On the role of sharp chains in the transport theorem
NASA Astrophysics Data System (ADS)
Falach, L.; Segev, R.
2016-03-01
A generalized transport theorem for convecting irregular domains is presented in the setting of Federer's geometric measure theory. A prototypical r-dimensional domain is viewed as a flat r-chain of finite mass in an open set of an n-dimensional Euclidean space. The evolution of such a generalized domain in time is assumed to follow a continuous succession of Lipschitz embedding so that the spatial gradient may be nonexistent in a subset of the domain with zero measure. The induced curve is shown to be continuous with respect to the flat norm and differential with respect to the sharp norm on currents in Rn. A time-dependent property is naturally assigned to the evolving region via the action of an r-cochain on the current associated with the domain. Applying a representation theorem for cochains, the properties are shown to be locally represented by an r-form. Using these notions, a generalized transport theorem is presented.
A note on trader Sharpe Ratios.
Coates, John M; Page, Lionel
2009-01-01
Traders in the financial world are assessed by the amount of money they make and, increasingly, by the amount of money they make per unit of risk taken, a measure known as the Sharpe Ratio. Little is known about the average Sharpe Ratio among traders, but the Efficient Market Hypothesis suggests that traders, like asset managers, should not outperform the broad market. Here we report the findings of a study conducted in the City of London which shows that a population of experienced traders attain Sharpe Ratios significantly higher than the broad market. To explain this anomaly we examine a surrogate marker of prenatal androgen exposure, the second-to-fourth finger length ratio (2D:4D), which has previously been identified as predicting a trader's long term profitability. We find that it predicts the amount of risk taken by traders but not their Sharpe Ratios. We do, however, find that the traders' Sharpe Ratios increase markedly with the number of years they have traded, a result suggesting that learning plays a role in increasing the returns of traders. Our findings present anomalous data for the Efficient Markets Hypothesis. PMID:19946367
Sharp comparison theorems for the Klein-Gordon equation in d dimensions
NASA Astrophysics Data System (ADS)
Hall, Richard L.; Zorin, Petr
2016-06-01
We establish sharp (or ’refined’) comparison theorems for the Klein-Gordon equation. We show that the condition Va ≤ Vb, which leads to Ea ≤ Eb, can be replaced by the weaker assumption Ua ≤ Ub which still implies the spectral ordering Ea ≤ Eb. In the simplest case, for d = 1, Ui(x) =∫0xV i(t)dt, i = a or b and for d > 1, Ui(r) =∫0rV i(t)td‑1dt, i = a or b. We also consider sharp comparison theorems in the presence of a scalar potential S (a ‘variable mass’) in addition to the vector term V (the time component of a four-vector). The theorems are illustrated by a variety of explicit detailed examples.
Assessment of the statistics of the Strehl ratio: predictions of central limit theorem analysis
NASA Astrophysics Data System (ADS)
Tyler, Glenn A.
2006-11-01
For a beam propagating through turbulence, the statistics of the Strehl ratio are determined by recognizing that the real and imaginary parts of the on-axis far-field pattern can be represented as the sum of many contributions from the aperture. With this in mind, the central limit theorem (CLT) can be used to develop the statistics of the real and imaginary parts of the optical field, which through the appropriate mathematical manipulations as described here can then be used to develop the probability distribution of the far-field irradiance. The results obtained in this way (which we call the CLT theory or analysis) provide an analytic expression that agrees with the results of detailed wave-optics simulations. This provides an approach by which the statistics of the Strehl ratio can be rapidly determined. A key feature of this work is that the analytic results depend on the values of a few relevant turbulence parameters that include r0,fG, and σ2l. Therefore, a measurement of these parameters at various sites of interest allows us to rapidly assess the detailed nature of the statistical fluctuations of the far-field irradiance that will be experienced at these locations.
NASA Astrophysics Data System (ADS)
Le Chenadec, Vincent; Pitsch, Heinz
2013-09-01
This paper presents a novel approach for solving the conservative form of the incompressible two-phase Navier-Stokes equations. In order to overcome the numerical instability induced by the potentially large density ratio encountered across the interface, the proposed method includes a Volume-of-Fluid type integration of the convective momentum transport, a monotonicity preserving momentum rescaling, and a consistent and conservative Ghost Fluid projection that includes surface tension effects. The numerical dissipation inherent in the Volume-of-Fluid treatment of the convective transport is localized in the interface vicinity, enabling the use of a kinetic energy conserving discretization away from the singularity. Two- and three-dimensional tests are presented, and the solutions shown to remain accurate at arbitrary density ratios. The proposed method is then successfully used to perform the detailed simulation of a round water jet emerging in quiescent air, therefore suggesting the applicability of the proposed algorithm to the computation of realistic turbulent atomization.
Le Chenadec, Vincent; Pitsch, Heinz
2013-09-15
This paper presents a novel approach for solving the conservative form of the incompressible two-phase Navier–Stokes equations. In order to overcome the numerical instability induced by the potentially large density ratio encountered across the interface, the proposed method includes a Volume-of-Fluid type integration of the convective momentum transport, a monotonicity preserving momentum rescaling, and a consistent and conservative Ghost Fluid projection that includes surface tension effects. The numerical dissipation inherent in the Volume-of-Fluid treatment of the convective transport is localized in the interface vicinity, enabling the use of a kinetic energy conserving discretization away from the singularity. Two- and three-dimensional tests are presented, and the solutions shown to remain accurate at arbitrary density ratios. The proposed method is then successfully used to perform the detailed simulation of a round water jet emerging in quiescent air, therefore suggesting the applicability of the proposed algorithm to the computation of realistic turbulent atomization.
Li Chao; Lovelace, Geoffrey
2008-03-15
Extreme-mass-ratio inspirals (EMRIs) and intermediate-mass-ratio inspirals (IMRIs) - binaries in which a stellar-mass object spirals into a massive black hole or other massive, compact body - are important sources of gravitational waves for LISA and LIGO, respectively. Thorne has speculated that the waves from EMRIs and IMRIs encode, in principle, all the details of (i) the central body's spacetime geometry (metric), (ii) the tidal coupling (energy and angular momentum exchange) between the central body and orbiting object, and (iii) the evolving orbital elements. Fintan Ryan has given a first partial proof that this speculation is correct: Restricting himself to nearly circular, nearly equatorial orbits and ignoring tidal coupling, Ryan proved that the central body's metric is encoded in the waves. In this paper we generalize Ryan's theorem. Retaining Ryan's restriction to nearly circular and nearly equatorial orbits, and dropping the assumption of no tidal coupling, we prove that Thorne's conjecture is nearly fully correct: the waves encode not only the central body's metric but also the evolving orbital elements and (in a sense slightly different from Thorne's conjecture) the evolving tidal coupling.
Caballero, David; Villanueva, Guillermo; Plaza, Jose Antonio; Mills, Christopher A; Samitier, Josep; Errachid, Abdelhamid
2010-01-01
The shape and dimensions of an atomic force microscope tip are crucial factors to obtain high resolution images at the nanoscale. When measuring samples with narrow trenches, inclined sidewalls near 90 degrees or nanoscaled structures, standard silicon atomic force microscopy (AFM) tips do not provide satisfactory results. We have combined deep reactive ion etching (DRIE) and focused ion beam (FIB) lithography techniques in order to produce probes with sharp rocket-shaped silicon AFM tips for high resolution imaging. The cantilevers were shaped and the bulk micromachining was performed using the same DRIE equipment. To improve the tip aspect ratio we used FIB nanolithography technique. The tips were tested on narrow silicon trenches and over biological samples showing a better resolution when compared with standard AFM tips, which enables nanocharacterization and nanometrology of high-aspect-ratio structures and nanoscaled biological elements to be completed, and provides an alternative to commercial high aspect ratio AFM tips. PMID:20352882
NASA Astrophysics Data System (ADS)
Elizarov, A. M.; Kalimullina, A. N.
2009-03-01
The lift/drag ratio of an airfoil placed in an incompressible attached flow is maximized taking into account the viscosity in the boundary-layer approximation. An exact solution is constructed. The situation when the resulting solutions are not in the admissible class of univalent flows is discussed. A procedure is proposed for determining physically feasible airfoils (with a univalent flow region) with a high lift/drag ratio. For this purpose, a class of airfoils is constructed that are determined by a twoparameter function approximating the found exact solution to the variational problem. For this class, the ranges of free parameters leading to physically feasible flows are found. The results are verified by computing a turbulent boundary layer using Eppler’s method, and airfoils with a high lift/drag ratio in an attached flow are detected.
NASA Astrophysics Data System (ADS)
Wyatt, Stephan
2004-08-01
The U.S. Navy"s SHAred Reconnaissance Pod (SHARP) employs the Recon/Optical, Inc. (ROI) CA-279 dual spectral band (visible/IR) digital cameras operating from an F-18E/F aircraft to perform low-to-high altitude reconnaissance missions. SHARP has proven itself combat worthy, with a rapid transition from development to operational deployment culminating in a highly reliable and effective reconnaissance capability for joint forces operating in Operation Iraqi Freedom (OIF). The U.S. Navy"s intelligence, surveillance and reconnaissance (ISR) roadmap transforms the SHARP system from being solely an independent reconnaissance sensor to a node in the growing Joint ISR network. ROI and the U.S. Navy have combined their resources to ensure the system"s transformation continues to follow the ISR road map. Pre-planned product improvements (P3I) for the CA-270 camera systems will lead the way in that transformation.
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.
Fluke, C
1992-10-01
All employees need to be very careful handling sharps to minimize risks to themselves and coworkers. The attention, awareness and attitude that lend themselves to safe practice can only be developed through thorough training and following correct procedures. If you have an accident/injury, report it immediately and follow your hospital's Exposure Control Plan. Many resources are available to further your learning in this area. If you are uncomfortable with your knowledge of infection control, Universal Precautions, sharps handling, etc., check with your supervisor, hospital library, and infection control staff for reference materials to increase your level of understanding. PMID:10121533
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
Cartland, H.; Fiske, P.; Greenwood, R.; Hargiss, D.; Heston, P.; Hinsey, N.; Hunter, J.; Massey, W.
1995-01-10
The worlds largest light gas gun at SHARP (Super High Altitude Research Project) is completed and in the past year has launched 9 scramjets. Typical masses and velocities are 5.9 kg at 2.8 km/sec.and 4.4 kg at 3.1 km/sec. In so doing SHARP launched the first fully functioning, hydrogen burning scramjet at mach 8. The SHARP launcher is unique in having a 4 inch diameter and 155 foot-long barrel. This enables lower acceleration launches than any other system. In addition the facility can deliver high energy projectiles to targets in the open air without having to contain the impact fragments. This allows one to track lethality test debris for several thousand feet.
An investigation of perceived sharpness and sharpness metrics
NASA Astrophysics Data System (ADS)
Zhang, Buyue; Allebach, Jan P.; Pizlo, Zygmunt
2005-01-01
Sharpness is an important attribute that contributes to the overall impression of image quality. As digital photography becomes more and more popular, digital photo enhancement has been a topic of great interest. In this paper, we investigate two issues related to digital photo sharpness. 1) How do we quantitatively measure the sharpness of a digital image? 2) What is the preferred sharpness of a digital image, and what is the relation between preferred sharpness and sharpness detection threshold? Both issues are of practical use to the digital photography market. First, we present the design and properties of three sharpness metrics to answer the first question. Next, we describe psychophysical experiments to investigate the second question. It is found that 1) the sharpness metric Digital Sharpness Scale (DSS) and Average Edge Transition Slope (AETS) are highly correlated to the perceived sharpness; 2) Both DSS and AETS predict sharpness equality with acceptable error; 3) the sharpness detection threshold is relatively consistent across subjects and across image contents, compared with the sharpness preference; 4) the average level of preferred sharpness is consistently higher than the detection threshold across image contents and across subjects, which implies that observers in general prefer a sharpened image to the original image; and 5) the preferred level of sharpness has a strong dependency on image content.
An investigation of perceived sharpness and sharpness metrics
NASA Astrophysics Data System (ADS)
Zhang, Buyue; Allebach, Jan P.; Pizlo, Zygmunt
2004-10-01
Sharpness is an important attribute that contributes to the overall impression of image quality. As digital photography becomes more and more popular, digital photo enhancement has been a topic of great interest. In this paper, we investigate two issues related to digital photo sharpness. 1) How do we quantitatively measure the sharpness of a digital image? 2) What is the preferred sharpness of a digital image, and what is the relation between preferred sharpness and sharpness detection threshold? Both issues are of practical use to the digital photography market. First, we present the design and properties of three sharpness metrics to answer the first question. Next, we describe psychophysical experiments to investigate the second question. It is found that 1) the sharpness metric Digital Sharpness Scale (DSS) and Average Edge Transition Slope (AETS) are highly correlated to the perceived sharpness; 2) Both DSS and AETS predict sharpness equality with acceptable error; 3) the sharpness detection threshold is relatively consistent across subjects and across image contents, compared with the sharpness preference; 4) the average level of preferred sharpness is consistently higher than the detection threshold across image contents and across subjects, which implies that observers in general prefer a sharpened image to the original image; and 5) the preferred level of sharpness has a strong dependency on image content.
NASA Astrophysics Data System (ADS)
Webster, Nathan A. S.; Pownceby, Mark I.; Madsen, Ian C.; Studer, Andrew J.; Manuel, James R.; Kimpton, Justin A.
2014-12-01
Effects of basicity, B (CaO:SiO2 ratio) on the thermal range, concentration, and formation mechanisms of silico-ferrite of calcium and aluminum (SFCA) and SFCA-I iron ore sinter bonding phases have been investigated using an in situ synchrotron X-ray diffraction-based methodology with subsequent Rietveld refinement-based quantitative phase analysis. SFCA and SFCA-I phases are the key bonding materials in iron ore sinter, and improved understanding of the effects of processing parameters such as basicity on their formation and decomposition may assist in improving efficiency of industrial iron ore sintering operations. Increasing basicity significantly increased the thermal range of SFCA-I, from 1363 K to 1533 K (1090 °C to 1260 °C) for a mixture with B = 2.48, to ~1339 K to 1535 K (1066 °C to 1262 °C) for a mixture with B = 3.96, and to ~1323 K to 1593 K (1050 °C to 1320 °C) at B = 4.94. Increasing basicity also increased the amount of SFCA-I formed, from 18 wt pct for the mixture with B = 2.48 to 25 wt pct for the B = 4.94 mixture. Higher basicity of the starting sinter mixture will, therefore, increase the amount of SFCA-I, considered to be more desirable of the two phases. Basicity did not appear to significantly influence the formation mechanism of SFCA-I. It did, however, affect the formation mechanism of SFCA, with the decomposition of SFCA-I coinciding with the formation of a significant amount of additional SFCA in the B = 2.48 and 3.96 mixtures but only a minor amount in the highest basicity mixture. In situ neutron diffraction enabled characterization of the behavior of magnetite after melting of SFCA produced a magnetite plus melt phase assemblage.
Back to Basics: Sharps Safety.
Spruce, Lisa
2016-07-01
Perioperative team members who handle sharp devices or equipment are at risk for sharps injuries. Because sharps injuries can expose individuals to potentially infectious diseases, safety practices should be followed at all times. Health care workers and patients are at risk when a sharps injury occurs, so protocols, including work practice and engineering controls, should be in place at every facility. This article provides guidance on the steps that can be followed to minimize risk of a sharps injury. PMID:27350353
Hardy-Littlewood theorem for trigonometric series with {alpha}-monotone coefficients
Dyachenko, Mikhail I; Nursultanov, Erlan D
2009-12-31
The Hardy-Littlewood theorem is established for trigonometric series with {alpha}-monotone coefficients. Inequalities of Hardy-Littlewood kind are proved. Examples of series demonstrating that the results obtained are sharp are constructed. Bibliography: 15 titles.
SHAred Reconnaissance Pod (SHARP) program
NASA Astrophysics Data System (ADS)
Kent, Dennis C.
2001-12-01
The SHAred Reconnaissance Pod (SHARP) Program is a United States Navy tactical reconnaissance program that culminates in the supply of visible and infrared imagery products to the fleet. The intent of the program is to provide the warfighter the most robust tactical reconnaissance capability possible in a timely manner. The SHARP concept is a multi-function reconnaissance pod, adaptable to several airborne platforms for tactical manned airborne reconnaissance. The genesis platform is the Navy F/A-18. With regard to multi-platform application, a smart pod approach has been pursued with most of the required functionality being incorporated into the pod. SHARP will replace the Tactical Airborne Reconnaissance Pod System (TARPS) flying on the Navy F-14. This paper outlines the SHARP Program requirements and acquisition approach, along with the SHARP system capabilities and operation.
