Generalized Dandelin’s Theorem

NASA Astrophysics Data System (ADS)

Kheyfets, A. L.

2017-11-01

The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.

Generalized Optical Theorem Detection in Random and Complex Media

NASA Astrophysics Data System (ADS)

Tu, Jing

energy while the optical theorem detectors are based on real physical energy. For reference, the optical theorem detectors are also compared with the matched filter approach which (unlike the optical theorem detectors) assumes perfect target and medium information. The practical implementation of the optical theorem detectors is based for certain random and complex media on the exploitation of time reversal focusing ideas developed in the past 20 years in electromagnetics and acoustics. In the final part of the dissertation, we also discuss the implementation of the optical theorem sensors for one-dimensional propagation systems such as transmission lines. We also present a new generalized likelihood ratio test for detection that exploits a prior data constraint based on the optical theorem. Finally, we also address the practical implementation of the optical theorem sensors for optical imaging systems, by means of holography. The later is the first holographic implementation the optical theorem for arbitrary scenes and targets.

SHARP Multiphysics Tutorials

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

Yu, Y. Q.; Shemon, E. R.; Mahadevan, Vijay S.

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-physicsmore » 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.« less

The geometric Mean Value Theorem

NASA Astrophysics Data System (ADS)

de Camargo, André Pierro

2018-05-01

In a previous article published in the American Mathematical Monthly, Tucker (Amer Math Monthly. 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying Rolle's theorem to a function like Although short and effective, such reasoning is not intuitive. Perhaps for this reason, Tucker classified the Mean Value Theorem as a technical existence theorem used to prove intuitively obvious statements. Moreover, he argued that there is nothing obvious about the Mean Value Theorem without the continuity of the derivative. Under so unfair discrimination, we felt the need to come to the defense of this beautiful theorem in order to clear up these misunderstandings.

Generalized quantum no-go theorems of pure states

NASA Astrophysics Data System (ADS)

Li, Hui-Ran; Luo, Ming-Xing; Lai, Hong

2018-07-01

Various results of the no-cloning theorem, no-deleting theorem and no-superposing theorem in quantum mechanics have been proved using the superposition principle and the linearity of quantum operations. In this paper, we investigate general transformations forbidden by quantum mechanics in order to unify these theorems. First, we prove that any useful information cannot be created from an unknown pure state which is randomly chosen from a Hilbert space according to the Harr measure. And then, we propose a unified no-go theorem based on a generalized no-superposing result. The new theorem includes the no-cloning theorem, no-anticloning theorem, no-partial-erasure theorem, no-splitting theorem, no-superposing theorem or no-encoding theorem as a special case. Moreover, it implies various new results. Third, we extend the new theorem into another form that includes the no-deleting theorem as a special case.

Pick's Theorem: What a Lemon!

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.

Approaching Cauchy's Theorem

ERIC Educational Resources Information Center

Garcia, Stephan Ramon; Ross, William T.

2017-01-01

We hope to initiate a discussion about various methods for introducing Cauchy's Theorem. Although Cauchy's Theorem is the fundamental theorem upon which complex analysis is based, there is no "standard approach." The appropriate choice depends upon the prerequisites for the course and the level of rigor intended. Common methods include…

Edge Sharpness Assessment by Parametric Modeling: Application to Magnetic Resonance Imaging.

PubMed

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.

Discovering the Theorem of Pythagoras

NASA Technical Reports Server (NTRS)

Lattanzio, Robert (Editor)

1988-01-01

In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.

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)

A fermionic de Finetti theorem

NASA Astrophysics Data System (ADS)

Krumnow, Christian; Zimborás, Zoltán; Eisert, Jens

2017-12-01

Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing one to bound the error made by mean-field approaches. Such theorems link the symmetry of a quantum state under the exchange of subsystems to negligible quantum correlations and are well understood and established in the context of distinguishable particles. In this work, we derive a de Finetti theorem for finite sized Majorana fermionic systems. It is shown, much reflecting the spirit of other quantum de Finetti theorems, that a state which is invariant under certain permutations of modes loses most of its anti-symmetric character and is locally well described by a mode separable state. We discuss the structure of the resulting mode separable states and establish in specific instances a quantitative link to the quality of the Hartree-Fock approximation of quantum systems. We hint at a link to generalized Pauli principles for one-body reduced density operators. Finally, building upon the obtained de Finetti theorem, we generalize and extend the applicability of Hudson's fermionic central limit theorem.

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.

Recurrence theorems: A unified account

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

Wallace, David, E-mail: david.wallace@balliol.ox.ac.uk

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.

From Einstein's theorem to Bell's theorem: a history of quantum non-locality

NASA Astrophysics Data System (ADS)

Wiseman, H. M.

2006-04-01

In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.

A quantum framework for likelihood ratios

NASA Astrophysics Data System (ADS)

Bond, Rachael L.; He, Yang-Hui; Ormerod, Thomas C.

The ability to calculate precise likelihood ratios is fundamental to science, from Quantum Information Theory through to Quantum State Estimation. However, there is no assumption-free statistical methodology to achieve this. For instance, in the absence of data relating to covariate overlap, the widely used Bayes’ theorem either defaults to the marginal probability driven “naive Bayes’ classifier”, or requires the use of compensatory expectation-maximization techniques. This paper takes an information-theoretic approach in developing a new statistical formula for the calculation of likelihood ratios based on the principles of quantum entanglement, and demonstrates that Bayes’ theorem is a special case of a more general quantum mechanical expression.

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.

The Parity Theorem Shuffle

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…

Riemannian and Lorentzian flow-cut theorems

NASA Astrophysics Data System (ADS)

Headrick, Matthew; Hubeny, Veronika E.

2018-05-01

We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.

The Levy sections theorem revisited

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio

2007-06-01

This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.

Sharps container

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.

A Novel Passive Tracking Scheme Exploiting Geometric and Intercept Theorems

PubMed Central

Zhou, Biao; Sun, Chao; Ahn, Deockhyeon; Kim, Youngok

2018-01-01

Passive tracking aims to track targets without assistant devices, that is, device-free targets. Passive tracking based on Radio Frequency (RF) Tomography in wireless sensor networks has recently been addressed as an emerging field. The passive tracking scheme using geometric theorems (GTs) is one of the most popular RF Tomography schemes, because the GT-based method can effectively mitigate the demand for a high density of wireless nodes. In the GT-based tracking scheme, the tracking scenario is considered as a two-dimensional geometric topology and then geometric theorems are applied to estimate crossing points (CPs) of the device-free target on line-of-sight links (LOSLs), which reveal the target’s trajectory information in a discrete form. In this paper, we review existing GT-based tracking schemes, and then propose a novel passive tracking scheme by exploiting the Intercept Theorem (IT). To create an IT-based CP estimation scheme available in the noisy non-parallel LOSL situation, we develop the equal-ratio traverse (ERT) method. Finally, we analyze properties of three GT-based tracking algorithms and the performance of these schemes is evaluated experimentally under various trajectories, node densities, and noisy topologies. Analysis of experimental results shows that tracking schemes exploiting geometric theorems can achieve remarkable positioning accuracy even under rather a low density of wireless nodes. Moreover, the proposed IT scheme can provide generally finer tracking accuracy under even lower node density and noisier topologies, in comparison to other schemes. PMID:29562621

Generalized Bloch theorem and topological characterization

NASA Astrophysics Data System (ADS)

Dobardžić, E.; Dimitrijević, M.; Milovanović, M. V.

2015-03-01

The Bloch theorem enables reduction of the eigenvalue problem of the single-particle Hamiltonian that commutes with the translational group. Based on a group theory analysis we present a generalization of the Bloch theorem that incorporates all additional symmetries of a crystal. The generalized Bloch theorem constrains the form of the Hamiltonian which becomes manifestly invariant under additional symmetries. In the case of isotropic interactions the generalized Bloch theorem gives a unique Hamiltonian. This Hamiltonian coincides with the Hamiltonian in the periodic gauge. In the case of anisotropic interactions the generalized Bloch theorem allows a family of Hamiltonians. Due to the continuity argument we expect that even in this case the Hamiltonian in the periodic gauge defines observables, such as Berry curvature, in the inverse space. For both cases we present examples and demonstrate that the average of the Berry curvatures of all possible Hamiltonians in the Bloch gauge is the Berry curvature in the periodic gauge.

Impossible colorings and Bell's theorem

NASA Astrophysics Data System (ADS)

Aravind, P. K.

1999-11-01

An argument due to Zimba and Penrose is generalized to show how all known non-coloring proofs of the Bell-Kochen-Specker (BKS) theorem can be converted into inequality-free proofs of Bell's nonlocality theorem. A compilation of many such inequality-free proofs is given.

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).

High-angular-resolution NIR astronomy with large arrays (SHARP I and SHARP II)

NASA Astrophysics Data System (ADS)

Hofmann, Reiner; Brandl, Bernhard; Eckart, Andreas; Eisenhauer, Frank; Tacconi-Garman, Lowell E.

1995-06-01

SHARP I and SHARP II are near infrared cameras for high-angular-resolution imaging. Both cameras are built around a 256 X 256 pixel NICMOS 3 HgCdTe array from Rockwell which is sensitive in the 1 - 2.5 micrometers range. With a 0.05'/pixel scale, they can produce diffraction limited K-band images at 4-m-class telescopes. For a 256 X 256 array, this pixel scale results in a field of view of 12.8' X 12.8' which is well suited for the observation of galactic and extragalactic near-infrared sources. Photometric and low resolution spectroscopic capabilities are added by photometric band filters (J, H, K), narrow band filters ((lambda) /(Delta) (lambda) approximately equals 100) for selected spectral lines, and a CVF ((lambda) /(Delta) (lambda) approximately equals 70). A cold shutter permits short exposure times down to about 10 ms. The data acquisition electronics permanently accepts the maximum frame rate of 8 Hz which is defined by the detector time constants (data rate 1 Mbyte/s). SHARP I has been especially designed for speckle observations at ESO's 3.5 m New Technology Telescope and is in operation since 1991. SHARP II is used at ESO's 3.6 m telescope together with the adaptive optics system COME-ON + since 1993. A new version of SHARP II is presently under test, which incorporates exchangeable camera optics for observations with scales of 0.035, 0.05, and 0.1'/pixel. The first scale extends diffraction limited observations down to the J-band, while the last one provides a larger field of view. To demonstrate the power of the cameras, images of the galactic center obtained with SHARP I, and images of the R136 region in 30 Doradus observed with SHARP II are presented.

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

NASA Astrophysics Data System (ADS)

Woolgar, Eric; Wylie, William

2016-02-01

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.

Discrete Jordan curve theorem

NASA Astrophysics Data System (ADS)

Chen, Li

1999-09-01

According to a general definition of discrete curves, surfaces, and manifolds (Li Chen, 'Generalized discrete object tracking algorithms and implementations, ' In Melter, Wu, and Latecki ed, Vision Geometry VI, SPIE Vol. 3168, pp 184 - 195, 1997.). This paper focuses on the Jordan curve theorem in 2D discrete spaces. The Jordan curve theorem says that a (simply) closed curve separates a simply connected surface into two components. Based on the definition of discrete surfaces, we give three reasonable definitions of simply connected spaces. Theoretically, these three definition shall be equivalent. We have proved the Jordan curve theorem under the third definition of simply connected spaces. The Jordan theorem shows the relationship among an object, its boundary, and its outside area. In continuous space, the boundary of an mD manifold is an (m - 1)D manifold. The similar result does apply to regular discrete manifolds. The concept of a new regular nD-cell is developed based on the regular surface point in 2D, and well-composed objects in 2D and 3D given by Latecki (L. Latecki, '3D well-composed pictures,' In Melter, Wu, and Latecki ed, Vision Geometry IV, SPIE Vol 2573, pp 196 - 203, 1995.).

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.

How sharp is sharp? Towards quantification of the sharpness and penetration ability of kitchen knives used in stabbings.

PubMed

Hainsworth, S V; Delaney, R J; Rutty, G N

2008-07-01

Stabbing is the most common method for violent death in the UK. As part of their investigation, forensic pathologists are commonly asked to estimate or quantify the degree of force required to create a wound. The force required to penetrate the skin and body by a knife is a complex function of the sharpness of the knife, the area of the body and alignment with cleavage lines of the skin, the angle of attack and the relative movement of the person stabbing relative to the victim being stabbed. This makes it difficult for the forensic pathologist to give an objective answer to the question; hence, subjective estimations are often used. One area where some degree of quantification is more tractable is in assessing how sharp an implement (particularly a knife) is. This paper presents results of a systematic study of how the different aspects of knife geometry influence sharpness and presents a simple test for assessing knife sharpness using drop testing. The results show that the radius of the blunt edge at the tip is important for controlling the penetration ability of a kitchen knife. Using high-speed video, it also gives insight into the mechanism of knife penetration into the skin. The results of the study will aid pathologists in giving a more informed answer to the question of the degree of force used in stabbing.

On the addition theorem of spherical functions

NASA Astrophysics Data System (ADS)

Shkodrov, V. G.

The addition theorem of spherical functions is expressed in two reference systems, viz., an inertial system and a system rigidly fixed to a planet. A generalized addition theorem of spherical functions and a particular addition theorem for the rigidly fixed system are derived. The results are applied to the theory of a planetary potential.

Analysis of sharpness increase by image noise

NASA Astrophysics Data System (ADS)

Kurihara, Takehito; Aoki, Naokazu; Kobayashi, Hiroyuki

2009-02-01

Motivated by the reported increase in sharpness by image noise, we investigated how noise affects sharpness perception. We first used natural images of tree bark with different amounts of noise to see whether noise enhances sharpness. Although the result showed sharpness decreased as noise amount increased, some observers seemed to perceive more sharpness with increasing noise, while the others did not. We next used 1D and 2D uni-frequency patterns as stimuli in an attempt to reduce such variability in the judgment. The result showed, for higher frequency stimuli, sharpness decreased as the noise amount increased, while sharpness of the lower frequency stimuli increased at a certain noise level. From this result, we thought image noise might reduce sharpness at edges, but be able to improve sharpness of lower frequency component or texture in image. To prove this prediction, we experimented again with the natural image used in the first experiment. Stimuli were made by applying noise separately to edge or to texture part of the image. The result showed noise, when added to edge region, only decreased sharpness, whereas when added to texture, could improve sharpness. We think it is the interaction between noise and texture that sharpens image.

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.…

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.

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

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

Woolgar, Eric, E-mail: ewoolgar@ualberta.ca; Wylie, William, E-mail: wwylie@syr.edu

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 tomore » 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.« less

On the symmetry foundation of double soft theorems

NASA Astrophysics Data System (ADS)

Li, Zhi-Zhong; Lin, Hung-Hwa; Zhang, Shun-Qing

2017-12-01

Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by employing current algebras, recent attempts of extending such an approach to known double soft theorems has been met with difficulties. In this work, we have traced the difficulty to two inequivalent expansion schemes, depending on whether the soft limit is taken asymmetrically or symmetrically, which we denote as type A and B respectively. The soft-behaviour for type A scheme can simply be derived from single soft theorems, and are thus non-perturbatively protected. For type B, the information of the four-point vertex is required to determine the corresponding soft theorems, and thus are in general not protected. This argument can be readily extended to general multi-soft theorems. We also ask whether unitarity can be emergent from locality together with the two kinds of soft theorems, which has not been fully investigated before.

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…

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)

SHARP: Spacecraft Health Automated Reasoning Prototype

NASA Technical Reports Server (NTRS)

Atkinson, David J.

1991-01-01

The planetary spacecraft mission OPS as applied to SHARP is studied. Knowledge systems involved in this study are detailed. SHARP development task and Voyager telecom link analysis were examined. It was concluded that artificial intelligence has a proven capability to deliver useful functions in a real time space flight operations environment. SHARP has precipitated major change in acceptance of automation at JPL. The potential payoff from automation using AI is substantial. SHARP, and other AI technology is being transferred into systems in development including mission operations automation, science data systems, and infrastructure applications.

Abel's theorem in the noncommutative case

NASA Astrophysics Data System (ADS)

Leitenberger, Frank

2004-03-01

We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel's theorem.

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.

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).

An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

NASA Astrophysics Data System (ADS)

Drivas, Theodore D.; Eyink, Gregory L.

2017-12-01

We prove that bounded weak solutions of the compressible Euler equations will conserve thermodynamic entropy unless the solution fields have sufficiently low space-time Besov regularity. A quantity measuring kinetic energy cascade will also vanish for such Euler solutions, unless the same singularity conditions are satisfied. It is shown furthermore that strong limits of solutions of compressible Navier-Stokes equations that are bounded and exhibit anomalous dissipation are weak Euler solutions. These inviscid limit solutions have non-negative anomalous entropy production and kinetic energy dissipation, with both vanishing when solutions are above the critical degree of Besov regularity. Stationary, planar shocks in Euclidean space with an ideal-gas equation of state provide simple examples that satisfy the conditions of our theorems and which demonstrate sharpness of our L 3-based conditions. These conditions involve space-time Besov regularity, but we show that they are satisfied by Euler solutions that possess similar space regularity uniformly in time.

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…

Ergodic theorem, ergodic theory, and statistical mechanics

PubMed Central

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

Kohn's theorem, Larmor's equivalence principle and the Newton-Hooke group

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

Gibbons, G.W., E-mail: gwg1@amtp.cam.ac.uk; Pope, C.N.; George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Texas A and M University, College Station, TX 77843-4242

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 systemmore » 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.« less

Logical errors on proving theorem

NASA Astrophysics Data System (ADS)

Sari, C. K.; Waluyo, M.; Ainur, C. M.; Darmaningsih, E. N.

2018-01-01

In tertiary level, students of mathematics education department attend some abstract courses, such as Introduction to Real Analysis which needs an ability to prove mathematical statements almost all the time. In fact, many students have not mastered this ability appropriately. In their Introduction to Real Analysis tests, even though they completed their proof of theorems, they achieved an unsatisfactory score. They thought that they succeeded, but their proof was not valid. In this study, a qualitative research was conducted to describe logical errors that students made in proving the theorem of cluster point. The theorem was given to 54 students. Misconceptions on understanding the definitions seem to occur within cluster point, limit of function, and limit of sequences. The habit of using routine symbol might cause these misconceptions. Suggestions to deal with this condition are described as well.

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.

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.

Unpacking Rouché's Theorem

ERIC Educational Resources Information Center

Howell, Russell W.; Schrohe, Elmar

2017-01-01

Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…

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

Implementing AORN recommended practices for sharps safety.

PubMed

Ford, Donna A

2014-01-01

Prevention of percutaneous sharps injuries in perioperative settings remains a challenge. Occupational transmission of bloodborne pathogens, not only from patients to health care providers but also from health care providers to patients, is a significant concern. Legislation and position statements geared toward ensuring the safety of patients and health care workers have not resulted in significantly reduced sharps injuries in perioperative settings. Awareness and understanding of the types of percutaneous injuries that occur in perioperative settings is fundamental to developing an effective sharps injury prevention program. The AORN "Recommended practices for sharps safety" clearly delineates evidence-based recommendations for sharps injury prevention. Perioperative RNs can lead efforts to change practice for the safety of patients and perioperative team members by promoting the elimination of sharps hazards; the use of engineering, work practice, and administrative controls; and the proper use of personal protective equipment, including double gloving. Copyright © 2014 AORN, Inc. Published by Elsevier Inc. All rights reserved.

Relationship between sharps disposal containers and Clostridium difficile infections in acute care hospitals.

PubMed

Pogorzelska-Maziarz, Monika

2015-10-01

Sharps disposal containers are ubiquitous in health care facilities; however, there is paucity of data on their potential role in pathogen transmission. This study assessed the relationship between use of single-use versus reusable sharps containers and rates of Clostridium difficile infections in a national sample of hospitals. A 2013 survey of 1,990 hospitals collected data on the use of sharps containers. Responses were linked to the 2012 Medicare Provider Analysis and Review dataset. Bivariate and multivariable negative binomial regression were conducted to examine differences in C difficile rates between hospitals using single-use versus reusable containers. There were 604 hospitals who completed the survey; of these, 539 provided data on use of sharps containers in 2012 (27% response rate). Hospitals had, on average, 289 beds (SD ± 203) and were predominantly non-for-profit (67%) and nonteaching (63%). Most used reusable sharps containers (72%). In bivariate regression, hospitals using single-use containers had significantly lower rates of C difficile versus hospitals using reusable containers (incidence rate ratio [IRR] = 0.846, P = .001). This relationship persisted in multivariable regression (IRR = 0.870, P = .003) after controlling for other hospital characteristics. This is the first study to show a link between use of single-use sharps containers and lower C difficile rates. Future research should investigate the potential for environmental contamination of reusable containers and the role they may play in pathogen transmission. Copyright © 2015 Association for Professionals in Infection Control and Epidemiology, Inc. Published by Elsevier Inc. All rights reserved.

S-HARP: A parallel dynamic spectral partitioner

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

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 Messagemore » 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.« less

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…

Mice Lacking the Circadian Modulators SHARP1 and SHARP2 Display Altered Sleep and Mixed State Endophenotypes of Psychiatric Disorders

PubMed Central

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

Lindeberg theorem for Gibbs-Markov dynamics

NASA Astrophysics Data System (ADS)

Denker, Manfred; Senti, Samuel; Zhang, Xuan

2017-12-01

A dynamical array consists of a family of functions \\{ fn, i: 1≤slant i≤slant k_n, n≥slant 1\\} and a family of initial times \\{τn, i: 1≤slant i≤slant k_n, n≥slant 1\\} . For a dynamical system (X, T) we identify distributional limits for sums of the form for suitable (non-random) constants s_n>0 and an, i\\in { R} . We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from Gibbs-Markov systems. Our results, which hold for more general dynamics, are stated in the context of Gibbs-Markov dynamical systems for convenience.

A Sharp methodology for VLSI layout

NASA Astrophysics Data System (ADS)

Bapat, Shekhar

1993-01-01

The layout problem for VLSI circuits is recognized as a very difficult problem and has been traditionally decomposed into the several seemingly independent sub-problems of placement, global routing, and detailed routing. Although this structure achieves a reduction in programming complexity, it is also typically accompanied by a reduction in solution quality. Most current placement research recognizes that the separation is artificial, and that the placement and routing problems should be solved ideally in tandem. We propose a new interconnection model, Sharp and an associated partitioning algorithm. The Sharp interconnection model uses a partitioning shape that roughly resembles the musical sharp 'number sign' and makes extensive use of pre-computed rectilinear Steiner trees. The model is designed to generate strategic routing information along with the partitioning results. Additionally, the Sharp model also generates estimates of the routing congestion. We also propose the Sharp layout heuristic that solves the layout problem in its entirety. The Sharp layout heuristic makes extensive use of the Sharp partitioning model. The use of precomputed Steiner tree forms enables the method to model accurately net characteristics. For example, the Steiner tree forms can model both the length of the net and more importantly its route. In fact, the tree forms are also appropriate for modeling the timing delays of nets. The Sharp heuristic works to minimize both the total layout area by minimizing total net length (thus reducing the total wiring area), and the congestion imbalances in the various channels (thus reducing the unused or wasted channel area). Our heuristic uses circuit element movements amongst the different partitioning blocks and selection of alternate minimal Steiner tree forms to achieve this goal. The objective function for the algorithm can be modified readily to include other important circuit constraints like propagation delays. The layout technique

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.

Tree-manipulating systems and Church-Rosser theorems.

NASA Technical Reports Server (NTRS)

Rosen, B. K.

1973-01-01

Study of a broad class of tree-manipulating systems called subtree replacement systems. The use of this framework is illustrated by general theorems analogous to the Church-Rosser theorem and by applications of these theorems. Sufficient conditions are derived for the Church-Rosser property, and their applications to recursive definitions, the lambda calculus, and parallel programming are discussed. McCarthy's (1963) recursive calculus is extended by allowing a choice between call-by-value and call-by-name. It is shown that recursively defined functions are single-valued despite the nondeterminism of the evaluation algorithm. It is also shown that these functions solve their defining equations in a 'canonical' manner.

Optimal no-go theorem on hidden-variable predictions of effect expectations

NASA Astrophysics Data System (ADS)

Blass, Andreas; Gurevich, Yuri

2018-03-01

No-go theorems prove that, under reasonable assumptions, classical hidden-variable theories cannot reproduce the predictions of quantum mechanics. Traditional no-go theorems proved that hidden-variable theories cannot predict correctly the values of observables. Recent expectation no-go theorems prove that hidden-variable theories cannot predict the expectations of observables. We prove the strongest expectation-focused no-go theorem to date. It is optimal in the sense that the natural weakenings of the assumptions and the natural strengthenings of the conclusion make the theorem fail. The literature on expectation no-go theorems strongly suggests that the expectation-focused approach is more general than the value-focused one. We establish that the expectation approach is not more general.

A Generalization of the Prime Number Theorem

ERIC Educational Resources Information Center

Bruckman, Paul S.

2008-01-01

In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiable…

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…

Gleason-Busch theorem for sequential measurements

NASA Astrophysics Data System (ADS)

Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah

2017-12-01

Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.

Double soft graviton theorems and Bondi-Metzner-Sachs symmetries

NASA Astrophysics Data System (ADS)

Anupam, A. H.; Kundu, Arpan; Ray, Krishnendu

2018-05-01

It is now well understood that Ward identities associated with the (extended) BMS algebra are equivalent to single soft graviton theorems. In this work, we show that if we consider nested Ward identities constructed out of two BMS charges, a class of double soft factorization theorems can be recovered. By making connections with earlier works in the literature, we argue that at the subleading order, these double soft graviton theorems are the so-called consecutive double soft graviton theorems. We also show how these nested Ward identities can be understood as Ward identities associated with BMS symmetries in scattering states defined around (non-Fock) vacua parametrized by supertranslations or superrotations.

Composite, ordered material having sharp surface features

DOEpatents

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.

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.

Scaling and scale invariance of conservation laws in Reynolds transport theorem framework

NASA Astrophysics Data System (ADS)

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.

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)…

The Holographic F Theorem

NASA Astrophysics Data System (ADS)

Taylor, Marika; Woodhead, William

2017-12-01

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension between 3/2 and 5/2. Therefore the strongest version of the F theorem is in general violated.

Fluctuation theorems in feedback-controlled open quantum systems: Quantum coherence and absolute irreversibility

NASA Astrophysics Data System (ADS)

Murashita, Yûto; Gong, Zongping; Ashida, Yuto; Ueda, Masahito

2017-10-01

The thermodynamics of quantum coherence has attracted growing attention recently, where the thermodynamic advantage of quantum superposition is characterized in terms of quantum thermodynamics. We investigate the thermodynamic effects of quantum coherent driving in the context of the fluctuation theorem. We adopt a quantum-trajectory approach to investigate open quantum systems under feedback control. In these systems, the measurement backaction in the forward process plays a key role, and therefore the corresponding time-reversed quantum measurement and postselection must be considered in the backward process, in sharp contrast to the classical case. The state reduction associated with quantum measurement, in general, creates a zero-probability region in the space of quantum trajectories of the forward process, which causes singularly strong irreversibility with divergent entropy production (i.e., absolute irreversibility) and hence makes the ordinary fluctuation theorem break down. In the classical case, the error-free measurement ordinarily leads to absolute irreversibility, because the measurement restricts classical paths to the region compatible with the measurement outcome. In contrast, in open quantum systems, absolute irreversibility is suppressed even in the presence of the projective measurement due to those quantum rare events that go through the classically forbidden region with the aid of quantum coherent driving. This suppression of absolute irreversibility exemplifies the thermodynamic advantage of quantum coherent driving. Absolute irreversibility is shown to emerge in the absence of coherent driving after the measurement, especially in systems under time-delayed feedback control. We show that absolute irreversibility is mitigated by increasing the duration of quantum coherent driving or decreasing the delay time of feedback control.

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…

Special ergodic theorems and dynamical large deviations

NASA Astrophysics Data System (ADS)

Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav

2012-11-01

Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.

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.

Out-of-time-order fluctuation-dissipation theorem

NASA Astrophysics Data System (ADS)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

On Pythagoras Theorem for Products of Spectral Triples

NASA Astrophysics Data System (ADS)

D'Andrea, Francesco; Martinetti, Pierre

2013-05-01

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.

Behold Mount Sharp!

NASA Image and Video Library

2012-08-06

This image taken by NASA Curiosity shows what lies ahead for the rover -- its main science target, informally called Mount Sharp. The rover shadow can be seen in the foreground, and the dark bands beyond are dunes.

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)).

Four Theorems on the Psychometric Function

PubMed Central

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 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…

Poisson's ratio of fiber-reinforced composites

NASA Astrophysics Data System (ADS)

Christiansson, Henrik; Helsing, Johan

1996-05-01

Poisson's ratio flow diagrams, that is, the Poisson's ratio versus the fiber fraction, are obtained numerically for hexagonal arrays of elastic circular fibers in an elastic matrix. High numerical accuracy is achieved through the use of an interface integral equation method. Questions concerning fixed point theorems and the validity of existing asymptotic relations are investigated and partially resolved. Our findings for the transverse effective Poisson's ratio, together with earlier results for random systems by other authors, make it possible to formulate a general statement for Poisson's ratio flow diagrams: For composites with circular fibers and where the phase Poisson's ratios are equal to 1/3, the system with the lowest stiffness ratio has the highest Poisson's ratio. For other choices of the elastic moduli for the phases, no simple statement can be made.

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.

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.

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.

Sharp Injuries Among Medical Students.

PubMed

Ghasemzadeh, Iman; Kazerooni, Mitra; Davoodian, Parivash; Hamedi, Yaghoob; Sadeghi, Payam

2015-03-30

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. 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. 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 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.

Quantization of Chirikov Map and Quantum KAM Theorem.

NASA Astrophysics Data System (ADS)

Shi, Kang-Jie

KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions

The SHARP Program: Giving Kids Chances to Excel

ERIC Educational Resources Information Center

Kenney, Rich

2007-01-01

In this article, the author describes the Sports, Habilitation, and Recreation Program (SHARP), a program of the Foundation for Blind Children in Phoenix, Arizona. The SHARP program aims to help children, who have visual impairments, achieve goals, develop independence, and make friends. One of the unique features of the SHARP program is that it…

Optimal Keno Strategies and the Central Limit Theorem

ERIC Educational Resources Information Center

Johnson, Roger W.

2006-01-01

For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…

The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities

NASA Astrophysics Data System (ADS)

Cain, George L., Jr.; González, Luis

2008-02-01

The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.

A Stochastic Version of the Noether Theorem

NASA Astrophysics Data System (ADS)

González Lezcano, Alfredo; Cabo Montes de Oca, Alejandro

2018-06-01

A stochastic version of the Noether theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied to two kinds of random covariant forces. One of them generated in an electrodynamic way and the other is defined in the rest frame of the particle as a function of the proper time. For both of them, it is shown the conservation of the mean value of a random drift momentum. The validity of the theorem makes clear that random systems can produce causal stochastic correlations between two faraway separated systems, that had interacted in the past. In addition possible connections of the discussion with the Ives Couder's experimental results are remarked.

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.

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…

Sharp Contradiction for Local-Hidden-State Model in Quantum Steering

PubMed Central

Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar

2016-01-01

In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell’s nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR’s original scenario is “steering”, i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox. PMID:27562658

Sharp Contradiction for Local-Hidden-State Model in Quantum Steering

NASA Astrophysics Data System (ADS)

Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar

2016-08-01

In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell’s nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR’s original scenario is “steering”, i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox.

Sharp Contradiction for Local-Hidden-State Model in Quantum Steering.

PubMed

Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar

2016-08-26

In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell's nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR's original scenario is "steering", i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox.

H-theorem in quantum physics.

PubMed

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.

H-theorem in quantum physics

PubMed Central

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

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.

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…

Four theorems on the psychometric function.

PubMed

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

Revisiting Ramakrishnan's approach to relatively. [Velocity addition theorem uniqueness

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

Nandi, K.K.; Shankara, T.S.

The conditions under which the velocity addition theorem (VAT) is formulated by Ramakrishnan gave rise to doubts about the uniqueness of the theorem. These conditions are rediscussed with reference to their algebraic and experimental implications. 9 references.

The Sharpness of Blades Used in Dermatologic Surgery.

