periodic Hamiltonian, Floquet theorem says that the time evolution operator can be written as U (t ,0 ) ≡P (t ) e-i/ℏ HFt with P (t +T )=P (t ) , and HF is Hermitian and time independent and called the Floquet Hamiltonian. In this work, we extend the Floquet theorem from closed to open systems described by a time-periodic Lindblad master equation with period T =2/π ω . We derive an expansion for the Lindbladian in powers of 1/ω . Two examples are presented to illustrate the theorem. We find that the results given by the Lindbladian expansion based on the open system Floquet theorem agree well with the exact dynamics in the high-frequency limit. It may find applications in quantum engineering with systems subject to decoherence.
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.
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.
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.
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)).
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.
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.
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.
Extending the Transport Theorem to Rough Domains of Integration.
Seguin, Brian; Hinz, Denis F; Fried, Eliot
2014-09-01
Transport theorems, such as that named after Reynolds, are an important tool in the field of continuum physics. Recently, Seguin and Fried used Harrison's theory of differential chains to establish a transport theorem valid for evolving domains that may become irregular. Evolving irregular domains occur in many different physical settings, such as phase transitions or fracture. Here, emphasizing concepts over technicalities, we present Harrison's theory of differential chains and the results of Seguin and Fried in a way meant to be accessible to researchers in continuum physics. We also show how the transport theorem applies to three concrete examples and approximate the resulting terms numerically. Furthermore, we discuss how the transport theorem might be used to weaken certain basic assumptions underlying the description of continua and the challenges associated with doing so.
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
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.
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.
Some functional limit theorems for compound Cox processes
Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.
2016-06-08
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
A study on arithmetical functions and the prime number theorem
NASA Astrophysics Data System (ADS)
Imm, Yeoh Saw
2014-06-01
In this paper, Leibniz triangle and suitable binomial coefficients were used to get the bounds of ψ (x) . Using the generalized convolution and the differentiation on generalized convolution of arithmetical functions, we get to prove Tatuzawa-Izeki identity. Selberg's asymptotic formula is included as a special case, which is the beginning of certain elementary proofs of the Prime Number Theorem. Integration is used on some related inequalities to provide a smoother elementary proof of the Prime Number Theorem.
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.
The virial theorem for systems subjected to sectionally defined potentials
NASA Astrophysics Data System (ADS)
Fernández, Francisco M.; Castro, Eduardo A.
1981-09-01
The correct formulation of the virial theorem for systems subjected to sectionally defined potentials is derived. It is shown that a trial wave function with an optimized scaling factor according to variational principles satisfies the virial theorem. Formal results are tested for a model reported by Ley-Koo and Rubinstein [J. Chem. Phys. 71, 351 (1979)] and results are analyzed in a comparative fashion.
On the Crooks fluctuation theorem and the Jarzynski equality
Chen, L. Y.
2008-01-01
The Jarzynski equality (JE) and the undergirding Crooks fluctuation theorem (CFT) have generated intense interest recently among researchers in physical and biological sciences. It has been held that the CFT has wider applicability than the JE. This note shows that the two are equally applicable and that their applicability is possibly limited to near-equilibrium processes, where the linear fluctuation-dissipation theorem holds. PMID:19044857
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.
Some functional limit theorems for compound Cox processes
NASA Astrophysics Data System (ADS)
Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.
2016-06-01
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
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.
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.
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.
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.
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.
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
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.
Formularies in integrated health systems: Sharp HealthCare.
Rizos, A L; Levy, E; Furnier, J; Crowley, K
1996-09-01
Formulary management implications are described for a California health system comprising 7 hospitals, 4 skilled-nursing centers, 22 medical clinics, 8 urgent care facilities, and a health maintenance organization. Sharp HealthCare serves nearly one million people in the San Diego area. A single institutional care division (ICD) pharmacy service has been created under the guidance of a steering committee comprising a pharmacy operations coordinator and a staff pharmacist from each site, the system pharmacy director, the system senior pharmacy information systems specialist, and the system senior clinical pharmacy specialist. Operations at each site are overseen by an operations coordinator instead of a pharmacy director. Functional teams reporting to the steering committee are standardized pharmacy processes, including formulary management; this is particularly important because the ICD has pharmacists and nurse per diem pools. Until 1995, formularies were independently managed at each site. Now, one system formulary is being developed. Standard policies and procedures, a nonformulary drug request form, and a monograph format have been completed. The hospitals' autonomous medical staffs have thus far elected to retain individual pharmacy and therapeutics (P&T) committees but approved a revamped formulary review process and system-wide P&T subcommittees. The computer system is being enhanced so that pharmacists will have access to applicable P&T committee-approved guidelines for drug use. Since vendors were advised that the system is establishing one formulary, Sharp has been able in some cases to achieve better pricing than it previously could through its purchasing group.
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.
More on soft theorems: Trees, loops, and strings
NASA Astrophysics Data System (ADS)
Bianchi, Massimo; He, Song; Huang, Yu-tin; Wen, Congkao
2015-09-01
We study soft theorems in a broader context, their universality in effective field theories and string theory, as well as continue the analysis of their fate at loop level. In effective field theories with F3 and R3 interactions, the soft theorems are not modified. However, for gravity theories with R2ϕ interactions, the sub-subleading order soft graviton theorem, which is beyond what is implied by the extended Bondi, van der Burg, Metzner, and Sachs symmetry, requires modifications at tree level for nonsupersymmetric theories and at loop level for N ≤4 supergravity due to anomalies. For open and closed superstrings at finite α', via explicit calculation for lower-point examples as well as world sheet operator product expansion analysis for arbitrary multiplicity, we show that scattering amplitudes satisfy the same soft theorem as their field-theory counterpart. This is no longer true for closed bosonic or heterotic strings due to the presence of R2ϕ interactions. We also consider loop corrections to gauge theories in the planar limit, where we show that tree-level soft gluon theorems are respected at the integrand level for 1 ≤N ≤4 SYM. Finally, we discuss the fate of soft theorems for finite loop amplitudes in pure Yang-Mills theory and gravity.