ERIC Educational Resources Information Center
Parameswaran, Revathy
2009-01-01
This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich concept images.…
The Interaction Equivalency Theorem
ERIC Educational Resources Information Center
Miyazoe, Terumi; Anderson, Terry
2010-01-01
This paper examines the key issues regarding The Interaction Equivalency Theorem posited by Anderson (2003a), which consists of the three interaction elements found in formal education courses among teacher, student, and content. It first examines the core concepts of the theorem and argues that two theses of different dimensions can be…
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…
Sharps injuries in ophthalmic practice
Ghauri, A-J; Amissah-Arthur, K N; Rashid, A; Mushtaq, B; Nessim, M; Elsherbiny, S
2011-01-01
Purpose Accidental sharps injuries are a potential route for transmission of blood-borne infection to healthcare workers. Ophthalmic staff in particular are at risk of sustaining such injuries due to the microsurgical nature of the speciality. Forthcoming European Union legislation aimed at reducing sharps injuries requires the development of risk-based sharps policy. The authors believe that this is the first study to assess the risks of sharps injuries and their management specific to ophthalmic practice within the European Union. Methods A retrospective review of all reported sharps injuries across three eye units in the UK over a period of 6 years was undertaken. Data were analysed to determine the circumstances surrounding the injury, occupation of the injured person, and whether appropriate actions were taken following incidents. Results A total of 68 sharps injuries were reported over the 6-year period. Nurses sustained 54.4% (n=37) of needlestick injuries, doctors 39.7% (n=27), and allied healthcare staff 5.9% (n=4). In all 51.5% (n=35) of sharps injuries occurred in the operating theatre, 30.9% (n=21) in the outpatient clinic, 13.2% (n=9) on the ophthalmic ward, and 4.4% (n=3) in unspecified locations. There was a median rate of 1.3 sharps injuries per 1000 surgical procedures per year and a range of 0.4–3.5 per 1000. Conclusions This study demonstrates the need to raise awareness of the unique risks of sharps injuries in ophthalmic practice. This is necessary in order to develop speciality-specific policy that promotes strategies to reduce such injuries, enhances the accuracy of reporting of such events, and provides guidance for appropriate management. PMID:21336251
The NASA Sharp Flight Experiment
NASA Technical Reports Server (NTRS)
Rasky, Daniel J.; Salute, Joan; Kolodziej, Paul; Bull, Jeffrey
1998-01-01
The Slender Hypersonic Aerothermodynamic Research Program (SHARP) was initiated by NASA Ames, and executed in partnership with Sandia National Laboratory and the US Air Force, to demonstrate sharp, passive leading edge designs for hypersonic vehicles, incorporating new ultra-high temperature ceramics (UHTC's). These new ceramic composites have been undergoing development, characterization and ground testing at NASA Ames for the last nine years. This paper will describe the background, flight objectives, design and pertinent flight results of SHARP, and some of the potential implications for future hypersonic vehicle designs.
ERIC Educational Resources Information Center
Benyi, Arpad; Casu, Ioan
2009-01-01
Pompeiu's theorem states that if ABC is an "equilateral" triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B,…
Sharp Hypervelocity Aerodynamic Research Probe
NASA Technical Reports Server (NTRS)
Bull, Jeffrey; Kolodziej, Paul; Rasky, Daniel J. (Technical Monitor)
1996-01-01
The objective of this flight demonstration is to deploy a slender-body hypervelocity aerodynamic research probe (SHARP) from an orbiting platform using a tether, deorbit and fly it along its aerothermal performance constraint, and recover it intact in mid-air. To accomplish this objective, two flight demonstrations are proposed. The first flight uses a blunt-body, tethered reentry experiment vehicle (TREV) to prove out tethered deployment technology for accurate entries, a complete SHARP electronics suite, and a new soft mid-air helicopter recovery technique. The second flight takes advantage of this launch and recovery capability to demonstrate revolutionary sharp body concepts for hypervelocity vehicles, enabled by new Ultra-High Temperature Ceramics (UHTCs) recently developed by Ames Research Center. Successful demonstration of sharp body hypersonic vehicle technologies could have radical impact on space flight capabilities, including: enabling global reentry cross range capability from Station, eliminating reentry communications blackout, and allowing new highly efficient launch systems incorporating air breathing propulsion and zeroth staging.
NASA Astrophysics Data System (ADS)
Pérez-Espigares, Carlos; Redig, Frank; Giardinà, Cristian
2015-08-01
For non-equilibrium systems of interacting particles and for interacting diffusions in d-dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.
Virial Theorem and Scale Transformations.
ERIC Educational Resources Information Center
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
A Schwinger disentangling theorem
Cross, Daniel J.; Gilmore, Robert
2010-10-15
Baker-Campbell-Hausdorff formulas are exceedingly useful for disentangling operators so that they may be more easily evaluated on particular states. We present such a disentangling theorem for general bilinear and linear combinations of multiple boson creation and annihilation operators. This work generalizes a classical result of Schwinger.
Weinberg, Steven
2008-09-15
It is shown that the generating function for tree graphs in the ''in-in'' formalism may be calculated by solving the classical equations of motion subject to certain constraints. This theorem is illustrated by application to the evolution of a single inflaton field in a Robertson-Walker background.
''CPT Theorem'' for Accelerators
Vladimir Shiltsev
2004-08-05
In this paper we attempt to reveal common features in evolution of various colliders' luminosity over commissioning periods. A simplified formula, ''CPT theorem'' or CP = T, is proposed which relates the time needed for commissioning T, the ''complexity'' of the machine C and performance increase goal P.
ERIC Educational Resources Information Center
Musto, Garrod
2010-01-01
Within his classroom, the author is often confronted by students who fail to see, or accept, the relevance of mathematics both to their lives and the world around them. One topic which is regularly perceived as being disconnected from people's daily lives is that of circle theorems, especially among less motivated students. In this article, the…
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.
ERIC Educational Resources Information Center
Abramovitz, Buma; Berezina, Miryam; Berman, Abraham; Shvartsman, Ludmila
2009-01-01
In this article we describe the process of studying the assumptions and the conclusion of a theorem. We tried to provide the students with exercises and problems where we discuss the following questions: What are the assumptions of a theorem and what are the conclusions? What is the geometrical meaning of a theorem? What happens when one or more…
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.
THE PARKER MAGNETOSTATIC THEOREM
Low, B. C.
2010-08-01
We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly conducting fluid bounded by a pair of rigid plates where each field is anchored, taking the plates perpendicular to the uniform field. Those force-free fields obtainable from the uniform field by continuous magnetic footpoint displacements at the plates have field topologies that are shown to be a restricted subset of the field topologies similarly created without imposing the force-free equilibrium condition. The theorem then follows from the deduction that a continuous nonequilibrium field with a topology not in that subset must find a force-free state containing tangential discontinuities.
NASA Astrophysics Data System (ADS)
Greaves, Hilary; Thomas, Teruji
2014-02-01
We provide a careful development and rigorous proof of the CPT theorem within the framework of mainstream (Lagrangian) quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches in the mainstream approach. We construct the CPT transformation for a general field directly, without appealing to the enumerative classification of representations, and in a manner that is clearly related to the requirements of our proof. Our approach applies equally in Minkowski spacetimes of any dimension at least three, and is in principle neutral between classical and quantum field theories: the quantum CPT theorem has a natural classical analogue. The key mathematical tool is that of complexification; this tool is central to the existing axiomatic proofs, but plays no overt role in the usual mainstream approaches to CPT.
NASA Astrophysics Data System (ADS)
Sarbicki, Gniewomir; Chruściński, Dariusz; Mozrzymas, Marek
2016-07-01
We analyse linear maps of operator algebras {{ B }}H({ H }) mapping the set of rank-k projectors onto the set of rank-l projectors surjectively. A complete characterisation of such maps for prime n={dim} { H } is provided. A particular case corresponding to k=l=1 is well known as Wigner’s theorem. Hence our result may be considered as a generalisation of this celebrated Wigner’s result.
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.
A sharp interface method for SPH
NASA Astrophysics Data System (ADS)
Zhang, Mingyu; Deng, Xiao-Long
2015-12-01
A sharp interface method (SIM) for smoothed particle hydrodynamics (SPH) has been developed to simulate two-phase flows with clear interfaces. The level set function is introduced to capture the interface implicitly. The interface velocity is used to evolve the level set function. The smoothness of the level set function helps to improve the accuracy of the interface curvature. Material discontinuity across the interface is dealt with by the ghost fluid method. The interface states are calculated by applying the jump conditions and are extended to the corresponding ghost fluid particles. The ghost fluid method helps to get smooth and stable calculation near the interface. The performance of the developed method is validated by benchmark tests. The developed SIM for SPH can be applied to simulate low speed two-phase flows of high density ratios with clear interface accurately and stably.
The virial theorem for the smoothly and sharply, penetrably and impenetrably confined hydrogen atom.
Katriel, Jacob; Montgomery, H E
2012-09-21
Confinement of atoms by finite or infinite boxes containing sharp (discontinuous) jumps has been studied since the fourth decade of the previous century, modelling the effect of external pressure. Smooth (continuous) counterparts of such confining potentials, that depend on a parameter such that in an appropriate limit they coincide with the sharp confining potentials, are investigated, with an emphasis on deriving the corresponding virial and Hellmann-Feynman theorems. PMID:22998251
Recurrence theorems: A unified account
Wallace, David
2015-02-15
I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.
A theorem in relativistic electronics
NASA Astrophysics Data System (ADS)
Yongjian, Yu
1990-04-01
This paper presents a theorem that connects the dispersion relation of the Electron Cyclotron Maser' and the oscillation equation of the Gyromonotron. This theorem gives us a simple way of obtaining the osscillating characteristics of the Gyromonotron provided that dispersion relation of the ECRM is given. Though the theorem is proved only with the case of ECRM and Gyromonotron, it holds for other kinds of Electron Masers, FEL4etc. and corresponding osscillators.
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.…
Roo: A parallel theorem prover
Lusk, E.L.; McCune, W.W.; Slaney, J.K.
1991-11-01
We describe a parallel theorem prover based on the Argonne theorem-proving system OTTER. The parallel system, called Roo, runs on shared-memory multiprocessors such as the Sequent Symmetry. We explain the parallel algorithm used and give performance results that demonstrate near-linear speedups on large problems.
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)
Correlation dimension Wonderland theorems
NASA Astrophysics Data System (ADS)
Carvalho, Silas L.; de Oliveira, César R.
2016-06-01
Existence of generic sets of self-adjoint operators, related to correlation dimensions of spectral measures, is investigated in separable Hilbert spaces. Typical results say that, given an orthonormal basis, the set of operators whose corresponding spectral measures are both 0-lower and 1-upper correlation dimensional is generic. The proofs rely on details of the relations among Fourier transform of spectral measures and Hausdorff and packing measures on the real line. Then such results are naturally combined with the Wonderland theorem. Applications are to classes of discrete one-dimensional Schrödinger operators and general (bounded) self-adjoint operators as well. Physical consequences include a proof of exotic dynamical behavior of singular continuous spectrum in some settings.
Composite, ordered material having sharp surface features
D'Urso, Brian R.; Simpson, John T.
2006-12-19
A composite material having sharp surface features includes a recessive phase and a protrusive phase, the recessive phase having a higher susceptibility to a preselected etchant than the protrusive phase, the composite material having an etched surface wherein the protrusive phase protrudes from the surface to form a sharp surface feature. The sharp surface features can be coated to make the surface super-hydrophobic.
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.
NASA Astrophysics Data System (ADS)
Guney, Veli Ugur
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible
'Sharpe', a clonal plum rootstock for peach
Technology Transfer Automated Retrieval System (TEKTRAN)
Sharpe clonal rootstock for peach is jointly released for grower trial by the U.S. Department of Agriculture, Agricultural Research Service (Byron, GA), and Florida Agricultural Experiment Station. Sharpe, previously tested as FLA1-1, was discovered in the wild and appears to be a hybrid of Chickas...
Electrokinetic instability: The sharp interface limit
NASA Astrophysics Data System (ADS)
Patankar, Neelesh A.
2011-01-01
An instability between two miscible liquid regions of identical mechanical properties but different electrical conductivities stressed by an external electric field parallel to the interface is studied. The problem is of interest due to its applications to mixing in microchannels. It is shown that the problem can be modeled by considering a sharp interface and an appropriate jump condition for the electrical conductivity. The transport of the electrical conductivity is governed by a diffusive equation. An infinite domain case and a shallow channel case are considered. It is shown that any velocity perturbation at the interface leads to a varying electrical conductivity in its vicinity due to the electromechanical coupling in the jump condition for the electrical conductivity. This in turns leads to a bulk charge density that gives a body force in the fluid equations. The body force generates a cellular motion that results in the instability. The results compare favorably with the experimental data and the numerical analysis for the diffuse interface case by Chen et al. [J. Fluid Mech. 524, 263 (2005)]. The critical condition for the instability is given in terms of a nondimensional parameter PΣ, which is a product of the Péclet number and another nondimensional parameter that depends on the conductivity ratio of the two liquids.
Nonrenormalization Theorems without Supersymmetry.
Cheung, Clifford; Shen, Chia-Hsien
2015-08-14
We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and antiholomorphic weights, (w,w[over ¯])=(n-h,n+h), where n and h are the number and sum over helicities of the particles created by that operator. We argue that an operator O_{i} can only be renormalized by an operator O_{j} if w_{i}≥w_{j} and w[over ¯]_{i}≥w[over ¯]_{j}, absent nonholomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally. PMID:26317712
Local virial and tensor theorems.
Cohen, Leon
2011-11-17
We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem. PMID:21863837
Robust sharp features infer from point clouds
NASA Astrophysics Data System (ADS)
Cao, Juming; Wushour, Slam; Yao, Xinhui; Li, NaiQian; Liang, Jin; Liang, Xinhe; Liu, Jianwei
2011-07-01
A novel sharp features extraction method is proposed in this paper. First, we calculate the displacement between the point and its local weighted average position and we label the point with salient this value as the candidate sharp feature points and we estimate the normal direction of those candidate sharp feature points by means of local PCA methods. Then we refine the normal estimated by inferring the orientation of the points near the candidate sharp feature region and bilateral filtering in the normal field of point clouds. At last we project the displacement between point and its local weighted average position along the direction of normal .We use value of this projection as the criteria of whether a point can be labeled as sharp feature. The extracted discrete sharp feature points are represented in the form of piecewised B-Spline lines. Experiment on both real scanner point clouds and synthesized point clouds show that our method of sharp features extraction are simple to be implemented and efficient for both space and time overhead as well as it robust to the noise ,outlier and un even sample witch are inherent in the point clouds.
A new approach to sharp Moser-Trudinger and Adams type inequalities: A rearrangement-free argument
NASA Astrophysics Data System (ADS)
Lam, Nguyen; Lu, Guozhen
The main purpose of this paper is two-fold. On the one hand, we will develop a new approach to establish sharp singular Moser-Trudinger and Adams type inequalities in unbounded domains of Euclidean spaces without using the standard symmetrization. On the other hand, we will prove the sharp singular Adams type inequality on high order Sobolev spaces W(Rn) of arbitrary integer order m (Theorem 1.1) which improves the results of Ruf and Sani (2013) [48] where sharp Adams inequalities were established for even m and those of the authors (Lam and Lu, 2012 [28,29]) for odd m but with different and more restricted norms. We first establish the sharp local singular Adams inequality on domains Ω in Rn of finite measure (Theorem 1.4). We take a perspective that any function in the high order Sobolev spaces W(Rn) can be represented as a Bessel potential. Thus, we can fully use the tools from harmonic analysis and the kernel properties of the polyharmonic operators (. Once we have established this sharp local Adams inequality, then we can adapt the rearrangement-free method we will develop in this paper to derive a global sharp Adams inequality from a local one. Our argument substantially simplifies those in Ruf and Sani (2013) [48] and Lam and Lu (2012) [28,29] and avoids the use of rather deep and complicated comparison principle of solutions to polyharmonic operators used in Ruf and Sani (2013) [48], Lam and Lu (2012) [28,29]. Moreover, our theorem holds on Sobolev spaces W(Rn) of any positive fractional order α
Treatment and disposal of contaminated sharps.
Palenik, C J; Miller, C H
1991-01-01
Dentists, like other health care workers, make an overt effort to protect themselves and their employees from infectious agents present in the body fluids of their patients. Of special concern are treatment-generated infectious waste materials, such as sharps. Sharps are items such as needles, sutures, scalpel blades, or broken glass which are capable of puncturing, cutting, or abrading tissue. Needles can cause occupational transmission of hepatitis B and AIDS. This article presents methods to safety store, treat, and dispose of sharps. All suggested procedures comply with current Indiana law, CDC guidelines, and EPA and OSHA regulations. PMID:1816346
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
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.