PubMed

Awadalla, Farah; Hexsel, Camile; Goldberg, Leonard H

2016-01-01

There are numerous blades available for use in dermatologic procedures. There are different advantages that are inhere.nt to different blades due to their shape and size. One aspect of the blade that is instrumental to its performance, but is not objectively defined, is sharpness. This information could be useful when choosing a blade for a particular procedure. This study aims to objectively define the sharpness of blades used in dermatologic surgery. The Sharpness Tester (Cutlery and Allied Trades Research Association, Sheffield, UK) was used to test the force in Newtons a blade requires to cut through a silicone cylinder. New blades were used to determine a standard for the sharpness of new blades. Blades used for surgery were tested to determine the sharpness after use. The sharpest blade is the double-edged razor blade (0.395 N) followed by the dermablade (0.46 N), plastic handled #15 (0.541 N), #15c (0.575 N), #10 (0.647 N), and the #15 blade (0.664 N). The sharpness of a blade is an important factor in its ability to perform a task and should be taken into account when choosing a particular blade for a particular procedure.

Kochen-Specker theorem studied with neutron interferometer.

PubMed

Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut

2011-04-01

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

Fully Quantum Fluctuation Theorems

NASA Astrophysics Data System (ADS)

Åberg, Johan

2018-02-01

Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

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…

Spacecraft Health Automated Reasoning Prototype (SHARP): The fiscal year 1989 SHARP portability evaluations task for NASA Solar System Exploration Division's Voyager project

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.

A Maximal Element Theorem in FWC-Spaces and Its Applications

PubMed Central

Hu, Qingwen; Miao, Yulin

2014-01-01

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672

H-theorem in quantum physics

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

Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.

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

H-theorem in quantum physics

DOE PAGES

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 virial theorem for massless electrons in graphene and other Dirac materials

NASA Astrophysics Data System (ADS)

Sokolik, A. A.; Zabolotskiy, A. D.; Lozovik, Yu. E.

2016-05-01

The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in the particular case of interacting massless electrons in graphene and other Dirac materials, the conventional virial theorem is violated. Starting from the tight-binding model, we derive the generalized virial theorem for Dirac electron systems, which contains an additional term associated with a momentum cutoff at the bottom of the energy band. Additionally, we derive the generalized virial theorem within the Dirac model using the minimization of the variational energy. The obtained theorem is illustrated by many-body calculations of the ground-state energy of an electron gas in graphene carried out in Hartree-Fock and self-consistent random-phase approximations. Experimental verification of the theorem in the case of graphene is discussed.

Strong converse theorems using Rényi entropies

NASA Astrophysics Data System (ADS)

Leditzky, Felix; Wilde, Mark M.; Datta, Nilanjana

2016-08-01

We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint arXiv:1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.

Strong converse theorems using Rényi entropies

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

Leditzky, Felix; Datta, Nilanjana; Wilde, Mark M.

We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint http://arxiv.org/abs/1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for themore » boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.« less

Understanding the Hospital Sharps Injury Reporting Pathway

PubMed Central

Boden, Leslie I.; Petrofsky, Yolanta V.; Hopcia, Karen; Wagner, Gregory R.; Hashimoto, Dean

2016-01-01

Introduction Patient-care workers are frequently exposed to sharps injuries, which can involve the risk of serious illness. Underreporting of these injuries can compromise prevention efforts. Materials and Methods We linked survey responses of 1572 non-physician patient-care workers with the Occupational Health Services (OHS) database at two academic hospitals. We determined whether survey respondents who said they had sharps injuries indicated that they had reported them and whether reported injuries were recorded in the OHS database. Results Respondents said that they reported 62 of 78 sharps injuries occurring over a 12-month period. Only 28 appeared in the OHS data. Safety practices were positively associated with respondents’ saying they reported sharps injuries but not with whether reported injuries appeared in the OHS data. Conclusions Administrators should consider creating reporting mechanisms that are simpler and more direct. Administrators and researchers should attempt to understand how incidents might be lost before they are recorded. PMID:25308763

Guided Discovery of the Nine-Point Circle Theorem and Its Proof

ERIC Educational Resources Information Center

Buchbinder, Orly

2018-01-01

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

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)

A remark on the energy conditions for Hawking's area theorem

NASA Astrophysics Data System (ADS)

Lesourd, Martin

2018-06-01

Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.

Behavior of healthcare workers after injuries from sharp instruments.

PubMed

Adib-Hajbaghery, Mohsen; Lotfi, Mohammad Sajjad

2013-09-01

Injuries with sharps are common occupational hazards for healthcare workers. Such injuries predispose the staff to dangerous infections such as hepatitis B, C and HIV. The present study was conducted to investigate the behaviors of healthcare workers in Kashan healthcare centers after needle sticks and injuries with sharps in 2012. A cross-sectional study was conducted on 298 healthcare workers of medical centers governed by Kashan University of Medical Sciences. A questionnaire was used in this study. The first part included questions about demographic characteristics. The second part of the questionnaire consisted of 16 items related to the sharp instrument injuries. For data analysis, descriptive and analytical statistics (chi-square, ANOVA and Pearson correlation coefficient) SPSS version 16.0 software was used. From a total of 298 healthcare workers, 114 (38.3%) had a history of injury from needles and sharp instruments in the last six months. Most needle stick and sharp instrument injuries had occurred among the operating room nurses and midwifes; 32.5% of injuries from sharp instruments occurred in the morning shift. Needles were responsible for 46.5% of injuries. The most common actions taken after needle stick injuries were compression (27.2%) and washing the area with soap and water (15.8%). Only 44.6% of the injured personnel pursued follow-up measures after a needle stick or sharp instrument injury. More than a half of the healthcare workers with needle stick or sharp instrument injury had refused follow-up for various reasons. The authorities should implement education programs along with protocols to be implemented after needle stick injuries or sharps.

A variational theorem for creep with applications to plates and columns

NASA Technical Reports Server (NTRS)

Sanders, J Lyell, Jr; Mccomb, Harvey G , Jr; Schlechte, Floyd R

1958-01-01

A variational theorem is presented for a body undergoing creep. Solutions to problems of the creep behavior of plates, columns, beams, and shells can be obtained by means of the direct methods of the calculus of variations in conjunction with the stated theorem. The application of the theorem is illustrated for plates and columns by the solution of two sample problems.

Matching factorization theorems with an inverse-error weighting

NASA Astrophysics Data System (ADS)

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea

2018-06-01

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.

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).

A no-hair theorem for black holes in f(R) gravity

NASA Astrophysics Data System (ADS)

Cañate, Pedro

2018-01-01

In this work we present a no-hair theorem which discards the existence of four-dimensional asymptotically flat, static and spherically symmetric or stationary axisymmetric, non-trivial black holes in the frame of f(R) gravity under metric formalism. Here we show that our no-hair theorem also can discard asymptotic de Sitter stationary and axisymmetric non-trivial black holes. The novelty is that this no-hair theorem is built without resorting to known mapping between f(R) gravity and scalar–tensor theory. Thus, an advantage will be that our no-hair theorem applies as well to metric f(R) models that cannot be mapped to scalar–tensor theory.

A Benes-like theorem for the shuffle-exchange graph

NASA Technical Reports Server (NTRS)

Schwabe, Eric J.

1992-01-01

One of the first theorems on permutation routing, proved by V. E. Beness (1965), shows that given a set of source-destination pairs in an N-node butterfly network with at most a constant number of sources or destinations in each column of the butterfly, there exists a set of paths of lengths O(log N) connecting each pair such that the total congestion is constant. An analogous theorem yielding constant-congestion paths for off-line routing in the shuffle-exchange graph is proved here. The necklaces of the shuffle-exchange graph play the same structural role as the columns of the butterfly in Beness' theorem.

3D near-surface soil response from H/V ambient-noise ratios

USGS Publications Warehouse

Wollery, E.W.; Street, R.

2002-01-01

The applicability of the horizontal-to-vertical (H/V) ambient-noise spectral ratio for characterizing earthquake site effects caused by nearsurface topography and velocity structures was evaluated at sites underlain by thick (i.e. >100 m) sediment deposits near the southern-end of the New Madrid seismic zone in the central United States. Three-component ambient-noise and velocity models derived from seismic (shearwave) refraction/reflection surveys showed that a relatively horizontal, sharp shear-wave velocity interface in the soil column resulted in an H/V spectral ratio with a single well-defined peak. Observations at sites with more than one sharp shear-wave velocity contrast and horizontally arranged soil layers resulted in at least two well-defined H/V spectral ratio peaks. Furthermore, at sites where there were sharp shear-wave velocity contrasts in nonhorizontal, near-surface soil layers, the H/V spectra exhibited a broad-bandwidth, relatively low amplitude signal instead of a single well-defined peak. ?? 2002 Elsevier Science Ltd. All rights reserved.

Enhancements to the SHARP Build System and NEK5000 Coupling

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

McCaskey, Alex; Bennett, Andrew R.; Billings, Jay Jay

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 inmore » 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

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.

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.

Some functional limit theorems for compound Cox processes

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

Korolev, Victor Yu.; Institute of Informatics Problems FRC CSC RAS; Chertok, A. V.

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.

An acoustofluidic micromixer based on oscillating sidewall sharp-edges†

PubMed Central

Huang, Po-Hsun; Xie, Yuliang; Ahmed, Daniel; Rufo, Joseph; Nama, Nitesh; Chen, Yuchao; Chan, Chung Yu; Huang, Tony Jun

2014-01-01

Rapid and homogeneous mixing inside a microfluidic channel is demonstrated via the acoustic streaming phenomenon induced by the oscillation of sidewall sharp-edges. By optimizing the design of the sharp-edges, excellent mixing performance and fast mixing speed can be achieved in a simple device, making our sharp-edge-based acoustic micromixer a promising candidate for a wide variety of applications. PMID:23896797

An acoustofluidic micromixer based on oscillating sidewall sharp-edges.

PubMed

Huang, Po-Hsun; Xie, Yuliang; Ahmed, Daniel; Rufo, Joseph; Nama, Nitesh; Chen, Yuchao; Chan, Chung Yu; Huang, Tony Jun

2013-10-07

Rapid and homogeneous mixing inside a microfluidic channel is demonstrated via the acoustic streaming phenomenon induced by the oscillation of sidewall sharp-edges. By optimizing the design of the sharp-edges, excellent mixing performance and fast mixing speed can be achieved in a simple device, making our sharp-edge-based acoustic micromixer a promising candidate for a wide variety of applications.

[Perceptual sharpness metric for visible and infrared color fusion images].

PubMed

Gao, Shao-Shu; Jin, Wei-Qi; Wang, Xia; Wang, Ling-Xue; Luo, Yuan

2012-12-01

For visible and infrared color fusion images, objective sharpness assessment model is proposed to measure the clarity of detail and edge definition of the fusion image. Firstly, the contrast sensitivity functions (CSF) of the human visual system is used to reduce insensitive frequency components under certain viewing conditions. Secondly, perceptual contrast model, which takes human luminance masking effect into account, is proposed based on local band-limited contrast model. Finally, the perceptual contrast is calculated in the region of interest (contains image details and edges) in the fusion image to evaluate image perceptual sharpness. Experimental results show that the proposed perceptual sharpness metrics provides better predictions, which are more closely matched to human perceptual evaluations, than five existing sharpness (blur) metrics for color images. The proposed perceptual sharpness metrics can evaluate the perceptual sharpness for color fusion images effectively.

Numerical investigation of rarefaction effects in the vicinity of a sharp leading edge

NASA Astrophysics Data System (ADS)

Pan, Shaowu; Gao, Zhenxun; Lee, Chunhian

2014-12-01

This paper presents a study of rarefaction effect on hypersonic flow over a sharp leading edge. Both continuum approach and kinetic method: a widely spread commercial Computational Fluid Dynamics-Navior-Stokes-Fourier (CFD-NSF) software - Fluent together with a direct simulation Monte Carlo (DSMC) code developed by the authors are employed for simulation of transition regime with Knudsen number ranging from 0.005 to 0.2. It is found that Fluent can predict the wall fluxes in the case of hypersonic argon flow over the sharp leading edge for the lowest Kn case (Kn = 0.005) in current paper while for other cases it also has a good agreement with DSMC except at the location near the sharp leading edge. Among all of the wall fluxes, it is found that coefficient of pressure is the most sensitive to rarefaction while heat transfer is the least one. A parameter based on translational nonequilibrium and a cut-off value of 0.34 is proposed for continuum breakdown in this paper. The structure of entropy and velocity profile in boundary layer is analyzed. Also, it is found that the ratio of heat transfer coefficient to skin friction coefficient remains uniform along the surface for the four cases in this paper.

Matching factorization theorems with an inverse-error weighting

DOE PAGES

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; ...

2018-04-03

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections tomore » the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H 0 boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. In conclusion, it is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.« less

Matching factorization theorems with an inverse-error weighting

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

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections tomore » the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H 0 boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. In conclusion, it is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.« less

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.

Unified quantum no-go theorems and transforming of quantum pure states in a restricted set

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

2017-12-01

The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.

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…

A theorem about Hamiltonian systems.

PubMed

Case, K M

1984-09-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation.

Generalized Fourier slice theorem for cone-beam image reconstruction.

PubMed

Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

2015-01-01

The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

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).

Mechanisms for Selective Single-Cell Reactivation during Offline Sharp-Wave Ripples and Their Distortion by Fast Ripples.

PubMed

Valero, Manuel; Averkin, Robert G; Fernandez-Lamo, Ivan; Aguilar, Juan; Lopez-Pigozzi, Diego; Brotons-Mas, Jorge R; Cid, Elena; Tamas, Gabor; Menendez de la Prida, Liset

2017-06-21

Memory traces are reactivated selectively during sharp-wave ripples. The mechanisms of selective reactivation, and how degraded reactivation affects memory, are poorly understood. We evaluated hippocampal single-cell activity during physiological and pathological sharp-wave ripples using juxtacellular and intracellular recordings in normal and epileptic rats with different memory abilities. CA1 pyramidal cells participate selectively during physiological events but fired together during epileptic fast ripples. We found that firing selectivity was dominated by an event- and cell-specific synaptic drive, modulated in single cells by changes in the excitatory/inhibitory ratio measured intracellularly. This mechanism collapses during pathological fast ripples to exacerbate and randomize neuronal firing. Acute administration of a use- and cell-type-dependent sodium channel blocker reduced neuronal collapse and randomness and improved recall in epileptic rats. We propose that cell-specific synaptic inputs govern firing selectivity of CA1 pyramidal cells during sharp-wave ripples. Copyright © 2017 Elsevier Inc. All rights reserved.

Formalization of the Integral Calculus in the PVS Theorem Prover

NASA Technical Reports Server (NTRS)

Butler, Ricky W.

2004-01-01

The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

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

A theorem about Hamiltonian systems

PubMed Central

Case, K. M.

1984-01-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation. PMID:16593515

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…

A uniform Tauberian theorem in dynamic games

NASA Astrophysics Data System (ADS)

Khlopin, D. V.

2018-01-01

Antagonistic dynamic games including games represented in normal form are considered. The asymptotic behaviour of value in these games is investigated as the game horizon tends to infinity (Cesàro mean) and as the discounting parameter tends to zero (Abel mean). The corresponding Abelian-Tauberian theorem is established: it is demonstrated that in both families the game value uniformly converges to the same limit, provided that at least one of the limits exists. Analogues of one-sided Tauberian theorems are obtained. An example shows that the requirements are essential even for control problems. Bibliography: 31 titles.

Limit Theorems for Dispersing Billiards with Cusps

NASA Astrophysics Data System (ADS)

Bálint, P.; Chernov, N.; Dolgopyat, D.

2011-12-01

Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting "intermittent" behavior that alternates between regular and chaotic patterns. Their statistical properties are therefore weak and delicate. They are characterized by a slow (power-law) decay of correlations, and as a result the classical central limit theorem fails. We prove that a non-classical central limit theorem holds, with a scaling factor of {sqrt{nlog n}} replacing the standard {sqrt{n}} . We also derive the respective Weak Invariance Principle, and we identify the class of observables for which the classical CLT still holds.

Computer Algebra Systems and Theorems on Real Roots of Polynomials

ERIC Educational Resources Information Center

Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.

2010-01-01

A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)

Surface-Wave Pulse Routing around Sharp Right Angles

NASA Astrophysics Data System (ADS)

Gao, Z.; Xu, H.; Gao, F.; Zhang, Y.; Luo, Y.; Zhang, B.

2018-04-01

Surface-plasmon polaritons (SPPs), or localized electromagnetic surface waves propagating on a metal-dielectric interface, are deemed promising information carriers for future subwavelength terahertz and optical photonic circuitry. However, surface waves fundamentally suffer from scattering loss when encountering sharp corners in routing and interconnection of photonic signals. Previous approaches enabling scattering-free surface-wave guidance around sharp corners are limited to either volumetric waveguide environments or extremely narrow bandwidth, being unable to guide a surface-wave pulse (SPP wave packet) on an on-chip platform. Here, in a surface-wave band-gap crystal implemented on a single metal surface, we demonstrate in time-domain routing a surface-wave pulse around multiple sharp right angles without perceptible scattering. Our work not only offers a solution to on-chip surface-wave pulse routing along an arbitrary path, but it also provides spatiotemporal information on the interplay between surface-wave pulses and sharp corners, both of which are desirable in developing high-performance large-scale integrated photonic circuits.

A Meinardus Theorem with Multiple Singularities

NASA Astrophysics Data System (ADS)

Granovsky, Boris L.; Stark, Dudley

2012-09-01

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.

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.

Generalized entropy production fluctuation theorems for quantum systems

NASA Astrophysics Data System (ADS)

Rana, Shubhashis; Lahiri, Sourabh; Jayannavar, A. M.

2013-02-01

Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for three different cases: (i) the system is evolving in isolation from its surroundings; (ii) the system being weakly coupled to a heat bath; and (iii) system in contact with reservoir using quantum Crooks fluctuation theorem. In case (iii), we build on the treatment carried out in [H. T. Quan and H. Dong, arxiv/cond-mat: 0812.4955], where a quantum trajectory has been defined as a sequence of alternating work and heat steps. The obtained entropy production fluctuation theorems retain the same form as in the classical case. The inequality of second law of thermodynamics gets modified in the presence of information. These fluctuation theorems are robust against intermediate measurements of any observable performed with respect to von Neumann projective measurements as well as weak or positive operator valued measurements.

Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

NASA Astrophysics Data System (ADS)

Li, Lei; Liu, Jian-Guo; Lu, Jianfeng

2017-10-01

We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.

Common fixed point theorems for maps under a contractive condition of integral type

NASA Astrophysics Data System (ADS)

Djoudi, A.; Merghadi, F.

2008-05-01

Two common fixed point theorems for mapping of complete metric space under a general contractive inequality of integral type and satisfying minimal commutativity conditions are proved. These results extend and improve several previous results, particularly Theorem 4 of Rhoades [B.E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 63 (2003) 4007-4013] and Theorem 4 of Sessa [S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (46) (1982) 149-153].

Investigation of micromixing by acoustically oscillated sharp-edges

PubMed Central

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

Investigation of micromixing by acoustically oscillated sharp-edges.

PubMed

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.

A Note on a Sampling Theorem for Functions over GF(q)n Domain

NASA Astrophysics Data System (ADS)

Ukita, Yoshifumi; Saito, Tomohiko; Matsushima, Toshiyasu; Hirasawa, Shigeichi

In digital signal processing, the sampling theorem states that any real valued function ƒ can be reconstructed from a sequence of values of ƒ that are discretely sampled with a frequency at least twice as high as the maximum frequency of the spectrum of ƒ. This theorem can also be applied to functions over finite domain. Then, the range of frequencies of ƒ can be expressed in more detail by using a bounded set instead of the maximum frequency. A function whose range of frequencies is confined to a bounded set is referred to as bandlimited function. And a sampling theorem for bandlimited functions over Boolean domain has been obtained. Here, it is important to obtain a sampling theorem for bandlimited functions not only over Boolean domain (GF(q)n domain) but also over GF(q)n domain, where q is a prime power and GF(q) is Galois field of order q. For example, in experimental designs, although the model can be expressed as a linear combination of the Fourier basis functions and the levels of each factor can be represented by GF(q)n, the number of levels often take a value greater than two. However, the sampling theorem for bandlimited functions over GF(q)n domain has not been obtained. On the other hand, the sampling points are closely related to the codewords of a linear code. However, the relation between the parity check matrix of a linear code and any distinct error vectors has not been obtained, although it is necessary for understanding the meaning of the sampling theorem for bandlimited functions. In this paper, we generalize the sampling theorem for bandlimited functions over Boolean domain to a sampling theorem for bandlimited functions over GF(q)n domain. We also present a theorem for the relation between the parity check matrix of a linear code and any distinct error vectors. Lastly, we clarify the relation between the sampling theorem for functions over GF(q)n domain and linear codes.

Fatal Injuries of Law Enforcement/Correctional Officers Attacked with Sharp-Edged Weapons.

PubMed

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.

Anomaly manifestation of Lieb-Schultz-Mattis theorem and topological phases

NASA Astrophysics Data System (ADS)

Cho, Gil Young; Hsieh, Chang-Tse; Ryu, Shinsei

2017-11-01

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that they can both be described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it were an internal symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly that is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gaplessness local in the parameter space.

An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

PubMed

Waller, Niels

2018-01-01

Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

Twelve years before the quantum no-cloning theorem

NASA Astrophysics Data System (ADS)

Ortigoso, Juan

2018-03-01

The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23-33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.

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.

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.)

Deriving robust noncontextuality inequalities from algebraic proofs of the Kochen-Specker theorem: the Peres-Mermin square

NASA Astrophysics Data System (ADS)

Krishna, Anirudh; Spekkens, Robert W.; Wolfe, Elie

2017-12-01

When a measurement is compatible with each of two other measurements that are incompatible with one another, these define distinct contexts for the given measurement. The Kochen-Specker theorem rules out models of quantum theory that satisfy a particular assumption of context-independence: that sharp measurements are assigned outcomes both deterministically and independently of their context. This notion of noncontextuality is not suited to a direct experimental test because realistic measurements always have some degree of unsharpness due to noise. However, a generalized notion of noncontextuality has been proposed that is applicable to any experimental procedure, including unsharp measurements, but also preparations as well, and for which a quantum no-go result still holds. According to this notion, the model need only specify a probability distribution over the outcomes of a measurement in a context-independent way, rather than specifying a particular outcome. It also implies novel constraints of context-independence for the representation of preparations. In this article, we describe a general technique for translating proofs of the Kochen-Specker theorem into inequality constraints on realistic experimental statistics, the violation of which witnesses the impossibility of a noncontextual model. We focus on algebraic state-independent proofs, using the Peres-Mermin square as our illustrative example. Our technique yields the necessary and sufficient conditions for a particular set of correlations (between the preparations and the measurements) to admit a noncontextual model. The inequalities thus derived are demonstrably robust to noise. We specify how experimental data must be processed in order to achieve a test of these inequalities. We also provide a criticism of prior proposals for experimental tests of noncontextuality based on the Peres-Mermin square.

The Heights of Mount Sharp

NASA Image and Video Library

2012-08-20

With the addition of four high-resolution Navigation Camera, or Navcam, images, taken on Aug. 18 Sol 12, Curiosity 360-degree landing-site panorama now includes the highest point on Mount Sharp visible from the rover.

One-range addition theorems for derivatives of Slater-type orbitals.

PubMed

Guseinov, Israfil

2004-06-01

Using addition theorems for STOs introduced by the author with the help of complete orthonormal sets of psi(alpha)-ETOs (Guseinov II (2003) J Mol Model 9:190-194), where alpha=1, 0, -1, -2, ..., a large number of one-range addition theorems for first and second derivatives of STOs are established. These addition theorems are especially useful for computation of multicenter-multielectron integrals over STOs that arise in the Hartree-Fock-Roothaan approximation and also in the Hylleraas function method, which play a significant role for the study of electronic structure and electron-nuclei interaction properties of atoms, molecules, and solids. The relationships obtained are valid for arbitrary quantum numbers, screening constants and location of STOs.

Some theorems and properties of multi-dimensional fractional Laplace transforms

NASA Astrophysics Data System (ADS)

Ahmood, Wasan Ajeel; Kiliçman, Adem

2016-06-01

The aim of this work is to study theorems and properties for the one-dimensional fractional Laplace transform, generalize some properties for the one-dimensional fractional Lapalce transform to be valid for the multi-dimensional fractional Lapalce transform and is to give the definition of the multi-dimensional fractional Lapalce transform. This study includes: dedicate the one-dimensional fractional Laplace transform for functions of only one independent variable with some of important theorems and properties and develop of some properties for the one-dimensional fractional Laplace transform to multi-dimensional fractional Laplace transform. Also, we obtain a fractional Laplace inversion theorem after a short survey on fractional analysis based on the modified Riemann-Liouville derivative.

Generalized Bezout's Theorem and its applications in coding theory

NASA Technical Reports Server (NTRS)

Berg, Gene A.; Feng, Gui-Liang; Rao, T. R. N.

1996-01-01

This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.

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.

A new blackhole theorem and its applications to cosmology and astrophysics

NASA Astrophysics Data System (ADS)

Wang, Shouhong; Ma, Tian

2015-04-01

We shall present a blackhole theorem and a theorem on the structure of our Universe, proved in a recently published paper, based on 1) the Einstein general theory of relativity, and 2) the cosmological principle that the universe is homogeneous and isotropic. These two theorems are rigorously proved using astrophysical dynamical models coupling fluid dynamics and general relativity based on a symmetry-breaking principle. With the new blackhole theorem, we further demonstrate that both supernovae explosion and AGN jets, as well as many astronomical phenomena including e.g. the recent reported are due to combined relativistic, magnetic and thermal effects. The radial temperature gradient causes vertical Benard type convection cells, and the relativistic viscous force (via electromagnetic, the weak and the strong interactions) gives rise to a huge explosive radial force near the Schwarzschild radius, leading e.g. to supernovae explosion and AGN jets.

An Application of the Perron-Frobenius Theorem to a Damage Model Problem.

DTIC Science & Technology

1985-04-01

RO-RI6I 20B AN APPLICATION OF THE PERRON - FROBENIUS THEOREM TO A ill I DAMAGOE MODEL PR BLEM.. (U) PITTSBURGH UNIV PA CENTER FOR I MULTIYARIATE...any copyright notation herein. * . .r * j * :h ~ ** . . .~. ~ % *~’ :. ~ ~ v 4 .% % %~ AN APPLICATION OF THE PERRON - FROBENIUS THEOREM TO A DAMAGE...University of Sheffield, U.K. S ~ Summry Using the Perron - Frobenius theorem, it is established that if’ (X,Y) is a random vector of non-negative

Markov Property of the Conformal Field Theory Vacuum and the a Theorem.

PubMed

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-06-30

We use strong subadditivity of entanglement entropy, Lorentz invariance, and the Markov property of the vacuum state of a conformal field theory to give new proof of the irreversibility of the renormalization group in d=4 space-time dimensions-the a theorem. This extends the proofs of the c and F theorems in dimensions d=2 and d=3 based on vacuum entanglement entropy, and gives a unified picture of all known irreversibility theorems in relativistic quantum field theory.

Fixed point theorems for generalized contractions in ordered metric spaces

NASA Astrophysics Data System (ADS)

O'Regan, Donal; Petrusel, Adrian

2008-05-01

The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, MEC. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petrusel, I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.

Guided discovery of the nine-point circle theorem and its proof

NASA Astrophysics Data System (ADS)

Buchbinder, Orly

2018-01-01

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through investigation in a dynamic geometry environment, and consequently prove it using a method of guided discovery. The paper concludes with a variety of suggestions for the ways in which the whole set of activities can be implemented in geometry classrooms.

A general Kastler-Kalau-Walze type theorem for manifolds with boundary

NASA Astrophysics Data System (ADS)

Wang, Jian; Wang, Yong

2016-11-01

In this paper, we establish a general Kastler-Kalau-Walze type theorem for any dimensional manifolds with boundary which generalizes the results in [Y. Wang, Lower-dimensional volumes and Kastler-Kalau-Walze type theorem for manifolds with boundary, Commun. Theor. Phys. 54 (2010) 38-42]. This solves a problem of the referee of [J. Wang and Y. Wang, A Kastler-Kalau-Walze type theorem for five-dimensional manifolds with boundary, Int. J. Geom. Meth. Mod. Phys. 12(5) (2015), Article ID: 1550064, 34 pp.], which is a general expression of the lower dimensional volumes in terms of the geometric data on the manifold.

A hierarchical generalization of the acoustic reciprocity theorem involving higher-order derivatives and interaction quantities.

PubMed

Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning

2016-10-01

An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.

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 B-field soft theorem and its unification with the graviton and dilaton

NASA Astrophysics Data System (ADS)

Di Vecchia, Paolo; Marotta, Raffaele; Mojaza, Matin

2017-10-01

In theories of Einstein gravity coupled with a dilaton and a two-form, a soft theorem for the two-form, known as the Kalb-Ramond B-field, has so far been missing. In this work we fill the gap, and in turn formulate a unified soft theorem valid for gravitons, dilatons and B-fields in any tree-level scattering amplitude involving the three massless states. The new soft theorem is fixed by means of on-shell gauge invariance and enters at the subleading order of the graviton's soft theorem. In contrast to the subsubleading soft behavior of gravitons and dilatons, we show that the soft behavior of B-fields at this order cannot be fully fixed by gauge invariance. Nevertheless, we show that it is possible to establish a gauge invariant decomposition of the amplitudes to any order in the soft expansion. We check explicitly the new soft theorem in the bosonic string and in Type II superstring theories, and furthermore demonstrate that, at the next order in the soft expansion, totally gauge invariant terms appear in both string theories which cannot be factorized into a soft theorem.

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…

The Geometric Mean Value Theorem

ERIC Educational Resources Information Center

de Camargo, André Pierro

2018-01-01

In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…

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.

Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

NASA Astrophysics Data System (ADS)

Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

2018-03-01

Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.

Fixed-point theorems for families of weakly non-expansive maps

NASA Astrophysics Data System (ADS)

Mai, Jie-Hua; Liu, Xin-He

2007-10-01

In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.

Circularly-symmetric complex normal ratio distribution for scalar transmissibility functions. Part I: Fundamentals

NASA Astrophysics Data System (ADS)

Yan, Wang-Ji; Ren, Wei-Xin

2016-12-01

Recent advances in signal processing and structural dynamics have spurred the adoption of transmissibility functions in academia and industry alike. Due to the inherent randomness of measurement and variability of environmental conditions, uncertainty impacts its applications. This study is focused on statistical inference for raw scalar transmissibility functions modeled as complex ratio random variables. The goal is achieved through companion papers. This paper (Part I) is dedicated to dealing with a formal mathematical proof. New theorems on multivariate circularly-symmetric complex normal ratio distribution are proved on the basis of principle of probabilistic transformation of continuous random vectors. The closed-form distributional formulas for multivariate ratios of correlated circularly-symmetric complex normal random variables are analytically derived. Afterwards, several properties are deduced as corollaries and lemmas to the new theorems. Monte Carlo simulation (MCS) is utilized to verify the accuracy of some representative cases. This work lays the mathematical groundwork to find probabilistic models for raw scalar transmissibility functions, which are to be expounded in detail in Part II of this study.

The impact of sharps injuries on student nurses: a systematic review.

PubMed

Hambridge, Kevin; Nichols, Andrew; Endacott, Ruth

2016-10-27

The purpose of this review was to discover the impact of sharps injuries in the student nurse population. Much is known and reported about sharps injuries in registered nurses, but there has been a lack of published evidence regarding sharps injuries within the student nurse population. A systematic review of nursing, health and psychology databases was conducted. The limits set were publications between 1980 and 2014 in the English language. Studies were identified then, following a rigorous critical and quality appraisal with validated tools, were selected for the systematic review. A total of 40 articles met the inclusion criteria, reporting studies conducted in 18 countries. Psychological and physical impacts of sharps injuries in student nurses were reported, such as fear, anxiety and depression, although these impacts were not quantified using a validated instrument. The impact of sharps injuries can be severe, both psychological and physical. This systematic review shows that further research is needed into this, especially in under-researched areas such as the UK, to establish the impact of sharps injuries within this population. Further research would also aid the education and prevention of this harmful problem. The review also emphasises the psychological issues relating to sharps injuries, the impact these can have on individuals and the support and counselling that student nurses require after injury. These findings highlight the potential psychological issues that can result from sharps injuries in this population.

Trace theorem for quasi-Fuchsian groups

NASA Astrophysics Data System (ADS)

Connes, A.; Sukochev, F. A.; Zanin, D. V.

2017-10-01

We complete the proof of the Trace Theorem in the quantized calculus for quasi-Fuchsian groups which was stated and sketched, but not fully proved, on pp. 322-325 of the book Noncommutative geometry of the first author. Bibliography: 34 titles.

End-point sharpness in thermometric titrimetry.