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.
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.
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.
Carnot{close_quote}s theorem as Noether{close_quote}s theorem for thermoacoustic engines
Smith, E. |
1998-09-01
Onset in thermoacoustic engines, the transition to spontaneous self-generation of oscillations, is studied here as both a dynamical critical transition and a limiting heat engine behavior. The critical transition is interesting because it occurs for both dissipative and conservative systems, with common scaling properties. When conservative, the stable oscillations above the critical point also implement a reversible engine cycle satisfying Carnot{close_quote}s theorem, a universal conservation law for entropy flux. While criticality in equilibrium systems is naturally associated with symmetries and universal conservation laws, these are usually exploited with global minimization principles, which dynamical critical systems may not have if dissipation is essential to their criticality. Acoustic heat engines furnish an example connecting equilibrium methods with dynamical and possibly even dissipative critical transitions: A reversible engine is shown to map, by a change of variables, to an equivalent system in apparent thermal equilibrium; a Noether symmetry in the equilibrium field theory implies Carnot{close_quote}s theorem for the engine. Under the same association, onset is shown to be a process of spontaneous symmetry breaking and the scaling of the quality factor predicted for both the reversible {ital and irreversible} engines is shown to arise from the Ginzburg-Landau description of the broken phase. {copyright} {ital 1998} {ital The American Physical Society}
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...
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...
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.
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.
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.
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 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
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.
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.
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.
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.
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.
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,
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
Curiosity Arm Over Marimba Target on Mount Sharp
2016-08-04
NASA's Curiosity Mars rover began close-up investigation of a target called "Marimba," on lower Mount Sharp, during the week preceding the fourth anniversary of the mission's dramatic sky-crane landing. The Navigation Camera (Navcam) on Curiosity's mast took this image on Aug. 2, 2016, during the 1,418th Martian day, or sol, since Curiosity landed inside Gale Crater on Aug. 6, 2012, Universal Time (Aug. 5, PDT). In this scene, the rover has extended its arm over a patch of bedrock selected as the target for rover's next drilling operation. The drilling collects rock powder for onboard laboratory analysis. The arm is positioned with the rover's wire-bristle Dust Removal Tool above the target. http://photojournal.jpl.nasa.gov/catalog/PIA20764
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.
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.
Carbon nanotube based sharp tips and soldering irons
NASA Astrophysics Data System (ADS)
Misra, Abha; Daraio, Chiara
2009-03-01
High energy electron beam machining has been proven a powerful tool to modify desired nanostructures for technological applications and to form molecular junctions and interconnections between carbon nanotubes. The development of the next generation of miniaturized electronic systems demands the integration of nanoelectronic components creating reliable mechanical and electrical contacts. At the same time, the development of scanning probe techniques and magnetic recording media require an ever decreasing tip size of ultrasharp magnetic read-write heads. We report on the nano-electron beam assisted fabrication of atomically sharp iron-based tips and on the creation of a nano-soldering iron for nano-interconnects using Fe-filled multiwalled carbon nanotubes (MWCNTs). Our technique allows also carving a MWCNT into a nanosoldering iron that was demonstrated capable of joining two separated halves of a tube. This approach could easily be extended to the interconnection of two largely dissimilar CNTs, between a CNT and a nanowire or between two nanowires.
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.
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.
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)].
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.
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.
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
Numerical prediction of interfacial instabilities: Sharp interface method (SIM)
NASA Astrophysics Data System (ADS)
Nourgaliev, R. R.; Liou, M.-S.; Theofanous, T. G.
2008-04-01
We introduce a sharp interface method (SIM) for the direct numerical simulation of unstable fluid-fluid interfaces. The method is based on the level set approach and the structured adaptive mesh refinement technology, endowed with a corridor of irregular, cut-cell grids that resolve the interfacial region to third-order spatial accuracy. Key in that regard are avoidance of numerical mixing, and a least-squares interpolation method that is supported by irregular datasets distinctly on each side of the interface. Results on test problems show our method to be free of the spurious current problem of the continuous surface force method and to converge, on grid refinement, at near-theoretical rates. Simulations of unstable Rayleigh-Taylor and viscous Kelvin-Helmholtz flows are found to converge at near-theoretical rates to the exact results over a wide range of conditions. Further, we show predictions of neutral-stability maps of the viscous Kelvin-Helmholtz flows (Yih instability), as well as self-selection of the most unstable wave-number in multimode simulations of Rayleigh-Taylor instability. All these results were obtained with a simple seeding of random infinitesimal disturbances of interface-shape, as opposed to seeding by a complete eigenmode. For other than elementary flows the latter would normally not be available, and extremely difficult to obtain if at all. Sample comparisons with our code adapted to mimic typical diffuse interface treatments were not satisfactory for shear-dominated flows. On the other hand the sharp dynamics of our method would appear to be compatible and possibly advantageous to any interfacial flow algorithm in which the interface is represented as a discrete Heaviside function.