A sharp interpolation between the Hölder and Gaussian Young inequalities
NASA Astrophysics Data System (ADS)
da Pelo, Paolo; Lanconelli, Alberto; Stan, Aurel I.
2016-03-01
We prove a very general sharp inequality of the Hölder-Young-type for functions defined on infinite dimensional Gaussian spaces. We begin by considering a family of commutative products for functions which interpolates between the pointwise and Wick products; this family arises naturally in the context of stochastic differential equations, through Wong-Zakai-type approximation theorems, and plays a key role in some generalizations of the Beckner-type Poincaré inequality. We then obtain a crucial integral representation for that family of products which is employed, together with a generalization of the classic Young inequality due to Lieb, to prove our main theorem. We stress that our main inequality contains as particular cases the Hölder inequality and Nelson’s hyper-contractive estimate, thus providing a unified framework for two fundamental results of the Gaussian analysis.
An evaluation based theorem prover
Degano, P.; Sirovich, F.
1985-01-01
A noninductive method for mechanical theorem proving is presented, which deals with a recursive class of theorems involving iterative functions and predicates. The method is based on the symbolic evaluation of the formula to be proved and requires no inductive step. Induction is avoided since a metatheorem is proved which establishes the conditions on the evaluation of any formula which are sufficient to assure that the formula actually holds. The proof of a supposed theorem consists in evaluating the formula and checking the conditions. The method applies to assertions that involve element-by-element checking of typed homogeneous sequences which are hierarchically constructed out of the primitive type consisting of the truth values. The sequences can be computed by means of iterative and ''accumulator'' functions. The paper includes the definition of a simple typed iterative language in which both predicates and functions are expressed. The language precisely defines the scope of the proof method. The method proves a wide variety of theorems about iterative functions on sequences, including that which states that REVERSE is its own inverse, and that it can be inversely distributed on APPEND, that FLATTEN can be distributed on APPEND and that each element of any sequence is a MEMBER of the sequence itself. Although the method is not complete, it does provide the basis for an extremely efficient tool to be used in a complete mechanical theorem prover.
Nambu-Goldstone theorem and spin-statistics theorem
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
New double soft emission theorems
NASA Astrophysics Data System (ADS)
Cachazo, Freddy; He, Song; Yuan, Ellis Ye
2015-09-01
We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, Dirac-Born-Infeld, Einstein-Maxwell-Scalar, nonlinear sigma model and Yang-Mills-Scalar. We use the recently found Cachazo-He-Yuan representation of these theories in order to give a simple proof of the leading order part of all these theorems.
No-go theorem for ergodicity and an Einstein relation.
Froemberg, D; Barkai, E
2013-08-01
We provide a simple no-go theorem for ergodicity and the generalized Einstein relation for anomalous diffusion processes. The theorem states that either ergodicity in the sense of equal time and ensemble averaged mean squared displacements (MSD) is broken, and/or the generalized Einstein relation for time averaged diffusivity and mobility is invalid, which is in complete contrast to normal diffusion processes. We also give a general relation for the time averages of drift and MSD for ergodic (in the MSD sense) anomalous diffusion processes, showing that the ratio of these quantities depends on the measurement time. The Lévy walk model is used to exemplify the no-go theorem. PMID:24032966
Khinchin Theorem and Anomalous Diffusion
NASA Astrophysics Data System (ADS)
Lapas, Luciano C.; Morgado, Rafael; Vainstein, Mendeli H.; Rubí, J. Miguel; Oliveira, Fernando A.
2008-12-01
A recent Letter [M. H. Lee, Phys. Rev. Lett. 98, 190601 (2007)PRLTAO0031-900710.1103/PhysRevLett.98.190601] has called attention to the fact that irreversibility is a broader concept than ergodicity, and that therefore the Khinchin theorem [A. I. Khinchin, Mathematical Foundations of Statistical Mechanics (Dover, New York, 1949)] may fail in some systems. In this Letter we show that for all ranges of normal and anomalous diffusion described by a generalized Langevin equation the Khinchin theorem holds.
Mixing rates and limit theorems for random intermittent maps
NASA Astrophysics Data System (ADS)
Bahsoun, Wael; Bose, Christopher
2016-04-01
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps {{T}α} using the full parameter range 0<α <∞ , in general. We derive a number of results around a common theme that illustrates in detail how the constituent map that is fastest mixing (i.e. smallest α) combined with details of the randomizing process, determines the asymptotic properties of the random transformation. Our key result (theorem 1.1) establishes sharp estimates on the position of return time intervals for the quenched dynamics. The main applications of this estimate are to limit laws (in particular, CLT and stable laws, depending on the parameters chosen in the range 0<α <1 ) for the associated skew product; these are detailed in theorem 3.2. Since our estimates in theorem 1.1 also hold for 1≤slant α <∞ we study a second class of random transformations derived from piecewise affine Gaspard-Wang maps, prove existence of an infinite (σ-finite) invariant measure and study the corresponding correlation asymptotics. To the best of our knowledge, this latter kind of result is completely new in the setting of random transformations.
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
Image sharpness function based on edge feature
NASA Astrophysics Data System (ADS)
Jun, Ni
2009-11-01
Autofocus technique has been widely used in optical tracking and measure system, but it has problem that when the autofocus device should to work. So, no-reference image sharpness assessment has become an important issue. A new Sharpness Function that can estimate current frame image be in focus or not is proposed in this paper. According to current image whether in focus or not and choose the time of auto focus automatism. The algorithm measures object typical edge and edge direction, and then get image local kurtosis information to determine the degree of image sharpness. It firstly select several grads points cross the edge line, secondly calculates edge sharpness value and get the cure of the kurtosis, according the measure precision of optical-equipment, a threshold value will be set beforehand. If edge kurtosis value is more than threshold, it can conclude current frame image is in focus. Otherwise, it is out of focus. If image is out of focus, optics system then takes autofocus program. This algorithm test several thousands of digital images captured from optical tracking and measure system. The results show high correlation with subjective sharpness assessment for s images of sky object.
Sharp bends of phononic crystal surface modes
NASA Astrophysics Data System (ADS)
Cicek, Ahmet; Salman, Aysevil; Adem Kaya, Olgun; Ulug, Bulent
2015-12-01
Sharp bending of surface waves at the interface of a two-dimensional phononic crystal (PnC) of steel cylinders in air and the method of using a diagonally offset cylindrical scatterer are numerically demonstrated by finite-element method simulations. The radii of the diagonally offset scatterer and the cylinder at the PnC corner, along with the distance between them, are treated as optimization parameters in the genetic algorithm optimization of sharp bends. Surface wave transmittance of at most 5% for the unmodified sharp bend is significantly enhanced to approximately 75% as a result of optimization. A series of transmittance peaks whose maxima increase exponentially, as their widths reduce, with increasing frequency is observed for the optimized sharp bend. The transmittance peaks appear at frequencies corresponding to integer plus half-beat periods, depending on the finite surface length. The optimal parameters are such that the cylinder radius at the PnC corner is not significantly modified, whereas a diagonally offset scatterer having a diameter of almost two periods and a shortest distance of about 0.7 periods between them is required for the strongest transmittance peak. Utilization of PnC surface sharp bends as acoustic ring resonators is demonstrated.
The cutting edge: Sharp biological materials
NASA Astrophysics Data System (ADS)
Meyers, M. A.; Lin, A. Y. M.; Lin, Y. S.; Olevsky, E. A.; Georgalis, S.
2008-03-01
Through hundreds of millions of years of evolution, organisms have developed a myriad of ingenious solutions to ensure and optimize survival and success. Biological materials that comprise organisms are synthesized at ambient temperature and pressure and mostly in aqueous environments. This process, mediated by proteins, limits the range of materials at the disposal of nature and therefore the design plays a pivotal role. This article focuses on sharp edges and serrations as important survival and predating mechanisms in a number of plants, insects, fishes, and mammals. Some plants have sharp edges covered with serrations. The proboscis of mosquitoes and stinger of bees are examples in insects. Serrations are a prominent feature in many fish teeth, and rodents have teeth that are sharpened continuously, ensuring their sharpness and efficacy. Some current bioinspired applications will also be reviewed.
On Sharp-Crested Gravity Waves
NASA Astrophysics Data System (ADS)
Lukomsky, Vasyl; Gandzha, Ivan; Tsekhmister, Yaroslav; Chalyi, Alexander
2004-11-01
In the framework of the canonical model of hydrodynamics, where fluid is assumed to be ideal and incompressible, waves are potential, two-dimensional, steady, and symmetric, we provide numerical evidence for the likely existence of sharp-crested gravity waves different from the well-known limiting Stokes wave with a 120^rc corner at the crest. To this end, the physical plane methods of ordinary and fractional Fourier approximations and the inverse plane Michell method were used. They all reveal new approximate irregular solutions that seem to represent a family of sharp-crested gravity waves with lesser amplitude (the through-to-crest height) than that of the limiting Stokes wave. Furthermore, Michell's method demonstrates the existence of a new family of sharp-crested subharmonic waves. We also provide a numerical justification for the conjecture of Grant that the 120^rc singularity of the limiting wave is formed from several coalescing 90^rc singularities.
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…
Discovering the Inscribed Angle Theorem
ERIC Educational Resources Information Center
Roscoe, Matt B.
2012-01-01
Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…
Illustrating the Central Limit Theorem
ERIC Educational Resources Information Center
Corcoran, Mimi
2016-01-01
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
Generalized Pump-restriction Theorem
Sinitsyn, Nikolai A; Chernyak, Vladimir Y
2008-01-01
We formulate conditions under which periodic modulations of parameters on a finite graph with stochastic transitions among its nodes do not lead to overall pump currents through any given link. Our theorem unifies previously known results with the new ones and provides a universal approach to explore futher restrictions on stochastic pump effect in non-adiabatically driven systems with detailed balance.
Equivalence theorem and infrared divergences
Torma, T.
1996-08-01
We look at the equivalence theorem as a statement about the absence of polynomial infrared divergences when {ital m}{sub {ital W}}{r_arrow}0. We prove their absence in a truncated toy model and conjecture that, if they exist at all, they are due to couplings between light particles. {copyright} {ital 1996 The American Physical Society.}
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.)
A Fundamental Theorem on Particle Acceleration
Xie, Ming
2003-05-01
A fundamental theorem on particle acceleration is derived from the reciprocity principle of electromagnetism and a rigorous proof of the theorem is presented. The theorem establishes a relation between acceleration and radiation, which is particularly useful for insightful understanding of and practical calculation about the first order acceleration in which energy gain of the accelerated particle is linearly proportional to the accelerating field.
Investigating the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Johnson, Heather L.
2010-01-01
The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were…
Generalizations of Ptolemy and Brahmagupta Theorems
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
Pythagorean Theorem Proofs: Connecting Interactive Websites
ERIC Educational Resources Information Center
Lin, Cheng-Yao
2007-01-01
There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)
Existence Theorems for Vortices in the Aharony-Bergman-Jaferis-Maldacena Model
NASA Astrophysics Data System (ADS)
Han, Xiaosen; Yang, Yisong
2015-01-01
A series of sharp existence and uniqueness theorems are established for the multiple vortex solutions in the supersymmetric Chern-Simons-Higgs theory formalism of Aharony, Bergman, Jaferis, and Maldacena, for which the Higgs bosons and Dirac fermions lie in the bifundamental representation of the general gauge symmetry group . The governing equations are of the BPS type and derived by Kim, Kim, Kwon, and Nakajima in the mass-deformed framework labeled by a continuous parameter.
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.
Forensic Veterinary Pathology: Sharp Injuries in Animals.
de Siqueira, A; Cuevas, S E Campusano; Salvagni, F A; Maiorka, P C
2016-09-01
Sharp-force injuries are injuries caused by a mechanical force using sharp objects against the skin. Sharp-force injuries are mainly classified as stab, incised, chop, and therapeutic wounds and are less frequent than blunt-force injuries in animals. The analysis of the edges of the wound is crucial, especially if more than one type of lesion is involved. It may be difficult to differentiate between sharp trauma and blunt trauma, because lacerations can resemble incised wounds. The accurate documentation and examination of these injuries may indicate the instrument involved, the relationship between the animal and the perpetrator, and the force of the stab. Situations in which this type of trauma occurs may involve social violence, accidents, hunting, veterinary medical management, and religious rituals. The causes of death related to this type of trauma include hypovolemic shock, pneumothorax, or asphyxiation due to aspiration of blood. Necropsy findings should provide objective and unbiased information about the cause and manner of death to aid the investigation and further judgment of a possible crime. PMID:27418586
A generalization of Bernoulli's theorem
Schaer, C. )
1993-05-15
The conservation of potential vorticity Q can be expressed as [partial derivative]([rho]Q)/[partial derivative]t + [del] [center dot] J = 0, where J denotes the total flux of potential vorticity. It is shown that J is related under statistically steady conditions to the Bernoulli function B by J = [del] [theta] [times] [del] B, where [theta] is the potential temperature. This relation is valid even in the nonhydrostatic limit and in the presence of arbitrary nonconservative forces (such as internal friction) and heating rates. In essence, it can be interpreted as a generalization of Bernoulli's theorem to the frictional and diabatic regime. The classical Bernoulli theorem-valid for inviscid adiabatic and steady flows-states that the intersections of surfaces at constant potential temperature and constant Bernoulli function yield streamlines. In the presence of frictional and diabatic effects, these intersections yield the flux lines along which potential vorticity is transported. 18 refs., 2 figs.
A Randomized Central Limit Theorem
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2010-05-01
The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√{n}), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √{n}. This Letter considers scaling schemes which are stochastic and non-uniform, and presents a "Randomized Central Limit Theorem" (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Lévy laws.
Navier Stokes Theorem in Hydrology
NASA Astrophysics Data System (ADS)
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
Recursion relations from soft theorems
NASA Astrophysics Data System (ADS)
Luo, Hui; Wen, Congkao
2016-03-01
We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large- z behaviour. This work is a generalization of the recursion relations recently obtained by Cheung et al. for amplitudes in scalar effective field theories with enhanced vanishing soft behaviours, which can be regarded as a special case of those with non-vanishing soft limits. We apply the recursion relations to tree-level amplitudes in various theories, including amplitudes in the Akulov-Volkov theory and amplitudes containing dilatons of spontaneously-broken conformal symmetry.
Aging Wiener-Khinchin Theorem.
Leibovich, N; Barkai, E
2015-08-21
The Wiener-Khinchin theorem shows how the power spectrum of a stationary random signal I(t) is related to its correlation function ⟨I(t)I(t+τ)⟩. We consider nonstationary processes with the widely observed aging correlation function ⟨I(t)I(t+τ)⟩∼t(γ)ϕ(EA)(τ/t) and relate it to the sample spectrum. We formulate two aging Wiener-Khinchin theorems relating the power spectrum to the time- and ensemble-averaged correlation functions, discussing briefly the advantages of each. When the scaling function ϕ(EA)(x) exhibits a nonanalytical behavior in the vicinity of its small argument we obtain the aging 1/f-type of spectrum. We demonstrate our results with three examples: blinking quantum dots, single-file diffusion, and Brownian motion in a logarithmic potential, showing that our approach is valid for a wide range of physical mechanisms. PMID:26340172
The Sharp Lepton Quandary: Reasonable cautions
Griffin, J.J.
1996-02-01
Surprisingly, the new APEX experiment designed to measure a definitive invariant mass distribution of the sharp pairs previously reported in similar heavy ion studies reports null results. Although it asserts no direct conflict with any data reported by EPOS/I, the APEX report nevertheless seems to have encouraged the view that the earlier (EPOS/I) observations were erroneous, and by extrapolation, that the whole (e{sup +}e{sup {minus}}) Puzzle data set can be dismissed as an unfortunate set of physically meaningless statistical fluctuations. We wish here to argue that such sweeping judgments should be postponed, on the grounds that (1) the published APEX analysis of their data is self-inconsistent, and can therefore sustain no valid inference about the EPOS/I data; (2) the data which supports the occurrence of sharp (e{sup +}e{sup {minus}}) pairs is much more extensive than the EPOS/I data, so that the APEX surprise must be considered as one episode in a much longer struggle finally to settle the question of whether these weak signals are significant or not; (3) a qualitative phenomenology exists which can organize the whole range of data of the Sharp Lepton Problem, and which suggests that (4) certain low energy (and low cost) experiments ought to be explored for their creation of sharp pairs; as follows: the study of pairs emitted following scattering of few MeV electron and positron beams from neutral U and Th atoms, and the study of pairs emitted following the resonant absorption of photons of 1.5 to 2.0 MeV on U and Th atoms. We first present a brief data-oriented history of the Sharp Lepton Problem, to show that no single unexpected null result can provide an adequate basis for rejecting the great range and quantity of data which evidences the occurrence of sharp pairs. We then consider the Quadronium Composite Particle Scenario for these processes, and its Quantum Electrodynamical implications, in support of the above recommendations.