PubMed

Tyrrell, H J

1967-07-01

It is shown that the sharpness of an end-point in a thermometric titration where the simple reaction A + B right harpoon over left harpoon AB takes place, depends on Kc(A') where K is the equilibrium constant for the reaction, and c(A') is the total concentration of the titrand (A) in the reaction mixture. The end-point is sharp if, (i) the enthalpy change in the reaction is not negligible, and (ii) Kc(A') > 10(3). This shows that it should, for example, be possible to titrate 0.1 M acid, pK(A) = 10, using a thennometric end-point. Some aspects of thermometric titrimetry when Kc(A') < 10(3) are also considered.

The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum

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

Alpay, Daniel, E-mail: dany@math.bgu.ac.il; Kimsey, David P., E-mail: dpkimsey@gmail.com; Colombo, Fabrizio, E-mail: fabrizio.colombo@polimi.it

In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The lack of a suitable notion ofmore » spectrum was a major obstruction to fully understand the spectral theorem for quaternionic normal operators. A prime motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti-self adjoint quaternionic operators which play a crucial role in the quaternionic quantum mechanics.« less

Refinement of Representation Theorems for Context-Free Languages

NASA Astrophysics Data System (ADS)

Fujioka, Kaoru

In this paper, we obtain some refinement of representation theorems for context-free languages by using Dyck languages, insertion systems, strictly locally testable languages, and morphisms. For instance, we improved the Chomsky-Schützenberger representation theorem and show that each context-free language L can be represented in the form L = h (D ∩ R), where D is a Dyck language, R is a strictly 3-testable language, and h is a morphism. A similar representation for context-free languages can be obtained, using insertion systems of weight (3, 0) and strictly 4-testable languages.

Don Sharp Home Improvements Information Sheet

EPA Pesticide Factsheets

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.

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.

Reduction theorems for optimal unambiguous state discrimination of density matrices

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

Raynal, Philippe; Luetkenhaus, Norbert; Enk, Steven J. van

2003-08-01

We present reduction theorems for the problem of optimal unambiguous state discrimination of two general density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank n and are described in a Hilbert space of dimensions 2n. We also show how to use the reduction theorems to discriminate unambiguously between N mixed states (N{>=}2)

Quantum no-singularity theorem from geometric flows

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

Noether’s second theorem and Ward identities for gauge symmetries

DOE PAGES

Avery, Steven G.; Schwab, Burkhard U. W.

2016-02-04

Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s secondmore » theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.« less

More on Weinberg's no-go theorem in quantum gravity

NASA Astrophysics Data System (ADS)

Nagahama, Munehiro; Oda, Ichiro

2018-05-01

We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.

Quantum Theory of Jaynes' Principle, Bayes' Theorem, and Information

NASA Astrophysics Data System (ADS)

Haken, Hermann

2014-12-01

After a reminder of Jaynes' maximum entropy principle and of my quantum theoretical extension, I consider two coupled quantum systems A,B and formulate a quantum version of Bayes' theorem. The application of Feynman's disentangling theorem allows me to calculate the conditional density matrix ρ (A|B) , if system A is an oscillator (or a set of them), linearly coupled to an arbitrary quantum system B. Expectation values can simply be calculated by means of the normalization factor of ρ (A|B) that is derived.

General self-tuning solutions and no-go theorem

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

Förste, Stefan; Kim, Jihn E.; Lee, Hyun Min, E-mail: forste@th.physik.uni-bonn.de, E-mail: jihnekim@gmail.com, E-mail: hyun.min.lee@kias.re.kr

2013-03-01

We consider brane world models with one extra dimension. In the bulk there is in addition to gravity a three form gauge potential or equivalently a scalar (by generalisation of electric magnetic duality). We find classical solutions for which the 4d effective cosmological constant is adjusted by choice of integration constants. No go theorems for such self-tuning mechanism are circumvented by unorthodox Lagrangians for the three form respectively the scalar. It is argued that the corresponding effective 4d theory always includes tachyonic Kaluza-Klein excitations or ghosts. Known no go theorems are extended to a general class of models with unorthodoxmore » Lagrangians.« less

Bell's Theorem and Einstein's "Spooky Actions" from a Simple Thought Experiment

ERIC Educational Resources Information Center

Kuttner, Fred; Rosenblum, Bruce

2010-01-01

In 1964 John Bell proved a theorem allowing the experimental test of whether what Einstein derided as "spooky actions at a distance" actually exist. We will see that they "do". Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at "any" level. And a simple, semi-classical derivation of…

A Bayesian perspective on Markovian dynamics and the fluctuation theorem

NASA Astrophysics Data System (ADS)

Virgo, Nathaniel

2013-08-01

One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.

Model Checking Failed Conjectures in Theorem Proving: A Case Study

NASA Technical Reports Server (NTRS)

Pike, Lee; Miner, Paul; Torres-Pomales, Wilfredo

2004-01-01

Interactive mechanical theorem proving can provide high assurance of correct design, but it can also be a slow iterative process. Much time is spent determining why a proof of a conjecture is not forthcoming. In some cases, the conjecture is false and in others, the attempted proof is insufficient. In this case study, we use the SAL family of model checkers to generate a concrete counterexample to an unproven conjecture specified in the mechanical theorem prover, PVS. The focus of our case study is the ROBUS Interactive Consistency Protocol. We combine the use of a mechanical theorem prover and a model checker to expose a subtle flaw in the protocol that occurs under a particular scenario of faults and processor states. Uncovering the flaw allows us to mend the protocol and complete its general verification in PVS.

Numerical analysis of mixing by sharp-edge-based acoustofluidic micromixer

NASA Astrophysics Data System (ADS)

Nama, Nitesh; Huang, Po-Hsun; Jun Huang, Tony; Costanzo, Francesco

2015-11-01

Recently, acoustically oscillated sharp-edges have been employed to realize rapid and homogeneous mixing at microscales (Huang, Lab on a Chip, 13, 2013). Here, we present a numerical model, qualitatively validated by experimental results, to analyze the acoustic mixing inside a sharp-edge-based micromixer. We extend our previous numerical model (Nama, Lab on a Chip, 14, 2014) to combine the Generalized Lagrangian Mean (GLM) theory with the convection-diffusion equation, while also allowing for the presence of a background flow as observed in a typical sharp-edge-based micromixer. We employ a perturbation approach to divide the flow variables into zeroth-, first- and second-order fields which are successively solved to obtain the Lagrangian mean velocity. The Langrangian mean velocity and the background flow velocity are further employed with the convection-diffusion equation to obtain the concentration profile. We characterize the effects of various operational and geometrical parameters to suggest potential design changes for improving the mixing performance of the sharp-edge-based micromixer. Lastly, we investigate the possibility of generation of a spatio-temporally controllable concentration gradient by placing sharp-edge structures inside the microchannel.

Enter the reverend: introduction to and application of Bayes' theorem in clinical ophthalmology.

PubMed

Thomas, Ravi; Mengersen, Kerrie; Parikh, Rajul S; Walland, Mark J; Muliyil, Jayprakash

2011-12-01

Ophthalmic practice utilizes numerous diagnostic tests, some of which are used to screen for disease. Interpretation of test results and many clinical management issues are actually problems in inverse probability that can be solved using Bayes' theorem. Use two-by-two tables to understand Bayes' theorem and apply it to clinical examples. Specific examples of the utility of Bayes' theorem in diagnosis and management. Two-by-two tables are used to introduce concepts and understand the theorem. The application in interpretation of diagnostic tests is explained. Clinical examples demonstrate its potential use in making management decisions. Positive predictive value and conditional probability. The theorem demonstrates the futility of testing when prior probability of disease is low. Application to untreated ocular hypertension demonstrates that the estimate of glaucomatous optic neuropathy is similar to that obtained from the Ocular Hypertension Treatment Study. Similar calculations are used to predict the risk of acute angle closure in a primary angle closure suspect, the risk of pupillary block in a diabetic undergoing cataract surgery, and the probability that an observed decrease in intraocular pressure is due to the medication that has been started. The examples demonstrate how data required for management can at times be easily obtained from available information. Knowledge of Bayes' theorem helps in interpreting test results and supports the clinical teaching that testing for conditions with a low prevalence has a poor predictive value. In some clinical situations Bayes' theorem can be used to calculate vital data required for patient management. © 2011 The Authors. Clinical and Experimental Ophthalmology © 2011 Royal Australian and New Zealand College of Ophthalmologists.

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 Here is the set of ergodic f-invariant measures, and for is the measure-theoretic entropy of f, is the largest Lyapunov exponent of the cocycle over f generated by , and is the smallest Lyapunov exponent of the differential of f.

Subleading soft graviton theorem for loop amplitudes

NASA Astrophysics Data System (ADS)

Sen, Ashoke

2017-11-01

Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.

Experimental Test of the Differential Fluctuation Theorem and a Generalized Jarzynski Equality for Arbitrary Initial States

NASA Astrophysics Data System (ADS)

Hoang, Thai M.; Pan, Rui; Ahn, Jonghoon; Bang, Jaehoon; Quan, H. T.; Li, Tongcang

2018-02-01

Nonequilibrium processes of small systems such as molecular machines are ubiquitous in biology, chemistry, and physics but are often challenging to comprehend. In the past two decades, several exact thermodynamic relations of nonequilibrium processes, collectively known as fluctuation theorems, have been discovered and provided critical insights. These fluctuation theorems are generalizations of the second law and can be unified by a differential fluctuation theorem. Here we perform the first experimental test of the differential fluctuation theorem using an optically levitated nanosphere in both underdamped and overdamped regimes and in both spatial and velocity spaces. We also test several theorems that can be obtained from it directly, including a generalized Jarzynski equality that is valid for arbitrary initial states, and the Hummer-Szabo relation. Our study experimentally verifies these fundamental theorems and initiates the experimental study of stochastic energetics with the instantaneous velocity measurement.

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.

[Overview of sharps injuries among health-care workers].

PubMed

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 Inside Gale Crater, Mars

NASA Image and Video Library

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.

Quantum regression theorem and non-Markovianity of quantum dynamics

NASA Astrophysics Data System (ADS)

Guarnieri, Giacomo; Smirne, Andrea; Vacchini, Bassano

2014-08-01

We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.

Sample Skewness as a Statistical Measurement of Neuronal Tuning Sharpness

PubMed Central

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

Entanglement, space-time and the Mayer-Vietoris theorem

NASA Astrophysics Data System (ADS)

Patrascu, Andrei T.

2017-06-01

Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality. While supported by our present intuition, a proof is far from obvious. In this article I present a first step towards such a proof, originating in what is known to algebraic topologists as the Mayer-Vietoris theorem. The main result of this work is the re-interpretation of the various morphisms arising when the Mayer-Vietoris theorem is used to assemble a torus-like topology from more basic subspaces on the torus in terms of quantum information theory resulting in a quantum entangler gate (Hadamard and c-NOT).

Bell - Kochen - Specker theorem for any finite dimension ?

NASA Astrophysics Data System (ADS)

Cabello, Adán; García-Alcaine, Guillermo

1996-03-01

The Bell - Kochen - Specker theorem against non-contextual hidden variables can be proved by constructing a finite set of `totally non-colourable' directions, as Kochen and Specker did in a Hilbert space of dimension n = 3. We generalize Kochen and Specker's set to Hilbert spaces of any finite dimension 0305-4470/29/5/016/img2, in a three-step process that shows the relationship between different kinds of proofs (`continuum', `probabilistic', `state-specific' and `state-independent') of the Bell - Kochen - Specker theorem. At the same time, this construction of a totally non-colourable set of directions in any dimension explicitly solves the question raised by Zimba and Penrose about the existence of such a set for n = 5.

Volumes of critical bubbles from the nucleation theorem

NASA Astrophysics Data System (ADS)

Wilemski, Gerald

2006-09-01

A corollary of the nucleation theorem due to Kashchiev [Nucleation: Basic Theory with Applications (Butterworth-Heinemann, Oxford, 2000)] allows the volume V* of a critical bubble to be determined from nucleation rate measurements. The original derivation was limited to one-component, ideal gas bubbles with a vapor density much smaller than that of the ambient liquid. Here, an exact result is found for multicomponent, nonideal gas bubbles. Provided a weak density inequality holds, this result reduces to Kashchiev's simple form which thus has a much broader range of applicability than originally expected. Limited applications to droplets are also mentioned, and the utility of the pT,x form of the nucleation theorem as a sum rule is noted.

Structure theorems and the dynamics of nitrogen catabolite repression in yeast

PubMed Central

Boczko, Erik M.; Cooper, Terrance G.; Gedeon, Tomas; Mischaikow, Konstantin; Murdock, Deborah G.; Pratap, Siddharth; Wells, K. Sam

2005-01-01

By using current biological understanding, a conceptually simple, but mathematically complex, model is proposed for the dynamics of the gene circuit responsible for regulating nitrogen catabolite repression (NCR) in yeast. A variety of mathematical “structure” theorems are described that allow one to determine the asymptotic dynamics of complicated systems under very weak hypotheses. It is shown that these theorems apply to several subcircuits of the full NCR circuit, most importantly to the URE2–GLN3 subcircuit that is independent of the other constituents but governs the switching behavior of the full NCR circuit under changes in nitrogen source. Under hypotheses that are fully consistent with biological data, it is proven that the dynamics of this subcircuit is simple periodic behavior in synchrony with the cell cycle. Although the current mathematical structure theorems do not apply to the full NCR circuit, extensive simulations suggest that the dynamics is constrained in much the same way as that of the URE2–GLN3 subcircuit. This finding leads to the proposal that mathematicians study genetic circuits to find new geometries for which structure theorems may exist. PMID:15814615

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.

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.

A Polarimetric Extension of the van Cittert-Zernike Theorem for Use with Microwave Interferometers

NASA Technical Reports Server (NTRS)

Piepmeier, J. R.; Simon, N. K.

2004-01-01

The van Cittert-Zernike theorem describes the Fourier-transform relationship between an extended source and its visibility function. Developments in classical optics texts use scalar field formulations for the theorem. Here, we develop a polarimetric extension to the van Cittert-Zernike theorem with applications to passive microwave Earth remote sensing. The development provides insight into the mechanics of two-dimensional interferometric imaging, particularly the effects of polarization basis differences between the scene and the observer.

Image sharpness assessment based on wavelet energy of edge area

NASA Astrophysics Data System (ADS)

Li, Jin; Zhang, Hong; Zhang, Lei; Yang, Yifan; He, Lei; Sun, Mingui

2018-04-01

Image quality assessment is needed in multiple image processing areas and blur is one of the key reasons of image deterioration. Although great full-reference image quality assessment metrics have been proposed in the past few years, no-reference method is still an area of current research. Facing this problem, this paper proposes a no-reference sharpness assessment method based on wavelet transformation which focuses on the edge area of image. Based on two simple characteristics of human vision system, weights are introduced to calculate weighted log-energy of each wavelet sub band. The final score is given by the ratio of high-frequency energy to the total energy. The algorithm is tested on multiple databases. Comparing with several state-of-the-art metrics, proposed algorithm has better performance and less runtime consumption.

Grand Canyon Similar to Mount Sharp

NASA Image and Video Library

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.

Mount Sharp Panorama in Raw Colors

NASA Image and Video Library

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.

First Sampling Hole in Mount Sharp

NASA Image and Video Library

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.

Testing subleading multiple soft graviton theorem for CHY prescription

NASA Astrophysics Data System (ADS)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2018-01-01

In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.

Analytic solution and pulse area theorem for three-level atoms

NASA Astrophysics Data System (ADS)

Shchedrin, Gavriil; O'Brien, Chris; Rostovtsev, Yuri; Scully, Marlan O.

2015-12-01

We report an analytic solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our analytic result and the numerical simulations. We use our solution to derive a pulse area theorem for three-level V and Λ systems without making the rotating wave approximation. Formulated as an energy conservation law, this pulse area theorem can be used to understand pulse propagation through three-level media.

Insulin stimulates the expression of the SHARP-1 gene via multiple signaling pathways.

PubMed

Takagi, K; Asano, K; Haneishi, A; Ono, M; Komatsu, Y; Yamamoto, T; Tanaka, T; Ueno, H; Ogawa, W; Tomita, K; Noguchi, T; Yamada, K

2014-06-01

The rat enhancer of split- and hairy-related protein-1 (SHARP-1) is a basic helix-loop-helix transcription factor. An issue of whether SHARP-1 is an insulin-inducible transcription factor was examined. Insulin rapidly increased the level of SHARP-1 mRNA both in vivo and in vitro. Then, signaling pathways involved with the increase of SHARP-1 mRNA by insulin were determined in H4IIE rat hepatoma cells. Pretreatments with LY294002, wortmannin, and staurosporine completely blocked the induction effect, suggesting the involvement of both phosphoinositide 3-kinase (PI 3-K) and protein kinase C (PKC) pathways. In fact, overexpression of a dominant negative form of atypical protein kinase C lambda (aPKCλ) significantly decreased the induction of the SHARP-1 mRNA. In addition, inhibitors for the small GTPase Rac or Jun N-terminal kinase (JNK) also blocked the induction of SHARP-1 mRNA by insulin. Overexpression of a dominant negative form of Rac1 prevented the activation by insulin. Furthermore, actinomycin D and cycloheximide completely blocked the induction of SHARP-1 mRNA by insulin. Finally, when a SHARP-1 expression plasmid was transiently transfected with various reporter plasmids into H4IIE cells, the promoter activity of PEPCK reporter plasmid was specifically decreased. Thus, we conclude that insulin induces the SHARP-1 gene expression at the transcription level via a both PI 3-K/aPKCλ/JNK- and a PI 3-K/Rac/JNK-signaling pathway; protein synthesis is required for this induction; and that SHARP-1 is a potential repressor of the PEPCK gene expression. © Georg Thieme Verlag KG Stuttgart · New York.

SHARPs - A Near-Real-Time Space Weather Data Product from HMI

NASA Astrophysics Data System (ADS)

Bobra, M.; Turmon, M.; Baldner, C.; Sun, X.; Hoeksema, J. T.

2012-12-01

A data product from the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO), called Space-weather HMI Active Region Patches (SHARPs), is now available through the SDO Joint Science Operations Center (JSOC) and the Virtual Solar Observatory. SHARPs are magnetically active regions identified on the solar disk and tracked automatically in time. SHARP data are processed within a few hours of the observation time. The SHARP data series contains active region-sized disambiguated vector magnetic field data in both Lambert Cylindrical Equal-Area and CCD coordinates on a 12 minute cadence. The series also provides simultaneous HMI maps of the line-of-sight magnetic field, continuum intensity, and velocity on the same ~0.5 arc-second pixel grid. In addition, the SHARP data series provides space weather quantities computed on the inverted, disambiguated, and remapped data. The values for each tracked region are computed and updated in near real time. We present space weather results for several X-class flares; furthermore, we compare said space weather quantities with helioseismic quantities calculated using ring-diagram analysis.

Pythagoras Theorem and Relativistic Kinematics

NASA Astrophysics Data System (ADS)

Mulaj, Zenun; Dhoqina, Polikron

2010-01-01

In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.

The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project

ERIC Educational Resources Information Center

Robiette, Alan G.

1975-01-01

Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)

A comprehensive numerical analysis of background phase correction with V-SHARP.

PubMed

Özbay, Pinar Senay; Deistung, Andreas; Feng, Xiang; Nanz, Daniel; Reichenbach, Jürgen Rainer; Schweser, Ferdinand

2017-04-01

Sophisticated harmonic artifact reduction for phase data (SHARP) is a method to remove background field contributions in MRI phase images, which is an essential processing step for quantitative susceptibility mapping (QSM). To perform SHARP, a spherical kernel radius and a regularization parameter need to be defined. In this study, we carried out an extensive analysis of the effect of these two parameters on the corrected phase images and on the reconstructed susceptibility maps. As a result of the dependence of the parameters on acquisition and processing characteristics, we propose a new SHARP scheme with generalized parameters. The new SHARP scheme uses a high-pass filtering approach to define the regularization parameter. We employed the variable-kernel SHARP (V-SHARP) approach, using different maximum radii (R m ) between 1 and 15 mm and varying regularization parameters (f) in a numerical brain model. The local root-mean-square error (RMSE) between the ground-truth, background-corrected field map and the results from SHARP decreased towards the center of the brain. RMSE of susceptibility maps calculated with a spatial domain algorithm was smallest for R m between 6 and 10 mm and f between 0 and 0.01 mm -1 , and for maps calculated with a Fourier domain algorithm for R m between 10 and 15 mm and f between 0 and 0.0091 mm -1 . We demonstrated and confirmed the new parameter scheme in vivo. The novel regularization scheme allows the use of the same regularization parameter irrespective of other imaging parameters, such as image resolution. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

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…

Surface-enhanced Raman scattering on periodic metal nanotips with tunable sharpness.

PubMed

Linn, Nicholas C; Sun, Chih-Hung; Arya, Ajay; Jiang, Peng; Jiang, Bin

2009-06-03

This paper reports on a scalable bottom-up technology for producing periodic gold nanotips with tunable sharpness as surface-enhanced Raman scattering (SERS) substrates. Inverted silicon pyramidal pits, which are templated from non-close-packed colloidal crystals prepared by a spin-coating technology, are used as structural templates to replicate arrays of polymer nanopyramids with nanoscale sharp tips. The deposition of a thin layer of gold on the polymer nanopyramids leads to the formation of SERS-active substrates with a high enhancement factor (up to 10(8)). The thickness of the deposited metal determines the sharpness of the nanotips and the resulting Raman enhancement factor. Finite-element electromagnetic modeling shows that the nanotips can significantly enhance the local electromagnetic field and the sharpness of nanotips greatly affects the SERS enhancement.

Electrostatic Hellmann-Feynman theorem applied to long-range interatomic forces - The hydrogen molecule.

NASA Technical Reports Server (NTRS)

Steiner, E.

1973-01-01

The use of the electrostatic Hellmann-Feynman theorem for the calculation of the leading term in the 1/R expansion of the force of interaction between two well-separated hydrogen atoms is discussed. Previous work has suggested that whereas this term is determined wholly by the first-order wavefunction when calculated by perturbation theory, the use of the Hellmann-Feynman theorem apparently requires the wavefunction through second order. It is shown how the two results may be reconciled and that the Hellmann-Feynman theorem may be reformulated in such a way that only the first-order wavefunction is required.

Explorations of the Gauss-Lucas Theorem

ERIC Educational Resources Information Center

Brilleslyper, Michael A.; Schaubroeck, Beth

2017-01-01

The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows…

Testing ground for fluctuation theorems: The one-dimensional Ising model

NASA Astrophysics Data System (ADS)

Lemos, C. G. O.; Santos, M.; Ferreira, A. L.; Figueiredo, W.

2018-04-01

In this paper we determine the nonequilibrium magnetic work performed on a Ising model and relate it to the fluctuation theorem derived some years ago by Jarzynski. The basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent, in a finite time, through nonequilibrium paths between the same thermodynamic states. We test the validity of this theorem by considering the one-dimensional Ising model where the free energy is exactly determined as a function of temperature and magnetic field. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system. We have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the Crooks relation are equally correct. We also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables. We have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process, while it decreases in the case of the forward process. The lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field.

Generalized chaos synchronization theorems for bidirectional differential equations and discrete systems with applications

NASA Astrophysics Data System (ADS)

Ji, Ye; Liu, Ting; Min, Lequan

2008-05-01

Two constructive generalized chaos synchronization (GCS) theorems for bidirectional differential equations and discrete systems are introduced. Using the two theorems, one can construct new chaos systems to make the system variables be in GCS. Five examples are presented to illustrate the effectiveness of the theoretical results.

Objective assessment of knife sharpness over a working day cutting meat.

PubMed

Savescu, Adriana; Cuny-Guerrier, Aude; Wild, Pascal; Reno, Gilles; Aublet-Cuvelier, Agnès; Claudon, Laurent

2018-04-01

Knife sharpness is one of multiple factors involved in musculoskeletal disorders in industrial meat cutting. The aim of this study was to objectively evaluate, in real working situations, how knife sharpness changed over a working day cutting meat, and to analyse the impact of sharpening, steeling and meat-cutting activities on these variations. Twenty-two meat-cutting workers from three different companies participated in the study. The methods included measurements of knife sharpness in relation to real work situations and consideration of the way meat-cutting and sharpening operations were organised. Results showed that the type of meat-cutting activities, the steeling strategy adopted by the worker, including the types of tool used, and the overall organisation of the sharpening task all had a significant influence on how knife sharpness evolved over a 2-h period and over an entire working day. To improve MSD prevention, sharpening and steeling operations should not be considered as independent activities, but taken into account as a continuity of working actions. Appropriate assessment of knife sharpness by meat cutters affects how they organise meat-cutting and sharpening tasks. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

Sharp Dissection versus Electrocautery for Radial Artery Harvesting

PubMed Central

Marzban, Mehrab; Arya, Reza; Mandegar, Mohammad Hossein; Karimi, Abbas Ali; Abbasi, Kiomars; Movahed, Namvar; Abbasi, Seyed Hesameddin

2006-01-01

Radial arteries have been increasingly used during the last decade as conduits for coronary artery revascularization. Although various harvesting techniques have been described, there has been little comparative study of arterial damage and patency. A radial artery graft was used in 44 consecutive patients, who were randomly divided into 2 groups. In the 1st group, the radial artery was harvested by sharp dissection and in the 2nd, by electrocautery. These groups were compared with regard to radial artery free flow, harvest time, number of clips used, complications, and endothelial damage. Radial artery free flow before and after intraluminal administration of papaverine was significantly greater in the electrocautery group (84.3 ± 50.7 mL/min and 109.7 ± 68.5 mL/min) than in the sharp-dissection group (52.9 ± 18.3 mL/min and 69.6 ± 28.2 mL/ min) (P =0.003). Harvesting time by electrocautery was significantly shorter (25.4 ± 4.3 min vs 34.4 ± 5.9 min) (P =0.0001). Electrocautery consumed an average of 9.76 clips, versus 22.45 clips consumed by sharp dissection. The 2 groups were not different regarding postoperative complications, except for 3 cases of temporary paresthesia of the thumb in the electrocautery group; histopathologic examination found no endothelial damage. We conclude that radial artery harvesting by electrocautery is faster and more economical than harvesting by sharp dissection and is associated with better intraoperative flow and good preservation of endothelial integrity. PMID:16572861

A Fascinating Application of Steiner's Theorem for Trapezium: Geometric Constructions Using Straightedge Alone

ERIC Educational Resources Information Center

Stupel, Moshe; Ben-Chaim, David

2013-01-01

Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this…

Short distance modification of the quantum virial theorem

NASA Astrophysics Data System (ADS)

Zhao, Qin; Faizal, Mir; Zaz, Zaid

2017-07-01

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

Generalized Friedland's theorem for C0-semigroups

NASA Astrophysics Data System (ADS)

Cichon, Dariusz; Jung, Il Bong; Stochel, Jan

2008-07-01

Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.

On Viviani's Theorem and Its Extensions

ERIC Educational Resources Information Center

Abboud, Elias

2010-01-01

Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…

Fixed Point Theorems for Hybrid Mappings

PubMed Central

Kamran, Tayyab; Karapinar, Erdal

2015-01-01

We obtain some fixed point theorems for two pairs of hybrid mappings using hybrid tangential property and quadratic type contractive condition. Our results generalize some results by Babu and Alemayehu and those contained therein. In the sequel, we introduce a new notion to generalize occasionally weak compatibility. Moreover, two concrete examples are established to illuminate the generality of our results. PMID:25629089

Representations of the language recognition problem for a theorem prover

NASA Technical Reports Server (NTRS)

Minker, J.; Vanderbrug, G. J.

1972-01-01

Two representations of the language recognition problem for a theorem prover in first order logic are presented and contrasted. One of the representations is based on the familiar method of generating sentential forms of the language, and the other is based on the Cocke parsing algorithm. An augmented theorem prover is described which permits recognition of recursive languages. The state-transformation method developed by Cordell Green to construct problem solutions in resolution-based systems can be used to obtain the parse tree. In particular, the end-order traversal of the parse tree is derived in one of the representations. An inference system, termed the cycle inference system, is defined which makes it possible for the theorem prover to model the method on which the representation is based. The general applicability of the cycle inference system to state space problems is discussed. Given an unsatisfiable set S, where each clause has at most one positive literal, it is shown that there exists an input proof. The clauses for the two representations satisfy these conditions, as do many state space problems.

Audit of sharp weapon deaths in metropolis of Karachi--an autopsy based study.

PubMed

Mirza, Farhat Hussain; Hasan, Qudsia; Memon, Akhtar Amin; Adil, Syeda Ezz-e-Rukhshan

2010-01-01

Sharp weapons are one of the most violent and abhorrent means of deaths. This study assesses the frequency of sharp weapon deaths in Karachi. This was a cross sectional study, and involves the deaths by sharp weapons autopsied in Karachi during Mar 2008-Feb 2009. This study reports that the frequency of sharp weapon deaths in Karachi is similar to some other studies conducted in different regions of Pakistan, yet it is very high as the population of Karachi is way more than any other metropolis of Pakistan. Our study reported that out of 2090 medico-legal deaths in Karachi during the study period, 91 deaths were due to sharp weapons, including 73 (80.2%) males and 18 (19.8%) females. 100% of the deaths were homicides, so none were suicides. Deaths were more frequent in age group ranging from 20-39 years (59.3%). Sharp weapon deaths continue to be a means of quite a number of deaths in Karachi. Such violence depicts intolerant and frustrated nature of the citizens.

A General No-Cloning Theorem for an infinite Multiverse

NASA Astrophysics Data System (ADS)

Gauthier, Yvon

2013-10-01

In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.

Stochastic thermodynamics, fluctuation theorems and molecular machines.

PubMed

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.

Reasoning by analogy as an aid to heuristic theorem proving.

NASA Technical Reports Server (NTRS)

Kling, R. E.

1972-01-01

When heuristic problem-solving programs are faced with large data bases that contain numbers of facts far in excess of those needed to solve any particular problem, their performance rapidly deteriorates. In this paper, the correspondence between a new unsolved problem and a previously solved analogous problem is computed and invoked to tailor large data bases to manageable sizes. This paper outlines the design of an algorithm for generating and exploiting analogies between theorems posed to a resolution-logic system. These algorithms are believed to be the first computationally feasible development of reasoning by analogy to be applied to heuristic theorem proving.

SHARP: A multi-mission AI system for spacecraft telemetry monitoring and diagnosis

NASA Technical Reports Server (NTRS)

Lawson, Denise L.; James, Mark L.

1989-01-01

The Spacecraft Health Automated Reasoning Prototype (SHARP) is a system designed to demonstrate automated health and status analysis for multi-mission spacecraft and ground data systems operations. Telecommunications link analysis of the Voyager II spacecraft is the initial focus for the SHARP system demonstration which will occur during Voyager's encounter with the planet Neptune in August, 1989, in parallel with real-time Voyager operations. The SHARP system combines conventional computer science methodologies with artificial intelligence techniques to produce an effective method for detecting and analyzing potential spacecraft and ground systems problems. The system performs real-time analysis of spacecraft and other related telemetry, and is also capable of examining data in historical context. A brief introduction is given to the spacecraft and ground systems monitoring process at the Jet Propulsion Laboratory. The current method of operation for monitoring the Voyager Telecommunications subsystem is described, and the difficulties associated with the existing technology are highlighted. The approach taken in the SHARP system to overcome the current limitations is also described, as well as both the conventional and artificial intelligence solutions developed in SHARP.

Heuristic analogy in Ars Conjectandi: From Archimedes' De Circuli Dimensione to Bernoulli's theorem.

PubMed

Campos, Daniel G

2018-02-01

This article investigates the way in which Jacob Bernoulli proved the main mathematical theorem that undergirds his art of conjecturing-the theorem that founded, historically, the field of mathematical probability. It aims to contribute a perspective into the question of problem-solving methods in mathematics while also contributing to the comprehension of the historical development of mathematical probability. It argues that Bernoulli proved his theorem by a process of mathematical experimentation in which the central heuristic strategy was analogy. In this context, the analogy functioned as an experimental hypothesis. The article expounds, first, Bernoulli's reasoning for proving his theorem, describing it as a process of experimentation in which hypothesis-making is crucial. Next, it investigates the analogy between his reasoning and Archimedes' approximation of the value of π, by clarifying both Archimedes' own experimental approach to the said approximation and its heuristic influence on Bernoulli's problem-solving strategy. The discussion includes some general considerations about analogy as a heuristic technique to make experimental hypotheses in mathematics. Copyright © 2018 Elsevier Ltd. All rights reserved.