On Harnack's theorem and extensions
NASA Astrophysics Data System (ADS)
Costa, Antonio F.; Parlier, Hugo
Harnack's theorem states that the fixed points of an orientation reversing involution of a compact orientable surface of genus g are a set of k disjoint simple closed geodesic where 0≤ k≤ g+1 . The first goal of this article is to give a purely geometric, complete and self-contained proof of this fact. In the case where the fixed curves of the involution do not separate the surface, we prove an extension of this theorem, by exhibiting the existence of auxiliary invariant curves with interesting properties. Although this type of extension is well known (see, for instance, Comment. Math. Helv. 57(4): 603-626 (1982) and Transl. Math. Monogr., vol. 225, Amer. Math. Soc., Providence, RI, 2004), our method also extends the theorem in the case where the surface has boundary. As a byproduct, we obtain a geometric method on how to obtain these auxiliary curves. As a consequence of these constructions, we obtain results concerning presentations of Non-Euclidean crystallographic groups and a new proof of a result on the set of points corresponding to real algebraic curves in the compactification of the Moduli space of complex curves of genus g , overline{M_{g}} . More concretely, we establish that given two real curves there is a path in overline{M_{g}} which passes through at most two singular curves, a result of M. Seppaelae (Ann. Sci. Ecole Norm. Sup. (4), 24(5), 519-544 (1991)).
Edge Sharpness Assessment by Parametric Modeling: Application to Magnetic Resonance Imaging
Ahmad, R; Ding, Y; Simonetti, OP
2015-01-01
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. PMID:26755895
SHARP/PRONGHORN Interoperability: Mesh Generation
Avery Bingham; Javier Ortensi
2012-09-01
Progress toward collaboration between the SHARP and MOOSE computational frameworks has been demonstrated through sharing of mesh generation and ensuring mesh compatibility of both tools with MeshKit. MeshKit was used to build a three-dimensional, full-core very high temperature reactor (VHTR) reactor geometry with 120-degree symmetry, which was used to solve a neutron diffusion critical eigenvalue problem in PRONGHORN. PRONGHORN is an application of MOOSE that is capable of solving coupled neutron diffusion, heat conduction, and homogenized flow problems. The results were compared to a solution found on a 120-degree, reflected, three-dimensional VHTR mesh geometry generated by PRONGHORN. The ability to exchange compatible mesh geometries between the two codes is instrumental for future collaboration and interoperability. The results were found to be in good agreement between the two meshes, thus demonstrating the compatibility of the SHARP and MOOSE frameworks. This outcome makes future collaboration possible.
Modeling the Geologic History of Mt. Sharp
NASA Technical Reports Server (NTRS)
Pascuzzo, A.; Allen, C.
2015-01-01
Gale is an approximately 155 km diameter crater located on the martian dichotomy boundary (5 deg S 138 deg E). Gale is estimated to have formed 3.8 - 3.5 Gya, in the late Noachian or early Hesperian. Mt. Sharp, at the center of Gale Crater, is a crescent shaped sedimentary mound that rises 5.2 km above the crater floor. Gale is one of the few craters that has a peak reaching higher than the rim of the crater wall. The Curiosity rover is currently fighting to find its way across a dune field at the northwest base of the mound searching for evidence of habitability. This study used orbital images and topographic data to refine models for the geologic history of Mt. Sharp by analyzing its morphological features. In addition, it assessed the possibility of a peak ring in Gale. The presence of a peak ring can offer important information to how Mt. Sharp was formed and eroded early in Gale's history.
Sharp neck injuries in suicidal intention.
Biétry, Damien; Exadaktylos, Aristomenis; Müller, Thomas; Zbären, Peter; Caversaccio, Marco; Arnold, Andreas
2015-12-01
Sharp neck injuries in suicidal intention often present as serious emergency situations with the need for an immediate diagnosis and treatment. We report our study of the clinical evolution of this emergency condition. This study investigates the cases of sharp neck injuries in suicidal intention treated at our institution between 2000 and 2010. Patient records were collected in a retrospectively reviewed and analyzed database. The current literature was compared to our findings. We found 36 cases (10 female and 26 male). The neck injuries were superficial and profound in 16 and 20 patients, respectively. Twenty-two patients were seen by the Head and Neck surgeon. A surgical neck exploration was necessary in 19 cases. Tracheal, laryngeal, pharyngeal and vascular injuries were found in one, five, three and three cases, respectively. The hospital stay ranged from 1 to 47 days. All the patients underwent emergency psychiatric assessment and were subsequently referred for psychiatric treatment. One patient died in the emergency room from an additional arterial injury to the wrist. Sharp neck injuries in suicidal intention treated with an interdisciplinary medical, surgical and psychiatric emergency assessment and treatment have low mortality and morbidity. PMID:25543307
NASA Astrophysics Data System (ADS)
Vandebril, Raf; van Barel, Marc
2006-05-01
In this paper we take a closer look at the nullity theorem as formulated by Markham and Fiedler in 1986. The theorem is a valuable tool in the computations with structured rank matrices: it connects ranks of subblocks of an invertible matrix A with ranks of other subblocks in his inverse A-1. A little earlier, Barrett and Feinsilver, 1981, proved a theorem very close to the nullity theorem, but restricted to semiseparable and tridiagonal matrices, which are each others inverses. We will adapt the ideas of Barrett and Feinsilver to come to a new, alternative proof of the nullity theorem, based on determinantal formulas.In the second part of the paper, we extend the nullity theorem to make it suitable for two types of decompositions, namely the LU and the QR-decomposition. These theorems relate the ranks of subblocks of the factors L, U and Q to the ranks of subblocks of the factored matrix. It is shown, that a combination of the nullity theorem and his extended versions is suitable to predict in an easy manner the structure of decompositions and/or of inverses of structured rank matrices, e.g., higher-order band, higher-order semiseparable, Hessenberg, and many other types of matrices.As examples, to show the power of the nullity theorem and the related theorems, we apply them to semiseparable and related matrices.
Current status of sharps waste management in the lower-level health facilities in Tanzania.
Manyele, Samwel V; Mujuni, Churchil M
2010-10-01
Sharps waste is part of infectious medical waste, management of which is a critical problem in Tanzanian health facilities. This study aimed at assessing the current status of sharps waste management in lower level health facilities (LLHFs) in Ilala Municipality in Tanzania. In this study a sample of 135 LLHFs (103 dispensaries, 13 clinics, 11 laboratories, and 8 health centers) was involved. The average number of workers per facility was 10, with positively skewed probability density function (up to 80 workers). The average patient-to-workers ratio was 5.87. About 59% of the LLHFs improvised sharps waste containers (SWCs). Sharps waste was transported by hands in 77% of LLHFs leading to high risks of exposure to needle stick injuries. Boots, aprons and masks were among the personal protective equipment (PPE) missing in most LLHFs, while latex gloves that cannot protect workers from injuries caused by sharps waste were readily available. Most facilities stored sharps waste for about 72 hours (before treatment), which is beyond the recommended maximum storage time of 24 hours. About 39.3% of LLHFs utilized on-site single-chamber incinerators for sharps waste treatment, which are of poor design, have rusted mechanical parts, short and rusted chimneys, and without automatic flame ignition burners. It is concluded that sharps waste management in LLHFs is poor, which puts workers, the public and the environment at risk of exposure to blood-borne pathogens. It is, therefore, important that the municipality should establish a waste processing center which will collect and incinerate all sharps waste. PMID:24409634
SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH ...
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Cosmological perturbations and the Weinberg theorem
NASA Astrophysics Data System (ADS)
Akhshik, Mohammad; Firouzjahi, Hassan; Jazayeri, Sadra
2015-12-01
The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.
Fluctuation theorem for partially masked nonequilibrium dynamics.
Shiraishi, Naoto; Sagawa, Takahiro
2015-01-01
We establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production satisfies the integral fluctuation theorem. Our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines. In particular, our result gives a unified fluctuation theorem for both autonomous and nonautonomous Maxwell's demons, where mutual information plays a crucial role. Furthermore, we derive a fluctuation-dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations. PMID:25679593
Fluctuation theorem for partially masked nonequilibrium dynamics
NASA Astrophysics Data System (ADS)
Shiraishi, Naoto; Sagawa, Takahiro
2015-01-01
We establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production satisfies the integral fluctuation theorem. Our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines. In particular, our result gives a unified fluctuation theorem for both autonomous and nonautonomous Maxwell's demons, where mutual information plays a crucial role. Furthermore, we derive a fluctuation-dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations.
A sharp-focusing schlieren optical deflectometer
NASA Technical Reports Server (NTRS)
Alvi, F. S.; Settles, G. S.; Weinstein, L. M.
1993-01-01
A new instrument capable of localized, nonintrusive turbulence measurements is developed by combining a focusing schlieren system with an optical deflectometer. This instrument records the fluctuating light intensity at a point in the focused schlieren image. Its capability is verified by making benchmark measurements of Kelvin-Helmholtz vortices produced in a low-speed axisymmetric mixing layer. The sharp-focusing effect is demonstrated both visually and quantitatively. The results show that the instrument is capable of optical turbulence measurements within a 4 mm depth-of-field.
Convex Regression with Interpretable Sharp Partitions
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.
An elementary derivation of the quantum virial theorem from Hellmann–Feynman theorem
NASA Astrophysics Data System (ADS)
İpekoğlu, Y.; Turgut, S.
2016-07-01
A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann–Feynman theorem produces the final statement of the virial theorem.
Status report on SHARP coupling framework.
Caceres, A.; Tautges, T. J.; Lottes, J.; Fischer, P.; Rabiti, C.; Smith, M. A.; Siegel, A.; Yang, W. S.; Palmiotti, G.
2008-05-30
This report presents the software engineering effort under way at ANL towards a comprehensive integrated computational framework (SHARP) for high fidelity simulations of sodium cooled fast reactors. The primary objective of this framework is to provide accurate and flexible analysis tools to nuclear reactor designers by simulating multiphysics phenomena happening in complex reactor geometries. Ideally, the coupling among different physics modules (such as neutronics, thermal-hydraulics, and structural mechanics) needs to be tight to preserve the accuracy achieved in each module. However, fast reactor cores in steady state mode represent a special case where weak coupling between neutronics and thermal-hydraulics is usually adequate. Our framework design allows for both options. Another requirement for SHARP framework has been to implement various coupling algorithms that are parallel and scalable to large scale since nuclear reactor core simulations are among the most memory and computationally intensive, requiring the use of leadership-class petascale platforms. This report details our progress toward achieving these goals. Specifically, we demonstrate coupling independently developed parallel codes in a manner that does not compromise performance or portability, while minimizing the impact on individual developers. This year, our focus has been on developing a lightweight and loosely coupled framework targeted at UNIC (our neutronics code) and Nek (our thermal hydraulics code). However, the framework design is not limited to just using these two codes.
After an exposure to sharps or body fluids
... htm After an exposure to sharps or body fluids To use the sharing features on this page, ... JavaScript. Being exposed to sharps (needles) or body fluids means that another person's blood or other body ...
77 FR 56647 - Lisa Jean Sharp: Debarment Order
Federal Register 2010, 2011, 2012, 2013, 2014
2012-09-13
... HUMAN SERVICES Food and Drug Administration Lisa Jean Sharp: Debarment Order AGENCY: Food and Drug... the Federal Food, Drug, and Cosmetic Act (the FD&C Act) permanently debarring Lisa Jean Sharp from... base this order on a finding that Lisa Jean Sharp was convicted of a felony under Federal law...
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…
NASA Astrophysics Data System (ADS)
Borghi, Riccardo
2014-03-01
In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.
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)
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…
The Classical Version of Stokes' Theorem Revisited
ERIC Educational Resources Information Center
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
A 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…
Visualizing the Central Limit Theorem through Simulation
ERIC Educational Resources Information Center
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
A Note on Morley's Triangle Theorem
ERIC Educational Resources Information Center
Mueller, Nancy; Tikoo, Mohan; Wang, Haohao
2012-01-01
In this note, we offer a proof of a variant of Morley's triangle theorem, when the exterior angles of a triangle are trisected. We also offer a generalization of Morley's theorem when angles of an "n"-gon are "n"-sected. (Contains 9 figures.)
A Note on Laplace's Expansion Theorem
ERIC Educational Resources Information Center
Janji, Milan
2005-01-01
A short proof of Laplace's expansion theorem is given. The proof is elementary and can be presented at any level of undergraduate studies where determinants are taught. It is derived directly from the definition so that the theorem may be used as a starting point for further investigation of determinants.
Hereditarily polaroid operators, SVEP and Weyl's theorem
NASA Astrophysics Data System (ADS)
Duggal, B. P.
2008-04-01
A Banach space operator is hereditarily polaroid, , if every part of T is polaroid. operators have SVEP. It is proved that if has SVEP and is a Riesz operator which commutes with T, then T+R satisfies generalized a-Browder's theorem. If, in particular, R is a quasi-nilpotent operator Q, then both T+Q and T*+Q* satisfy generalized a-Browder's theorem; furthermore, if Q is injective, then also T+Q satisfies Weyl's theorem. If is an algebraic operator which commutes with the polynomially operator T, then T+N is polaroid and has SVEP, f(T+N) satisfies generalized Weyl's theorem for every function f which is analytic on a neighbourhood of [sigma](T+N), and f(T+N)* satisfies generalized a-Weyl's theorem for every function f which is analytic on, and constant on no component of, a neighbourhood of [sigma](T+N).
SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS
THIEDE, ERIK; VAN KOTEN, BRIAN; WEARE, JONATHAN
2015-01-01
For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations. PMID:26491218
5426 Sharp: A Probable Hungaria Binary
NASA Astrophysics Data System (ADS)
Warner, Brian D.; Benishek, Vladimir; Ferrero, Andrea
2015-07-01
Initial CCD photometry observations of the Hungaria asteroid 5426 Sharp in 2014 December and 2015 January at the Center of Solar System Studies-Palmer Divide Station in Landers, CA, showed attenuations from the general lightcurve, indicating the possibility of the asteroid being a binary system. The secondary period was almost exactly an Earth day, prompting a collaboration to be formed with observers in Europe, which eventually allowed establishing two periods: P1 = 4.5609 ± 0.0003 h, A1 = 0.18 ± 0.01 mag and P2 = 24.22 ± 0.02 h, A2 = 0.08 ± 0.01 mag. No mutual events, i.e., occultations and/or eclipses, were seen, therefore the asteroid is considered a probable and not confirmed binary
NASA Astrophysics Data System (ADS)
Ruderman, M. S.; Petrukhin, N. S.; Pelinovsky, E.
2016-04-01
We study kink oscillations of thin magnetic tubes. We assume that the density inside and outside the tube (and possibly also the cross-section radius) can vary along the tube. This variation is assumed to be of such a form that the kink speed is symmetric with respect to the tube centre and varies monotonically from the tube ends to the tube centre. Then we prove a theorem stating that the ratio of periods of the fundamental mode and first overtone is a monotonically increasing function of the ratio of the kink speed at the tube centre and the tube ends. In particular, it follows from this theorem that the period ratio is lower than two when the kink speed increases from the tube ends to its centre, while it is higher than two when the kink speed decreases from the tube ends to its centre. The first case is typical for non-expanding coronal magnetic loops, and the second for prominence threads. We apply the general results to particular problems. First we consider kink oscillations of coronal magnetic loops. We prove that, under reasonable assumptions, the ratio of the fundamental period to the first overtone is lower than two and decreases when the loop size increases. The second problem concerns kink oscillations of prominence threads. We consider three internal density profiles: generalised parabolic, Gaussian, and Lorentzian. Each of these profiles contain the parameter α that is responsible for its sharpness. We calculate the dependence of the period ratio on the ratio of the mean to the maximum density. For all considered values of α we find that a formula relating the period ratio and the ratio of the mean and maximum density suggested by Soler, Goossens, and Ballester ( Astron. Astrophys. 575, A123, 2015) gives a sufficiently good approximation to the exact dependence.
Singlet and triplet instability theorems
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Singlet and triplet instability theorems
NASA Astrophysics Data System (ADS)
Yamada, Tomonori; Hirata, So
2015-09-01
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Singlet and triplet instability theorems.
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions. PMID:26395692
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.
Geometric optics and the "hairy ball theorem"
NASA Astrophysics Data System (ADS)
Bormashenko, Edward; Kazachkov, Alexander
Applications of the hairy ball theorem to the geometrical optics are discussed. When the ideal mirror, topologically equivalent to a sphere, is illuminated at every point, the "hairy ball theorem" prescribes the existence of at least one point at which the incident light will be normally reflected. For the more general case of the surface, topologically equivalent to a sphere, which is both reflecting and refracting the "hairy ball theorem" predicts the existence of at least one point, at which the incident light will be normally reflected and also normally refracted.
How sharp is the sharp Archean Moho? Example from eastern Superior Province
NASA Astrophysics Data System (ADS)
Levin, Vadim; VanTongeren, Jill A.; Servali, Andrea
2016-03-01
The Superior Province of North America has not experienced major internal deformation for nearly 2.8 Gyr, preserving the Archean crust in its likely original state. We present seismological evidence for a sharp (less than 1 km) crust-mantle boundary beneath three distinct Archean terranes and for a more vertically extensive boundary at sites likely affected by the 1.2-0.9 Ga Grenville orogeny. At all sites crustal thickness is smaller than expected for the primary crust produced by melting under higher mantle potential temperature conditions of Archean time. Reduced thickness and an abrupt contrast in seismic properties at the base of the undisturbed Archean crust are consistent with density sorting and loss of the residues through gravitational instability facilitated by higher temperatures in the upper mantle at the time of formation. Similar sharpness of crust-mantle boundary in disparate Archean terranes suggests that it is a universal feature of the Archean crustal evolution.
The effective field theory of inflation models with sharp features
Bartolo, Nicola; Cannone, Dario; Matarrese, Sabino E-mail: dario.cannone@pd.infn.it
2013-10-01
We describe models of single-field inflation with small and sharp step features in the potential (and sound speed) of the inflaton field, in the context of the Effective Field Theory of Inflation. This approach allows us to study the effects of features in the power-spectrum and in the bispectrum of curvature perturbations, from a model-independent point of view, by parametrizing the features directly with modified ''slow-roll'' parameters. We can obtain a self-consistent power-spectrum, together with enhanced non-Gaussianity, which grows with a quantity β that parametrizes the sharpness of the step. With this treatment it is straightforward to generalize and include features in other coefficients of the effective action of the inflaton field fluctuations. Our conclusion in this case is that, excluding extrinsic curvature terms, the only interesting effects at the level of the bispectrum could arise from features in the first slow-roll parameter ε or in the speed of sound c{sub s}. Finally, we derive an upper bound on the parameter β from the consistency of the perturbative expansion of the action for inflaton perturbations. This constraint can be used for an estimation of the signal-to-noise ratio, to show that the observable which is most sensitive to features is the power-spectrum. This conclusion would change if we consider the contemporary presence of a feature and a speed of sound c{sub s} < 1, as, in such a case, contributions from an oscillating folded configuration can potentially make the bispectrum the leading observable for feature models.
Janati, A Bruce; AlGhasab, Naif Saad; Alshammari, Raed Ayed; saad AlGhassab, Abdulmohsen; Al-Aslami Yossef Fahad
2016-06-01
There exists a paucity of data in the EEG literature on characteristics of "atypical" interictal epileptiform discharges (IEDs), including sharp slow waves (SSWs). This article aims to address the clinical, neurophysiological, and neuropathological significance of SSW The EEGs of 920 patients at a tertiary-care facility were prospectively reviewed over a period of one year. Thirty-six patients had SSWs in their EEG. Of these, 6 patients were excluded because of inadequate clinical data. The clinical and neuroimaging data of the remaining 30 patients were then retrospectively collected and reviewed, and the findings were correlated. The data revealed that SSWs were rare and age-related EEG events occurring primarily in the first two decades of life. All patients with SSWs had documented epilepsy, presenting clinically with partial or generalized epilepsy. It is notable that one-third of the patients with SSWs had chronic or static central nervous system (CNS) pathology, particularly congenital CNS anomalies. Though more than one mechanism may be involved in the pathogenesis of SSWs, this research indicates that the most compelling theory is a deeply seated cortical generator giving rise to this EEG pattern. The presence of SSWs should alert clinicians to the presence of partial or generalized epilepsy or an underlying chronic or static CNS pathology, in particular congenital CNS anomalies, underscoring the significance of brain magnetic resonance imaging in the work-up of this population. PMID:27373055
Sharp Tips on the Atomic Force Microscope
NASA Technical Reports Server (NTRS)
2008-01-01
This image shows the eight sharp tips of the NASA's Phoenix Mars Lander's Atomic Force Microscope, or AFM. The AFM is part of Phoenix's Microscopy, Electrochemistry, and Conductivity Analyzer, or MECA.
The microscope maps the shape of particles in three dimensions by scanning them with one of the tips at the end of a beam. For the AFM image taken, the tip at the end of the upper right beam was used. The tip pointing up in the enlarged image is the size of a smoke particle at its base, or 2 microns. This image was taken with a scanning electron microscope before Phoenix launched on August 4, 2007.
The AFM was developed by a Swiss-led consortium in collaboration with Imperial College London.
The Phoenix Mission is led by the University of Arizona, Tucson, on behalf of NASA. Project management of the mission is by NASA's Jet Propulsion Laboratory, Pasadena, Calif. Spacecraft development is by Lockheed Martin Space Systems, Denver.
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).
Stability of sharp reaction fronts in porous rocks and implications for non-sharp reaction zones
NASA Astrophysics Data System (ADS)
Wangen, Magnus
2014-05-01
The flow of reactive fluids in the subsurface, like for instance acids, may create reaction fronts. A sharp reaction front is an idealization of the narrow zone where the reaction takes place. Narrow reaction zones are studied with a one-component reaction transport model, where a first order reaction changes the porosity. The porosity field is coupled to the permeability field, where an increasing porosity leads to an increasing permeability. Therefore, the reaction has a feed-back on the flow field. We have derived 1D approximate solutions for the change in concentration and porosity across the reaction zone. These solutions are used to derive a condition for reaction fronts to be narrow. The condition gives a minimum reaction rate necessary for 90% of the reaction to be restricted to the given area. Sharp fronts are idealizations of narrow fronts that are more amendable for analytical treatment. A condition has recently been derived for the stability of sharp reaction fronts in homogeneous porous medium using linear stability analysis. The condition gives that a perturbation of a flat reaction front of any wave-length becomes unstable if the permeability behind the front increases. The front instability grows faster for short wave lengths than for long wave lengths. Similarly, the perturbations of the front will die out if the permeability behind the front decreases, and short wave length perturbations will die out faster than long wave length perturbations. It is a condition that applies for both 2D and 3D porous media. Numerical experiments are shown that demonstrate the front stability criterion, when the fronts are narrow, but not sharp. The sharp front approximation turns out to be useful for the interpretation of reactions that are not sufficiently fast to give narrow reaction zones, when the reaction alters the porosity- and the permeability fields. Dissolution is an important example of reactions that increase the porosity and therefore the permeability
Undecidability Theorem and Quantum Randomness
NASA Astrophysics Data System (ADS)
Berezin, Alexander A.
2005-04-01
As scientific folklore has it, Kurt Godel was once annoyed by question whether he sees any link between his Undecidability Theorem (UT) and Uncertainty Relationship. His reaction, however, may indicate that he probably felt that such a hidden link could indeed exist but he was unable clearly formulate it. Informational version of UT (G.J.Chaitin) states impossibility to rule out algorithmic compressibility of arbitrary digital string. Thus, (mathematical) randomness can only be disproven, not proven. Going from mathematical to physical (mainly quantum) randomness, we encounter seemingly random acts of radioactive decays of isotopes (such as C14), emission of excited atoms, tunneling effects, etc. However, our notion of quantum randomness (QR) may likely hit similarly formidable wall of physical version of UT leading to seemingly bizarre ideas such as Everett many world model (D.Deutsch) or backward causation (J.A.Wheeler). Resolution may potentially lie in admitting some form of Aristotelean final causation (AFC) as an ultimate foundational principle (G.W.Leibniz) connecting purely mathematical (Platonic) grounding aspects with it physically observable consequences, such as plethora of QR effects. Thus, what we interpret as QR may eventually be manifestation of AFC in which UT serves as delivery vehicle. Another example of UT/QR/AFC connection is question of identity (indistinguishability) of elementary particles (are all electrons exactly the same or just approximately so to a very high degree?).
Comparison theorems for causal diamonds
NASA Astrophysics Data System (ADS)
Berthiere, Clément; Gibbons, Gary; Solodukhin, Sergey N.
2015-09-01
We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the redshift factor which, as we show explicitly in the spherically symmetric case, is monotonic in the radial direction, and it takes its maximal value at the center. As a by-product of our discussion we rederive Bishop's inequality without assuming the positivity of the spatial Ricci tensor. We then generalize our considerations to arbitrary, static and not necessarily spherically symmetric, asymptotically flat spacetimes. In the case of spacetimes with a horizon our generalization involves the so-called domain of dependence. The respective volume, expressed in terms of the duration measured by a distant observer compared with the volume of the domain in Minkowski spacetime, exhibits behaviors which differ if d =4 or d >4 . This peculiarity of four dimensions is due to the logarithmic subleading term in the asymptotic expansion of the metric near infinity. In terms of the invariant duration measured by a comoving observer associated with the diamond we establish an inequality which is universal for all d . We suggest some possible applications of our results including comparison theorems for entanglement entropy, causal set theory, and fundamental limits on computation.
Exchange fluctuation theorem for correlated quantum systems.
Jevtic, Sania; Rudolph, Terry; Jennings, David; Hirono, Yuji; Nakayama, Shojun; Murao, Mio
2015-10-01
We extend the exchange fluctuation theorem for energy exchange between thermal quantum systems beyond the assumption of molecular chaos, and describe the nonequilibrium exchange dynamics of correlated quantum states. The relation quantifies how the tendency for systems to equilibrate is modified in high-correlation environments. In addition, a more abstract approach leads us to a "correlation fluctuation theorem". Our results elucidate the role of measurement disturbance for such scenarios. We show a simple application by finding a semiclassical maximum work theorem in the presence of correlations. We also present a toy example of qubit-qudit heat exchange, and find that non-classical behaviour such as deterministic energy transfer and anomalous heat flow are reflected in our exchange fluctuation theorem. PMID:26565174
One-loop soft theorems via dual superconformal symmetry
NASA Astrophysics Data System (ADS)
Brandhuber, Andreas; Hughes, Edward; Spence, Bill; Travaglini, Gabriele
2016-03-01
We study soft theorems at one loop in planar {N}=4 super Yang-Mills theory through finite order in the infrared regulator and to subleading order in the soft parameter δ. In particular, we derive a universal constraint from dual superconformal symmetry, which we use to bootstrap subleading log δ behaviour. Moreover, we determine the complete infrared-finite subleading soft contribution of n-point MHV amplitudes using momentum twistors. Finally, we compute the subleading log δ behaviour of one-loop NMHV ratio functions at six and seven points, finding that universality holds within but not between helicity sectors.
Sahoo- and Wayment-Type Integral Mean Value Theorems
ERIC Educational Resources Information Center
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
NASA Astrophysics Data System (ADS)
Fishman, S.; Soffer, A.
2016-07-01
We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.
Douma, Huub; Vasconcelos, Ivan; Snieder, Roel
2011-05-01
By analyzing correlation-type reciprocity theorems for wavefields in perturbed media, it is shown that the correlation-type reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem. This reciprocity theorem, in contrast to the generalized optical theorem, allows for inhomogeneous background properties and does not make use of a far-field condition. This theorem specializes to the generalized optical theorem when considering a finite-size scatterer embedded in a homogeneous background medium and when utilizing the far-field condition. Moreover, it is shown that the reciprocity theorem for the scattered field is responsible for the cancellation of non-physical (spurious) arrivals in seismic interferometry, and as such provides the mathematical description of such arrivals. Even though here only acoustic waves are treated, the presented treatment is not limited to such wavefields and can be generalized to general wavefields. Therefore, this work provides the framework for deriving equivalents of the generalized optical theorem for general wavefields. PMID:21568381
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…
No-hair theorem for the Galileon.
Hui, Lam; Nicolis, Alberto
2013-06-14
We consider a Galileon field coupled to gravity. The standard no-hair theorems do not apply because of the Galileon's peculiar derivative interactions. We prove that, nonetheless, static spherically symmetric black holes cannot sustain nontrivial Galileon profiles. Our theorem holds for trivial boundary conditions and for cosmological ones, and regardless of whether there are nonminimal couplings between the Galileon and gravity of the covariant Galileon type. PMID:25165906
Noether's second theorem for BRST symmetries
Bashkirov, D.; Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2005-05-01
We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles Y{yields}X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.
The matrix Euler-Fermat theorem
NASA Astrophysics Data System (ADS)
Arnol'd, Vladimir I.
2004-12-01
We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem.
Aerothermal/FEM Analysis of Hypersonic Sharp Leading Edges
NASA Technical Reports Server (NTRS)
Kolodziej, Paul; Bull, Jeffrey D.; Kowalski, Thomas R.; Rasky, Daniel J. (Technical Monitor)
1995-01-01
Advanced hypersonic vehicles, like wave riders, will have sharp leading edges to minimize drag. These designs require accurate finite element modeling (FEM) of the thermal-structural behavior of a diboride ceramic matrix composite sharp leading edge. By coupling the FEM solver to an engineering model of the aerothermodynamic heating environment the impact of non catalytic surfaces, rarefied flow effects, and multidimensional conduction on the performance envelopes of sharp leading edges can be examined.
[Sharp's syndrome. Clinical, immunological and nosographic aspects].
Scagliusi, P; Muratore, M; Martiradonna, A; Berlingerio, G; Carrozzo, M
1980-12-15
LE cells, ds-DNA antibodies (radioimmunoassay), antinuclear antibodies (ANA) by indirect immunofluorescence (IFI) and anti-ENA antibodies have been sought in 150 clinical cases observed over a 5-year period in the Rheumatology Division of Bari University. For the latter, three parallel techniques were adopted on each serum, each completed by RNA-sensitivity assay for the demonstration of anti-RNP, i.e. IFI, passive haemoagglutination (PHA) and controimmunoelectrophoresis (CIE). The series included systemic lupus erythematodes (SLE), 30 cases; rheumatoid arthritis (RA), 30 cases; progressive systemic sclerosis (PSS), 12 cases; unclassified connective tissue disease (UCTD), 8 cases; mixed connective tissue disease (MCTD), 7 cases; Sjögren's syndrome (SS), 4 cases; dermatomyositis (DM), 3 cases; overlap syndromes (PSS-SLE, SS-SLE), 2 cases; rheumatological and internal miscellanea, 54 cases, LE cells and ds-DNA antibodies were found exclusively in SLE; the anti-ENA were found in various groups of diseases, while the anti-RNP were only demonstrated in the 7 MCTD and in some SLE. Of the three techniques for demonstrating anti-ENA, the PHA proved most sensitive and CIE most specific, whereas IFI was considered most suitable for clinical screening. The clinical aspects of the 7 MCTD faithfully followed the disease picture described by Sharp, but some overlap-syndromes and the unclassified connective tissue diseases did not present anti-RNP. It is also pointed out that nephropathy is not rare in MCTD and that the clinical course of the disease is not always benign. To conclude, it is considered that MCTD merits nosographic autonomy, but further investigations are recommended for more exact nosographical typing of connective tissue diseases. PMID:6161325
Optical theorem detectors for active scatterers
NASA Astrophysics Data System (ADS)
Marengo, Edwin A.; Tu, Jing
2015-10-01
We develop a new theory of the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. It applies to arbitrary lossless backgrounds and quite general probing fields. The derived formulation holds for arbitrary passive scatterers, which can be dissipative, as well as for the more general class of active scatterers which are composed of a (passive) scatterer component and an active, radiating (antenna) component. The generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks and invisible scatterers and wireless communications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a novel reactive optical theorem related to the reactive power changes. The developed approach naturally leads to three optical theorem indicators or statistics which can be used to detect changes or targets in unknown complex media. The paper includes numerical simulation results that illustrate the application of the derived optical theorem results to change detection in complex and random media.