A Formally-Verified Decision Procedure for Univariate Polynomial Computation Based on Sturm's Theorem

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony J.; Munoz, Cesar A.

2014-01-01

Sturm's Theorem is a well-known result in real algebraic geometry that provides a function that computes the number of roots of a univariate polynomial in a semiopen interval. This paper presents a formalization of this theorem in the PVS theorem prover, as well as a decision procedure that checks whether a polynomial is always positive, nonnegative, nonzero, negative, or nonpositive on any input interval. The soundness and completeness of the decision procedure is proven in PVS. The procedure and its correctness properties enable the implementation of a PVS strategy for automatically proving existential and universal univariate polynomial inequalities. Since the decision procedure is formally verified in PVS, the soundness of the strategy depends solely on the internal logic of PVS rather than on an external oracle. The procedure itself uses a combination of Sturm's Theorem, an interval bisection procedure, and the fact that a polynomial with exactly one root in a bounded interval is always nonnegative on that interval if and only if it is nonnegative at both endpoints.

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

NASA Astrophysics Data System (ADS)

Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

2018-04-01

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem.

PubMed

Altürk, Ahmet

2016-01-01

Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.

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.

Learning-assisted theorem proving with millions of lemmas☆

PubMed Central

Kaliszyk, Cezary; Urban, Josef

2015-01-01

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck. PMID:26525678

Averages of ratios of the Riemann zeta-function and correlations of divisor sums

NASA Astrophysics Data System (ADS)

Conrey, Brian; Keating, Jonathan P.

2017-10-01

Nonlinearity has published articles containing a significant number-theoretic component since the journal was first established. We examine one thread, concerning the statistics of the zeros of the Riemann zeta function. We extend this by establishing a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of Möbius and divisor functions. Specifically, we prove that the ratios conjecture and an arithmetic correlations conjecture imply the same result. This provides new support for the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe. Our main theorem generalises a recent calculation pertaining to the special case of two-over-two ratios.

Injuries caused by sharp instruments among healthcare workers--international and Polish perspectives.

PubMed

Goniewicz, Mariusz; Włoszczak-Szubzda, Anna; Niemcewicz, Marcin; Witt, Magdalena; Marciniak-Niemcewicz, Anna; Jarosz, Mirosław Jerzy

2012-01-01

Health care workers (HCW) worldwide are especially exposed to injury by sharp instruments in the course of their duty. The most often executed procedures with injury risk are: intramuscular or subcutaneous injection (22%), taking blood samples, or during intravenous cannulation (20%), and repeatedly replacing the cap on an already used needle (30%). Even a minor sharp injury with only a small loss of blood carries the risk of transfer of over 20 pathogens: Hepatitis B Virus (HBV), Hepatitis C Virus (HCV), HIV/AIDS virus, malaria, syphilis, tuberculosis, brucellosis, herpes virus and diphtheria. The World Health Organization (WHO) estimates that more than two million health care workers experience the stressful event of a percutaneous injury with a contaminated sharp object each year (25-90% of them, however, remain unreported). These exposures result in about 16,000 infections with HCV, 66,000 with HBV and about 1,000 (200-5000) with HIV, which lead to about 1,100 deaths or significant disability. Exposures to sharp injuries and their consequences are highly preventable through simple interventions, such as HBV vaccination, education and providing containers for sharp instruments. Specific guidelines, similar to the American Occupational Safety and Health Administration (OSHA) regulations that have lowered by up to 88% of needle stabbing incidents, should be introduced by the European Union (EU) and other countries. The results of a review of reports leads to the following conclusions: 1) elaboration and implementation of new State regulations, especially in EU countries and in countries where such regulations do not exist; 2) the training of health care personnel should always be undertaken for new employees, and periodically for those already employed; 3) periodical control by appointed inspectors of knowledge of procedures for the prevention of injuries by sharp instruments among health care workers; 4) introducing and training in the use of equipment, which can

Migdal's theorem and electron-phonon vertex corrections in Dirac materials

NASA Astrophysics Data System (ADS)

Roy, Bitan; Sau, Jay D.; Das Sarma, S.

2014-04-01

Migdal's theorem plays a central role in the physics of electron-phonon interactions in metals and semiconductors, and has been extensively studied theoretically for parabolic band electronic systems in three-, two-, and one-dimensional systems over the last fifty years. In the current work, we theoretically study the relevance of Migdal's theorem in graphene and Weyl semimetals which are examples of 2D and 3D Dirac materials, respectively, with linear and chiral band dispersion. Our work also applies to 2D and 3D topological insulator systems. In Fermi liquids, the renormalization of the electron-phonon vertex scales as the ratio of sound (vs) to Fermi (vF) velocity, which is typically a small quantity. In two- and three-dimensional quasirelativistic systems, such as undoped graphene and Weyl semimetals, the one loop electron-phonon vertex renormalization, which also scales as η =vs/vF as η →0, is, however, enhanced by an ultraviolet logarithmic divergent correction, arising from the linear, chiral Dirac band dispersion. Such enhancement of the electron-phonon vertex can be significantly softened due to the logarithmic increment of the Fermi velocity, arising from the long range Coulomb interaction, and therefore, the electron-phonon vertex correction does not have a logarithmic divergence at low energy. Otherwise, the Coulomb interaction does not lead to any additional renormalization of the electron-phonon vertex. Therefore, electron-phonon vertex corrections in two- and three-dimensional Dirac fermionic systems scale as vs/vF0, where vF0 is the bare Fermi velocity, and small when vs≪vF0. These results, although explicitly derived for the intrinsic undoped systems, should hold even when the chemical potential is tuned away from the Dirac points.

Use of the reciprocity theorem for a closed form solution of scattering of the lowest axially symmetric torsional wave mode by a defect in a pipe.

PubMed

Lee, Jaesun; Achenbach, Jan D; Cho, Younho

2018-03-01

Guided waves can effectively be used for inspection of large scale structures. Surface corrosion is often found as major defect type in large scale structures such as pipelines. Guided wave interaction with surface corrosion can provide useful information for sizing and classification. In this paper, the elastodynamic reciprocity theorem is used to formulate and solve complicated scattering problems in a simple manner. The approach has already been applied to scattering of Rayleigh and Lamb waves by defects to produce closed form solutions of amplitude of scattered waves. In this paper, the scattering of the lowest axially symmetric torsional mode, which is widely used in commercial applications, is analyzed by the reciprocity theorem. In the present paper, the theorem is used to determine the scattering of the lowest torsional mode by a tapered defect that was earlier considered experimentally and numerically by the finite element method. It is shown that by the presented method it is simple to obtain the ratio of amplitudes of scattered torsional modes for a tapered notch. The results show a good agreement with earlier numerical results. The wave field superposition technique in conjunction with the reciprocity theorem simplifies the solution of the scattering problem to yield a closed form solution which can play a significant role in quantitative signal interpretation. Copyright © 2017 Elsevier B.V. All rights reserved.

Communication. Kinetics of scavenging of small, nucleating clusters. First nucleation theorem and sum rules

DOE PAGES

Malila, Jussi; McGraw, Robert; Laaksonen, Ari; ...

2015-01-07

Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of subcritical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here we extend the kinetic derivation of the first nucleation theorem to give amore » general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them.« less

Generalization of the Ehrenfest theorem to quantum systems with periodical boundary conditions

NASA Astrophysics Data System (ADS)

Sanin, Andrey L.; Bagmanov, Andrey T.

2005-04-01

A generalization of Ehrenfest's theorem is discussed. For this purpose the quantum systems with periodical boundary conditions are being revised. The relations for time derivations of mean coordinate and momentum are derived once again. In comparison with Ehrenfest's theorem and its conventional quantities, the additional local terms occur which are caused boundaries. Because of this, the obtained new relations can be named as generalized. An example for using these relations is given.

Kohn's theorem in a superfluid Fermi gas with a Feshbach resonance

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

Ohashi, Y.

2004-12-01

We investigate the dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential. According to Kohn's theorem, the frequency of this collective mode is not affected by an interaction between the atoms and is always equal to the trap frequency. This remarkable property, however, does not necessarily hold in an approximate theory. We explicitly prove that the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA), including a coupling between fluctuations in the density and Cooper channels, is consistent with both Kohn's theorem as well as Goldstone's theorem. This proof can be immediately extended to the strong-coupling superfluid theorymore » developed by Nozieres and Schmitt-Rink (NSR), where the effect of superfluid fluctuations is included within the Gaussian level. As a result, the NSR-GRPA formalism can be used to study collective modes in the BCS-BEC crossover region in a manner which is consistent with Kohn's theorem. We also include the effect of a Feshbach resonance and a condensate of the associated molecular bound states. A detailed discussion is given of the unusual nature of the Kohn mode eigenfunctions in a Fermi superfluid, in the presence and absence of a Feshbach resonance. When the molecular bosons feel a different trap frequency from the Fermi atoms, the dipole frequency is shown to depend on the strength of effective interaction associated with the Feshbach resonance.« less

Novel Soft-Pion Theorem for Long-Range Nuclear Parity Violation.

PubMed

Feng, Xu; Guo, Feng-Kun; Seng, Chien-Yeah

2018-05-04

The parity-odd effect in the standard model weak neutral current reveals itself in the long-range parity-violating nuclear potential generated by the pion exchanges in the ΔI=1 channel with the parity-odd pion-nucleon coupling constant h_{π}^{1}. Despite decades of experimental and theoretical efforts, the size of this coupling constant is still not well understood. In this Letter, we derive a soft-pion theorem relating h_{π}^{1} and the neutron-proton mass splitting induced by an artificial parity-even counterpart of the ΔI=1 weak Lagrangian and demonstrate that the theorem still holds exact at the next-to-leading order in the chiral perturbation theory. A considerable amount of simplification is expected in the study of h_{π}^{1} by using either lattice or other QCD models following its reduction from a parity-odd proton-neutron-pion matrix element to a simpler spectroscopic quantity. The theorem paves the way to much more precise calculations of h_{π}^{1}, and thus a quantitative test of the strangeness-conserving neutral current interaction of the standard model is foreseen.

Applying the multivariate time-rescaling theorem to neural population models

PubMed Central

Gerhard, Felipe; Haslinger, Robert; Pipa, Gordon

2011-01-01

Statistical models of neural activity are integral to modern neuroscience. Recently, interest has grown in modeling the spiking activity of populations of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing. However any statistical model must be validated by an appropriate goodness-of-fit test. Kolmogorov-Smirnov tests based upon the time-rescaling theorem have proven to be useful for evaluating point-process-based statistical models of single-neuron spike trains. Here we discuss the extension of the time-rescaling theorem to the multivariate (neural population) case. We show that even in the presence of strong correlations between spike trains, models which neglect couplings between neurons can be erroneously passed by the univariate time-rescaling test. We present the multivariate version of the time-rescaling theorem, and provide a practical step-by-step procedure for applying it towards testing the sufficiency of neural population models. Using several simple analytically tractable models and also more complex simulated and real data sets, we demonstrate that important features of the population activity can only be detected using the multivariate extension of the test. PMID:21395436

Novel Soft-Pion Theorem for Long-Range Nuclear Parity Violation

NASA Astrophysics Data System (ADS)

Feng, Xu; Guo, Feng-Kun; Seng, Chien-Yeah

2018-05-01

The parity-odd effect in the standard model weak neutral current reveals itself in the long-range parity-violating nuclear potential generated by the pion exchanges in the Δ I =1 channel with the parity-odd pion-nucleon coupling constant hπ1 . Despite decades of experimental and theoretical efforts, the size of this coupling constant is still not well understood. In this Letter, we derive a soft-pion theorem relating hπ1 and the neutron-proton mass splitting induced by an artificial parity-even counterpart of the Δ I =1 weak Lagrangian and demonstrate that the theorem still holds exact at the next-to-leading order in the chiral perturbation theory. A considerable amount of simplification is expected in the study of hπ1 by using either lattice or other QCD models following its reduction from a parity-odd proton-neutron-pion matrix element to a simpler spectroscopic quantity. The theorem paves the way to much more precise calculations of hπ1, and thus a quantitative test of the strangeness-conserving neutral current interaction of the standard model is foreseen.

Gauge Invariance and the Goldstone Theorem

NASA Astrophysics Data System (ADS)

Guralnik, Gerald S.

This paper was originally created for and printed in the "Proceedings of seminar on unified theories of elementary particles" held in Feldafing, Germany from July 5 to 16, 1965 under the auspices of the Max-Planck-Institute for Physics and Astrophysics in Munich. It details and expands upon the 1964 Guralnik, Hagen, and Kibble paper demonstrating that the Goldstone theorem does not require physical zero mass particles in gauge theories.

Sharps Injuries and Other Blood and Body Fluid Exposures Among Home Health Care Nurses and Aides

PubMed Central

Markkanen, Pia K.; Galligan, Catherine J.; Kriebel, David; Chalupka, Stephanie M.; Kim, Hyun; Gore, Rebecca J.; Sama, Susan R.; Laramie, Angela K.; Davis, Letitia

2009-01-01

Objectives. We quantified risks of sharp medical device (sharps) injuries and other blood and body fluid exposures among home health care nurses and aides, identified risk factors, assessed the use of sharps with safety features, and evaluated underreporting in workplace-based surveillance. Methods. We conducted a questionnaire survey and workplace-based surveillance, collaborating with 9 home health care agencies and 2 labor unions from 2006 to 2007. Results. Approximately 35% of nurses and 6.4% of aides had experienced at least 1 sharps injury during their home health care career; corresponding figures for other blood and body fluid exposures were 15.1% and 6.7%, respectively. Annual sharps injuries incidence rates were 5.1 per 100 full-time equivalent (FTE) nurses and 1.0 per 100 FTE aides. Medical procedures contributing to sharps injuries were injecting medications, administering fingersticks and heelsticks, and drawing blood. Other contributing factors were sharps disposal, contact with waste, and patient handling. Sharps with safety features frequently were not used. Underreporting of sharps injuries to the workplace-based surveillance system was estimated to be about 50%. Conclusions. Sharps injuries and other blood and body fluid exposures are serious hazards for home health care nurses and aides. Improvements in hazard intervention are needed. PMID:19890177

Needlestick and Sharps Injuries in Dermatologic Surgery: A Review of Preventative Techniques and Post-exposure Protocols

PubMed Central

Monroe, Holly; Orengo, Ida; Rosen, Theodore

2016-01-01

Background: Needlestickand sharps injuries are the leading causes of morbidity in the dermatologicfield. Among medical specialties, surgeons and dermatologists have the highest rates of needlestickand sharps injuries.The high rates of needlestickand sharps injuries in dermatology not only apply to physicians, but also to nurses, physician assistants, and technicians in the demnatologic field. Needlestickand sharps injuries are of great concern due to the monetary, opportunity, social, and emotional costs associated with their occurrence. Objective: A review of preventative techniques and post-exposure protocols for the majortypes of sharps injuries encountered in dermatologic practice. Design: The terms “needle-stick injuryT’sharps injuryTdermatologic surgery? “post-exposure prophylaxis,”and “health-care associated injury” were used in combinations to search the PubMed database. Relevant studies were reviewed for validity and included. Results The authors discuss the major types of sharps injuries that occur in the dermatologic surgery setting and summarize preventative techniques with respect to each type of sharps injury.The authors also summarize and discuss relevant post-exposure protocols in the event of a sharps injury. Conclusion: The adoption of the discussed methods, techniques, practices, and attire can result in the elimination of the vast majority of dermatologic sharps injuries. PMID:27847548

Special relativity theorem and Pythagoras’s magic

NASA Astrophysics Data System (ADS)

Korkmaz, S. D.; Aybek, E. C.; Örücü, M.

2016-03-01

In the modern physics unit included in the course curriculum of grade 10 physics introduced in the 2007-2008 education year, the aim is that students at this grade level are aware of any developments which constitute modern physics and may be considered new, and interpret whether mass, length and time values of the motions at any velocities close to the speed of light vary or not. One of the scientific concepts and subjects among the final ones to be learned in the unit of modern physics with 12 course hours includes the special relativity theorem and its results. The special relativity theorem, the foundation of which was laid by Einstein in 1905, has three significant predictions proven by experiments and observations: time extension, dimensional shortening and mass relativity. At the first stage of this study, a simple and fast solution that uses the Pythagorean relation for problems and must be treated by using the mathematical expressions of the predictions as specified above is given, and this way of solution was taught while the relativity subject was explained to the secondary education students who are fifteen years old from grade 10 in the 2013-2014 education year. At the second stage of the study, a qualitative study is released together with grade 11 students who are sixteen years old in 2014-2015, who learnt to solve any problems in both methods, while the special relativity subject is discussed in the physics course in grade 10. The findings of the study show that the students have a misconception on the relativity theorem and prefer to solve any relativity-related problems by using the Pythagorean method constituting the first stage of this study.

Answering Junior Ant's "Why" for Pythagoras' Theorem

ERIC Educational Resources Information Center

Pask, Colin

2002-01-01

A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…

Fermat's Last Theorem for Factional and Irrational Exponents

ERIC Educational Resources Information Center

Morgan, Frank

2010-01-01

Fermat's Last Theorem says that for integers n greater than 2, there are no solutions to x[superscript n] + y[superscript n] = z[superscript n] among positive integers. What about rational exponents? Irrational n? Negative n? See what an undergraduate senior seminar discovered.

SHARP-B2: Flight Test Objectives, Project Implementation and Initial Results

NASA Technical Reports Server (NTRS)

Salute, Joan; Bull, Jeff; Rasky, Dan; Keese, David; Arnold, Jim (Technical Monitor)

2001-01-01

On September 28, 2000 the SHARP-B2 flight experiment was launched from Vandenberg Air Force Base, California. SHARP-B2 is the 2nd Ballistic flight test in the SHARP (Slender Hypervelocity Aerothermodynamic Research Probes) program which develops and tests new thermal protection materials and sharp body concepts. The flight tested Ultra-High Temperature Ceramics (UHTCs), which may radically change the design and performance of future aerospace vehicles. The new designs may overturn an age-old tenet of aerodynamics: that blunt-body aerospace vehicles, but not those with sharp leading edges, can survive the searing temperatures created as the vehicles tear through the atmosphere. Sharp leading edges offer numerous advantages over the blunt-body design currently in use. They could allow a space shuttle or crew return vehicle to maneuver in space more like an airplane and potentially allow astronauts to return to Earth from anywhere on orbit. They may allow improved astronaut safety by decreasing the risk of aborting into the ocean. They may reduce the electromagnetic interference that causes the communications blackouts that plague reentering blunt-body space vehicles. Reducing the amount of drag could lead to a reduction in propulsion requirements. Planetary probes could make use of sharp-body technology for aerobraking and to maximize their maneuvering capability. SHARP-B2 was a joint effort among NASA Ames, Sandia National Laboratories, the U.S. Air Force and the U.S. Army. It was funded by the Pathfinder Program at NASA's Marshall Space Flight Center. The SHARP-B2 payload was carried aboard a U.S. Air Force Minuteman III missile carrying a modified Mk 12A reentry vehicle (RV), which blasted off from Vandenberg Air Force Base near Lompoc, CA, at 3:01 a.m. PDT on Sept. 28. The RV was equipped with four 5. 1 inch-long strakes, or sharp leading edges. Each strake contained three UHTCs: ZrB2/SiC/C; ZrB2/SiC; and HfB2/SiC. Once it reached an altitude of about 400

Weapon Use in Korean Homicide: Differences Between Homicides Involving Sharp and Blunt Instruments.

PubMed

Park, Jisun; Son, Hyeonseo

2017-10-23

On the basis of information regarding 276 homicides committed in South Korea between 1987 and 2008, we compared offenders' and victims' characteristics, injury locations, weapon-related behavior, and offending behavior between homicides involving sharp and blunt instruments. The victims of sharp-force homicide were much younger relative to those of blunt-force homicide. In addition, homicides involving blunt instruments were more likely to be committed by offenders who lived with the victims. Most sharp-force homicides involved injuries to the torso, while blunt-force homicides involved mainly head injuries. Furthermore, perpetrators of sharp-force homicides tended to preselect their weapons, while those of blunt-force homicides were likely to use weapons of opportunity. Logistic regression analysis identified a number of factors, including injury location and body transportation, which significantly predicted weapon type. As this was the first South Korean study to compare sharp- and blunt-force homicides, the results have practical implications for homicide investigations. © 2017 American Academy of Forensic Sciences.

The Hawking-Penrose Singularity Theorem for C 1,1-Lorentzian Metrics

NASA Astrophysics Data System (ADS)

Graf, Melanie; Grant, James D. E.; Kunzinger, Michael; Steinbauer, Roland

2018-06-01

We show that the Hawking-Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of C 1,1-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for C 1,1-metrics, and of C 0-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.

Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

NASA Astrophysics Data System (ADS)

Benaych-Georges, Florent; Guionnet, Alice; Male, Camille

2014-07-01

We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.

Generalization of the Bogoliubov-Zubarev Theorem for Dynamic Pressure to the Case of Compressibility

NASA Astrophysics Data System (ADS)

Rudoi, Yu. G.

2018-01-01

We present the motivation, formulation, and modified proof of the Bogoliubov-Zubarev theorem connecting the pressure of a dynamical object with its energy within the framework of a classical description and obtain a generalization of this theorem to the case of dynamical compressibility. In both cases, we introduce the volume of the object into consideration using a singular addition to the Hamiltonian function of the physical object, which allows using the concept of the Bogoliubov quasiaverage explicitly already on a dynamical level of description. We also discuss the relation to the same result known as the Hellmann-Feynman theorem in the framework of the quantum description of a physical object.

Optical theorem for acoustic non-diffracting beams and application to radiation force and torque

PubMed Central

Zhang, Likun; Marston, Philip L.

2013-01-01

Acoustical and optical non-diffracting beams are potentially useful for manipulating particles and larger objects. An extended optical theorem for a non-diffracting beam was given recently in the context of acoustics. The theorem relates the extinction by an object to the scattering at the forward direction of the beam’s plane wave components. Here we use this theorem to examine the extinction cross section of a sphere centered on the axis of the beam, with a non-diffracting Bessel beam as an example. The results are applied to recover the axial radiation force and torque on the sphere by the Bessel beam. PMID:24049681

Randomized central limit theorems: A unified theory.

PubMed

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

Transient quantum fluctuation theorems and generalized measurements

NASA Astrophysics Data System (ADS)

Prasanna Venkatesh, B.; Watanabe, Gentaro; Talkner, Peter

2014-01-01

The transient quantum fluctuation theorems of Crooks and Jarzynski restrict and relate the statistics of work performed in forward and backward forcing protocols. So far, these theorems have been obtained under the assumption that the work is determined by two projective energy measurements, one at the end, and the other one at the beginning of each run of the protocol. We found that one can replace these two projective measurements only by special error-free generalized energy measurements with pairs of tailored, protocol-dependent post-measurement states that satisfy detailed balance-like relations. For other generalized measurements, the Crooks relation is typically not satisfied. For the validity of the Jarzynski equality, it is sufficient that the first energy measurements are error-free and the post-measurement states form a complete orthonormal set of elements in the Hilbert space of the considered system. Additionally, the effects of the second energy measurements must have unit trace. We illustrate our results by an example of a two-level system for different generalized measurements.

Transient quantum fluctuation theorems and generalized measurements

NASA Astrophysics Data System (ADS)

Prasanna Venkatesh, B.; Watanabe, Gentaro; Talkner, Peter

2014-05-01

The transient quantum fluctuation theorems of Crooks and Jarzynski restrict and relate the statistics of work performed in forward and backward forcing protocols. So far, these theorems have been obtained under the assumption that the work is determined by two projective energy measurements, one at the end, and the other one at the beginning of each run of the protocol.We found that one can replace these two projective measurements only by special error-free generalized energy measurements with pairs of tailored, protocol-dependent post-measurement states that satisfy detailed balance-like relations. For other generalized measurements, the Crooks relation is typically not satisfied. For the validity of the Jarzynski equality, it is sufficient that the first energy measurements are error-free and the post-measurement states form a complete orthonormal set of elements in the Hilbert space of the considered system. Additionally, the effects of the second energy measurements must have unit trace. We illustrate our results by an example of a two-level system for different generalized measurements.

Mount Sharp Panorama in White-Balanced Colors

NASA Image and Video Library

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.

Oscillation theorems for second order nonlinear forced differential equations.

PubMed

Salhin, Ambarka A; Din, Ummul Khair Salma; Ahmad, Rokiah Rozita; Noorani, Mohd Salmi Md

2014-01-01

In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature.

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…

Nonuniform sampling theorems for random signals in the linear canonical transform domain

NASA Astrophysics Data System (ADS)

Shuiqing, Xu; Congmei, Jiang; Yi, Chai; Youqiang, Hu; Lei, Huang

2018-06-01

Nonuniform sampling can be encountered in various practical processes because of random events or poor timebase. The analysis and applications of the nonuniform sampling for deterministic signals related to the linear canonical transform (LCT) have been well considered and researched, but up to now no papers have been published regarding the various nonuniform sampling theorems for random signals related to the LCT. The aim of this article is to explore the nonuniform sampling and reconstruction of random signals associated with the LCT. First, some special nonuniform sampling models are briefly introduced. Second, based on these models, some reconstruction theorems for random signals from various nonuniform samples associated with the LCT have been derived. Finally, the simulation results are made to prove the accuracy of the sampling theorems. In addition, the latent real practices of the nonuniform sampling for random signals have been also discussed.

Cone and trumpet concentrators in light of the general edge-ray theorem

NASA Astrophysics Data System (ADS)

Ries, Harald; Spirkl, Wolfgang; Winston, Roland

1995-08-01

Cone and trumpet are nonimaging concentrators which do not obey the traditional edge-ray principle. The latter states that edge rays from the source should be transferred to the edge of the target. These concentrators have traditionally been described in terms of the heuristic flow line principle. The edge-ray theorem has been generalized to include nonimaging reflectors with multiple reflections. One includes all multiply reflected rays as an auxiliary domain. The general edge-ray theorem then states that the edge rays to the union of source and auxiliary domain must be reflected to edge of the union of target and auxiliary domain by the first reflection. We show the setup for which cone and trumpet constitute perfect nonimaging concentrators in the light of the generalized edge-ray theorem. We discuss the cases where cones are very good approximations for the solutions of nonimaging problems.

Fan beam image reconstruction with generalized Fourier slice theorem.

PubMed

Zhao, Shuangren; Yang, Kang; Yang, Kevin

2014-01-01

For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.

Zero-Bounded Limits as a Special Case of the Squeeze Theorem for Evaluating Single-Variable and Multivariable Limits

ERIC Educational Resources Information Center

Gkioulekas, Eleftherios

2013-01-01

Many limits, typically taught as examples of applying the "squeeze" theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful…

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

PubMed Central

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

A generalized measurement equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry

NASA Astrophysics Data System (ADS)

Carozzi, T. D.; Woan, G.

2009-05-01

We derive a generalized van Cittert-Zernike (vC-Z) theorem for radio astronomy that is valid for partially polarized sources over an arbitrarily wide field of view (FoV). The classical vC-Z theorem is the theoretical foundation of radio astronomical interferometry, and its application is the basis of interferometric imaging. Existing generalized vC-Z theorems in radio astronomy assume, however, either paraxiality (narrow FoV) or scalar (unpolarized) sources. Our theorem uses neither of these assumptions, which are seldom fulfiled in practice in radio astronomy, and treats the full electromagnetic field. To handle wide, partially polarized fields, we extend the two-dimensional (2D) electric field (Jones vector) formalism of the standard `Measurement Equation' (ME) of radio astronomical interferometry to the full three-dimensional (3D) formalism developed in optical coherence theory. The resulting vC-Z theorem enables full-sky imaging in a single telescope pointing, and imaging based not only on standard dual-polarized interferometers (that measure 2D electric fields) but also electric tripoles and electromagnetic vector-sensor interferometers. We show that the standard 2D ME is easily obtained from our formalism in the case of dual-polarized antenna element interferometers. We also exploit an extended 2D ME to determine that dual-polarized interferometers can have polarimetric aberrations at the edges of a wide FoV. Our vC-Z theorem is particularly relevant to proposed, and recently developed, wide FoV interferometers such as Low Frequency Array (LOFAR) and Square Kilometer Array (SKA), for which direction-dependent effects will be important.

Diverse Terrain Types on Mount Sharp, Mars

NASA Image and Video Library

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

Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann's H-theorem (1868-1877)

NASA Astrophysics Data System (ADS)

Badino, M.

2011-11-01

An intricate, long, and occasionally heated debate surrounds Boltzmann's H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt's 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the first part, I discuss the development of Boltzmann's research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt's challenge and Boltzmann's response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject.

On Kronecker-Capelli type theorems for infinite systems

NASA Astrophysics Data System (ADS)

Fedorov, Foma M.; Potapova, Sargylana V.

2017-11-01

On the basis of the new concept of the decrement of an infinite matrices and determinants, we studied the inconsistency of a general infinite systems of linear algebraic equations. We proved the theorem on inconsistency of a infinite system when the decrement of its matrix is nonzero.

A Pseudo-Reversing Theorem for Rotation and its Application to Orientation Theory

DTIC Science & Technology

2012-03-01

approach to the task of constructing the appropriate course a ship must steer in order for the wind to appear to come from some given direction with some...axes, although the theorem doesn’t actually require such axes. The Pseudo-Reversing Theorem can often be invoked to give a different pedagogical basis to...of validity will quickly become obvious when it’s implemented on a computer. It does not seem to me that a great deal of pedagogical effort has found

Generalized virial theorem and pressure relation for a strongly correlated Fermi gas

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

Tan, Shina

2008-12-15

For a two-component Fermi gas in the unitarity limit (i.e., with infinite scattering length), there is a well-known virial theorem, first shown by J.E. Thomas et al. A few people rederived this result, and extended it to few-body systems, but their results are all restricted to the unitarity limit. Here I show that there is a generalized virial theorem for FINITE scattering lengths. I also generalize an exact result concerning the pressure to the case of imbalanced populations.

Central Limit Theorems for the Shrinking Target Problem

NASA Astrophysics Data System (ADS)

Haydn, Nicolai; Nicol, Matthew; Vaienti, Sandro; Zhang, Licheng

2013-12-01

Suppose B i := B( p, r i ) are nested balls of radius r i about a point p in a dynamical system ( T, X, μ). The question of whether T i x∈ B i infinitely often (i.o.) for μ a.e. x is often called the shrinking target problem. In many dynamical settings it has been shown that if diverges then there is a quantitative rate of entry and for μ a.e. x∈ X. This is a self-norming type of strong law of large numbers. We establish self-norming central limit theorems (CLT) of the form (in distribution) for a variety of hyperbolic and non-uniformly hyperbolic dynamical systems, the normalization constants are . Dynamical systems to which our results apply include smooth expanding maps of the interval, Rychlik type maps, Gibbs-Markov maps, rational maps and, in higher dimensions, piecewise expanding maps. For such central limit theorems the main difficulty is to prove that the non-stationary variance has a limit in probability.

SHARP: A multi-mission artificial intelligence system for spacecraft telemetry monitoring and diagnosis

NASA Technical Reports Server (NTRS)

Lawson, Denise L.; James, Mark L.

1989-01-01

The Spacecraft Health Automated Reasoning Prototype (SHARP) is a system designed to demonstrate automated health and status analysis for multi-mission spacecraft and ground data systems operations. Telecommunications link analysis of the Voyager 2 spacecraft is the initial focus for the SHARP system demonstration which will occur during Voyager's encounter with the planet Neptune in August, 1989, in parallel with real time Voyager operations. The SHARP system combines conventional computer science methodologies with artificial intelligence techniques to produce an effective method for detecting and analyzing potential spacecraft and ground systems problems. The system performs real time analysis of spacecraft and other related telemetry, and is also capable of examining data in historical context. A brief introduction is given to the spacecraft and ground systems monitoring process at the Jet Propulsion Laboratory. The current method of operation for monitoring the Voyager Telecommunications subsystem is described, and the difficulties associated with the existing technology are highlighted. The approach taken in the SHARP system to overcome the current limitations is also described, as well as both the conventional and artificial intelligence solutions developed in SHARP.

Bayes' Theorem: An Old Tool Applicable to Today's Classroom Measurement Needs. ERIC/AE Digest.

ERIC Educational Resources Information Center

Rudner, Lawrence M.

This digest introduces ways of responding to the call for criterion-referenced information using Bayes' Theorem, a method that was coupled with criterion-referenced testing in the early 1970s (see R. Hambleton and M. Novick, 1973). To illustrate Bayes' Theorem, an example is given in which the goal is to classify an examinee as being a master or…

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.

Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities

NASA Astrophysics Data System (ADS)

Hamada, Yuta; Shiu, Gary

2018-05-01

We show that the soft photon, gluon, and graviton theorems can be understood as the Ward-Takahashi identities of large gauge transformation, i.e., diffeomorphism that does not fall off at spatial infinity. We found infinitely many new identities which constrain the higher order soft behavior of the gauge bosons and gravitons in scattering amplitudes of gauge and gravity theories. Diagrammatic representations of these soft theorems are presented.

ENVIRONMENTAL TECHNOLOGY VERIFICATION REPORT, HVLP COATING EQUIPMENT, SHARPE MANUFACTURING COMPANY PLATINUM 2012 HVLP SPRAY GUN

EPA Science Inventory

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...

Projection-slice theorem based 2D-3D registration

NASA Astrophysics Data System (ADS)

van der Bom, M. J.; Pluim, J. P. W.; Homan, R.; Timmer, J.; Bartels, L. W.

2007-03-01

In X-ray guided procedures, the surgeon or interventionalist is dependent on his or her knowledge of the patient's specific anatomy and the projection images acquired during the procedure by a rotational X-ray source. Unfortunately, these X-ray projections fail to give information on the patient's anatomy in the dimension along the projection axis. It would be very profitable to provide the surgeon or interventionalist with a 3D insight of the patient's anatomy that is directly linked to the X-ray images acquired during the procedure. In this paper we present a new robust 2D-3D registration method based on the Projection-Slice Theorem. This theorem gives us a relation between the pre-operative 3D data set and the interventional projection images. Registration is performed by minimizing a translation invariant similarity measure that is applied to the Fourier transforms of the images. The method was tested by performing multiple exhaustive searches on phantom data of the Circle of Willis and on a post-mortem human skull. Validation was performed visually by comparing the test projections to the ones that corresponded to the minimal value of the similarity measure. The Projection-Slice Theorem Based method was shown to be very effective and robust, and provides capture ranges up to 62 degrees. Experiments have shown that the method is capable of retrieving similar results when translations are applied to the projection images.

Orbit-averaged quantities, the classical Hellmann-Feynman theorem, and the magnetic flux enclosed by gyro-motion

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

Perkins, R. J., E-mail: rperkins@pppl.gov; Bellan, P. M.

Action integrals are often used to average a system over fast oscillations and obtain reduced dynamics. It is not surprising, then, that action integrals play a central role in the Hellmann-Feynman theorem of classical mechanics, which furnishes the values of certain quantities averaged over one period of rapid oscillation. This paper revisits the classical Hellmann-Feynman theorem, rederiving it in connection to an analogous theorem involving the time-averaged evolution of canonical coordinates. We then apply a modified version of the Hellmann-Feynman theorem to obtain a new result: the magnetic flux enclosed by one period of gyro-motion of a charged particle inmore » a non-uniform magnetic field. These results further demonstrate the utility of the action integral in regards to obtaining orbit-averaged quantities and the usefulness of this formalism in characterizing charged particle motion.« less

The incidence of coring with blunt versus sharp needles.

PubMed

Wani, Tariq; Wadhwa, Anupama; Tobias, Joseph D

2014-03-01

With the advent of safety needles to prevent inadvertent needle sticks in the operating room (OR), a potentially new issue has arisen. These needles may result in coring, or the shaving off of fragments of the rubber stopper, when the needle is pierced through the rubber stopper of the medication vial. These fragments may be left in the vial and then drawn up with the medication and possibly injected into patients. The current study prospectively evaluated the incidence of coring when blunt and sharp needles were used to pierce rubber topped vials. We also evaluated the incidence of coring in empty medication vials with rubber tops. The rubber caps were then pierced with either an18-gauge sharp hypodermic needle or a blunt plastic (safety) needle. Coring occurred in 102 of 250 (40.8%) vials when a blunt needle was used versus 9 of 215 (4.2%) vials with a sharp needle (P < 0.0001). A significant incidence of coring was demonstrated when a blunt plastic safety needle was used. This situation is potentially a patient safety hazard and methods to eliminate this problem are needed. Copyright © 2014 Elsevier Inc. All rights reserved.

After an exposure to sharps or body fluids

MedlinePlus

... the area with soap and water. For a splash exposure to the nose, mouth, or skin, flush ... designing, implementing, and evaluating a sharps injury prevention program. www.cdc.gov/sharpssafety/pdf/sharpsworkbook_2008.pdf . ...

Randomized central limit theorems: A unified theory

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

Understanding sharps injuries in home healthcare: The Safe Home Care qualitative methods study to identify pathways for injury prevention.

PubMed

Markkanen, Pia; Galligan, Catherine; Laramie, Angela; Fisher, June; Sama, Susan; Quinn, Margaret

2015-04-11

Home healthcare is one of the fastest growing sectors in the United States. Percutaneous injuries from sharp medical devices (sharps) are a source of bloodborne pathogen infections among home healthcare workers and community members. Sharps use and disposal practices in the home are highly variable and there is no comprehensive analysis of the system of sharps procurement, use and disposal in home healthcare. This gap is a barrier to effective public health interventions. The objectives of this study were to i) identify the full range of pathways by which sharps enter and exit the home, stakeholders involved, and barriers for using sharps with injury prevention features; and ii) assess the leverage points for preventive interventions. This study employed qualitative research methods to develop two systems maps of the use of sharps and prevention of sharps injuries in home healthcare. Twenty-six in-depth interview sessions were conducted including home healthcare agency clinicians, public health practitioners, sharps device manufacturers, injury prevention advocates, pharmacists and others. Interview transcripts were audio-recorded and analyzed thematically using NVIVO qualitative research analysis software. Analysis of supporting archival material also was conducted. All findings guided development of the two maps. Sharps enter the home via multiple complex pathways involving home healthcare providers and home users. The providers reported using sharps with injury prevention features. However, home users' sharps seldom had injury prevention features and sharps were commonly re-used for convenience and cost-savings. Improperly discarded sharps present hazards to caregivers, waste handlers, and community members. The most effective intervention potential exists at the beginning of the sharps systems maps where interventions can eliminate or minimize sharps injuries, in particular with needleless treatment methods and sharps with injury prevention features

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

NASA Technical Reports Server (NTRS)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

Viète's Formula and an Error Bound without Taylor's Theorem

ERIC Educational Resources Information Center

Boucher, Chris

2018-01-01

This note presents a derivation of Viète's classic product approximation of pi that relies on only the Pythagorean Theorem. We also give a simple error bound for the approximation that, while not optimal, still reveals the exponential convergence of the approximation and whose derivation does not require Taylor's Theorem.

Mount Sharp 'Photobombs' Curiosity

NASA Image and Video Library

2018-01-31

This self-portrait of NASA's Curiosity Mars rover shows the vehicle on Vera Rubin Ridge, which it's been investigating for the past several months. Directly behind the rover is the start of a clay-rich slope scientists are eager to begin exploring. In the coming week, Curiosity will begin to climb this slope. North is on the left and west is on the right, with Gale Crater's rim on the horizon of both edges. Poking up just behind Curiosity's mast is Mount Sharp, photobombing the robot's selfie. Curiosity landed on Mars five years ago with the intention of studying lower Mount Sharp, where it will remain for all of its time on Mars. The mountain's base provides access to layers formed over millions of years. These layers formed in the presence of water -- likely due to a lake or lakes that sat at the bottom of the mountain, which sits inside of Gale Crater. This mosaic was assembled from dozens of images taken by Curiosity's Mars Hands Lens Imager (MAHLI). They were all taken on Jan. 23, 2018, during Sol 1943. The view does not include the rover's arm nor the MAHLI camera itself, except in the miniature scene reflected upside down in the parabolic mirror at the top of the mast. That mirror is part of Curiosity's Chemistry and Camera (ChemCam) instrument. MAHLI appears in the center of the mirror. Wrist motions and turret rotations on the arm allowed MAHLI to acquire the mosaic's component images. The arm was positioned out of the shot in the images, or portions of images, that were used in this mosaic. A full-resolution image is available at https://photojournal.jpl.nasa.gov/catalog/PIA22207

Birkhoff theorem and conformal Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Ferrando, Joan Josep; Sáez, Juan Antonio

2015-06-01

We analyze the main geometric conditions imposed by the hypothesis of the Jebsen-Birkhoff theorem. We show that the result (existence of an additional Killing vector) does not necessarily require a three-dimensional isometry group on two-dimensional orbits but only the existence of a conformal Killing-Yano tensor. In this approach the (additional) isometry appears as the known invariant Killing vector that the -metrics admit.

Fluctuation theorem for the effusion of an ideal gas.

PubMed

Cleuren, B; Van den Broeck, C; Kawai, R

2006-08-01

The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.

Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper

NASA Technical Reports Server (NTRS)

Schumann, Johann; Koga, Dennis (Technical Monitor)

1999-01-01

In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).

The Two-Component Virial Theorem and the Physical Properties of Stellar Systems.

PubMed

Dantas; Ribeiro; Capelato; de Carvalho RR

2000-01-01

Motivated by present indirect evidence that galaxies are surrounded by dark matter halos, we investigate whether their physical properties can be described by a formulation of the virial theorem that explicitly takes into account the gravitational potential term representing the interaction of the dark halo with the baryonic or luminous component. Our analysis shows that the application of such a "two-component virial theorem" not only accounts for the scaling relations displayed by, in particular, elliptical galaxies, but also for the observed properties of all virialized stellar systems, ranging from globular clusters to galaxy clusters.

Causality and a -theorem constraints on Ricci polynomial and Riemann cubic gravities

NASA Astrophysics Data System (ADS)

Li, Yue-Zhou; Lü, H.; Wu, Jun-Bao

2018-01-01

In this paper, we study Einstein gravity extended with Ricci polynomials and derive the constraints on the coupling constants from the considerations of being ghost-free, exhibiting an a -theorem and maintaining causality. The salient feature is that Einstein metrics with appropriate effective cosmological constants continue to be solutions with the inclusion of such Ricci polynomials and the causality constraint is automatically satisfied. The ghost-free and a -theorem conditions can only be both met starting at the quartic order. We also study these constraints on general Riemann cubic gravities.

Experimental demonstration that a free-falling aerosol particle obeys a fluctuation theorem

NASA Astrophysics Data System (ADS)

Wong, Chun-Shang; Goree, J.; Gopalakrishnan, Ranganathan

2018-05-01

We investigate the fluctuating motion of an aerosol particle falling in air. Using a Millikan-like setup, we tracked a 1-μ m sphere falling at its terminal velocity. We observe occurrences of particles undergoing upward displacements against the force of gravity, so that negative work is done briefly. These negative-work events have a probability that is shown to obey the work fluctuation theorem. This experimental confirmation of the theorem's applicability to aerosols leads us to develop and demonstrate an application: an in situ measurement of an aerosol particle's mass.

Sharps injury reduction: a six-year, three-phase study comparing use of a small patient-room sharps disposal container with a larger engineered container

PubMed Central

Naisoro, W

2014-01-01

A 350-bed Sydney hospital noted excessive container-associated sharps injuries (CASI) using small sharps containers and compared the effect from 2004 to 2010 of using a larger container engineered to reduce CASI. In Phase 1 (Ph1), disposable 1.4L containers (BD Australia) were carried to/from patients’ rooms. In Phase 2 (Ph2), this stopped and a safety-engineered 32L reusable container (the Device; Sharpsmart, SteriHealth) was mounted in medication stations only and sharps were carried to and from patient rooms using kidney dishes. In Phase 3 (Ph3), the Device was wall-mounted in patient rooms. Sharps injuries were categorised as ‘during-procedure’, ‘after-procedure but before disposal’, ‘CASI’, and ‘improper disposal SI’. Disposal-related SI comprised CASI plus improper-disposal SI. Injuries per 100 full-time-equivalent staff were analysed using Chi2; p ≤ 0.05; and relative risk and 95% confidence limits were calculated. In Ph1 (small containers) 19.4% of SI were CASI and transport injuries were zero. In Ph2 (Device in medication station) CASI fell 94.9% (p <0.001); Disposal-related SI fell 71.1% (p=0.002) but transport injuries rose significantly. In Ph3 (Device in patient room) zero CASI occurred (p<0.001); Disposal-related SI fell 83.1% (p=0.001). Recapping SI fell 85.1% (p=0.01) with the Device. The Device’s volume, large aperture, passive overfill-protection and close-at-hand siting are postulated as SI reduction factors. PMID:28989381

Application of the Feynman-tree theorem together with BCFW recursion relations

NASA Astrophysics Data System (ADS)

Maniatis, M.

2018-03-01

Recently, it has been shown that on-shell scattering amplitudes can be constructed by the Feynman-tree theorem combined with the BCFW recursion relations. Since the BCFW relations are restricted to tree diagrams, the preceding application of the Feynman-tree theorem is essential. In this way, amplitudes can be constructed by on-shell and gauge-invariant tree amplitudes. Here, we want to apply this method to the electron-photon vertex correction. We present all the single, double, and triple phase-space tensor integrals explicitly and show that the sum of amplitudes coincides with the result of the conventional calculation of a virtual loop correction.

Externalities and the Coase Theorem: A Diagrammatic Presentation

ERIC Educational Resources Information Center

Halteman, James

2005-01-01

In intermediate microeconomic textbooks the reciprocal nature of externalities is presented using numerical examples of costs and benefits. This treatment of the Coase theorem obscures the fact that externality costs and benefits are best understood as being on a continuum where costs vary with the degree of intensity of the externality. When…

Postoperative pain and neuropathy after caesarean operation featuring blunt or sharp opening of the fascia: a randomised, parallel group, double-blind study.

PubMed

Yazici Yilmaz, Fatma; Aydogan Mathyk, Begum; Yildiz, Serhat; Yenigul, Nefise Nazli; Saglam, Ceren

2018-03-21

The purpose of this study was to compare postoperative pain and neuropathy after primary caesarean sections with either blunt or sharp fascial expansions. A total of 123 women undergoing primary caesarean sections were included in the study. The sharp group had 61 patients, and the blunt group had 62. In the sharp group, the fascia was incised sharply and extended using scissors. In blunt group, the fascia was bluntly opened by lateral finger-pulling. The primary outcome was postoperative pain. The long-term chronic pain scores were significantly lower in the blunt group during mobilisation (p = .012 and p = .022). Neuropathy was significantly more prevalent in the sharp group at both 1 and 3 months postoperatively (p = .043 and p = .016, respectively). The odds ratio (OR) and 95%CI for postoperative neuropathy at 1 and 3 months were as follows; OR 3.71, 95%CI 0.97-14.24 and OR 5.67, 95%CI 1.18-27.08, respectively. The OR for postoperative pain after 3 months was 3.26 (95%CI 1.09-9.73). The prevelance of postsurgical neuropathy and chronic pain at 3 months were significantly lower in the blunt group. Blunt fascial opening reduces the complication rate of postoperative pain and neuropathy after caesarean sections. Impact statement What is already known on this subject? The anatomic relationship of the abdominal fascia and the anterior abdominal wall nerves is a known fact. The fascia during caesarean sections can be opened by either a sharp or blunt extension. Data on the isolated impact of different fascial incisions on postoperative pain is limited. What do the results of this study add? The postoperative pain scores on the incision area are lower in the bluntly opened group compared to the sharp fascial incision group. By extending the fascia bluntly, a decrease in trauma and damage to nerves was observed. What are the implications of these findings for clinical practice and/or future research? The lateral extension of the fascia during

Confidence Hills -- The First Mount Sharp Drilling Site

NASA Image and Video Library

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.

77 FR 52061 - Notice of Proposed Exemption Involving Sharp HealthCare Located in San Diego, CA

Federal Register 2010, 2011, 2012, 2013, 2014

2012-08-28

...This document contains a notice of pendency (the Notice) before the Department of Labor (the Department) of a proposed individual exemption from certain prohibited transaction restrictions of the Employee Retirement Income Security Act of 1974 (the Act or ERISA). The transactions involve the Sharp HealthCare Health and Dental Plan (the Plan). The proposed exemption, if granted, would affect the Plan, its participants and beneficiaries, Sharp Healthcare (Sharp), and the Sharp Health Plan (the HMO).

Sharp-front wave of strong magnetic field diffusion in solid metal

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

Xiao, Bo; Gu, Zhuo-wei; Kan, Ming-xian

When a strong magnetic field diffuses into a solid metal, if the metal's resistance possesses an abrupt rise at some critical temperature and the magnetic field strength is above some critical value, the magnetic field will diffuse into the metal in the form of a sharp-front wave. Formulas for the critical conditions under which a sharp-front magnetic diffusion wave emerges and a formula for the wave-front velocity are derived in this work.

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.

A Perron-Frobenius Type of Theorem for Quantum Operations

NASA Astrophysics Data System (ADS)

Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng

2017-10-01

We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1. We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1, the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.

A double commutant theorem for Murray–von Neumann algebras

PubMed Central

Liu, Zhe

2012-01-01

Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double commutant theorem characterizes von Neumann algebras as those for which , where , the commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double commutant theorem for Murray–von Neumann algebras. PMID:22543165

Common Coupled Fixed Point Theorems for Two Hybrid Pairs of Mappings under φ-ψ Contraction

PubMed Central

Handa, Amrish

2014-01-01

We introduce the concept of (EA) property and occasional w-compatibility for hybrid pair F : X × X → 2X and f : X → X. We also introduce common (EA) property for two hybrid pairs F, G : X → 2X and f, g : X → X. We establish some common coupled fixed point theorems for two hybrid pairs of mappings under φ-ψ contraction on noncomplete metric spaces. An example is also given to validate our results. We improve, extend and generalize several known results. The results of this paper generalize the common fixed point theorems for hybrid pairs of mappings and essentially contain fixed point theorems for hybrid pair of mappings. PMID:27340688

A QUANTITATIVE TEST OF THE NO-HAIR THEOREM WITH Sgr A* USING STARS, PULSARS, AND THE EVENT HORIZON TELESCOPE

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

Psaltis, Dimitrios; Wex, Norbert; Kramer, Michael

The black hole in the center of the Milky Way, Sgr A*, has the largest mass-to-distance ratio among all known black holes in the universe. This property makes Sgr A* the optimal target for testing the gravitational no-hair theorem. In the near future, major developments in instrumentation will provide the tools for high-precision studies of its spacetime via observations of relativistic effects in stellar orbits, in the timing of pulsars, and in horizon-scale images of its accretion flow. We explore here the prospect of measuring the properties of the black hole spacetime using all of these three types of observations.more » We show that the correlated uncertainties in the measurements of the black hole spin and quadrupole moment using the orbits of stars and pulsars are nearly orthogonal to those obtained from measuring the shape and size of the shadow the black hole casts on the surrounding emission. Combining these three types of observations will therefore allow us to assess and quantify systematic biases and uncertainties in each measurement and lead to a highly accurate, quantitative test of the gravitational no-hair theorem.« less

A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems

NASA Astrophysics Data System (ADS)

Dragičević, D.; Froyland, G.; González-Tokman, C.; Vaienti, S.

2018-06-01

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of the spectral method, commonly used in limit laws for deterministic maps, to the general random setting. We achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of Lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter. While some versions of the LDP and CLT have previously been proved with other techniques, the local central limit theorem is, to our knowledge, a completely new result, and one that demonstrates the strength of our method. Applications include non-autonomous (piecewise) expanding maps, defined by random compositions of the form {T_{σ^{n-1} ω} circ\\cdotscirc T_{σω}circ T_ω}. An important aspect of our results is that we only assume ergodicity and invertibility of the random driving {σ:Ω\\toΩ} ; in particular no expansivity or mixing properties are required.

A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems

NASA Astrophysics Data System (ADS)

Dragičević, D.; Froyland, G.; González-Tokman, C.; Vaienti, S.

2018-01-01

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of the spectral method, commonly used in limit laws for deterministic maps, to the general random setting. We achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of Lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter. While some versions of the LDP and CLT have previously been proved with other techniques, the local central limit theorem is, to our knowledge, a completely new result, and one that demonstrates the strength of our method. Applications include non-autonomous (piecewise) expanding maps, defined by random compositions of the form {T_{σ^{n-1} ω} circ\\cdotscirc T_{σω}circ T_ω} . An important aspect of our results is that we only assume ergodicity and invertibility of the random driving {σ:Ω\\toΩ} ; in particular no expansivity or mixing properties are required.

How to (properly) strengthen Bell's theorem using counterfactuals

NASA Astrophysics Data System (ADS)

Bigaj, Tomasz

Bell's theorem in its standard version demonstrates that the joint assumptions of the hidden-variable hypothesis and the principle of local causation lead to a conflict with quantum-mechanical predictions. In his latest counterfactual strengthening of Bell's theorem, Stapp attempts to prove that the locality assumption itself contradicts the quantum-mechanical predictions in the Hardy case. His method relies on constructing a complex, non-truth functional formula which consists of statements about measurements and outcomes in some region R, and whose truth value depends on the selection of a measurement setting in a space-like separated location L. Stapp argues that this fact shows that the information about the measurement selection made in L has to be present in R. I give detailed reasons why this conclusion can and should be resisted. Next I correct and formalize an informal argument by Shimony and Stein showing that the locality condition coupled with Einstein's criterion of reality is inconsistent with quantum-mechanical predictions. I discuss the possibility of avoiding the inconsistency by rejecting Einstein's criterion rather than the locality assumption.

Making Sense of Bell's Theorem and Quantum Nonlocality

NASA Astrophysics Data System (ADS)

Boughn, Stephen

2017-05-01

Bell's theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell's theorem and its many extensions have led to the claim that quantum mechanics and by inference nature herself are nonlocal in the sense that a measurement on a system by an observer at one location has an immediate effect on a distant entangled system (one with which the original system has previously interacted). Einstein was repulsed by such "spooky action at a distance" and was led to question whether quantum mechanics could provide a complete description of physical reality. In this paper I argue that quantum mechanics does not require spooky action at a distance of any kind and yet it is entirely reasonable to question the assumption that quantum mechanics can provide a complete description of physical reality. The magic of entangled quantum states has little to do with entanglement and everything to do with superposition, a property of all quantum systems and a foundational tenet of quantum mechanics.

Discover the pythagorean theorem using interactive multimedia learning

NASA Astrophysics Data System (ADS)

Adhitama, I.; Sujadi, I.; Pramudya, I.

2018-04-01

In learning process students are required to play an active role in learning. They do not just accept the concept directly from teachers, but also build their own knowledge so that the learning process becomes more meaningful. Based on the observation, when learning Pythagorean theorem, students got difficulty on determining hypotenuse. One of the solution to solve this problem is using an interactive multimedia learning. This article aims to discuss the interactive multimedia as learning media for students. This was a Research and Development (R&D) by using ADDIE model of development. The results obtained was multimedia which was developed proper for students as learning media. Besides, on Phytagorian theorem learning activity we also compare Discovery Learning (DL) model with interactive multimedia and DL without interactive multimedia, and obtained that DL with interactive gave positive effect better than DL without interactive multimedia. It was also obtainde that interactive multimedia can attract and increase the interest ot the students on learning math. Therefore, the use of interactive multimedia on DL procees can improve student learning achievement.

Focusing optical waves with a rotationally symmetric sharp-edge aperture

NASA Astrophysics Data System (ADS)

Hu, Yanwen; Fu, Shenhe; Li, Zhen; Yin, Hao; Zhou, Jianying; Chen, Zhenqiang

2018-04-01

While there has been various kinds of patterned structures proposed for wave focusing, these patterned structures usually involve complicated lithographic techniques since the element size of the patterned structures should be precisely controlled in microscale or even nanoscale. Here we propose a new and straightforward method for focusing an optical plane wave in free space with a rotationally symmetric sharp-edge aperture. The focusing phenomenon of wave is realized by superposition of a portion of the higher-order symmetric plane waves generated from the sharp edges of the apertures, in contrast to previously focusing techniques which usually depend on a curved phase. We demonstrate both experimentally and theoretically the focusing effect with a series of apertures having different rotational symmetry, and find that the intensity of the hotspots could be controlled by the symmetric strength of the sharp-edge apertures. The presented results would advance the conventional wisdom that light would diffract in all directions and become expanding when it propagates through an aperture. The proposed method is easy to be processed, and might open potential applications in interferometry, image, and superresolution.

On direct theorems for best polynomial approximation

NASA Astrophysics Data System (ADS)

Auad, A. A.; AbdulJabbar, R. S.

2018-05-01

This paper is to obtain similarity for the best approximation degree of functions, which are unbounded in L p,α (A = [0,1]), which called weighted space by algebraic polynomials. {E}nH{(f)}p,α and the best approximation degree in the same space on the interval [0,2π] by trigonometric polynomials {E}nT{(f)}p,α of direct wellknown theorems in forms the average modules.

Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED.

PubMed

Fodor, Z; Hoelbling, C; Krieg, S; Lellouch, L; Lippert, Th; Portelli, A; Sastre, A; Szabo, K K; Varnhorst, L

2016-08-19

In a previous Letter [Borsanyi et al., Phys. Rev. Lett. 111, 252001 (2013)] we determined the isospin mass splittings of the baryon octet from a lattice calculation based on N_{f}=2+1 QCD simulations to which QED effects have been added in a partially quenched setup. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. Our ensembles include 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. For the parameter which quantifies violations to Dashen's theorem, we obtain ϵ=0.73(2)(5)(17), where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, m_{u}=2.27(6)(5)(4) and m_{d}=4.67(6)(5)(4)  MeV in the modified minimal subtraction scheme at 2  GeV and the isospin breaking ratios m_{u}/m_{d}=0.485(11)(8)(14), R=38.2(1.1)(0.8)(1.4), and Q=23.4(0.4)(0.3)(0.4). Our results exclude the m_{u}=0 solution to the strong CP problem by more than 24 standard deviations.

Central limit theorems under special relativity

PubMed Central

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

Central limit theorems under special relativity.

PubMed

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.

Three-dimensional vibrations of cylindrical elastic solids with V-notches and sharp radial cracks

NASA Astrophysics Data System (ADS)

McGee, O. G.; Kim, J. W.

2010-02-01

This paper provides free vibration data for cylindrical elastic solids, specifically thick circular plates and cylinders with V-notches and sharp radial cracks, for which no extensive previously published database is known to exist. Bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick V-notched plate under transverse vibratory motion, and three-dimensional (3-D) normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a V-notched cylindrical elastic solid under 3-D free vibration. A theoretical analysis is done in this work utilizing a variational Ritz procedure including these essential singularity effects. The procedure incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of " edge functions" that explicitly model the 3-D stress singularities which exist along a reentrant terminus edge (i.e., α>180°) of the V-notch. The first set of polynomials guarantees convergence to exact frequencies, as sufficient terms are retained. The second set of edge functions—in addition to representing the corner stress singularities—substantially accelerates the convergence of frequency solutions. This is demonstrated through extensive convergence studies that have been carried out by the investigators. Numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various V-notch angles and depths. The relative depth of the V-notch is defined as (1- c/ a), and the notch angle is defined as (360°- α). For a very small notch angle (1° or less), the notch may be regarded as a "sharp radial crack." Accurate (four significant figure) frequencies are presented for a wide spectrum of notch angles (360°- α), depths (1- c/ a), and thickness ratios ( a/ h for plates and h/ a for cylinders). An extended database of frequencies for completely free thick sectorial, semi-circular, and

Sharp Crater Rim with Dark Material and Boulders

NASA Image and Video Library

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.

An Elementary Proof of a Converse Mean-Value Theorem

ERIC Educational Resources Information Center

Almeida, Ricardo

2008-01-01

We present a new converse mean value theorem, with a rather elementary proof. [The work was supported by Centre for Research on Optimization and Control (CEOC) from the "Fundacaopara a Ciencia e a Tecnologia" FCT, co-financed by the European Community Fund FEDER/POCTI.

Notes on breeding sharp-shinned hawks and cooper’s hawks in Barnwell County, South Carolina

Treesearch

Mark Vukovich; John C. Kilgo

2009-01-01

Breeding records of Accipiter striatus (Sharp-shinned Hawks) in the southeastern US are scattered and isolated. We documented a Sharp-shinned Hawk and Accipiter cooperii (Cooper’s Hawk) nest while conducting a telemetry study on Melanerpes erythrocephalus (Red-headed Woodpeckers) in Barnwell County, SC in 2006 and 2007. We report the first known nest of a Sharp-shinned...

Analogues of Chernoff's theorem and the Lie-Trotter theorem

NASA Astrophysics Data System (ADS)

Neklyudov, Alexander Yu

2009-10-01

This paper is concerned with the abstract Cauchy problem \\dot x=\\mathrm{A}x, x(0)=x_0\\in\\mathscr{D}(\\mathrm{A}), where \\mathrm{A} is a densely defined linear operator on a Banach space \\mathbf X. It is proved that a solution x(\\,\\cdot\\,) of this problem can be represented as the weak limit \\lim_{n\\to\\infty}\\{\\mathrm F(t/n)^nx_0\\}, where the function \\mathrm F\\colon \\lbrack 0,\\infty)\\mapsto\\mathscr L(\\mathrm X) satisfies the equality \\mathrm F'(0)y=\\mathrm{A}y, y\\in\\mathscr{D}(\\mathrm{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 \\mathrm{C} to be closable and for its closure to be the generator of a C_0-semigroup. Also, we obtain new criteria for the sum of two generators of C_0-semigroups to be the generator of a C_0-semigroup and for the Lie-Trotter formula to hold. Bibliography: 13 titles.

The Holographic Electron Density Theorem, de-quantization, re-quantization, and nuclear charge space extrapolations of the Universal Molecule Model

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2017-11-01

Two strongly related theorems on non-degenerate ground state electron densities serve as the basis of "Molecular Informatics". The Hohenberg-Kohn theorem is a statement on global molecular information, ensuring that the complete electron density contains the complete molecular information. However, the Holographic Electron Density Theorem states more: the local information present in each and every positive volume density fragment is already complete: the information in the fragment is equivalent to the complete molecular information. In other words, the complete molecular information provided by the Hohenberg-Kohn Theorem is already provided, in full, by any positive volume, otherwise arbitrarily small electron density fragment. In this contribution some of the consequences of the Holographic Electron Density Theorem are discussed within the framework of the "Nuclear Charge Space" and the Universal Molecule Model. In the Nuclear Charge Space" the nuclear charges are regarded as continuous variables, and in the more general Universal Molecule Model some other quantized parameteres are also allowed to become "de-quantized and then re-quantized, leading to interrelations among real molecules through abstract molecules. Here the specific role of the Holographic Electron Density Theorem is discussed within the above context.

The generalized Lyapunov theorem and its application to quantum channels

NASA Astrophysics Data System (ADS)

Burgarth, Daniel; Giovannetti, Vittorio

2007-05-01

We give a simple and physically intuitive necessary and sufficient condition for a map acting on a compact metric space to be mixing (i.e. infinitely many applications of the map transfer any input into a fixed convergency point). This is a generalization of the 'Lyapunov direct method'. First we prove this theorem in topological spaces and for arbitrary continuous maps. Finally we apply our theorem to maps which are relevant in open quantum systems and quantum information, namely quantum channels. In this context, we also discuss the relations between mixing and ergodicity (i.e. the property that there exists only a single input state which is left invariant by a single application of the map) showing that the two are equivalent when the invariant point of the ergodic map is pure.

Sharp plasma pinnacle structure based on shockwave for an improved laser wakefield accelerator

NASA Astrophysics Data System (ADS)

Fang, Ming; Zhang, Zhijun; Wang, Wentao; Liu, Jiansheng; Li, Ruxin

2018-07-01

We created a sharp plasma pinnacle structure for localized electron injection and controlled acceleration in a laser wakefield accelerator. The formation of this shockwave-based pinnacle structure was investigated using aerodynamic theory. Details and scaling laws for the shockwave angle, shock position, shock width, and density ratio were experimentally and theoretically presented. Such work is crucial to yielding an expected plasma density distribution in a laser–plasma experiment but has had little discussion in the literature. Compared with the commonly used shock downramp structure, the particle-in-cell simulations demonstrated that the e beam injected in the created pinnacle structure could be accelerated to higher energy with much smaller root-mean-square relative energy spread. Moreover, this study indicated that the beam charge and transverse emittance can be tuned by the shock angle.

A monotonicity preserving conservative sharp interface flow solver for high density ratio two-phase flows

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

Le Chenadec, Vincent, E-mail: vlechena@stanford.edu; Pitsch, Heinz; Institute for Combustion Technology, RWTH Aachen, Templergraben 64, 52056 Aachen

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-dimensionalmore » 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.« less

Gibbs-Curie-Wulff Theorem in Organic Materials: A Case Study on the Relationship between Surface Energy and Crystal Growth.