Enhancements to the SHARP Build System and NEK5000 Coupling
McCaskey, Alex; Bennett, Andrew R.; Billings, Jay Jay
2014-10-01
The SHARP project for the Department of Energy's Nuclear Energy Advanced Modeling and Simulation (NEAMS) program provides a multiphysics framework for coupled simulations of advanced nuclear reactor designs. It provides an overall coupling environment that utilizes custom interfaces to couple existing physics codes through a common spatial decomposition and unique solution transfer component. As of this writing, SHARP couples neutronics, thermal hydraulics, and structural mechanics using PROTEUS, Nek5000, and Diablo respectively. This report details two primary SHARP improvements regarding the Nek5000 and Diablo individual physics codes: (1) an improved Nek5000 coupling interface that lets SHARP achieve a vast increase in overall solution accuracy by manipulating the structure of the internal Nek5000 spatial mesh, and (2) the capability to seamlessly couple structural mechanics calculations into the framework through improvements to the SHARP build system. The Nek5000 coupling interface now uses a barycentric Lagrange interpolation method that takes the vertex-based power and density computed from the PROTEUS neutronics solver and maps it to the user-specified, general-order Nek5000 spectral element mesh. Before this work, SHARP handled this vertex-based solution transfer in an averaging-based manner. SHARP users can now achieve higher levels of accuracy by specifying any arbitrary Nek5000 spectral mesh order. This improvement takes the average percentage error between the PROTEUS power solution and the Nek5000 interpolated result down drastically from over 23 % to just above 2 %, and maintains the correct power profile. We have integrated Diablo into the SHARP build system to facilitate the future coupling of structural mechanics calculations into SHARP. Previously, simulations involving Diablo were done in an iterative manner, requiring a large amount manual work, and left only as a task for advanced users. This report will detail a new Diablo build system that
Stability theorems for multidimensional linear systems with variable parameters
NASA Technical Reports Server (NTRS)
Shrivastava, S. K.
1981-01-01
A Liapunov-type approach is used to derive two equivalent theorems which govern the stability of coupled linear systems with varying multiple parameters. The theorems generalize some of the existing theorems applicable to systems with constant parameters and the Sonin-Polya theorem applicable to a single-degree-of-freedom system with variable coefficients. As an illustration, the proposed theorems are applied to mechanical systems with varying inertia, stiffness, gyroscopic, and damping terms, and velocity and position-dependent forces.
Kharitonov's theorem: Generalizations and algorithms
NASA Technical Reports Server (NTRS)
Rublein, George
1989-01-01
In 1978, the Russian mathematician V. Kharitonov published a remarkably simple necessary and sufficient condition in order that a rectangular parallelpiped of polynomials be a stable set. Here, stable is taken to mean that the polynomials have no roots in the closed right-half of the complex plane. The possibility of generalizing this result was studied by numerous authors. A set, Q, of polynomials is given and a necessary and sufficient condition that the set be stable is sought. Perhaps the most general result is due to Barmish who takes for Q a polytope and proceeds to construct a complicated nonlinear function, H, of the points in Q. With the notion of stability which was adopted, Barmish asks that the boundary of the closed right-half plane be swept, that the set G is considered = to (j(omega)(bar) - infinity is less than omega is less than infinity) and for each j(omega)(sigma)G, require H(delta) is greater than 0. Barmish's scheme has the merit that it describes a true generalization of Kharitonov's theorem. On the other hand, even when Q is a polyhedron, the definition of H requires that one do an optimization over the entire set of vertices, and then a subsequent optimization over an auxiliary parameter. In the present work, only the case where Q is a polyhedron is considered and the standard definition of stability described, is used. There are straightforward generalizations of the method to the case of discrete stability or to cases where certain root positions are deemed desirable. The cases where Q is non-polyhedral are less certain as candidates for the method. Essentially, a method of geometric programming was applied to the problem of finding maximum and minimum angular displacements of points in the Nyquist locus (Q(j x omega)(bar) - infinity is less than omega is less than infinity). There is an obvious connection with the boundary sweeping requirement of Barmish.
'Sharpe', a new Armillaria resistant rootstock for peach
Technology Transfer Automated Retrieval System (TEKTRAN)
Sharpe clonal rootstock for peach is jointly released for grower trial by the U.S. Department of Agriculture, Agricultural Research Service (Byron, GA) and Florida Agricultural Experiment Station. Sharpe, previously tested as FLA1-1, was discovered in the wild and appears to be a hybrid of Chickasa...
Ergodic theorem, ergodic theory, and statistical mechanics
Moore, Calvin C.
2015-01-01
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697
Ergodic theorem, ergodic theory, and statistical mechanics.
Moore, Calvin C
2015-02-17
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
Soft theorems from effective field theory
NASA Astrophysics Data System (ADS)
Larkoski, Andrew J.; Neill, Duff; Stewart, Iain W.
2015-06-01
The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate this explicitly both at tree-level and at one-loop. The effective theory correctly describes these configurations, and we generalize the Low-Burnett-Kroll theorem into a new one-loop subleading soft theorem for amplitudes. Our analysis is presented in a manner that illustrates the wider utility of using effective theory techniques to understand the perturbative S-matrix.
Generalized fluctuation theorems for classical systems
NASA Astrophysics Data System (ADS)
Agarwal, G. S.; Dattagupta, Sushanta
2015-11-01
The fluctuation theorem has a very special place in the study of nonequilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen fluctuation theorem which is in terms of the distribution of the work p (W )/p (-W )=exp(α W ) . We derive the general form of the fluctuation theorems for an arbitrary multidimensional Gaussian Markov process. Interestingly, the parameter α is by no means universal, hitherto taken for granted in the case of linear Gaussian processes. As a matter of fact, conditions under which α does become a universal parameter 1 /K T are found to be rather restrictive. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is nontrivial. The generalized theorems are equally valid for nonequilibrium steady states and could be especially important in the presence of anisotropic diffusion.
Anti-Bell - Refutation of Bell's theorem
NASA Astrophysics Data System (ADS)
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
Shahmoradi, Ali; Reinecke, Lisa; Kroos, Christina; Wichert, Sven P.; Oster, Henrik; Wehr, Michael C.; Taneja, Reshma; Hirrlinger, Johannes; Rossner, Moritz J.
2014-01-01
Increasing evidence suggests that clock genes may be implicated in a spectrum of psychiatric diseases, including sleep and mood related disorders as well as schizophrenia. The bHLH transcription factors SHARP1/DEC2/BHLHE41 and SHARP2/DEC1/BHLHE40 are modulators of the circadian system and SHARP1/DEC2/BHLHE40 has been shown to regulate homeostatic sleep drive in humans. In this study, we characterized Sharp1 and Sharp2 double mutant mice (S1/2-/-) using online EEG recordings in living animals, behavioral assays and global gene expression profiling. EEG recordings revealed attenuated sleep/wake amplitudes and alterations of theta oscillations. Increased sleep in the dark phase is paralleled by reduced voluntary activity and cortical gene expression signatures reveal associations with psychiatric diseases. S1/2-/- mice display alterations in novelty induced activity, anxiety and curiosity. Moreover, mutant mice exhibit impaired working memory and deficits in prepulse inhibition resembling symptoms of psychiatric diseases. Network modeling indicates a connection between neural plasticity and clock genes, particularly for SHARP1 and PER1. Our findings support the hypothesis that abnormal sleep and certain (endo)phenotypes of psychiatric diseases may be caused by common mechanisms involving components of the molecular clock including SHARP1 and SHARP2. PMID:25340473
Theoretical performance characteristics of sharp-lip inlets at subsonic speeds
NASA Technical Reports Server (NTRS)
Fradenburgh, Evan A; Demarquis, D Wyatt
1954-01-01
A method is presented for the estimation of the subsonic-flight-speed characteristics of sharp-lip inlets applicable to supersonic aircraft. The analysis, based on a simple momentum balance consideration, permits the computation of inlet-pressure-recovery mass-flow relations and additive-drag coefficients for forward velocities from zero to the speed of sound. The penalties for operation of a sharp-lip inlet at velocity ratios other than 1.0 may be severe; at lower velocity ratios an additive drag is incurred that is not cancelled by lip suction, while at higher velocity ratios, unavoidable losses in inlet total pressure will result. In particular, at the take-off condition, the total pressure and the mass flow for a choked inlet are only 79 percent of the values ideally attainable with a rounded lip. The test specimens were polished and unnotched. The manufacturer of the material, the Aluminum Company of America, has made axial-load tests on 24S-T4 and 75S-T6 rod material. The test techniques used at the three laboratories are described in detail; the test results are presented and are compared with each other and with results obtained on unpolished sheet by the National Bureau of Standards. Experimental data obtained at zero speed with a sharp-lip supersonic inlet model were in substantial agreement with the theoretical results. (author)
Causality, Bell's theorem, and Ontic Definiteness
NASA Astrophysics Data System (ADS)
Henson, Joe
2011-03-01
Bell's theorem shows that the reasonable relativistic causal principle known as ``local causality'' is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while dropping any of the better-known assumptions of Bell's theorem. However, another assumption of Bell's theorem is the use of classical logic. One part of this assumption is the principle of ontic definiteness, that is, that it must in principle be possible to assign definite truth values to all propositions treated in the theory. Once the logical setting is clarified somewhat, it can be seen that rejecting this principle does not in any way undermine the type of causal principle used by Bell. Without ontic definiteness, the deterministic causal condition known as Einstein Locality succeeds in banning superluminal influence (including signalling) whilst allowing correlations that violate Bell's inequalities. Objections to altering logic, and the consequences for operational and realistic viewpoints, are also addressed.
Equilibrium fluctuation theorems compatible with anomalous response
NASA Astrophysics Data System (ADS)
Velazquez, L.; Curilef, S.
2010-12-01
Previously, we have derived a generalization of the canonical fluctuation relation between heat capacity and energy fluctuations C = β2langδU2rang, which is able to describe the existence of macrostates with negative heat capacities C < 0. In this work, we extend our previous results for an equilibrium situation with several control parameters to account for the existence of states with anomalous values in other response functions. Our analysis leads to the derivation of three different equilibrium fluctuation theorems: the fundamental and the complementary fluctuation theorems, which represent the generalization of two fluctuation identities already obtained in previous works, and the associated fluctuation theorem, a result that has no counterpart in the framework of Boltzmann-Gibbs distributions. These results are applied to study the anomalous susceptibility of a ferromagnetic system, in particular, the case of the 2D Ising model.
S-HARP: A parallel dynamic spectral partitioner
Sohn, A.; Simon, H.
1998-01-01
Computational science problems with adaptive meshes involve dynamic load balancing when implemented on parallel machines. This dynamic load balancing requires fast partitioning of computational meshes at run time. The authors present in this report a fast parallel dynamic partitioner, called S-HARP. The underlying principles of S-HARP are the fast feature of inertial partitioning and the quality feature of spectral partitioning. S-HARP partitions a graph from scratch, requiring no partition information from previous iterations. Two types of parallelism have been exploited in S-HARP, fine grain loop level parallelism and coarse grain recursive parallelism. The parallel partitioner has been implemented in Message Passing Interface on Cray T3E and IBM SP2 for portability. Experimental results indicate that S-HARP can partition a mesh of over 100,000 vertices into 256 partitions in 0.2 seconds on a 64 processor Cray T3E. S-HARP is much more scalable than other dynamic partitioners, giving over 15 fold speedup on 64 processors while ParaMeTiS1.0 gives a few fold speedup. Experimental results demonstrate that S-HARP is three to 10 times faster than the dynamic partitioners ParaMeTiS and Jostle on six computational meshes of size over 100,000 vertices.
Behavior of Healthcare Workers After Injuries From Sharp Instruments
Adib-Hajbaghery, Mohsen; Lotfi, Mohammad Sajjad
2013-01-01
Background 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. Objectives 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. Materials and Methods 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. Results 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. Conclusions 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. PMID:24350157
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.
Asymptotic symmetries and subleading soft graviton theorem
NASA Astrophysics Data System (ADS)
Campiglia, Miguel; Laddha, Alok
2014-12-01
Motivated by the equivalence between the soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the Bondi, van der Burg, Metzner and Sachs (BMS) group, we propose a new extension (different from the so-called extended BMS) of the BMS group that is a semidirect product of supertranslations and Diff(S2) . We propose a definition for the canonical generators associated with the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.
Complementary Variational Theorems for inhomogeneous superconductors
NASA Astrophysics Data System (ADS)
Choy, T. C.
1997-03-01
Complementary variational theorems are derived for an inhomogeneous London (local) superconductor in which both the magnetic permeability μ(r) and the London penetration length λ_L(r) vary randomly in space (T.C. Choy, Physical Review B (1997) (to appear)). An essential feature is the close coupling between magnetic and supercurrent polarisation effects, developed self-consistently in this work. Using these theorems and a suitable ansatz for the single particle polarisabilities, we obtained complementary bounds for a composite superconductor near Tc and T=0^circ K. Our results may be important for the empirical study of systems containing magnetic (normal) and superconducting mixtures, including the high Tc oxide superconductors.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime. PMID:17813892
Jarzynski's theorem for lattice gauge theory
NASA Astrophysics Data System (ADS)
Caselle, Michele; Costagliola, Gianluca; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-08-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a nonequilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.
A variational proof of Thomson's theorem
NASA Astrophysics Data System (ADS)
Fiolhais, Miguel C. N.; Essén, Hanno; Gouveia, Tomé M.
2016-08-01
Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.
Characterizing curves satisfying the Gauss-Christoffel theorem
NASA Astrophysics Data System (ADS)
Berriochoa, E.; Cachafeiro, A.
2009-12-01
In this paper we obtain the reciprocal of the classical Gauss theorem for quadrature formulas. Indeed we characterize the support of the measures having quadrature formulas with the exactness given in the Gauss theorem.
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.
Hearing Aids May Help Keep Seniors' Minds Sharp
... nih.gov/medlineplus/news/fullstory_158532.html Hearing Aids May Help Keep Seniors' Minds Sharp Ability to ... people with hearing loss. "We know that hearing aids can keep older adults with hearing loss more ...
Hearing Aids May Help Keep Seniors' Minds Sharp
... https://medlineplus.gov/news/fullstory_158532.html Hearing Aids May Help Keep Seniors' Minds Sharp Ability to ... people with hearing loss. "We know that hearing aids can keep older adults with hearing loss more ...
Generalized Misner-Sharp energy in f(R) gravity
Cai Ronggen; Cao Liming; Ohta, Nobuyoshi; Hu Yapeng
2009-11-15
We study generalized Misner-Sharp energy in f(R) gravity in a spherically symmetric space-time. We find that unlike the cases of Einstein gravity and Gauss-Bonnet gravity, the existence of the generalized Misner-Sharp energy depends on a constraint condition in the f(R) gravity. When the constraint condition is satisfied, one can define a generalized Misner-Sharp energy, but it cannot always be written in an explicit quasilocal form. However, such a form can be obtained in a Friedmann-Robertson-Walker universe and for static spherically symmetric solutions with constant scalar curvature. In the Friedmann-Robertson-Walker universe, the generalized Misner-Sharp energy is nothing but the total matter energy inside a sphere with radius r, which acts as the boundary of a finite region under consideration. The case of scalar-tensor gravity is also briefly discussed.
Analytical solutions for beams passing apertures with sharp boundaries
NASA Astrophysics Data System (ADS)
Luz, Eitam; Granot, Er’el; Malomed, Boris A.
2016-07-01
An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the condition that the thickness of its edges is much smaller than any other length scale in the beam’s initial profile. The approximation can be easily generalized for any beam whose initial profile has several sharp features. Therefore, this method can be used as a tool to investigate the diffraction of beams on complex obstacles. The analytical results are compared to numerical solutions and experimental findings, which demonstrates high accuracy of the approximation. For an initially uniform field confined by sharp boundaries, this solution becomes exact for any propagation distance and any sharpness of the edges. Thus, it can be used as an efficient tool to represent the beams, produced by series of slits with a complex structure, in terms of the exact analytical solution.
Method of forming a sharp edge on an optical device
NASA Technical Reports Server (NTRS)
Fleetwood, C. M.; Rice, S. H.
1980-01-01
A sharp edge is formed on an optical device by placing the optical device in a holding mechanism; grinding one surface so that it and a surface of the holding mechanism are co-planar; and polishing both the surface of the optical device and the surface of the holding mechanism with felt until an edge on the surface of the optical device adjacent to the surface of the holding mechanism obtains a desired sharpness.
The sharp constant in Markov's inequality for the Laguerre weight
Sklyarov, Vyacheslav P
2009-06-30
We prove that the polynomial of degree n that deviates least from zero in the uniformly weighted metric with Laguerre weight is the extremal polynomial in Markov's inequality for the norm of the kth derivative. Moreover, the corresponding sharp constant does not exceed (8{sup k} n {exclamation_point} k {exclamation_point})/((n-k){exclamation_point} (2k){exclamation_point}). For the derivative of a fixed order this bound is asymptotically sharp as n{yields}{infinity}. Bibliography: 20 items.
Tennis Rackets and the Parallel Axis Theorem
NASA Astrophysics Data System (ADS)
Christie, Derek
2014-04-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
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…
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.
Student Thinking Strategies in Reconstructing Theorems
ERIC Educational Resources Information Center
Siswono, Tatag Yuli Eko
2005-01-01
A mathematics university student as a future mathematician should have the ability to find "new" mathematics structures or construct theorems based on particular axioms. That ability can be created by using problem posing tasks. To do the tasks, students with different abilities will use different thinking strategies. To understand them exactly,…
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.
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…
An Elementary Proof of Pick's Theorem.
ERIC Educational Resources Information Center
Pullman, Howard W.
1979-01-01
Pick's Theorem, a statement of the relationship between the area of a polygonal region on a lattice and its interior and boundary lattice points, is familiar to those whose students have participated in activities and discovery lessons using the geoboard. The proof presented, although rather long, is well within the grasp of the average geometry…
Areas and the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Vajiac, A.; Vajiac, B.
2008-01-01
We present a concise, yet self-contained module for teaching the notion of area and the Fundamental Theorem of Calculus for different groups of students. This module contains two different levels of rigour, depending on the class it used for. It also incorporates a technological component. (Contains 6 figures.)
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.
An extension theorem for conformal gauge singularities
Luebbe, Christian; Tod, Paul
2009-11-15
We analyze conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem along a congruence of timelike conformal geodesics.
The Binomial Theorem Tastes the Rainbow.
ERIC Educational Resources Information Center
Cuff, Carolyn K.
1998-01-01
Discusses the commercial for Skittles candies and asks the question "How many flavor combinations can you find?" Focuses on the modeling for a Skittles exercise which includes a brief outline of the mathematical modeling process. Guides students in the use of the binomial theorem and Pascal's triangle in this activity. (ASK)
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.
Ptolemy's Theorem and Familiar Trigonometric Identities.
ERIC Educational Resources Information Center
Bidwell, James K.
1993-01-01
Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)
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…
Codimension- p Paley-Wiener theorems
NASA Astrophysics Data System (ADS)
Yang, Yan; Qian, Tao; Sommen, Frank
2007-04-01
We obtain the generalized codimension- p Cauchy-Kovalevsky extension of the exponential function e^{i
An Ordinary but Surprisingly Powerful Theorem
ERIC Educational Resources Information Center
Sultan, Alan
2009-01-01
Being a mathematician, the author started to wonder if there are any theorems in mathematics that seem very ordinary on the outside, but when applied, have surprisingly far reaching consequences. The author thought about this and came up with the following unlikely candidate which follows immediately from the definition of the area of a rectangle…
Reflection theorem for Lorentz-Minkowski spaces
NASA Astrophysics Data System (ADS)
Lee, Nam-Hoon
2016-07-01
We generalize the reflection theorem of the Lorentz-Minkowski plane to that of the Lorentz-Minkowski spaces of higher dimensions. As a result, we show that an isometry of the Lorentz-Minkowski spacetime is a composition of at most 5 reflections.
Sharps management and the disposal of clinical waste.
Blenkharn, J Ian
Dangerous errors in clinical waste management continue to occur and inappropriate items find their way into clinical waste sacks that are not designed to hold sharp or heavy items, or fluids. Although great attention is given to the safe use of sharps, needles still find their way into waste sacks instead of a sharps bin. Sharps injuries among ancillary and support staff, and waste handlers working in the disposal sector, can occur at a rate greater than for health-care staff. Blood and body fluid exposures from carelessly packaged clinical waste are similarly common, with almost 100% of waste handlers having blood splashes on their clothing within four hours of starting a shift. Blood splashes are also common on the outside surfaces of sharps bins and on the frames supporting clinical waste sacks. Using forensic techniques, blood residues invisible to the naked eye can be detected on all surfaces of most sharps bins and on the bench top, walls and floor where the bins were positioned. Care is required when disposing of clinical waste, to protect and maintain the immediate environment from contamination, and to ensure the safety of those who come into contact with waste as it passes along the disposal chain. PMID:19633596
An improved image sharpness assessment method based on contrast sensitivity
NASA Astrophysics Data System (ADS)
Zhang, Li; Tian, Yan; Yin, Yili
2015-10-01
An image sharpness assessment method based on the property of Contrast Sensitivity Function (CSF) was proposed to realize the sharpness assessment of unfocused image. Firstly, image was performed the two-dimensional Discrete Fourier Transform (DFT), and intermediate frequency coefficients and high frequency coefficients are divided into two parts respectively. Secondly the four parts were performed the inverse Discrete Fourier Transform (IDFT) to obtain subimages. Thirdly, using Range Function evaluates the four sub-image sharpness value. Finally, the image sharpness is obtained through the weighted sum of the sub-image sharpness value. In order to comply with the CSF characteristics, weighting factor is setting based on the Contrast Sensitivity Function. The new algorithm and four typical evaluation algorithm: Fourier, Range , Variance and Wavelet are evaluated based on the six quantitative evaluation index, which include the width of steep part of focusing curve, the ration of sharpness, the steepness, the variance of float part of focusing curve, the factor of local extreme and the sensitivity. On the other hand, the effect of noise, and image content on algorithm is analyzed in this paper. The experiment results show that the new algorithm has better performance of sensitivity, anti-nose than the four typical evaluation algorithms. The evaluation results are consistent with human visual characteristics.
The hazard of sharp force injuries: Factors influencing outcome.
Kristoffersen, Stine; Normann, Stig-André; Morild, Inge; Lilleng, Peer Kåre; Heltne, Jon-Kenneth
2016-01-01
The risk of dying from sharp force injury is difficult to ascertain. To the best of our knowledge, no study has been performed in Norway regarding mortality due to sharp force injury or factors that impact survival. Thus, the objective of the present study was to investigate and assess mortality in subjects with sharp force injury. This retrospective study comprises data on 136 subjects (34 female, 102 male) with suspected severe sharp force injury (self-inflicted or inflicted by others) admitted to Haukeland University Hospital between 2001 and 2010. The majority of subjects were intoxicated, and the injury was most often inflicted by a knife. The incidence of sharp force injury in Western Norway is similar to the incidence in other European countries. Almost half of the subjects with self-inflicted injury died. In cases with injury inflicted by another individual, one in five died. Mortality rates were higher in those with penetrating chest injuries than those with penetrating abdominal injuries and higher in cases with cardiac injury compared to pleural or lung injury. Sharp force injury can be fatal, but the overall mortality rate in this study was 29%. Factors influencing mortality rate were the number of injuries, the topographic regions of the body injured, the anatomical organs/structures inflicted, and emergency measures performed. PMID:26599374
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.
Implications of Tracey's theorem to asynchronous sequential circuit design
NASA Technical Reports Server (NTRS)
Gopalakrishnan, S.; Kim, G.; Maki, G.
1990-01-01
Tracey's Theorem has long been recognized as essential in generating state assignments for asynchronous sequential circuits. This paper shows that Tracey's Theorem also has a significant impact in generating the design equations. Moreover, this theorem is important to the fundamental understanding of asynchronous sequential operation. The results of this work simplify asynchronous logic design. Moreover, detection of safe circuits is made easier.
Using Dynamic Geometry to Explore Non-Traditional Theorems
ERIC Educational Resources Information Center
Wares, Arsalan
2010-01-01
The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…
Local theorems in strengthened form for lattice random variables.
NASA Technical Reports Server (NTRS)
Mason, J. D.
1971-01-01
Investigation of some conditions which are sufficient for a sequence of independent integral-valued lattice random variables to satisfy a local theorem in strengthened form. A number of theorems giving the conditions under which the investigated sequence satisfies a local theorem in strengthened form are proven with the aid of lemmas derived by Kruglov (1968).
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).
Sahoo- and Wayment-type integral mean value theorems
NASA Astrophysics Data System (ADS)
Tiryaki, Aydin; Çakmak, Devrim
2010-06-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment [An integral mean value theorem, Math. Gazette 54 (1970), pp. 300-301] and Sahoo [Some results related to the integral mean value theorem, Int. J. Math. Ed. Sci. Tech. 38(6) (2007), pp. 818-822]. The importance of our results are illustrated by interesting examples.
Sharp Adams type inequalities in Sobolev spaces W(Rn) for arbitrary integer m
NASA Astrophysics Data System (ADS)
Lam, Nguyen; Lu, Guozhen
The main purpose of our paper is to prove sharp Adams type inequalities in unbounded domains of Rn for the Sobolev space W(Rn) for any positive integer m less than n. Our results complement those of Ruf and Sani (in press) [35] where such inequalities have been established for even integer m. We extend the main techniques of Ruf and Sani (in press) [35], which are the combinations of the comparison principle of Talenti (1976) [36] and Trombetti and Vázquez (1985) [38] for polyharmonic operators and a symmetrization argument together with constructions of radial auxiliary functions, to the case when m is odd. Moreover, we offer a completely different but much simpler approach to prove the comparison principle using the power of Bessel potentials and the Riesz rearrangement (see Remarks 3.2 and 3.3). This approach is of independent interest and works for any differential operators with appropriate radial kernels. As corollaries of our main theorems, we will derive the Adams type inequalities in the case when n=2m for all positive integer m by using different Sobolev norms.
Investigation of micromixing by acoustically oscillated sharp-edges.
Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco
2016-03-01
Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel. PMID:27158292
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).
Aging and nonergodicity beyond the Khinchin theorem
Burov, S.; Metzler, R.; Barkai, E.
2010-01-01
The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin’s theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics. PMID:20624984
Aging and nonergodicity beyond the Khinchin theorem.
Burov, S; Metzler, R; Barkai, E
2010-07-27
The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin's theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics. PMID:20624984
An analogue of a theorem of Kurzweil
NASA Astrophysics Data System (ADS)
Simmons, David
2015-05-01
A theorem of Kurzweil ('55) on inhomogeneous Diophantine approximation states that if θ is an irrational number, then the following are equivalent: (A) for every decreasing positive function ψ such that \\sumq = 1^∞ \\psi(q) = ∞ , and for almost every s\\in R , there exist infinitely many q\\in N such that ‖qθ - s‖ < ψ(q), and (B) θ is badly approximable. This theorem is not true if one adds to condition (A) the hypothesis that the function q ↦ qψ(q) is decreasing. In this paper we find a condition on the continued fraction expansion of θ which is equivalent to the modified version of condition (A). This expands on a recent paper of Kim (2014 Nonlinearity 27 1985-97).
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
A torus bifurcation theorem with symmetry
NASA Technical Reports Server (NTRS)
Vangils, S. A.; Golubitsky, M.
1989-01-01
Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.
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.
A THEOREM ON CENTRAL VELOCITY DISPERSIONS
An, Jin H.; Evans, N. Wyn E-mail: nwe@ast.cam.ac.uk
2009-08-20
It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere (SIS), the logarithmic cusp slope {gamma} of the tracers must be given exactly by {gamma} = 2{beta}, where {beta} is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the SIS, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging velocity dispersion also traces the behavior of the potential. The implication of our theorem on projected quantities is also discussed. We argue that our theorem should be understood as a warning against interpreting results based on simplifying assumptions such as isotropy and spherical symmetry.
A generalized antenna theorem for broadband pulses
NASA Astrophysics Data System (ADS)
Johnson, Michael A.
1989-03-01
Using a very general argument, one can place an upper limit on the fluence that can be delivered to a distant point by passing a pulse with finite energy through an aperture of finite area. Based on a time-dependent form of Huygen's principle, shown is the maximum possible fluence produced by an arbitrary scalar field passing through an aperture to an observation point is about equal to the fluence produced by a nearly monochromatic pulse of the same energy. This fictitious pulse uniformly illuminates the aperture and converges to a geometric focal spot at the observation point. The frequency of the monochromatic wave is made equal to the aperture-averaged root-mean-square frequency of the actual diffracting field. Thus, a pulse with arbitrary time dependence satisfies an antenna theorem very similar to the more well-known version of the theorem satisfied by monochromatic waves.
Construction of momentum theorem using cross moments
NASA Astrophysics Data System (ADS)
Hahm, T. S.; Wang, Lu; Diamond, P. H.
2009-11-01
Charney-Drazin theorem has been extended to Hasegawa Wakatani system for zonal flow problem in magnetic fusion [P.H. Diamond, et al., Plasma Phys. Control. Fusion 50, 124018 (2008)]. For this model, the guiding center density is the potential vorticity and zonal flow is influenced by the particle flux. In this work we construct momentum theorems in terms of a hierarchy of cross moments
Volume integral theorem for exotic matter
Nandi, Kamal Kanti; Zhang Yuanzhong; Kumar, K.B. Vijaya
2004-12-15
We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well-known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.
Wigner-Araki-Yanase theorem on distinguishability
Miyadera, Takayuki; Imai, Hideki
2006-08-15
The presence of an additive-conserved quantity imposes a limitation on the measurement process. According to the Wigner-Araki-Yanase theorem, perfect repeatability and distinguishability of the apparatus cannot be attained simultaneously. Instead of repeatability, in this paper, the distinguishability in both systems is examined. We derive a trade-off inequality between the distinguishability of the final states on the system and the one on the apparatus. An inequality shows that perfect distinguishability of both systems cannot be attained simultaneously.
Tests of the lattice index theorem
Jordan, Gerald; Hoellwieser, Roman; Faber, Manfried; Heller, Urs M.
2008-01-01
We investigate the lattice index theorem and the localization of the zero modes for thick classical center vortices. For nonorientable spherical vortices, the index of the overlap Dirac operator differs from the topological charge although the traces of the plaquettes deviate only by a maximum of 1.5% from trivial plaquettes. This may be related to the fact that even in Landau gauge some links of these configuration are close to the nontrivial center elements.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Sharpness of Spike Initiation in Neurons Explained by Compartmentalization
Brette, Romain
2013-01-01
In cortical neurons, spikes are initiated in the axon initial segment. Seen at the soma, they appear surprisingly sharp. A standard explanation is that the current coming from the axon becomes sharp as the spike is actively backpropagated to the soma. However, sharp initiation of spikes is also seen in the input–output properties of neurons, and not only in the somatic shape of spikes; for example, cortical neurons can transmit high frequency signals. An alternative hypothesis is that Na channels cooperate, but it is not currently supported by direct experimental evidence. I propose a simple explanation based on the compartmentalization of spike initiation. When Na channels are placed in the axon, the soma acts as a current sink for the Na current. I show that there is a critical distance to the soma above which an instability occurs, so that Na channels open abruptly rather than gradually as a function of somatic voltage. PMID:24339755
Joint probability distributions and fluctuation theorems
NASA Astrophysics Data System (ADS)
García-García, Reinaldo; Lecomte, Vivien; Kolton, Alejandro B.; Domínguez, Daniel
2012-02-01
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation-dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators.
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.
Coherent cyclotron motion beyond Kohn's theorem
NASA Astrophysics Data System (ADS)
Maag, T.; Bayer, A.; Baierl, S.; Hohenleutner, M.; Korn, T.; Schüller, C.; Schuh, D.; Bougeard, D.; Lange, C.; Huber, R.; Mootz, M.; Sipe, J. E.; Koch, S. W.; Kira, M.
2016-02-01
In solids, the high density of charged particles makes many-body interactions a pervasive principle governing optics and electronics. However, Walter Kohn found in 1961 that the cyclotron resonance of Landau-quantized electrons is independent of the seemingly inescapable Coulomb interaction between electrons. Although this surprising theorem has been exploited in sophisticated quantum phenomena, such as ultrastrong light-matter coupling, superradiance and coherent control, the complete absence of nonlinearities excludes many intriguing possibilities, such as quantum-logic protocols. Here, we use intense terahertz pulses to drive the cyclotron response of a two-dimensional electron gas beyond the protective limits of Kohn's theorem. Anharmonic Landau ladder climbing and distinct terahertz four- and six-wave mixing signatures occur, which our theory links to dynamic Coulomb effects between electrons and the positively charged ion background. This new context for Kohn's theorem unveils previously inaccessible internal degrees of freedom of Landau electrons, opening up new realms of ultrafast quantum control for electrons.