PubMed

Li, Rongjin; Zhang, Xiaotao; Dong, Huanli; Li, Qikai; Shuai, Zhigang; Hu, Wenping

2016-02-24

The equilibrium crystal shape and shape evolution of organic crystals are found to follow the Gibbs-Curie-Wulff theorem. Organic crystals are grown by the physical vapor transport technique and exhibit exactly the same shape as predicted by the Gibbs-Curie-Wulff theorem under optimal conditions. This accordance provides concrete proof for the theorem. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Bell's Theorem and Einstein's `Spooky Actions' from a Simple Thought Experiment

NASA Astrophysics Data System (ADS)

Kuttner, Fred; Rosenblum, Bruce

2010-02-01

In 1964 John Bell proved a theorem2 allowing the experimental test of whether what Einstein derided as "spooky actions at a distance" actually exist. We will see that they do. Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at any level. And a simple, semi-classical derivation of the quantum theory result can be given for physics students. These entanglement phenomena are today applied in industrial laboratories and are increasingly discussed in the popular literature. Unfortunately, they are also misappropriated by the purveyors of pseudoscience, something physicists have a responsibility to address.3 Students can be intrigued by the quantum strangeness physics has encountered at a boundary of our discipline.

Optical theorem for two-dimensional (2D) scalar monochromatic acoustical beams in cylindrical coordinates.

PubMed

Mitri, F G

2015-09-01

The optical theorem for plane waves is recognized as one of the fundamental theorems in optical, acoustical and quantum wave scattering theory as it relates the extinction cross-section to the forward scattering complex amplitude function. Here, the optical theorem is extended and generalized in a cylindrical coordinates system for the case of 2D beams of arbitrary character as opposed to plane waves of infinite extent. The case of scalar monochromatic acoustical wavefronts is considered, and generalized analytical expressions for the extinction, absorption and scattering cross-sections are derived and extended in the framework of the scalar resonance scattering theory. The analysis reveals the presence of an interference scattering cross-section term describing the interaction between the diffracted Franz waves with the resonance elastic waves. The extended optical theorem in cylindrical coordinates is applicable to any object of arbitrary geometry in 2D located arbitrarily in the beam's path. Related investigations in optics, acoustics and quantum mechanics will benefit from this analysis in the context of wave scattering theory and other phenomena closely connected to it, such as the multiple scattering by a cloud of particles, as well as the resulting radiation force and torque. Copyright © 2015 Elsevier B.V. All rights reserved.

Late onset Pott's paraplegia in patients with upper thoracic sharp kyphosis.

PubMed

Zhang, Zhengfeng

2012-02-01

The purpose of this study was to determine the clinical results of patients with late onset upper thoracic sharp Pott's kyphosis and to predict the prognosis for Pott's paraplegics. The study included five patients who developed late onset upper thoracic (T1-T4) sharp Pott's kyphosis/kyphoscoliosis within a period from 19 to 37 years after the active disease was healed. The kyphosis angle of the patients ranged from 95° to 105°. Among them, three patients suffered onset of paraplegia ranging from 26 to 31 years after spinal tuberculosis was healed. The duration of neurological deterioration before surgery ranged from four to five years. All patients underwent decompressive surgery with an attempt to correct the curve. Neurological status was evaluated using the ASIA impairment classification and the motor score. Postoperatively, kyphosis correction ranged from 20° to 30° for five patients. No neurological deficit occurred in two patients with normal neurological status. Two ASIA D paraplegics remained unchanged after surgery and no further improvement was found at one year follow-up. One ASIA C paralysis deteriorated neurologically to ASIA B after surgery and persisted to a deterioration of neurological status at one year follow-up. Upper thoracic sharp Pott's kyphosis and neurological deficits occur progressively. The neurological recovery or improvement of Pott's paraplegics with upper thoracic severe sharp kyphosis results in poor prognosis after decompressive surgery.

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.

No-Hair Theorem for Black Holes in Astrophysical Environments

NASA Astrophysics Data System (ADS)

Gürlebeck, Norman

2015-04-01

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

No-hair theorem for black holes in astrophysical environments.

PubMed

Gürlebeck, Norman

2015-04-17

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

Development of the Adult Scale of Hostility and Aggression: Reactive-Proactive (A-SHARP)

ERIC Educational Resources Information Center

Matlock, Scott Thomas; Aman, Michael G.

2011-01-01

In this study, the authors developed the Adult Scale of Hostility and Aggression Reactive-Proactive (A-SHARP). Sixty-one caregivers rated 512 individuals with intellectual and developmental disabilities on the A-SHARP. Exploratory factor analysis revealed 5 factors on the Problem Scale: (a) Verbal Aggression, (b) Physical Aggression, (c) Hostile…

Maintaining knife sharpness in industrial meat cutting: A matter of knife or meat cutter ability.

PubMed

Karltun, J; Vogel, K; Bergstrand, M; Eklund, J

2016-09-01

Knife sharpness is imperative in meat cutting. The aim of this study was to compare the impact of knife blade steel quality with meat cutters' individual ability to maintain the cutting edge sharp in an industrial production setting. Twelve meat cutters in two different companies using three different knives during normal production were studied in this quasi-experimental study. Methods included were measuring knife cutting force before and after knife use, time knives were used, ratings of sharpness and discomfort and interviews. Results showed that the meat cutters' skill of maintaining sharpness during work had a much larger effect on knife sharpness during work than the knife steel differences. The ability was also related to feelings of discomfort and to physical exertion. It was found that meat cutters using more knives were more likely to suffer from discomfort in the upper limbs, which is a risk for developing MSD. Copyright © 2016 Elsevier Ltd. All rights reserved.

Lacosamide and Levetiracetam Have No Effect on Sharp-Wave Ripple Rate.

PubMed

Kudlacek, Jan; Chvojka, Jan; Posusta, Antonin; Kovacova, Lubica; Hong, Seung Bong; Weiss, Shennan; Volna, Kamila; Marusic, Petr; Otahal, Jakub; Jiruska, Premysl

2017-01-01

Pathological high-frequency oscillations are a novel marker used to improve the delineation of epileptogenic tissue and, hence, the outcome of epilepsy surgery. Their practical clinical utilization is curtailed by the inability to discriminate them from physiological oscillations due to frequency overlap. Although it is well documented that pathological HFOs are suppressed by antiepileptic drugs (AEDs), the effect of AEDs on normal HFOs is not well known. In this experimental study, we have explored whether physiological HFOs (sharp-wave ripples) of hippocampal origin respond to AED treatment. The results show that application of a single dose of levetiracetam or lacosamide does not reduce the rate of sharp-wave ripples. In addition, it seems that these new generation drugs do not negatively affect the cellular and network mechanisms involved in sharp-wave ripple generation, which may provide a plausible explanation for the absence of significant negative effects on cognitive functions of these drugs, particularly on memory.

Geometric Demonstration of the Fundamental Theorems of the Calculus

ERIC Educational Resources Information Center

Sauerheber, Richard D.

2010-01-01

After the monumental discovery of the fundamental theorems of the calculus nearly 350 years ago, it became possible to answer extremely complex questions regarding the natural world. Here, a straightforward yet profound demonstration, employing geometrically symmetric functions, describes the validity of the general power rules for integration and…

A report on SHARP (Spacecraft Health Automated Reasoning Prototype) and the Voyager Neptune encounter

NASA Technical Reports Server (NTRS)

Martin, R. G. (Editor); Atkinson, D. J.; James, M. L.; Lawson, D. L.; Porta, H. J.

1990-01-01

The development and application of the Spacecraft Health Automated Reasoning Prototype (SHARP) for the operations of the telecommunications systems and link analysis functions in Voyager mission operations are presented. An overview is provided of the design and functional description of the SHARP system as it was applied to Voyager. Some of the current problems and motivations for automation in real-time mission operations are discussed, as are the specific solutions that SHARP provides. The application of SHARP to Voyager telecommunications had the goal of being a proof-of-capability demonstration of artificial intelligence as applied to the problem of real-time monitoring functions in planetary mission operations. AS part of achieving this central goal, the SHARP application effort was also required to address the issue of the design of an appropriate software system architecture for a ground-based, highly automated spacecraft monitoring system for mission operations, including methods for: (1) embedding a knowledge-based expert system for fault detection, isolation, and recovery within this architecture; (2) acquiring, managing, and fusing the multiple sources of information used by operations personnel; and (3) providing information-rich displays to human operators who need to exercise the capabilities of the automated system. In this regard, SHARP has provided an excellent example of how advanced artificial intelligence techniques can be smoothly integrated with a variety of conventionally programmed software modules, as well as guidance and solutions for many questions about automation in mission operations.

Null conformal Killing-Yano tensors and Birkhoff theorem

NASA Astrophysics Data System (ADS)

Ferrando, Joan Josep; Sáez, Juan Antonio

2016-04-01

We study the space-times admitting a null conformal Killing-Yano tensor whose divergence defines a Killing vector. We analyze the similarities and differences with the recently studied non null case (Ferrando and Sáez in Gen Relativ Gravit 47:1911, 2015). The results by Barnes concerning the Birkhoff theorem for the case of null orbits are analyzed and generalized.

A Theorem and its Application to Finite Tampers

DOE R&D Accomplishments Database

Feynman, R. P.

1946-08-15

A theorem is derived which is useful in the analysis of neutron problems in which all neutrons have the same velocity. It is applied to determine extrapolated end-points, the asymptotic amplitude from a point source, and the neutron density at the surface of a medium. Formulas fro the effect of finite tampers are derived by its aid, and their accuracy discussed.

Needlestick and Sharp Instruments Injuries among Brazilian Dentistry Students

PubMed Central

Fernandes, Liege Helena Freitas; Nunes, Wanúbia Barbosa; Silva, Larissa Costa; Wanderley, Rayssa Lucena; Barros, Criseuda Maria Benício; Cavalcanti, Alessandro Leite

2017-01-01

Background: The occurrence of occupational accidents is common among students and dentists. The present study is aimed to evaluate the prevalence and characteristics of needlestick and sharp instrument injuries among dentistry students. Materials and Methods: A documentary research was carried out with data being obtained from the analysis of 137 medical records of injuries caused by needlestick and sharp instruments occurring in the period from 2012 to 2016 and were analyzed regarding the characteristics of the victim (gender and age) and the accident (year, time, environment, and time interval between exposure and search for care). Data were organized in the Statistical Package for Social Sciences software version 18 and were presented through descriptive statistics. Results: The occurrence of accidents was high (43.1%), with the predominance of female victims (66.1%) and aged up to 23 years (55.9%). The majority of events occurred in the afternoon (54.4%), in the clinical setting (70.7%), and in 75% of the cases, the search for care occurred within 2 h after exposure. Conclusion: Accidents with needlestick and sharp instruments have high frequency and involve mainly female students. They are more common in the afternoon and in the clinical setting and the time interval was between exposure and the search for care complied with recommendations of the Brazilian legislation. PMID:28566861

Aspects of AdS/CFT: Conformal Deformations and the Goldstone Equivalence Theorem

NASA Astrophysics Data System (ADS)

Cantrell, Sean Andrew

The AdS/CFT correspondence provides a map from the states of theories situated in AdSd+1 to those in dual conformal theories in a d-dimensional space. The correspondence can be used to establish certain universal properties of some theories in one space by examining the behave of general objects in the other. In this thesis, we develop various formal aspects of AdS/CFT. Conformal deformations manifest in the AdS/CFT correspondence as boundary conditions on the AdS field. Heretofore, double-trace deformations have been the primary focus in this context. To better understand multitrace deformations, we revisit the relationship between the generating AdS partition function for a free bulk theory and the boundary CFT partition function subject to arbitrary conformal deformations. The procedure leads us to a formalism that constructs bulk fields from boundary operators. We independently replicate the holographic RG flow narrative to go on to interpret the brane used to regulate the AdS theory as a renormalization scale. The scale-dependence of the dilatation spectrum of a boundary theory in the presence of general deformations can be thus understood on the AdS side using this formalism. The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal

FAST TRACK COMMUNICATION: Singularity theorems based on trapped submanifolds of arbitrary co-dimension

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Senovilla, José M. M.

2010-08-01

Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a unification of the several possibilities for the boundary conditions in the traditional theorems and their generalization to an arbitrary co-dimension is achieved. The classical convergence conditions must be replaced by a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of the co-dimension 1, 2 or n.

The Relevance of Culturally Based Curriculum and Instruction: The Case of Nancy Sharp

ERIC Educational Resources Information Center

Lipka, Jerry; Sharp, Nancy; Brenner, Betsy; Yanez, Evelyn; Sharp, Ferdinand

2005-01-01

Ms. Sharp's case is particularly instructive as it shows how this experienced Yup'ik teacher steeped in the traditions of her culture effectively implemented a culturally based math module. Ms. Sharp's pedagogical creatively allowed her to authentically bring together a core academic content area, math, with Yup'ik traditions, knowledge, and ways…

Induction of the SHARP-2 mRNA level by insulin is mediated by multiple signaling pathways.

PubMed

Kanai, Yukiko; Asano, Kosuke; Komatsu, Yoshiko; Takagi, Katsuhiro; Ono, Moe; Tanaka, Takashi; Tomita, Koji; Haneishi, Ayumi; Tsukada, Akiko; Yamada, Kazuya

2017-02-01

The rat enhancer of split- and hairy-related protein-2 (SHARP-2) is an insulin-inducible transcription factor which represses transcription of the rat phosphoenolpyruvate carboxykinase gene. In this study, a regulatory mechanism of the SHARP-2 mRNA level by insulin was analyzed. Insulin rapidly induced the level of SHARP-2 mRNA. This induction was blocked by inhibitors for phosphoinositide 3-kinase (PI 3-K), protein kinase C (PKC), and mammalian target of rapamycin (mTOR), actinomycin D, and cycloheximide. Whereas an adenovirus infection expressing a dominant negative form of atypical PKC lambda (aPKCλ) blocked the insulin-induction of the SHARP-2 mRNA level, insulin rapidly activated the mTOR. Insulin did not enhance transcriptional activity from a 3.7 kb upstream region of the rat SHARP-2 gene. Thus, we conclude that insulin induces the expression of the rat SHARP-2 gene at the transcription level via both a PI 3-K/aPKCλ- and a PI 3-K/mTOR- pathways and that protein synthesis is required for this induction.

Sharp-tailed Grouse Restoration; Colville Tribes Restore Habitat for Sharp-tailed Grouse, Annual Report 2002-2003.

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

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 Crawfordmore » 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.« less

A faunistic study of genus Chasmogenus Sharp, 1882 of China (Coleoptera, Hydrophilidae).

PubMed

Jia, Fenglong; Tang, Yu-Dan

2018-01-01

Chasmogenus Sharp, 1882 is newly reported from the Chinese Mainland. A new species, C. parorbus sp. n. , is described from China (Yunnan). Chasmogenus orbus Watanabe, 1987 is reported from Hong Kong, the first record outside Japan. Chasmogenus abnormalis (Sharp, 1890) is reported from the Chinese mainland for the first time. The male genitalia of each species are illustrated. A key to the Chinese species of the genus is provided.

Occurrence of Greater Sage-Grouse X Sharp-tailed Grouse hybrids in Alberta

USGS Publications Warehouse

Aldridge, Cameron L.; Oyler-McCance, S.J.; Brigham, R.M.

2001-01-01

Two distinct grouse were regularly observed at two Greater Sage-Grouse (Centrocercus urophasianus) leks in both 1999 and 2000 in southeastern Alberta. Physically and behaviorally, the birds exhibited characteristics of both Greater Sage-Grouse and Sharp-tailed Grouse (Tympanuchus phasianellus), suggesting they were hybrids. DNA analyses of blood and feather samples indicated that both birds were males with Greater Sage-Grouse mothers and thus, fathers that were likely Sharp-tailed Grouse.

Tree-oriented interactive processing with an application to theorem-proving, appendix E

NASA Technical Reports Server (NTRS)

Hammerslag, David; Kamin, Samuel N.; Campbell, Roy H.

1985-01-01

The concept of unstructured structure editing and ted, an editor for unstructured trees, is described. Ted is used to manipulate hierarchies of information in an unrestricted manner. The tool was implemented and applied to the problem of organizing formal proofs. As a proof management tool, it maintains the validity of a proof and its constituent lemmas independently from the methods used to validate the proof. It includes an adaptable interface which may be used to invoke theorem provers and other aids to proof construction. Using ted, a user may construct, maintain, and verify formal proofs using a variety of theorem provers, proof checkers, and formatters.

Farmer Brown v. Rancher Wyatt: Teaching the Coase Theorem

ERIC Educational Resources Information Center

Gourley, Patrick

2018-01-01

The Coase Theorem is a fundamental tenet of environmental economics and is taught to thousands of principles of microeconomics students each year. Its counterintuitive conclusion, that a Pareto optimal solution can result between private parties regardless of the initial allocation of property rights over a scarce resource, is difficult for…

Improving Conceptions in Analytical Chemistry: The Central Limit Theorem

ERIC Educational Resources Information Center

Rodriguez-Lopez, Margarita; Carrasquillo, Arnaldo, Jr.

2006-01-01

This article describes the central limit theorem (CLT) and its relation to analytical chemistry. The pedagogic rational, which argues for teaching the CLT in the analytical chemistry classroom, is discussed. Some analytical chemistry concepts that could be improved through an understanding of the CLT are also described. (Contains 2 figures.)

Understanding the Sampling Distribution and the Central Limit Theorem.

ERIC Educational Resources Information Center

Lewis, Charla P.

The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…

Catastrophe optics of sharp-edge diffraction.

PubMed

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.

Sharp Central Venous Recanalization in Hemodialysis Patients: A Single-Institution Experience

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

Arabi, Mohammad, E-mail: marabi2004@hotmail.com; Ahmed, Ishtiaq; Mat’hami, Abdulaziz

PurposeWe report our institutional experience with sharp central venous recanalization in chronic hemodialysis patients who failed standard techniques.Materials and MethodsSince January 2014, a series of seven consecutive patients (four males and three females), mean age 35 years (18–65 years), underwent sharp central venous recanalization. Indications included obtaining hemodialysis access (n = 6) and restoration of superior vena cava (SVC) patency to alleviate occlusion symptoms and restore fistula function (n = 1). The transseptal needle was used for sharp recanalization in six patients, while it could not be introduced in one patient due to total occlusion of the inferior vena cava. Instead, transmediastinal SVC access using Chibamore » needle was obtained.ResultsTechnical success was achieved in all cases. SVC recanalization achieved symptoms’ relief and restored fistula function in the symptomatic patient. One patient underwent arteriovenous fistula creation on the recanalized side 3 months after the procedure. The remaining catheters were functional at median follow-up time of 9 months (1–14 months). Two major complications occurred including a right hemothorax and a small hemopericardium, which were managed by covered stent placement across the perforated SVC.ConclusionSharp central venous recanalization using the transseptal needle is feasible technique in patients who failed standard recanalization procedures. The potential high risk of complications necessitates thorough awareness of anatomy and proper technical preparedness.« less

The Space High Angular Resolution Probe for the Infrared (SHARP-IR)

NASA Technical Reports Server (NTRS)

Rinehart, S. A.; Rizzo, M. J.; Leisawitz, D. T.; Staguhn, J. G.; Dipirro, M.; Mentzell, J. E.; Juanola-Parramon, R.; Dhabal, A.; Mundy, L. G.; Moseley, S. H.;

Poynting Theorem, Relativistic Transformation of Total Energy-Momentum and Electromagnetic Energy-Momentum Tensor

NASA Astrophysics Data System (ADS)

Kholmetskii, Alexander; Missevitch, Oleg; Yarman, Tolga

2016-02-01

We address to the Poynting theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy-momentum. We show that this inconsistency stems from the incorrect application of Poynting theorem to a system of discrete point-like charges, when the terms of self-interaction in the product {\\varvec{j}} \\cdot {\\varvec{E}} (where the current density {\\varvec{j}} and bound electric field {\\varvec{E}} are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy-momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy-momentum tensor.

Generalized fluctuation-dissipation theorem as a test of the Markovianity of a system

NASA Astrophysics Data System (ADS)

Willareth, Lucian; Sokolov, Igor M.; Roichman, Yael; Lindner, Benjamin

2017-04-01

We study how well a generalized fluctuation-dissipation theorem (GFDT) is suited to test whether a stochastic system is not Markovian. To this end, we simulate a stochastic non-equilibrium model of the mechanosensory hair bundle from the inner ear organ and analyze its spontaneous activity and response to external stimulation. We demonstrate that this two-dimensional Markovian system indeed obeys the GFDT, as long as i) the averaging ensemble is sufficiently large and ii) finite-size effects in estimating the conjugated variable and its susceptibility can be neglected. Furthermore, we test the GFDT also by looking only at a one-dimensional projection of the system, the experimentally accessible position variable. This reduced system is certainly non-Markovian and the GFDT is somewhat violated but not as drastically as for the equilibrium fluctuation-dissipation theorem. We explore suitable measures to quantify the violation of the theorem and demonstrate that for a set of limited experimental data it might be difficult to decide whether the system is Markovian or not.

Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation

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

Mundt, Michael; Kuemmel, Stephan; Leeuwen, Robert van

2007-05-15

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of Na{sub 5} and Na{sub 9}{sup +}, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.

An Experiment on a Physical Pendulum and Steiner's Theorem

ERIC Educational Resources Information Center

Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.

2010-01-01

Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…

Splitting hairs: differentiating between entomological activity, taphonomy, and sharp force trauma on hair.

PubMed

Mazzarelli, Debora; Vanin, Stefano; Gibelli, Daniele; Maistrello, Lara; Porta, Davide; Rizzi, Agostino; Cattaneo, Cristina

2015-03-01

The analysis of hair can provide useful information for the correct evaluation of forensic cases, but studies of trauma on hair are extremely rare. Hair may present lesions caused by traumatic events or by animals: in fact, signs of sharp force weapons on hair may provide important information for the reconstruction of the manner of death, and, for example, may suggest fetishist practice. This study stemmed from a judicial case where it was fundamental to distinguish between sharp force lesions and insect activity on hair. In order to highlight differences between sharp force lesions and insect feeding activity, different experiments were performed with high power microscopy: hair samples were subjected to several lesions by blunt and sharp force trauma; then samples were used as pabulum for two taxa of insects: the common clothes moth (Tineola bisselliella Lepidoptera, Tineidae) and the carpet beetle (Anthrenus sp., Coleoptera, Dermestidae). Hairs were examined from a macroscopic and microscopic point of view by stereomicroscopy and scanning electron microscopy (SEM): the morphological characteristics of the lesions obtained from the different experimental samples were compared. Results show that sharp force trauma produces lesions with regular edges, whereas insects leave concave lesions caused by their "gnawing" activity. These two types of lesions are easily distinguishable from breaking and tearing using SEM. This study demonstrates that insect activity leaves very specific indications on hair and sheds some light on different hair lesions that may be found in forensic cases.

Relativistic H-theorem and nonextensive kinetic theory

NASA Astrophysics Data System (ADS)

Silva, R.; Lima, J. A. S.

2003-08-01

In 1988 Tsallis proposed a striking generalization of the Boltzmann-Gibbs entropy functional form given by [1] (1) where kB is Boltzmann's constant, pi is the probability of the i-th microstate, and the parameter q is any real number. Nowadays, the q-thermostatistics associated with Sq is being hailed as the possible basis of a theoretical framework appropriate to deal with nonextensive settings. There is a growing body of evidence suggesting that Sq provides a convenient frame for the thermostatistical analysis of many physical systems and processes ranging from the laboratory scale to the astrophysical domain [2]. However, all the basic results, including the proof of the H-theorem has been worked in the classical non-relativistic domain [3]. In this context we discuss the relativistic kinetic foundations of the Tsallis' nonextensive approach through the full Boltzmann's transport equation. Our analysis follows from a nonextensive generalization of the "molecular chaos hypothesis". For q > 0, the q-transport equation satisfies a relativistic H-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by the relativistic Tsallis' q-nonextensive velocity distribution. References [1] C. Tsallis, J. Stat. Phys. 52, 479 (1988). [2] J. A. S. Lima, R. Silva, and J. Santos, Astron. and Astrophys. 396, 309 (2002). [3] J. A. S. Lima, R. Silva, and A. R. Plastino, Phys. Rev. Lett. 86, 2938 (2001).

Chondrules in the Sharps H3 chondrite - Evidence for intergroup compositional differences among ordinary chondrite chondrules

NASA Technical Reports Server (NTRS)

Rubin, Alan E.; Pernicka, Ernst

1989-01-01

Bulk compositions of 19 chondrules and one matrix-rich sample from H3.4 Sharps were determined by instrumental neutron activation analysis. Samples were characterized petrographically, and mineral compositions were determined by electron microprobe analysis. There is constancy among ordinary chondrite (OC) groups in the compositional interrelationships of different chondrule types; e.g., in H3 as well as L3 and LL3 chondrites, porphyritic chondrules are more refractory than nonporphyritic chondrules. Precursor components of H3 chondrules are closely related to those of LL3 chondrules. The mean Ir/Ni, Ir/Co, and Ir/Au ratios of H3 chondrules differ from the corresponding ratios of LL3 chondrules at the 99, 90, and 79 percent confidence levels, respectively. The ratios in H3 chondrules exceed those in LL3 chondrules by amounts similar to those by which H whole-rocks exceed LL whole-rocks. These data suggest that there are primary systematic differences in bulk composition between H and LL chondrules. These differences support the inference that chondrule formation occurred after major nebular fractionation events had established the observed bulk compositional differences among OC groups.

Color Variations on Mount Sharp, Mars White Balanced

NASA Image and Video Library

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

Learning in neural networks based on a generalized fluctuation theorem

NASA Astrophysics Data System (ADS)

Hayakawa, Takashi; Aoyagi, Toshio

2015-11-01

Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.

Flow Control Over Sharp-Edged Wings

DTIC Science & Technology

2007-07-01

Gad-el-Hak (2001) as the ability to actively or passively manipulate a flow field to effect a desired change. The challenge is to achieve that change...combinations. Been able to independently control both is a great challenge . These requirements may appear too stringent for the sharp- edged airfoils...06 0𔄁 08 09 lic Vlc Figure 22: Pressure distributions for Model B at a=13 °. Stations I (left); 2 (right) 1 , -2 1 F - [12 1 -6a -16 08 -08 06 -06

Bayes` theorem and quantitative risk assessment

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

Kaplan, S.

1994-12-31

This paper argues that for a quantitative risk analysis (QRA) to be useful for public and private decision making, and for rallying the support necessary to implement those decisions, it is necessary that the QRA results be ``trustable.`` Trustable means that the results are based solidly and logically on all the relevant evidence available. This, in turn, means that the quantitative results must be derived from the evidence using Bayes` theorem. Thus, it argues that one should strive to make their QRAs more clearly and explicitly Bayesian, and in this way make them more ``evidence dependent`` than ``personality dependent.``

Soft theorems for shift-symmetric cosmologies

NASA Astrophysics Data System (ADS)

Finelli, Bernardo; Goon, Garrett; Pajer, Enrico; Santoni, Luca

2018-03-01

We derive soft theorems for single-clock cosmologies that enjoy a shift symmetry. These so-called consistency conditions arise from a combination of a large diffeomorphism and the internal shift symmetry and fix the squeezed limit of all correlators with a soft scalar mode. As an application, we show that our results reproduce the squeezed bispectrum for ultra-slow-roll inflation, a particular shift-symmetric, nonattractor model which is known to violate Maldacena's consistency relation. Similar results have been previously obtained by Mooij and Palma using background-wave methods. Our results shed new light on the infrared structure of single-clock cosmological spacetimes.

Mean energy of some interacting bosonic systems derived by virtue of the generalized Hellmann-Feynman theorem

NASA Astrophysics Data System (ADS)

Fan, Hong-yi; Xu, Xue-xiang

2009-06-01

By virtue of the generalized Hellmann-Feynman theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications of the Hellmann-Feynman theorem and may enrich the theory of quantum statistics.

Subleading soft theorem for multiple soft gravitons

NASA Astrophysics Data System (ADS)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2017-12-01

We derive the subleading soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. Our results are valid to all orders in perturbation theory when the number of non-compact space-time dimensions is six or more, but only for tree amplitudes for five or less non-compact space-time dimensions due to enhanced contribution to loop amplitudes from the infrared region.

An Extension of the Mean Value Theorem for Integrals

ERIC Educational Resources Information Center

Khalili, Parviz; Vasiliu, Daniel

2010-01-01

In this note we present an extension of the mean value theorem for integrals. The extension we consider is motivated by an older result (here referred as Corollary 2), which is quite classical for the literature of Mathematical Analysis or Calculus. We also show an interesting application for computing the sum of a harmonic series.

Two Theorems on Dissipative Energy Losses in Capacitor Systems

ERIC Educational Resources Information Center

Newburgh, Ronald

2005-01-01

This article examines energy losses in charge motion in two capacitor systems. In the first charge is transferred from a charged capacitor to an uncharged one through a resistor. In the second a battery charges an originally uncharged capacitor through a resistance. Analysis leads to two surprising general theorems. In the first case the fraction…

The Unforgettable Experience of a Workshop on Pythagoras Theorem

ERIC Educational Resources Information Center

Arwani, Salima Shahzad

2011-01-01

The author conducted a workshop with colleagues in which awareness of Pythagoras' theorem was raised. This workshop was an unforgettable event in the author's life because it was the first time that she had interacted with teachers from a different school system, and it allowed her to develop presentation skills and confidence in her own…

The detailed balance principle and the reciprocity theorem between photocarrier collection and dark carrier distribution in solar cells

NASA Astrophysics Data System (ADS)

Rau, Uwe; Brendel, Rolf

1998-12-01

It is shown that a recently described general relationship between the local collection efficiency of solar cells and the dark carrier concentration (reciprocity theorem) directly follows from the principle of detailed balance. We derive the relationship for situations where transport of charge carriers occurs between discrete states as well as for the situation where electronic transport is described in terms of continuous functions. Combining both situations allows to extend the range of applicability of the reciprocity theorem to all types of solar cells, including, e.g., metal-insulator-semiconductor-type, electrochemical solar cells, as well as the inclusion of the impurity photovoltaic effect. We generalize the theorem further to situations where the occupation probability of electronic states is governed by Fermi-Dirac statistics instead of Boltzmann statistics as underlying preceding work. In such a situation the reciprocity theorem is restricted to small departures from equilibrium.

Experimental measurement of binding energy, selectivity, and allostery using fluctuation theorems.

PubMed

Camunas-Soler, Joan; Alemany, Anna; Ritort, Felix

2017-01-27

Thermodynamic bulk measurements of binding reactions rely on the validity of the law of mass action and the assumption of a dilute solution. Yet, important biological systems such as allosteric ligand-receptor binding, macromolecular crowding, or misfolded molecules may not follow these assumptions and may require a particular reaction model. Here we introduce a fluctuation theorem for ligand binding and an experimental approach using single-molecule force spectroscopy to determine binding energies, selectivity, and allostery of nucleic acids and peptides in a model-independent fashion. A similar approach could be used for proteins. This work extends the use of fluctuation theorems beyond unimolecular folding reactions, bridging the thermodynamics of small systems and the basic laws of chemical equilibrium. Copyright © 2017, American Association for the Advancement of Science.

A Prototype Embedding of Bluespec System Verilog in the PVS Theorem Prover

NASA Technical Reports Server (NTRS)

Richards, Dominic; Lester, David

2010-01-01

Bluespec SystemVerilog (BSV) is a Hardware Description Language based on the guarded action model of concurrency. It has an elegant semantics, which makes it well suited for formal reasoning. To date, a number of BSV designs have been verified with hand proofs, but little work has been conducted on the application of automated reasoning. We present a prototype shallow embedding of BSV in the PVS theorem prover. Our embedding is compatible with the PVS model checker, which can automatically prove an important class of theorems, and can also be used in conjunction with the powerful proof strategies of PVS to verify a broader class of properties than can be achieved with model checking alone.

Quantum probability rule: a generalization of the theorems of Gleason and Busch

NASA Astrophysics Data System (ADS)

Barnett, Stephen M.; Cresser, James D.; Jeffers, John; Pegg, David T.

2014-04-01

Busch's theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleason's theorem. Here we show that a further generalization is possible by reducing the number of quantum postulates used by Busch. We do not assume that the positive measurement outcome operators are effects or that they form a probability operator measure. We derive a more general probability rule from which the standard rule can be obtained from the normal laws of probability when there is no measurement outcome information available, without the need for further quantum postulates. Our general probability rule has prediction-retrodiction symmetry and we show how it may be applied in quantum communications and in retrodictive quantum theory.

Singlet-triplet splittings from the virial theorem and single-particle excitation energies

NASA Astrophysics Data System (ADS)

Becke, Axel D.

2018-01-01

The zeroth-order (uncorrelated) singlet-triplet energy difference in single-particle excited configurations is 2Kif, where Kif is the Coulomb self-energy of the product of the transition orbitals. Here we present a non-empirical, virial-theorem argument that the correlated singlet-triplet energy difference should be half of this, namely, Kif. This incredibly simple result gives vertical HOMO-LUMO excitation energies in small-molecule benchmarks as good as the popular TD-B3LYP time-dependent approach to excited states. For linear acenes and nonlinear polycyclic aromatic hydrocarbons, the performance is significantly better than TD-B3LYP. In addition to the virial theorem, the derivation borrows intuitive pair-density concepts from density-functional theory.

The Hartman-Grobman theorem for semilinear hyperbolic evolution equations

NASA Astrophysics Data System (ADS)

Hein, Marie-Luise; Prüss, Jan

2016-10-01

The famous Hartman-Grobman theorem for ordinary differential equations is extended to abstract semilinear hyperbolic evolution equations in Banach spaces by means of simple direct proof. It is also shown that the linearising map is Hölder continuous. Several applications to abstract and specific damped wave equations are given, to demonstrate the strength of our results.

Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos

ERIC Educational Resources Information Center

Boozer, A. D.

2011-01-01

We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…

Remarkable features in lattice-parameter ratios of crystals. II. Monoclinic and triclinic crystals.

PubMed

de Gelder, R; Janner, A

2005-06-01

The frequency distributions of monoclinic crystals as a function of the lattice-parameter ratios resemble the corresponding ones of orthorhombic crystals: an exponential component, with more or less pronounced sharp peaks, with in general the most important peak at the ratio value 1. In addition, the distribution as a function of the monoclinic angle beta has a sharp peak at 90 degrees and decreases sensibly at larger angles. Similar behavior is observed for the three triclinic angular parameters alpha, beta and gamma, with characteristic differences between the organic and metal-organic, bio-macromolecular and inorganic crystals, respectively. The general behavior observed for the hexagonal, tetragonal, orthorhombic, monoclinic and triclinic crystals {in the first part of this series [de Gelder & Janner (2005). Acta Cryst. B61, 287-295] and in the present case} is summarized and commented. The data involved represent 366 800 crystals, with lattice parameters taken from the Cambridge Structural Database, CSD (294 400 entries), the Protein Data Bank, PDB (18 800 entries), and the Inorganic Crystal Structure Database, ICSD (53 600 entries). A new general structural principle is suggested.

Research in advanced formal theorem-proving techniques

NASA Technical Reports Server (NTRS)

Rulifson, J. F.

1971-01-01

The present status is summarized of a continuing research program aimed at the design and implementation of a language for expressing problem-solving procedures in several areas of artificial intelligence, including program synthesis, robot planning, and theorem proving. Notations, concepts, and procedures common to the representation and solution of many of these problems were abstracted and incorporated as features into the language. The areas of research covered are described, and abstracts of six papers that contain extensive description and technical detail of the work are presented.

Morera-type theorems in the hyperbolic disc

NASA Astrophysics Data System (ADS)

Volchkov, V. V.; Volchkov, V. V.

2018-02-01

Let G be the group of conformal automorphisms of the unit disc {D}=\\{z\\in{C}\\colon \\vert z\\vert<1\\}. We study the problem of the holomorphicity of functions f on {D} satisfying the equation where γ\\varrho=\\{z\\in{C}\\colon \\vert z\\vert=\\varrho\\} and ρ\\in(0,1) is fixed. We find exact conditions for holomorphicity in terms of the boundary behaviour of such functions. A by-product of our work is a new proof of the Berenstein-Pascuas two-radii theorem.

Analysis of regulatory mechanisms of an insulin-inducible SHARP-2 gene by (S)-Equol.

PubMed

Haneishi, Ayumi; Takagi, Katsuhiro; Asano, Kosuke; Yamamoto, Taichi; Tanaka, Takashi; Nakamura, Soichiro; Noguchi, Tamio; Yamada, Kazuya

2012-09-01

Small compounds that activate the insulin-dependent signaling pathway have potential therapeutic applications in controlling type 2 diabetes mellitus. The rat enhancer of split- and hairy-related protein-2 (SHARP-2) is an insulin-inducible transcription factor that decreases expression of the phosphoenolpyruvate carboxykinase gene, a gluconeogenic enzyme gene. In this study, we screened for soybean isoflavones that can induce the rat SHARP-2 gene expression and analyzed their mechanism(s). Genistein and (S)-Equol, a metabolite of daidzein, induced rat SHARP-2 gene expression in H4IIE rat hepatoma cells. The (S)-Equol induction was mediated by both the phosphoinositide 3-kinase- and protein kinase C (PKC)-pathways. When a dominant negative form of atypical PKC lambda (aPKCλ) was expressed, the induction of SHARP-2 mRNA level by (S)-Equol was inhibited. In addition, Western blot analyses showed that (S)-Equol rapidly activated both aPKCλ and classical PKC alpha. Furthermore, the (S)-Equol induction was inhibited by treatment with a RNA polymerase inhibitor or a protein synthesis inhibitor. Finally, a reporter gene assay revealed that the transcriptional stimulation by (S)-Equol was mediated by nucleotide sequences located between -4687 and -4133 of the rat SHARP-2 gene. Thus, we conclude that (S)-Equol is an useful dietary supplement to control type 2 diabetes mellitus. Copyright © 2012 Elsevier Inc. All rights reserved.

Entropy Inequalities for Stable Densities and Strengthened Central Limit Theorems

NASA Astrophysics Data System (ADS)

Toscani, Giuseppe

2016-10-01

We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy functionals along the sequence we prove convergence with explicit rate in various norms to a Lévy centered density of parameter λ >1 . This introduces a new information-theoretic approach to the central limit theorem for stable laws, in which the main argument is shown to be the relative fractional Fisher information, recently introduced in Toscani (Ricerche Mat 65(1):71-91, 2016). In particular, it is proven that, with respect to the relative fractional Fisher information, the Lévy density satisfies an analogous of the logarithmic Sobolev inequality, which allows to pass from the monotonicity and decay to zero of the relative fractional Fisher information in the standardized sum to the decay to zero in relative entropy with an explicit decay rate.

View from west sharp perspective, foundry/propeller shop. Naval Base ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

View from west sharp perspective, foundry/propeller shop. - Naval Base Philadelphia-Philadelphia Naval Shipyard, Foundry-Propeller Shop, North of Porter Avenue, west of Third Street West, Philadelphia, Philadelphia County, PA

Verification of the FtCayuga fault-tolerant microprocessor system. Volume 2: Formal specification and correctness theorems

NASA Technical Reports Server (NTRS)

Bickford, Mark; Srivas, Mandayam

1991-01-01

Presented here is a formal specification and verification of a property of a quadruplicately redundant fault tolerant microprocessor system design. A complete listing of the formal specification of the system and the correctness theorems that are proved are given. The system performs the task of obtaining interactive consistency among the processors using a special instruction on the processors. The design is based on an algorithm proposed by Pease, Shostak, and Lamport. The property verified insures that an execution of the special instruction by the processors correctly accomplishes interactive consistency, providing certain preconditions hold, using a computer aided design verification tool, Spectool, and the theorem prover, Clio. A major contribution of the work is the demonstration of a significant fault tolerant hardware design that is mechanically verified by a theorem prover.

Formal reasoning about systems biology using theorem proving

PubMed Central

Hasan, Osman; Siddique, Umair; Tahar, Sofiène

2017-01-01

System biology provides the basis to understand the behavioral properties of complex biological organisms at different levels of abstraction. Traditionally, analysing systems biology based models of various diseases have been carried out by paper-and-pencil based proofs and simulations. However, these methods cannot provide an accurate analysis, which is a serious drawback for the safety-critical domain of human medicine. In order to overcome these limitations, we propose a framework to formally analyze biological networks and pathways. In particular, we formalize the notion of reaction kinetics in higher-order logic and formally verify some of the commonly used reaction based models of biological networks using the HOL Light theorem prover. Furthermore, we have ported our earlier formalization of Zsyntax, i.e., a deductive language for reasoning about biological networks and pathways, from HOL4 to the HOL Light theorem prover to make it compatible with the above-mentioned formalization of reaction kinetics. To illustrate the usefulness of the proposed framework, we present the formal analysis of three case studies, i.e., the pathway leading to TP53 Phosphorylation, the pathway leading to the death of cancer stem cells and the tumor growth based on cancer stem cells, which is used for the prognosis and future drug designs to treat cancer patients. PMID:28671950

Conservative sharp debridement: the professional and legal issues.

PubMed

Ashworth, Jenny; Chivers, Marc

2002-06-01

In recent years there has been much debate over the use of conservative sharp debridement in the treatment of certain wound types. Here it is discussed in relation to increasing the speed of wound healing in slow-to-heal wounds. The authors examine education and skill competence in relation to the professional's duty of care to patients with wounds.

SU(p,q) coherent states and a Gaussian de Finetti theorem

NASA Astrophysics Data System (ADS)

Leverrier, Anthony

2018-04-01

We prove a generalization of the quantum de Finetti theorem when the local space is an infinite-dimensional Fock space. In particular, instead of considering the action of the permutation group on n copies of that space, we consider the action of the unitary group U(n) on the creation operators of the n modes and define a natural generalization of the symmetric subspace as the space of states invariant under unitaries in U(n). Our first result is a complete characterization of this subspace, which turns out to be spanned by a family of generalized coherent states related to the special unitary group SU(p, q) of signature (p, q). More precisely, this construction yields a unitary representation of the noncompact simple real Lie group SU(p, q). We therefore find a dual unitary representation of the pair of groups U(n) and SU(p, q) on an n(p + q)-mode Fock space. The (Gaussian) SU(p, q) coherent states resolve the identity on the symmetric subspace, which implies a Gaussian de Finetti theorem stating that tracing over a few modes of a unitary-invariant state yields a state close to a mixture of Gaussian states. As an application of this de Finetti theorem, we show that the n × n upper-left submatrix of an n × n Haar-invariant unitary matrix is close in total variation distance to a matrix of independent normal variables if n3 = O(m).

The Adiabatic Theorem and Linear Response Theory for Extended Quantum Systems

NASA Astrophysics Data System (ADS)

Bachmann, Sven; De Roeck, Wojciech; Fraas, Martin

2018-03-01

The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter ɛ. Under suitable assumptions the solution of the time-inhomogenous equation stays close to an instantaneous fixpoint. In the present paper, we prove an adiabatic theorem with an error bound that is independent of the number of degrees of freedom. Our setup is that of quantum spin systems where the manifold of ground states is separated from the rest of the spectrum by a spectral gap. One important application is the proof of the validity of linear response theory for such extended, genuinely interacting systems. In general, this is a long-standing mathematical problem, which can be solved in the present particular case of a gapped system, relevant e.g. for the integer quantum Hall effect.

SHARP Demonstration Flight: Video Broadcast System for Research in Intelligent Flight Characterization and Control

NASA Technical Reports Server (NTRS)

Kitts, Christopher

2001-01-01

The NASA Ames Research Center (Thermal Protection Materials and Systems Branch) is investigating new ceramic materials for the thermal protection of atmospheric entry vehicles. An incremental approach to proving the capabilities of these materials calls for a lifting entry flight test of a sharp leading edge component on the proposed SHARP (Slender Hypervelocity Aerothermodynamic Research Probe) vehicle. This flight test will establish the aerothermal performance constraint under real lifting entry conditions. NASA Ames has been developing the SHARP test flight with SSDL (responsible for the SHARP S I vehicle avionics), Montana State University (responsible for the SHARP S I vehicle airframe), the Wickman Spacecraft and Propulsion Company (responsible for the sounding rocket and launch operations), and with the SCU Intelligent Robotics Program, The SCU team was added well after the rest of the development team had formed. The SCU role was to assist with the development of a real-time video broadcast system which would relay onboard flight video to a communication groundstation. The SCU team would also assist with general vehicle preparation as well as flight operations. At the time of the submission of the original SCU proposal, a test flight in Wyoming was originally targeted for September 2000. This date was moved several times into the Fall of 2000. It was then postponed until the Spring of 2001, and later pushed into late Summer 2001. To date, the flight has still not taken place. These project delays resulted in SCU requesting several no-cost extensions to the project. Based on the most recent conversations with the project technical lead, Paul Kolodjiez, the current plan is for the overall SHARP team to assemble what exists of the vehicle, to document the system, and to 'mothball' the vehicle in anticipation of future flight and funding opportunities.

Driving Skills Training for Older Adults: An Assessment of DriveSharp.

PubMed

Johnston, Katherine A; Borkenhagen, David; Scialfa, Charles T

2015-12-01

RÉSUMÉ Les procédures de formation cognitive informatique visent à augmenter la sécurité en améliorant les compétences relatives à la conduite, comme la vitesse-de-traitement et le Useful Field of View. L'étude actuelle a évalué l'efficacité du DriveSharp dans la formation des conducteurs âgés dans un cadre de classe réaliste. Les participants (n = 24) ont assisté à 10 heures de cours de DriveSharp pendant 5 semaines. Les séances pré- et post-test ont evalués améliorations sur un essai dynamique de la perception du risque, Trails A et Trails B. Un groupe de contrôle (n = 18) a terminé seulement les séances pré- et post-test. En classe, les temps de formation étaient plus bas que prévus. L'amélioration des participants aux jeux ont stabilisée après la première évaluation, et le groupe de DriveSharp n'a pas démontré une amélioration significative des performances sur les tests, par rapport au groupe de contrôle. Parmi plusieurs questions relatives à la facilité d'utilisation, les plus problématiques étaient le malentendudes objectifs de la tâche et la différence entre la formation et l'évaluation. Il y a plusieurs implications pour ceux qui utilisent DriveSharp pour améliorer la sécurité des conducteurs âgés.

Thermodynamic laws and equipartition theorem in relativistic Brownian motion.

PubMed

Koide, T; Kodama, T

2011-06-01

We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.

Radial fingering under arbitrary viscosity and density ratios

NASA Astrophysics Data System (ADS)

Anjos, Pedro H. A.; Dias, Eduardo O.; Miranda, José A.

2017-08-01

We study viscous fingering formation in radial Hele-Shaw cell geometry considering the combined action of capillary and inertial effects for arbitrary values of viscosity and density ratios. We tackle the problem by employing a perturbative mode-coupling approach and focus our attention on weakly nonlinear stages of the dynamics. If inertial effects are neglected, our theoretical results indicate that the shape of the resulting interfacial patterns is significantly affected by changes in the viscosity ratio. Under such conditions, the growing fingers tend to proliferate through a repeated ramification process (e.g., by finger bifurcation, quadrifurcation, etc.) as the capillary number is increased. Nevertheless, we find that this scenario is dramatically altered when inertia is taken into account. When inertia is relevant, the conventional finger splitting morphologies are replaced by three-lobed structures, characterized by the occurrence of sidebranching phenomena. We verify that slightly different types of sidebranched patterns arise, presenting either wide or sharp fingertips, for a range of capillary numbers and density ratios.

A no-go theorem for monodromy inflation

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

Andriot, David, E-mail: david.andriot@aei.mpg.de

2016-03-01

We study the embedding of the monodromy inflation mechanism by E. Silverstein and A. Westphal (2008) in a concrete compactification setting. To that end, we look for an appropriate vacuum of type IIA supergravity, corresponding to the minimum of the inflaton potential. We prove a no-go theorem on the existence of such a vacuum, using ten-dimensional equations of motion. Anti-de Sitter and Minkowski vacua are ruled out; de Sitter vacua are not excluded, but have a lower bound on their cosmological constant which is too high for phenomenology.

Noncommutative gauge theories and Kontsevich's formality theorem

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schupp, P.; Wess, J.

2001-09-01

The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a "Mini Seiberg-Witten map" that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor.

The virtual-casing principle and Helmholtz's theorem

DOE PAGES

Hanson, J. D.

2015-09-10

The virtual-casing principle is used in plasma physics to convert a Biot–Savart integration over a current distribution into a surface integral over a surface that encloses the current. In many circumstances, use of virtual casing can significantly speed up the computation of magnetic fields. In this paper, a virtual-casing principle is derived for a general vector field with arbitrary divergence and curl. This form of the virtual-casing principle is thus applicable to both magnetostatic fields and electrostatic fields. The result is then related to Helmholtz's theorem.

A mathematical proof and example that Bayes's Theorem is fundamental to actuarial estimates of sexual recidivism risk.

PubMed

Donaldson, Theodore; Wollert, Richard

2008-06-01

Expert witnesses in sexually violent predator (SVP) cases often rely on actuarial instruments to make risk determinations. Many questions surround their use, however. Bayes's Theorem holds much promise for addressing these questions. Some experts nonetheless claim that Bayesian analyses are inadmissible in SVP cases because they are not accepted by the relevant scientific community. This position is illogical because Bayes's Theorem is simply a probabilistic restatement of the way that frequency data are combined to arrive at whatever recidivism rates are paired with each test score in an actuarial table. This article presents a mathematical proof and example validating this assertion. The advantages and implications of a logic model that combines Bayes's Theorem and the null hypothesis are also discussed.

Noether's Theorem and its Inverse of Birkhoffian System in Event Space Based on Herglotz Variational Problem

NASA Astrophysics Data System (ADS)

Tian, X.; Zhang, Y.

2018-03-01

Herglotz variational principle, in which the functional is defined by a differential equation, generalizes the classical ones defining the functional by an integral. The principle gives a variational principle description of nonconservative systems even when the Lagrangian is independent of time. This paper focuses on studying the Noether's theorem and its inverse of a Birkhoffian system in event space based on the Herglotz variational problem. Firstly, according to the Herglotz variational principle of a Birkhoffian system, the principle of a Birkhoffian system in event space is established. Secondly, its parametric equations and two basic formulae for the variation of Pfaff-Herglotz action of a Birkhoffian system in event space are obtained. Furthermore, the definition and criteria of Noether symmetry of the Birkhoffian system in event space based on the Herglotz variational problem are given. Then, according to the relationship between the Noether symmetry and conserved quantity, the Noether's theorem is derived. Under classical conditions, Noether's theorem of a Birkhoffian system in event space based on the Herglotz variational problem reduces to the classical ones. In addition, Noether's inverse theorem of the Birkhoffian system in event space based on the Herglotz variational problem is also obtained. In the end of the paper, an example is given to illustrate the application of the results.

On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem

PubMed Central

Li, Jiawei; Kendall, Graham

2015-01-01

In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games. PMID:26288088

Variational Implicit Solvation with Solute Molecular Mechanics: From Diffuse-Interface to Sharp-Interface Models.

PubMed

Li, Bo; Zhao, Yanxiang

2013-01-01

Central in a variational implicit-solvent description of biomolecular solvation is an effective free-energy functional of the solute atomic positions and the solute-solvent interface (i.e., the dielectric boundary). The free-energy functional couples together the solute molecular mechanical interaction energy, the solute-solvent interfacial energy, the solute-solvent van der Waals interaction energy, and the electrostatic energy. In recent years, the sharp-interface version of the variational implicit-solvent model has been developed and used for numerical computations of molecular solvation. In this work, we propose a diffuse-interface version of the variational implicit-solvent model with solute molecular mechanics. We also analyze both the sharp-interface and diffuse-interface models. We prove the existence of free-energy minimizers and obtain their bounds. We also prove the convergence of the diffuse-interface model to the sharp-interface model in the sense of Γ-convergence. We further discuss properties of sharp-interface free-energy minimizers, the boundary conditions and the coupling of the Poisson-Boltzmann equation in the diffuse-interface model, and the convergence of forces from diffuse-interface to sharp-interface descriptions. Our analysis relies on the previous works on the problem of minimizing surface areas and on our observations on the coupling between solute molecular mechanical interactions with the continuum solvent. Our studies justify rigorously the self consistency of the proposed diffuse-interface variational models of implicit solvation.

A rare case of a sharp foreign body on the vocal cord.

PubMed

Nor Hisyam, C I; Misron, K; Mohamad, I

2017-01-01

A foreign body (FB) in the upper aerodigestive tract is a common clinical problem that presents as as acute emergency. Sharp FB, such as fish bone or chicken bone, commonly lodges in the tonsil, base of tongue, vallecula or pyriform fossa. Dislodgement of a FB into the laryngopharynx is very rare and specifically onto the vocal cord is extremely uncommon. This case report illustrates a rare case of a sharp FB that was dislodged into the airway and stuck on to the right vocal cord, which was removed under local anaesthesia.

Convex Regression with Interpretable Sharp Partitions

PubMed Central

Petersen, Ashley; Simon, Noah; Witten, Daniela

2016-01-01

We consider the problem of predicting an outcome variable on the basis of a small number of covariates, using an interpretable yet non-additive model. We propose convex regression with interpretable sharp partitions (CRISP) for this task. CRISP partitions the covariate space into blocks in a data-adaptive way, and fits a mean model within each block. Unlike other partitioning methods, CRISP is fit using a non-greedy approach by solving a convex optimization problem, resulting in low-variance fits. We explore the properties of CRISP, and evaluate its performance in a simulation study and on a housing price data set. PMID:27635120

A Layer Framework to Investigate Student Understanding and Application of the Existence and Uniqueness Theorems of Differential Equations

ERIC Educational Resources Information Center

Raychaudhuri, D.

2007-01-01

The focus of this paper is on student interpretation and usage of the existence and uniqueness theorems for first-order ordinary differential equations. The inherent structure of the theorems is made explicit by the introduction of a framework of layers concepts-conditions-connectives-conclusions, and we discuss the manners in which students'…

Black holes, information, and the universal coefficient theorem

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

Patrascu, Andrei T.

2016-07-15

General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article, I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by the demanding invariance of the laws of physics to the change of coefficient structures in cohomology.

Rowlands' Duality Principle: A Generalization of Noether's Theorem?

NASA Astrophysics Data System (ADS)

Karam, Sabah E.

This paper will examine a physical principle that has been used in making valid predictions and generalizes established conservation laws. In a previous paper it was shown how Rowlands' zero-totality condition could be viewed as a generalization of Newton's third law of motion. In this paper it will be argued that Rowlands' Duality Principle is a generalization of Noether's Theorem and that the two principles taken together are truly foundational principles that have tamed Metaphysics.

Individual and Collective Analyses of the Genesis of Student Reasoning Regarding the Invertible Matrix Theorem in Linear Algebra

ERIC Educational Resources Information Center

Wawro, Megan Jean

2011-01-01

In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

Glimpse of Bagnold Dunes Edging Mount Sharp

NASA Image and Video Library

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

Improvement in perception of image sharpness through the addition of noise and its relationship with memory texture

NASA Astrophysics Data System (ADS)

Wan, Xiazi; Kobayashi, Hiroyuki; Aoki, Naokazu

2015-03-01

In a preceding study, we investigated the effects of image noise on the perception of image sharpness using white noise, and one- and two-dimensional single-frequency sinusoidal patterns as stimuli. This study extends our preceding study by evaluating natural color images, rather than black-and-white patterns. The results showed that the effect of noise in improving image sharpness perception is more evident in blurred images than in sharp images. This is consistent with the results of the preceding study. In another preceding study, we proposed "memory texture" to explain the preferred granularity of images, as a concept similar to "memory color" for preferred color reproduction. We observed individual differences in type of memory texture for each object, that is, white or 1/f noise. This study discusses the relationship between improvement of sharpness perception by adding noise, and the memory texture, following its individual differences. We found that memory texture is one of the elements that affect sharpness perception.

Applications of the theorem of Pythagoras in R3

NASA Astrophysics Data System (ADS)

Srinivasan, V. K.

2010-01-01

Three distinct points ? and ? with ? are taken, respectively on the x, y and the z-axes of a rectangular coordinate system in ? Using the converse of the theorem of Pythagoras, it is shown that the triangle ? can never be a right-angled triangle. The result seems to be intuitive, but nevertheless requires a proof. As an application, some intuitive results about a tetrahedron are confirmed.

Consistency relations for sharp inflationary non-Gaussian features

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

Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris

If cosmic inflation suffered tiny time-dependent deviations from the slow-roll regime, these would induce the existence of small scale-dependent features imprinted in the primordial spectra, with their shapes and sizes revealing information about the physics that produced them. Small sharp features could be suppressed at the level of the two-point correlation function, making them undetectable in the power spectrum, but could be amplified at the level of the three-point correlation function, offering us a window of opportunity to uncover them in the non-Gaussian bispectrum. In this article, we show that sharp features may be analyzed using only data coming frommore » the three point correlation function parametrizing primordial non-Gaussianity. More precisely, we show that if features appear in a particular non-Gaussian triangle configuration (e.g. equilateral, folded, squeezed), these must reappear in every other configuration according to a specific relation allowing us to correlate features across the non-Gaussian bispectrum. As a result, we offer a method to study scale-dependent features generated during inflation that depends only on data coming from measurements of non-Gaussianity, allowing us to omit data from the power spectrum.« less

Does the Coase theorem hold in real markets? An application to the negotiations between waterworks and farmers in Denmark.

PubMed

Abildtrup, Jens; Jensen, Frank; Dubgaard, Alex

2012-01-01

The Coase theorem depends on a number of assumptions, among others, perfect information about each other's payoff function, maximising behaviour and zero transaction costs. An important question is whether the Coase theorem holds for real market transactions when these assumptions are violated. This is the question examined in this paper. We consider the results of Danish waterworks' attempts to establish voluntary cultivation agreements with Danish farmers. A survey of these negotiations shows that the Coase theorem is not robust in the presence of imperfect information, non-maximising behaviour and transaction costs. Thus, negotiations between Danish waterworks and farmers may not be a suitable mechanism to achieve efficiency in the protection of groundwater quality due to violations of the assumptions of the Coase theorem. The use of standard schemes or government intervention (e.g. expropriation) may, under some conditions, be a more effective and cost efficient approach for the protection of vulnerable groundwater resources in Denmark. Copyright © 2011 Elsevier Ltd. All rights reserved.

STABILITY OF GAS CLOUDS IN GALACTIC NUCLEI: AN EXTENDED VIRIAL THEOREM

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

Chen, Xian; Cuadra, Jorge; Amaro-Seoane, Pau, E-mail: xchen@astro.puc.cl, E-mail: jcuadra@astro.puc.cl, E-mail: Pau.Amaro-Seoane@aei.mpg.de

2016-03-10

Cold gas entering the central 1–10{sup 2} pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH) to turn on an active galactic nucleus (AGN). The conventional criteria to assess the stability of these clouds, such as the Jeans criterion and Roche (or tidal) limit, are insufficient here, because they assume the dominance of self-gravity in binding a cloud, and neglect external agents, such as pressure and tidal forces, which are common in galactic nuclei. We formulatemore » a new scheme for judging this stability. We first revisit the conventional Virial theorem, taking into account an external pressure, to identify the correct range of masses that lead to stable clouds. We then extend the theorem to further include an external tidal field, which is equally crucial for the stability in the region of our interest—in dense star clusters, around SMBHs. We apply our extended Virial theorem to find new solutions to controversial problems, namely, the stability of the gas clumps in AGN tori, the circum-nuclear disk in the Galactic Center, and the central molecular zone of the Milky Way. The masses we derive for these structures are orders of magnitude smaller than the commonly used Virial masses (equivalent to the Jeans mass). Moreover, we prove that these clumps are stable, contrary to what one would naively deduce from the Roche (tidal) limit.« less

Haemothorax following bullectomy caused by a sharp edge of the Endoloop.

PubMed

Otsuka, Hajime; Hata, Yoshinobu; Takagi, Keigo; Sato, Fumitomo

2013-05-01

A 22-year old man presented with a massive haemothorax 25 days after bullectomy for a spontaneous pneumothorax. Thoracoscopic surgery revealed ongoing bleeding from the chest wall caused by a sharp edge of the Endoloop Ligature (Ethicon Endo-Surgery) used to resect the remaining small part of the lung at the earlier staple bullectomy. The point where bleeding was occurring was clipped and covered using a collagen patch coated with human fibrinogen and thrombin. The protruding sharp edge of the Endoloop was excised together with the surrounding lung tissue, using a stapler. Although prevention of this type of complication is difficult, awareness of the potential problem may help in managing such extremely rare events.

Haemothorax following bullectomy caused by a sharp edge of the Endoloop

PubMed Central

Otsuka, Hajime; Hata, Yoshinobu; Takagi, Keigo; Sato, Fumitomo

2013-01-01

A 22-year old man presented with a massive haemothorax 25 days after bullectomy for a spontaneous pneumothorax. Thoracoscopic surgery revealed ongoing bleeding from the chest wall caused by a sharp edge of the Endoloop Ligature (Ethicon Endo-Surgery) used to resect the remaining small part of the lung at the earlier staple bullectomy. The point where bleeding was occurring was clipped and covered using a collagen patch coated with human fibrinogen and thrombin. The protruding sharp edge of the Endoloop was excised together with the surrounding lung tissue, using a stapler. Although prevention of this type of complication is difficult, awareness of the potential problem may help in managing such extremely rare events. PMID:23407693

Relationship of intentional self-harm using sharp objects with depressive and dissociative tendencies in pre-adolescence-adolescence.

PubMed

Sho, Noriko; Oiji, Arata; Konno, Chizue; Toyohara, Koji; Minami, Tatsuya; Arai, Takashi; Seike, Yoji

2009-06-01

The objectives of the present study were to (i) evaluate the prevalence of children and adolescents who have engaged in intentional self-harm using a sharp object; and (ii) investigate the relationship between self-harm with sharp objects and depressive tendencies or dissociative tendencies. A total of 1938 students in grades 5-12 in Yokohama, Japan, were enrolled, and they completed anonymous self-report questionnaires including a question about intentional self-harm with a sharp object, the Depression Self-Rating Scale for Children (DSRSC) and the Adolescent Dissociative Experiences Scale (A-DES). The prevalence of self-harm using sharp object was 5.4% among male 5th-6th graders, 4.0% among female 5th-6th graders, 5.3% among male 7th-9th graders, 15.1% among female 7th-9th graders, 6.6% among male 10th-12th graders, and 9.6% among female 10th-12th graders. Categorical regression analysis showed that a small amount of variance in self-harm by sharp object was explained by DSRSC and A-DES scores. Self-harm with a sharp object was prevalent among pre-adolescents and adolescents and was associated with depressive and dissociative tendencies.

The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: SHARPs - Space-Weather HMI Active Region Patches

NASA Astrophysics Data System (ADS)

Bobra, M. G.; Sun, X.; Hoeksema, J. T.; Turmon, M.; Liu, Y.; Hayashi, K.; Barnes, G.; Leka, K. D.

2014-09-01

A new data product from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) called Space-weather HMI Active Region Patches ( SHARPs) is now available. SDO/HMI is the first space-based instrument to map the full-disk photospheric vector magnetic field with high cadence and continuity. The SHARP data series provide maps in patches that encompass automatically tracked magnetic concentrations for their entire lifetime; map quantities include the photospheric vector magnetic field and its uncertainty, along with Doppler velocity, continuum intensity, and line-of-sight magnetic field. Furthermore, keywords in the SHARP data series provide several parameters that concisely characterize the magnetic-field distribution and its deviation from a potential-field configuration. These indices may be useful for active-region event forecasting and for identifying regions of interest. The indices are calculated per patch and are available on a twelve-minute cadence. Quick-look data are available within approximately three hours of observation; definitive science products are produced approximately five weeks later. SHARP data are available at jsoc.stanford.edu and maps are available in either of two different coordinate systems. This article describes the SHARP data products and presents examples of SHARP data and parameters.

From the necessary to the possible: the genesis of the spin-statistics theorem

NASA Astrophysics Data System (ADS)

Blum, Alexander

2014-12-01

The spin-statistics theorem, which relates the intrinsic angular momentum of a single particle to the type of quantum statistics obeyed by a system of many such particles, is one of the central theorems in quantum field theory and the physics of elementary particles. It was first formulated in 1939/40 by Wolfgang Pauli and his assistant Markus Fierz. This paper discusses the developments that led up to this first formulation, starting from early attempts in the late 1920s to explain why charged matter particles obey Fermi-Dirac statistics, while photons obey Bose-Einstein statistics. It is demonstrated how several important developments paved the way from such general philosophical musings to a general (and provable) theorem, most notably the use of quantum field theory, the discovery of new elementary particles, and the generalization of the notion of spin. It is also discussed how the attempts to prove a spin-statistics connection were driven by Pauli from formal to more physical arguments, culminating in Pauli's 1940 proof. This proof was a major success for the beleaguered theory of quantum field theory and the methods Pauli employed proved essential for the renaissance of quantum field theory and the development of renormalization techniques in the late 1940s.

On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator

ERIC Educational Resources Information Center

Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru

2009-01-01

The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.

The stratigraphy and evolution of lower Mount Sharp from spectral, morphological, and thermophysical orbital data sets.

PubMed

Fraeman, A A; Ehlmann, B L; Arvidson, R E; Edwards, C S; Grotzinger, J P; Milliken, R E; Quinn, D P; Rice, M S

2016-09-01

We have developed a refined geologic map and stratigraphy for lower Mount Sharp using coordinated analyses of new spectral, thermophysical, and morphologic orbital data products. The Mount Sharp group consists of seven relatively planar units delineated by differences in texture, mineralogy, and thermophysical properties. These units are (1-3) three spatially adjacent units in the Murray formation which contain a variety of secondary phases and are distinguishable by thermal inertia and albedo differences, (4) a phyllosilicate-bearing unit, (5) a hematite-capped ridge unit, (6) a unit associated with material having a strongly sloped spectral signature at visible near-infrared wavelengths, and (7) a layered sulfate unit. The Siccar Point group consists of the Stimson formation and two additional units that unconformably overlie the Mount Sharp group. All Siccar Point group units are distinguished by higher thermal inertia values and record a period of substantial deposition and exhumation that followed the deposition and exhumation of the Mount Sharp group. Several spatially extensive silica deposits associated with veins and fractures show that late-stage silica enrichment within lower Mount Sharp was pervasive. At least two laterally extensive hematitic deposits are present at different stratigraphic intervals, and both are geometrically conformable with lower Mount Sharp strata. The occurrence of hematite at multiple stratigraphic horizons suggests redox interfaces were widespread in space and/or in time, and future measurements by the Mars Science Laboratory Curiosity rover will provide further insights into the depositional settings of these and other mineral phases.

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.

A Hybrid Common Fixed Point Theorem under Certain Recent Properties

PubMed Central

Imdad, Mohammad

2014-01-01

We prove a common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings via common limit range property. Our result improves some results from the existing literature, especially the ones contained in Sintunavarat and Kumam (2009). Some illustrative and interesting examples to highlight the realized improvements are also furnished. PMID:24592191

A Gleason-Type Theorem for Any Dimension Based on a Gambling Formulation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco

2017-07-01

Based on a gambling formulation of quantum mechanics, we derive a Gleason-type theorem that holds for any dimension n of a quantum system, and in particular for n=2. The theorem states that the only logically consistent probability assignments are exactly the ones that are definable as the trace of the product of a projector and a density matrix operator. In addition, we detail the reason why dispersion-free probabilities are actually not valid, or rational, probabilities for quantum mechanics, and hence should be excluded from consideration.

Autonomous quantum to classical transitions and the generalized imaging theorem

NASA Astrophysics Data System (ADS)

Briggs, John S.; Feagin, James M.

2016-03-01

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. Here we prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Currently, the quantum to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.

Autonomous quantum to classical transitions and the generalized imaging theorem

DOE PAGES

Briggs, John S.; Feagin, James M.

2016-03-16

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. We prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Now, the quantummore » to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.« less

Design of multiplier-less sharp transition width non-uniform filter banks using gravitational search algorithm

NASA Astrophysics Data System (ADS)

Bindiya T., S.; Elias, Elizabeth

2015-01-01

In this paper, multiplier-less near-perfect reconstruction tree-structured filter banks are proposed. Filters with sharp transition width are preferred in filter banks in order to reduce the aliasing between adjacent channels. When sharp transition width filters are designed as conventional finite impulse response filters, the order of the filters will become very high leading to increased complexity. The frequency response masking (FRM) method is known to result in linear-phase sharp transition width filters with low complexity. It is found that the proposed design method, which is based on FRM, gives better results compared to the earlier reported results, in terms of the number of multipliers when sharp transition width filter banks are needed. To further reduce the complexity and power consumption, the tree-structured filter bank is made totally multiplier-less by converting the continuous filter bank coefficients to finite precision coefficients in the signed power of two space. This may lead to performance degradation and calls for the use of a suitable optimisation technique. In this paper, gravitational search algorithm is proposed to be used in the design of the multiplier-less tree-structured uniform as well as non-uniform filter banks. This design method results in uniform and non-uniform filter banks which are simple, alias-free, linear phase and multiplier-less and have sharp transition width.

Application of the SHARP Toolkit to Sodium-Cooled Fast Reactor Challenge Problems

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

Shemon, E. R.; Yu, Y.; Kim, T. K.

The Simulation-based High-efficiency Advanced Reactor Prototyping (SHARP) toolkit is under development by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) Campaign of the U.S. Department of Energy, Office of Nuclear Energy. To better understand and exploit the benefits of advanced modeling simulations, the NEAMS Campaign initiated the “Sodium-Cooled Fast Reactor (SFR) Challenge Problems” task, which include the assessment of hot channel factors (HCFs) and the demonstration of zooming capability using the SHARP toolkit. If both challenge problems are resolved through advanced modeling and simulation using the SHARP toolkit, the economic competitiveness of a SFR can be significantly improved. The effortsmore » in the first year of this project focused on the development of computational models, meshes, and coupling procedures for multi-physics calculations using the neutronics (PROTEUS) and thermal-hydraulic (Nek5000) components of the SHARP toolkit, as well as demonstration of the HCF calculation capability for the 100 MWe Advanced Fast Reactor (AFR-100) design. Testing the feasibility of the SHARP zooming capability is planned in FY 2018. The HCFs developed for the earlier SFRs (FFTF, CRBR, and EBR-II) were reviewed, and a subset of these were identified as potential candidates for reduction or elimination through high-fidelity simulations. A one-way offline coupling method was used to evaluate the HCFs where the neutronics solver PROTEUS computes the power profile based on an assumed temperature, and the computational fluid dynamics solver Nek5000 evaluates the peak temperatures using the neutronics power profile. If the initial temperature profile used in the neutronics calculation is reasonably accurate, the one-way offline method is valid because the neutronics power profile has weak dependence on small temperature variation. In order to get more precise results, the proper temperature profile for initial neutronics calculations was obtained

Summer High School Apprenticeship Research Program (SHARP) of the National Aeronautics and Space Administration

NASA Technical Reports Server (NTRS)

1984-01-01

A total of 125 talented high school students had the opportunity to gain first hand experience about science and engineering careers by working directly with a NASA scientist or engineer during the summer. This marked the fifth year of operation for NASA's Summer High School Apprenticehsip Research Program (SHARP). Ferguson Bryan served as the SHARP contractor and worked closely with NASA staff at Headquarters and the eight participating sites to plan, implement, and evaluate the Program. The main objectives were to strengthen SHARP and expand the number of students in the Program. These eight sites participated in the Program: Ames Research Center North, Ames' Dryden Flight Research Facility, Goddard Space Flight Center, Goddard's Wallops Flight Facility, Kennedy Space Center, Langley Research Center, Lewis Research Center, and Marshall Space Flight Center.

Four Proofs of the Converse of the Chinese Remainder Theorem

ERIC Educational Resources Information Center

Dobbs, D. E.

2008-01-01

Four proofs, designed for classroom use in varying levels of courses on abstract algebra, are given for the converse of the classical Chinese Remainder Theorem over the integers. In other words, it is proved that if m and n are integers greater than 1 such that the abelian groups [double-struck z][subscript m] [direct sum] [double-struck…

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,…

Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

NASA Astrophysics Data System (ADS)

Sumin, M. I.

2015-06-01

A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.

Enhanced Transmissions Through Three-dimensional Cascade Sharp Waveguide Bends Using C-slit Diaphragms.

PubMed

Yang, Rui; Hu, Bowei; Zhang, Aofang; Gao, Dongxing; Wang, Hui; Shi, Ayuan; Lei, Zhenya; Yang, Pei

2017-03-21

Transmission properties through sharp rectangular waveguide bends are investigated to determine the cut-off bending angles of the wave propagation. We show that a simple metallic diaphragm at the bending corner with properly devised sub-wavelength defect apertures of C-slits would be readily to turn on the transmissions with scarce reflections of the propagating modes, while preserving the integrity of the transmitting fields soon after the bends. In particularly, our design also demonstrates the capability of eliminating all the unwanted cavity resonant transmissions that exist in the three-dimensional cascade sharp waveguide bends, and solely let the desired signals travel along the whole passage of the waveguide. The present approach, using C-slit diaphragms to support the sharp bending behaviors of the guided waves with greatly enhanced transmissions, would be especially effective in constructing novel waveguides and pave the way for the development of more compact and miniaturized electromagnetic systems that exploit these waveguide bends.

A no-hair theorem for stars in Horndeski theories

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

Lehébel, A.; Babichev, E.; Charmousis, C., E-mail: antoine.lehebel@th.u-psud.fr, E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr

We consider a generic scalar-tensor theory involving a shift-symmetric scalar field and minimally coupled matter fields. We prove that the Noether current associated with shift-symmetry vanishes in regular, spherically symmetric and static spacetimes. We use this fact to prove the absence of scalar hair for spherically symmetric and static stars in Horndeski and beyond theories. We carefully detail the validity of this no-hair theorem.

Implementing Metamathematics as an Approach to Automatic Theorem Proving

DTIC Science & Technology

1989-01-01

study of artifcial intelligence . Prominent pioneers in theic ranks are the likes of Allen Newel, Herbert Simon, and John McCarthy. On the other hand, the...researchers of diverse interests. There are those interested in studying intelligence , espe- cially reasoning. They argue that reasoning and problem solving...are critical to integce and that proving theorems is intelligent behavior. People with those interests will usually associate themselves with the

Implementation of mutual information and bayes theorem for classification microarray data

NASA Astrophysics Data System (ADS)

Dwifebri Purbolaksono, Mahendra; Widiastuti, Kurnia C.; Syahrul Mubarok, Mohamad; Adiwijaya; Aminy Ma’ruf, Firda

2018-03-01

Microarray Technology is one of technology which able to read the structure of gen. The analysis is important for this technology. It is for deciding which attribute is more important than the others. Microarray technology is able to get cancer information to diagnose a person’s gen. Preparation of microarray data is a huge problem and takes a long time. That is because microarray data contains high number of insignificant and irrelevant attributes. So, it needs a method to reduce the dimension of microarray data without eliminating important information in every attribute. This research uses Mutual Information to reduce dimension. System is built with Machine Learning approach specifically Bayes Theorem. This theorem uses a statistical and probability approach. By combining both methods, it will be powerful for Microarray Data Classification. The experiment results show that system is good to classify Microarray data with highest F1-score using Bayesian Network by 91.06%, and Naïve Bayes by 88.85%.

The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup

NASA Astrophysics Data System (ADS)

Lehrer, G. I.; Zhang, R. B.

2017-01-01

We give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space. In this way, super Schur-Weyl-Brauer duality is established between the orthosymplectic supergroup of superdimension ( m|2 n) and the Brauer algebra with parameter m - 2 n. The result may be interpreted either in terms of the group scheme OSp( V) over C, where V is a finite dimensional super space, or as a statement about the orthosymplectic Lie supergroup over the infinite dimensional Grassmann algebra {Λ}. We take the latter point of view here, and also state a corresponding theorem for the orthosymplectic Lie superalgebra, which involves an extra invariant generator, the super-Pfaffian.

Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect

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

Macdougall, James, E-mail: jbm34@mail.fresnostate.edu; Singleton, Douglas, E-mail: dougs@csufresno.edu

2014-04-15

Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect—the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology ofmore » the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed.« less

The stratigraphy and evolution of lower Mount Sharp from spectral, morphological, and thermophysical orbital data sets

PubMed Central

Ehlmann, B. L.; Arvidson, R. E.; Edwards, C. S.; Grotzinger, J. P.; Milliken, R. E.; Quinn, D. P.; Rice, M. S.

2016-01-01

Abstract We have developed a refined geologic map and stratigraphy for lower Mount Sharp using coordinated analyses of new spectral, thermophysical, and morphologic orbital data products. The Mount Sharp group consists of seven relatively planar units delineated by differences in texture, mineralogy, and thermophysical properties. These units are (1–3) three spatially adjacent units in the Murray formation which contain a variety of secondary phases and are distinguishable by thermal inertia and albedo differences, (4) a phyllosilicate‐bearing unit, (5) a hematite‐capped ridge unit, (6) a unit associated with material having a strongly sloped spectral signature at visible near‐infrared wavelengths, and (7) a layered sulfate unit. The Siccar Point group consists of the Stimson formation and two additional units that unconformably overlie the Mount Sharp group. All Siccar Point group units are distinguished by higher thermal inertia values and record a period of substantial deposition and exhumation that followed the deposition and exhumation of the Mount Sharp group. Several spatially extensive silica deposits associated with veins and fractures show that late‐stage silica enrichment within lower Mount Sharp was pervasive. At least two laterally extensive hematitic deposits are present at different stratigraphic intervals, and both are geometrically conformable with lower Mount Sharp strata. The occurrence of hematite at multiple stratigraphic horizons suggests redox interfaces were widespread in space and/or in time, and future measurements by the Mars Science Laboratory Curiosity rover will provide further insights into the depositional settings of these and other mineral phases. PMID:27867788

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

NASA Astrophysics Data System (ADS)

Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.

2008-11-01

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Isotopic ratios in outbursting comet C/2015 ER61

NASA Astrophysics Data System (ADS)

Yang, Bin; Hutsemékers, Damien; Shinnaka, Yoshiharu; Opitom, Cyrielle; Manfroid, Jean; Jehin, Emmanuël; Meech, Karen J.; Hainaut, Olivier R.; Keane, Jacqueline V.; Gillon, Michaël

2018-02-01

Isotopic ratios in comets are critical to understanding the origin of cometary material and the physical and chemical conditions in the early solar nebula. Comet C/2015 ER61 (PANSTARRS) underwent an outburst with a total brightness increase of 2 magnitudes on the night of 2017 April 4. The sharp increase in brightness offered a rare opportunity to measure the isotopic ratios of the light elements in the coma of this comet. We obtained two high-resolution spectra of C/2015 ER61 with UVES/VLT on the nights of 2017 April 13 and 17. At the time of our observations, the comet was fading gradually following the outburst. We measured the nitrogen and carbon isotopic ratios from the CN violet (0, 0) band and found that 12C/13C = 100 ± 15, 14N/15N = 130 ± 15. In addition, we determined the 14N/15N ratio from four pairs of NH2 isotopolog lines and measured 14N/15N = 140 ± 28. The measured isotopic ratios of C/2015 ER61 do not deviate significantly from those of other comets.

Cellular compartmentation follows rules: The Schnepf theorem, its consequences and exceptions: A biological membrane separates a plasmatic from a non-plasmatic phase.

PubMed

Moog, Daniel; Maier, Uwe G

2017-08-01

Is the spatial organization of membranes and compartments within cells subjected to any rules? Cellular compartmentation differs between prokaryotic and eukaryotic life, because it is present to a high degree only in eukaryotes. In 1964, Prof. Eberhard Schnepf formulated the compartmentation rule (Schnepf theorem), which posits that a biological membrane, the main physical structure responsible for cellular compartmentation, usually separates a plasmatic form a non-plasmatic phase. Here we review and re-investigate the Schnepf theorem by applying the theorem to different cellular structures, from bacterial cells to eukaryotes with their organelles and compartments. In conclusion, we can confirm the general correctness of the Schnepf theorem, noting explicit exceptions only in special cases such as endosymbiosis and parasitism. © 2017 WILEY Periodicals, Inc.

Curiosity Rover on Mount Sharp, Seen from Mars Orbit

NASA Image and Video Library

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

Liouville type theorems of a nonlinear elliptic equation for the V-Laplacian

NASA Astrophysics Data System (ADS)

Huang, Guangyue; Li, Zhi

2018-03-01

In this paper, we consider Liouville type theorems for positive solutions to the following nonlinear elliptic equation: Δ _V u+aulog u=0, where a is a nonzero real constant. By using gradient estimates, we obtain upper bounds of |\

TESTING THE NO-HAIR THEOREM WITH OBSERVATIONS IN THE ELECTROMAGNETIC SPECTRUM. II. BLACK HOLE IMAGES

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

Johannsen, Tim; Psaltis, Dimitrios, E-mail: timj@physics.arizona.ed, E-mail: dpsaltis@email.arizona.ed

2010-07-20

According to the no-hair theorem, all astrophysical black holes are fully described by their masses and spins. This theorem can be tested observationally by measuring (at least) three different multipole moments of the spacetimes of black holes. In this paper, we analyze images of black holes within a framework that allows us to calculate observables in the electromagnetic spectrum as a function of the mass, spin, and, independently, the quadrupole moment of a black hole. We show that a deviation of the quadrupole moment from the expected Kerr value leads to images of black holes that are either prolate ormore » oblate depending on the sign and magnitude of the deviation. In addition, there is a ring-like structure around the black hole shadow with a diameter of {approx}10 black hole masses that is substantially brighter than the image of the underlying accretion flow and that is independent of the astrophysical details of accretion flow models. We show that the shape of this ring depends directly on the mass, spin, and quadrupole moment of the black hole and can be used for an independent measurement of all three parameters. In particular, we demonstrate that this ring is highly circular for a Kerr black hole with a spin a {approx}< 0.9 M, independent of the observer's inclination, but becomes elliptical and asymmetric if the no-hair theorem is violated. Near-future very long baseline interferometric observations of Sgr A* will image this ring and may allow for an observational test of the no-hair theorem.« less

Cannula Versus Sharp Needle for Placement of Soft Tissue Fillers: An Observational Cadaver Study.

PubMed

van Loghem, Jani A J; Humzah, Dalvi; Kerscher, Martina

2017-12-13

Soft-tissue fillers have become important products for facial rejuvenation. Deep fat compartments and facial bones lose volume during the natural aging process. For the most natural-looking results, deep volumetric injections at strategic sites are therefore preferred. Supraperiosteal placement is performed with a sharp needle or a non-traumatic cannula. The primary objective was to determine whether there is a difference in precision between supraperiosteal placement with a sharp needle compared with a non-traumatic cannula in cadaver specimens. A secondary objective was to analyze the safety profiles of both injection techniques. Cadaver heads were injected with dye material and soft-tissue fillers at multiple aesthetic facial sites on the supraperiosteum and subsequently dissected for observation of dye and filler placement. The non-traumatic cannula technique resulted in product being confined to the deep anatomic layers. In contrast, with the sharp needle technique, material was placed in multiple anatomic layers, from the periosteum to more superficial skin layers. For both techniques results were consistent for all facial sites. Although direct extrapolation from cadavers to the in vivo situation cannot be made, cannulae showed more precision in placement of product. With the sharp needle, the material was injected on the periosteum, and then migrated in a retrograde direction along the trajectory of the needle path, ending up in multiple anatomic layers. The sharp needle technique also showed a higher complication risk with intra-arterial injection occurring, even though the needle tip was positioned on the periosteum and the product was injected with the needle in constant contact with the periosteum. © 2016 The American Society for Aesthetic Plastic Surgery, Inc. Reprints and permission: journals.permissions@oup.com

GENERAL VIEW OF SHARP FREEZE ROOM ON LEVEL 2; LOOKING ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

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

Ripples Beside Pahrump Hills Outcrop at Base of Mount Sharp

NASA Image and Video Library

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.

Possible violation of the optical theorem in LHC experiments

NASA Astrophysics Data System (ADS)

Kupczynski, M.

2014-12-01

The optical theorem (OT), allowing the determination of the total cross section for a hadron-hadron scattering from the imaginary part of the forward elastic scattering amplitude, is believed to be an unavoidable consequence of the conservation of probability and of the unitary S matrix. This is a fundamental theorem which contains an imaginary part of the forward elastic scattering amplitude that is not directly measurable. The impossibility of scattering phenomena without the elastic channel is considered to be a part of the quantum magic. However, if one takes seriously the idea that the hadrons are extended particles, one may define a unitary S matrix such that one cannot prove the OT. Moreover, data violating the OT do exist, but they are not conclusive due to the uncertainties related to the extrapolation of the differential elastic cross-section to the forward direction. These results were published several years ago, but they were forgotten. In this paper we will recall these results in an understandable way, and we will give the additional arguments why the OT can be violated in high energy strong interaction scattering and why it should be tested and not simply used as a tool in LHC experiments.

Entropic nonadditivity, H theorem, and nonlinear Klein-Kramers equations.

PubMed

Dos Santos, M A F; Lenzi, E K

2017-11-01

We use the H theorem to establish the entropy and the entropic additivity law for a system composed of subsystems, with the dynamics governed by the Klein-Kramers equations, by considering relations among the dynamics of these subsystems and their entropies. We start considering the subsystems governed by linear Klein-Kramers equations and verify that the Boltzmann-Gibbs entropy is appropriated to this dynamics, leading us to the standard entropic additivity, S_{BG}^{(1∪2)}=S_{BG}^{1}+S_{BG}^{2}, consistent with the fact that the distributions of the subsystem are independent. We then extend the dynamics of these subsystems to independent nonlinear Klein-Kramers equations. For this case, the results show that the H theorem is verified for a generalized entropy, which does not preserve the standard entropic additivity for independent distributions. In this scenario, consistent results are obtained when a suitable coupling among the nonlinear Klein-Kramers equations is considered, in which each subsystem modifies the other until an equilibrium state is reached. This dynamics, for the subsystems, results in the Tsallis entropy for the system and, consequently, verifies the relation S_{q}^{(1∪2)}=S_{q}^{1}+S_{q}^{2}+(1-q)S_{q}^{1}S_{q}^{2}/k, which is a nonadditive entropic relation.

The generalized second law implies a quantum singularity theorem

NASA Astrophysics Data System (ADS)

Wall, Aron C.

2013-08-01

The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose’s original singularity theorem, it implies that spacetime is null-geodesically incomplete inside black holes, and to the past of spatially infinite Friedmann-Robertson-Walker cosmologies. If space is finite instead, the generalized second law requires that there only be a finite amount of entropy producing processes in the past, unless there is a reversal of the arrow of time. In asymptotically flat spacetime, the generalized second law also rules out traversable wormholes, negative masses, and other forms of faster-than-light travel between asymptotic regions, as well as closed timelike curves. Furthermore it is impossible to form baby universes which eventually become independent of the mother universe, or to restart inflation. Since the semiclassical approximation is used only in regions with low curvature, it is argued that the results may hold in full quantum gravity. The introduction describes the second law and its time-reverse, in ordinary and generalized thermodynamics, using either the fine-grained or the coarse-grained entropy. (The fine-grained version is used in all results except those relating to the arrow of time.)

Developing a new solar radiation estimation model based on Buckingham theorem

NASA Astrophysics Data System (ADS)

Ekici, Can; Teke, Ismail

2018-06-01

While the value of solar radiation can be expressed physically in the days without clouds, this expression becomes difficult in cloudy and complicated weather conditions. In addition, solar radiation measurements are often not taken in developing countries. In such cases, solar radiation estimation models are used. Solar radiation prediction models estimate solar radiation using other measured meteorological parameters those are available in the stations. In this study, a solar radiation estimation model was obtained using Buckingham theorem. This theory has been shown to be useful in predicting solar radiation. In this study, Buckingham theorem is used to express the solar radiation by derivation of dimensionless pi parameters. This derived model is compared with temperature based models in the literature. MPE, RMSE, MBE and NSE error analysis methods are used in this comparison. Allen, Hargreaves, Chen and Bristow-Campbell models in the literature are used for comparison. North Dakota's meteorological data were used to compare the models. Error analysis were applied through the comparisons between the models in the literature and the model that is derived in the study. These comparisons were made using data obtained from North Dakota's agricultural climate network. In these applications, the model obtained within the scope of the study gives better results. Especially, in terms of short-term performance, it has been found that the obtained model gives satisfactory results. It has been seen that this model gives better accuracy in comparison with other models. It is possible in RMSE analysis results. Buckingham theorem was found useful in estimating solar radiation. In terms of long term performances and percentage errors, the model has given good results.

Assessing the Time Dependence of Reconnection With Poynting's Theorem: MMS Observations

NASA Astrophysics Data System (ADS)

Genestreti, K. J.; Cassak, P. A.; Varsani, A.; Burch, J. L.; Nakamura, R.; Wang, S.

2018-04-01

We investigate the time dependence of electromagnetic-field-to-plasma energy conversion in the electron diffusion region of asymmetric magnetic reconnection. To do so, we consider the terms in Poynting's theorem. In a steady state there is a perfect balance between the divergence of the electromagnetic energy flux ∇·S→ and the conversion between electromagnetic field and particle energy J→·E→. This energy balance is demonstrated with a particle-in-cell simulation of reconnection. We also evaluate each of the terms in Poynting's theorem during an observation of a magnetopause reconnection region by Magnetospheric Multiscale (MMS). We take the equivalence of both sides of Poynting's theorem as an indication that the errors associated with the approximation of each term with MMS data are small. We find that, for this event, balance between J→·E→=-∇·S→ is only achieved for a small fraction of the energy conversion region at/near the X-point. Magnetic energy was rapidly accumulating on either side of the current sheet at roughly 3 times the predicted energy conversion rate. Furthermore, we find that while J→·E→>0 and ∇·S→<0 are observed, as is expected for reconnection, the energy accumulation is driven by the overcompensation for J→·E→ by -∇·S→>J→·E→. We note that due to the assumptions necessary to do this calculation, the accurate evaluation of ∇·S→ may not be possible for every MMS-observed reconnection event; but, if possible, this is a simple approach to determine if reconnection is or is not in a steady state.

Ultra-sharp plasmonic resonances from monopole optical nanoantenna phased arrays

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

Li, Shi-Qiang; Bruce Buchholz, D.; Zhou, Wei

Diffractively coupled plasmonic resonances possess both ultra-sharp linewidths and giant electric field enhancement around plasmonic nanostructures. They can be applied to create a new generation of sensors, detectors, and nano-optical devices. However, all current designs require stringent index-matching at the resonance condition that limits their applicability. Here, we propose and demonstrate that it is possible to relieve the index-matching requirement and to induce ultra-sharp plasmon resonances in an ordered vertically aligned optical nano-antenna phased array by transforming a dipole resonance to a monopole resonance with a mirror plane. Due to the mirror image effect, the monopole resonance not only retainedmore » the dipole features but also enhanced them. The engineered resonances strongly suppressed the radiative decay channel, resulting in a four-order of magnitude enhancement in local electric field and a Q-factor greater than 200.« less

Fluctuation theorem for entropy production during effusion of a relativistic ideal gas.

PubMed

Cleuren, B; Willaert, K; Engel, A; Van den Broeck, C

2008-02-01

The probability distribution of the entropy production for the effusion of a relativistic ideal gas is calculated explicitly. This result is then extended to include particle and antiparticle pair production and annihilation. In both cases, the fluctuation theorem is verified.

Hybridization between Dusky Grouse and Sharp-tailed Grouse

USGS Publications Warehouse

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.

Restoring the consistency with the contact density theorem of a classical density functional theory of ions at a planar electrical double layer.

PubMed

Gillespie, Dirk

2014-11-01

Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991)PLRAAN1050-294710.1103/PhysRevA.44.5025] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993)JCPSA60021-960610.1063/1.464569], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied.

Towards a sharp-interface volume-of-fluid methodology for modeling evaporation

NASA Astrophysics Data System (ADS)

Pathak, Ashish; Raessi, Mehdi

2017-11-01

In modeling evaporation, the diffuse-interface (one-domain) formulation yields inaccurate results. Recent efforts approaching the problem via a sharp-interface (two-domain) formulation have shown significant improvements. The reasons behind their better performance are discussed in the present work. All available sharp-interface methods, however, exclusively employ the level-set. In the present work, we develop a sharp-interface evaporation model in a volume-of-fluid (VOF) framework in order to leverage its mass-conserving property as well as its ability to handle large topographical changes. We start with a critical review of the assumptions underlying the mathematical equations governing evaporation. For example, it is shown that the assumption of incompressibility can only be applied in special circumstances. The famous D2 law used for benchmarking is valid exclusively to steady-state test problems. Transient is present over significant lifetime of a micron-size droplet. Therefore, a 1D spherical fully transient model is developed to provide a benchmark transient solution. Finally, a 3D Cartesian Navier-Stokes evaporation solver is developed. Some preliminary validation test-cases are presented for static and moving drop evaporation. This material is based upon work supported by the Department of Energy, Office of Energy Efficiency and Renewable Energy and the Department of Defense, Tank and Automotive Research, Development, and Engineering Center, under Award Number DEEE0007292.

Emulation of anamorphic imaging on the SHARP extreme ultraviolet mask microscope

DOE PAGES

Benk, Markus P.; Wojdyla, Antoine; Chao, Weilun; ...

2016-07-12

The SHARP high-numerical aperture actinic reticle review project is a synchrotron-based, extreme ultraviolet (EUV) microscope dedicated to photomask research. SHARP emulates the illumination and imaging conditions of current EUV lithography scanners and those several generations into the future. An anamorphic imaging optic with increased mask-side numerical aperture (NA) in the horizontal and increased demagnification in the vertical direction has been proposed in this paper to overcome limitations of current multilayer coatings and extend EUV lithography beyond 0.33 NA. Zoneplate lenses with an anamorphic 4×/8× NA of 0.55 are fabricated and installed in the SHARP microscope to emulate anamorphic imaging. SHARP’smore » Fourier synthesis illuminator with a range of angles exceeding the collected solid angle of the newly designed elliptical zoneplates can produce arbitrary angular source spectra matched to anamorphic imaging. A target with anamorphic dense features down to 50-nm critical dimension is fabricated using 40 nm of nickel as the absorber. In a demonstration experiment, anamorphic imaging at 0.55 4×/8× NA and 6 deg central ray angle (CRA) is compared with conventional imaging at 0.5 4× NA and 8 deg CRA. A significant contrast loss in horizontal features is observed in the conventional images. Finally, the anamorphic images show the same image quality in the horizontal and vertical directions.« less

Emulation of anamorphic imaging on the SHARP extreme ultraviolet mask microscope

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

Benk, Markus P.; Wojdyla, Antoine; Chao, Weilun

The SHARP high-numerical aperture actinic reticle review project is a synchrotron-based, extreme ultraviolet (EUV) microscope dedicated to photomask research. SHARP emulates the illumination and imaging conditions of current EUV lithography scanners and those several generations into the future. An anamorphic imaging optic with increased mask-side numerical aperture (NA) in the horizontal and increased demagnification in the vertical direction has been proposed in this paper to overcome limitations of current multilayer coatings and extend EUV lithography beyond 0.33 NA. Zoneplate lenses with an anamorphic 4×/8× NA of 0.55 are fabricated and installed in the SHARP microscope to emulate anamorphic imaging. SHARP’smore » Fourier synthesis illuminator with a range of angles exceeding the collected solid angle of the newly designed elliptical zoneplates can produce arbitrary angular source spectra matched to anamorphic imaging. A target with anamorphic dense features down to 50-nm critical dimension is fabricated using 40 nm of nickel as the absorber. In a demonstration experiment, anamorphic imaging at 0.55 4×/8× NA and 6 deg central ray angle (CRA) is compared with conventional imaging at 0.5 4× NA and 8 deg CRA. A significant contrast loss in horizontal features is observed in the conventional images. Finally, the anamorphic images show the same image quality in the horizontal and vertical directions.« less

Hollow structure formation of intense ion beams with sharp edge in background plasmas

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

Hu, Zhang-Hu; Wang, You-Nian, E-mail: ynwang@dlut.edu.cn

The transport of intense ion beams with sharp radial beam edge in plasmas has been studied with two-dimensional electromagnetic particle simulations. The initial solid beam evolves into a hollow beam due to the nonlinear sharp transverse force peak in the regions of beam edge. The magnitude and nonlinearity of this peak are enhanced as the ion beam travels further into the plasma, due to the self-consistent interactions between the beam ions and the plasma electrons. This structure formation is shown to be independent on the beam radius.

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

Engaging Sharp-Leadenhall: An Interdisciplinary Faculty Collaboration in Service-Learning

ERIC Educational Resources Information Center

Falk, Audrey; Durington, Matthew; Lankford, Elsa

2012-01-01

This article reports on an interdisciplinary collaboration in the context of service-learning. Faculty members from the disciplines of family studies, anthropology, and media production worked collaboratively to develop and implement service-learning projects involving their classes and Sharp-Leadenhall, one of the oldest historically…