Sample Skewness as a Statistical Measurement of Neuronal Tuning Sharpness
Samonds, Jason M.; Potetz, Brian R.; Lee, Tai Sing
2014-01-01
We propose using the statistical measurement of the sample skewness of the distribution of mean firing rates of a tuning curve to quantify sharpness of tuning. For some features, like binocular disparity, tuning curves are best described by relatively complex and sometimes diverse functions, making it difficult to quantify sharpness with a single function and parameter. Skewness provides a robust nonparametric measure of tuning curve sharpness that is invariant with respect to the mean and variance of the tuning curve and is straightforward to apply to a wide range of tuning, including simple orientation tuning curves and complex object tuning curves that often cannot even be described parametrically. Because skewness does not depend on a specific model or function of tuning, it is especially appealing to cases of sharpening where recurrent interactions among neurons produce sharper tuning curves that deviate in a complex manner from the feedforward function of tuning. Since tuning curves for all neurons are not typically well described by a single parametric function, this model independence additionally allows skewness to be applied to all recorded neurons, maximizing the statistical power of a set of data. We also compare skewness with other nonparametric measures of tuning curve sharpness and selectivity. Compared to these other nonparametric measures tested, skewness is best used for capturing the sharpness of multimodal tuning curves defined by narrow peaks (maximum) and broad valleys (minima). Finally, we provide a more formal definition of sharpness using a shape-based information gain measure and derive and show that skewness is correlated with this definition. PMID:24555451
Deler-Hernández, Albert; Fikáček, Martin
2016-01-01
In order to understand the identity of the Central American species of the genus Phaenonotum Sharp, 1882, the type specimens of the species described by Sharp (1882) deposited in the David Sharp collection in the Natural History Museum in London have been re-examined. The following species are redescribed: Phaenonotum apicale Sharp, 1882, Phaenonotum collare Sharp, 1882, Phaenonotum dubium Sharp, 1882 (confirmed as junior synonym of Phaenonotum exstriatum (Say, 1835)), Phaenonotum laevicolle Sharp, 1882, Phaenonotum rotundulum Sharp, 1882 and Phaenonotum tarsale Sharp, 1882. Lectotypes are designated for Phaenonotum apicale, Phaenonotum collare, Phaenonotum rotundulum and Phaenonotum tarsale. External diagnostic characters and morphology of male genitalia are illustrated. A table summarizing diagnostic characters allowing the identification of the species is provided. PMID:27110202
Deler-Hernández, Albert; Fikáček, Martin
2016-01-01
Abstract In order to understand the identity of the Central American species of the genus Phaenonotum Sharp, 1882, the type specimens of the species described by Sharp (1882) deposited in the David Sharp collection in the Natural History Museum in London have been re-examined. The following species are redescribed: Phaenonotum apicale Sharp, 1882, Phaenonotum collare Sharp, 1882, Phaenonotum dubium Sharp, 1882 (confirmed as junior synonym of Phaenonotum exstriatum (Say, 1835)), Phaenonotum laevicolle Sharp, 1882, Phaenonotum rotundulum Sharp, 1882 and Phaenonotum tarsale Sharp, 1882. Lectotypes are designated for Phaenonotum apicale, Phaenonotum collare, Phaenonotum rotundulum and Phaenonotum tarsale. External diagnostic characters and morphology of male genitalia are illustrated. A table summarizing diagnostic characters allowing the identification of the species is provided. PMID:27110202
Hippocampal sharp-wave ripples in waking and sleeping states.
Roumis, Demetris K; Frank, Loren M
2015-12-01
Waking and sleeping states are privileged periods for distinct mnemonic processes. In waking behavior, rapid retrieval of previous experience aids memory-guided decision making. In sleep, a gradual series of reactivated associations supports consolidation of episodes into memory networks. Synchronized bursts of hippocampal place cells during events called sharp-wave ripples communicate associated neural patterns across distributed circuits in both waking and sleeping states. Differences between sleep and awake sharp-wave ripples, and in particular the accuracy of recapitulated experience, highlight their state-dependent roles in memory processes. PMID:26011627
Karlsson, T; Ormstad, K; Rajs, J
1988-03-01
A total of 89 cases of sharp force suicide that had been committed in the Stockholm area in Sweden from 1972 through 1984 were investigated. The series showed a male preponderance, sex ratio 3.3, and among males a shift towards the age group 40 to 49 years of age. An impact of cultural/ethnic factors was indicated by the overrepresentation of Finnish and Hungarian immigrants. A psychiatric diagnosis had been ascribed in 22 cases, and addiction to drugs or alcohol in 23. Previous attempts at self-destruction were recorded in 11 cases, only 1 of which was by sharp force. Classical indicators of suicidal intent, for example, suicide notes and the presence of hesitation injuries, were found in 28 and 80%, respectively. A preference for certain anatomical locations (throat, precordium, epigastrium, wrists) was confirmed as was the tendency to expose the skin before inflicting suicidal wounds. As compared to homicidal precordial stabs whose entrance wounds usually run vertically, horizontal or upwards/left-slanting stabs are strongly suggestive of suicide. Although cases were encountered where several "rules of thumb" concerning homicidal versus suicidal patterns were violated, our series contained no case of injuries to the backside of the trunk and no case of more than one wound piercing the left ventricle of the heart. Multiple chest wounds transecting costal or sternal bone were however not uncommon, and, along with the use of bizarre tools and objects like wood chisels or pieces of glass, illustrated the determination of suicidal intent. Toxicological analysis was positive for drugs in 22 and for alcohol in 27 cases. Blood alcohol levels were roughly similar to those found in victims of homicidal sharp force, whereas drug levels tended to be lower or higher in suicides. PMID:3373161
NASA Astrophysics Data System (ADS)
Aime, C.
2013-10-01
Context. This study focuses on an instrument able to monitor the corona close to the solar limb. Aims: We study the performance of externally occulted solar coronagraphs. We compute the shape of the umbra and penumbra produced by the occulter at the entrance aperture of the telescope and compare levels of rejection obtained for a circular occulter with a sharp or smooth transmission at the edge. Methods: We show that the umbral pattern in an externally occulted coronagraph can be written as a convolution product between the occulter diffraction pattern and an image of the Sun. We then focus on the analysis to circular symmetric occulters. We first derive an analytical expression using two Lommel series for the Fresnel diffraction pattern produced by a sharp-edged circular occulter. Two different expressions are used for inside and outside the occulter's geometric shadow. We verify that a numerical approach that directly solves the Huygens-Fresnel integral gives the same result. This suggests that the numerical computation can be used for a circular occulter with any variable transmission. Results: With the objective of observing the solar corona a few minutes from limb, a sharp-edged circular occulter of a few meters cannot produce an umbra darker than 10-4 of the direct sunlight. The same occulter, having an apodization zone of a few percent of the diameter (3 cm for a 1.5 m occulter), darkers the umbra down to 10-8 of the direct sunlight for linear transmission and to 10-12 for Sonine or cosine bell transmissions. An investigation for an apodized occulter with manufacturing defaults is quickly performed. Conclusions: It has been possible to numerically demonstrate the large superiority of apodized circular occulters with respect to the sharp-edged ones. These occulters allow the theoretical observation of the very limb-close corona with not yet obtained contrast ratios.
Emulation of anamorphic imaging on the SHARP EUV mask microscope
NASA Astrophysics Data System (ADS)
Benk, Markus P.; Wojdyla, Antoine; Chao, Weilun; Salmassi, Farhad; Oh, Sharon; Wang, Yow-Gwo; Miyakawa, Ryan H.; Naulleau, Patrick P.; Goldberg, Kenneth A.
2016-03-01
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 several generations into the future. An anamorphic imaging optic with increased mask side-NA in the horizontal and increased demagnification in the vertical direction has been proposed to overcome limitations of current multilayer coatings and extend EUV lithography beyond 0.33 NA.1 Zoneplate lenses with an anamorphic 4x/8x NA of 0.55 are fabricated and installed in the SHARP microscope to emulate anamorphic imaging. SHARP's 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 4x/8xNA and 6° central ray angle is compared to conventional imaging at 0.5 4xNA and 8° central ray angle. A significant contrast loss in horizontal features is observed in the conventional images. The anamorphic images show the same image quality in the horizontal and vertical directions.
A Validity Scale for the Sharp Consumer Satisfaction Scales.
ERIC Educational Resources Information Center
Tanner, Barry A.; Stacy, Webb, Jr.
1985-01-01
A validity scale for the Sharp Consumer Satisfaction Scale was developed and used in experiments to assess patients' satisfaction with community mental health centers. The scale discriminated between clients who offered suggestions and those who did not. It also improved researcher's ability to predict true scores from obtained scores. (DWH)
8. RHODES DITCH: VIEW TO SOUTHEAST, SHOWING SHARP 'U' CONTOURED ...
8. RHODES DITCH: VIEW TO SOUTHEAST, SHOWING SHARP 'U' CONTOURED ABOVE SWALE. DITCH IS ALSO VISIBLE IN DISTANCE, RUNNING HORIZONTALLY ACROSS PHOTO, ON FAR HILLSIDE. - Natomas Ditch System, Rhodes Ditch, West of Bidwell Street, north of U.S. Highway 50, Folsom, Sacramento County, CA
Adding a MOAB Geometry Interface to SHARP Structural Mechanics
Ferencz, R M; Hodge, N E
2012-05-28
The authors briefly summarize the development of, and test experience with, an initial data interface between the structural mechanics code Diablo and the SHARP reactor simulation system data hub MOAB. That interface has been exercised both to write MOAB databases from Diablo, and then also to use such a database to read in part of a simulation definition for a subsequent Diablo execution. All enhancements are integrated into the central Diablo source repository. The SHARP software system for advanced simulation of nuclear reactors and power plant systems is sponsored by DOE's Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SHARP has been architected as a federation of single-physics simulation tools to permit flexibility in programming langugages and leveraging of past and on-going investments. Solution of multi-physics problems will be coordinated by, and data passed through, a central 'hub'. SHARP's hub implementation is utilizing MOAB: a Mesh-Oriented datABase. This same data hub approach is also intended to enable multi-resolution simulations, e.g, lower-dimension plant-scale simulations can be informed by high-fidelity 3D models of particular critical components.
No-reference image sharpness assessment in autoregressive parameter space.
Gu, Ke; Zhai, Guangtao; Lin, Weisi; Yang, Xiaokang; Zhang, Wenjun
2015-10-01
In this paper, we propose a new no-reference (NR)/blind sharpness metric in the autoregressive (AR) parameter space. Our model is established via the analysis of AR model parameters, first calculating the energy- and contrast-differences in the locally estimated AR coefficients in a pointwise way, and then quantifying the image sharpness with percentile pooling to predict the overall score. In addition to the luminance domain, we further consider the inevitable effect of color information on visual perception to sharpness and thereby extend the above model to the widely used YIQ color space. Validation of our technique is conducted on the subsets with blurring artifacts from four large-scale image databases (LIVE, TID2008, CSIQ, and TID2013). Experimental results confirm the superiority and efficiency of our method over existing NR algorithms, the stateof-the-art blind sharpness/blurriness estimators, and classical full-reference quality evaluators. Furthermore, the proposed metric can be also extended to stereoscopic images based on binocular rivalry, and attains remarkably high performance on LIVE3D-I and LIVE3D-II databases. PMID:26054063
Sharp Technologies as Applied to a Crew Transfer Vehicle (CTV)
NASA Technical Reports Server (NTRS)
Cappuccio, Gelsomina; Kinney, David; Reuther, James; Saunders, David
2003-01-01
This viewgraph presentation reviews the efforts of Ames Research Center to develop Slender Hypersonic Aerothermodynamic Research Probes (SHARP) technologies as applied to the new Crew Transfer Vehicle (CTV). Amongst these technologies are ultra high temperature ceramics (UHTC). The results of Computational Fluid Dynamic simulations on prospective designs of the CTV are shown as well as wind tunnel test results.
GENERAL VIEW OF SHARP FREEZE ROOM ON LEVEL 2; LOOKING ...
GENERAL VIEW OF SHARP FREEZE ROOM ON LEVEL 2; LOOKING WEST; PIPES ON CEILING CARRIED COMPRESSED AMMONIA; NOTE NONBEARING GLAZED TILE WALLS BETWEEN COLUMNS; FLOORS ARE BRICK - Rath Packing Company, Cooler Building, Sycamore Street between Elm & Eighteenth Streets, Waterloo, Black Hawk County, IA
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,…
[Overview of sharps injuries among health-care workers].
Gopar-Nieto, Rodrigo; Juárez-Pérez, Cuauhtémoc Arturo; Cabello-López, Alejandro; Haro-García, Luis Cuauhtémoc; Aguilar-Madrid, Guadalupe
2015-01-01
Sharps injuries are one of the most frequent health-care related accidents. It is estimated globally that 35 million workers are at risk; in Mexico there is no data available for this type of injuries. They are associated with lack of training, instrument and procedure risk, fatigue and stress. The occupational distribution is nurses 45 %, technicians 20 %, doctors 20 % and maintenance workers 5 %. The most commonly associated procedures are injection, venipuncture, suture, and insertion and manipulation of IV catheters. Hepatitis B is the most commonly transmitted agent. Emotional distress is huge as well as the cost of prophylaxis and follow-up. More than half of the injuries are not notified. The most common reasons for not reporting are: the belief that the exposure has low risk of infection, the lack of knowledge of reporting systems and the assumption that it is difficult to notify. Many strategies have been created to reduce the incidence of sharps injuries, such as: identifying the risk of blood exposure, the creation of politics to minimize the risk, the education and training to create a safe workplace, the enhancing of the reporting system, the use of double-gloving and using safety-engineered sharps devices. In many countries these politics have reduced the incidence of sharps injuries as well as the economic burden. PMID:25984621
Extending Bell's Theorem: Ruling out Paramater Independent Hidden Variable Theories
NASA Astrophysics Data System (ADS)
Leegwater, G. J.
2016-03-01
Bell's Theorem may well be the best known result in the foundations of quantum mechanics. Here, it is presented as stating that for any hidden variable theory the combination of the conditions Parameter Independence, Outcome Independence, Source Independence and Compatibility with Quantum Theory leads to a contradiction. Based on work by Roger Colbeck and Renato Renner, an extension of Bell's Theorem is considered. In this extension the theorem is strengthened by replacing Outcome Independence by a strictly weaker condition.
A unified optical theorem for scalar and vectorial wave fields.
Wapenaar, Kees; Douma, Huub
2012-05-01
The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers. PMID:22559339
Fatou type theorems for series in Mittag-Leffler functions
NASA Astrophysics Data System (ADS)
Paneva-Konovska, Jordanka
2012-11-01
In studying the behaviour of series, defined by means of the Mittag-Leffler functions, on the boundary of its domain of convergence in the complex plane, we give analogues of the classical theorems for the power series like Cauchy-Hadamard, Abel, as well as Fatou theorems. The asymptotic formulae for the Mittag-Leffler functions in the cases of "large" values of indices that are used in the proofs of the convergence theorems for the considered series are also provided.
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)…
Generalized acceleration theorem for spatiotemporal Bloch waves
Arlinghaus, Stephan; Holthaus, Martin
2011-08-01
A representation is put forward for wave functions of quantum particles in periodic lattice potentials subjected to homogeneous time-periodic forcing, based on an expansion with respect to Bloch-like states which embody both the spatial and the temporal periodicity. It is shown that there exists a generalization of Bloch's famous acceleration theorem which grows out of this representation and captures the effect of a weak probe force applied in addition to a strong dressing force. Taken together, these elements point at a ''dressing and probing'' strategy for coherent wave-packet manipulation, which could be implemented in present experiments with optical lattices.
Flory Theorem for Structurally Asymmetric Mixtures
NASA Astrophysics Data System (ADS)
Dobrynin, Andrey; Sun, Frank; Shirvanyants, David; Rubinstein, Gregory; Rubinstein, Michael; Sheiko, Sergei; Lee, Hyung-Il; Matyjaszewski, Krzysztof
2008-03-01
The generalization of the Flory theorem for structurally asymmetric mixtures was derived and tested by direct visualization of conformational transformations of brushlike macromolecules embedded in a melt of linear chains. Swelling of a brush molecule was shown to be controlled not only by the degree of polymerization of the surrounding linear chains, NB, but also by the degree of polymerization of the brush's side chains, N, which determines the structural asymmetry of the mixed species. The boundaries of the swelling region were established by scaling analysis as N^2
Flory Theorem for Structurally Asymmetric Mixtures
NASA Astrophysics Data System (ADS)
Sun, Frank C.; Dobrynin, Andrey V.; Shirvanyants, David; Lee, Hyung-Il; Matyjaszewski, Krzysztof; Rubinstein, Gregory J.; Rubinstein, Michael; Sheiko, Sergei S.
2007-09-01
The generalization of the Flory theorem for structurally asymmetric mixtures was derived and tested by direct visualization of conformational transformations of brushlike macromolecules embedded in a melt of linear chains. Swelling of a brush molecule was shown to be controlled not only by the degree of polymerization (DP) of the surrounding linear chains, NB, but also by the DP of the brush’s side chains, N, which determines the structural asymmetry of the mixed species. The boundaries of the swelling region were established by scaling analysis as N2
Generating Test Templates via Automated Theorem Proving
NASA Technical Reports Server (NTRS)
Kancherla, Mani Prasad
1997-01-01
Testing can be used during the software development process to maintain fidelity between evolving specifications, program designs, and code implementations. We use a form of specification-based testing that employs the use of an automated theorem prover to generate test templates. A similar approach was developed using a model checker on state-intensive systems. This method applies to systems with functional rather than state-based behaviors. This approach allows for the use of incomplete specifications to aid in generation of tests for potential failure cases. We illustrate the technique on the cannonical triangle testing problem and discuss its use on analysis of a spacecraft scheduling system.
No-cloning theorem on quantum logics
Miyadera, Takayuki; Imai, Hideki
2009-10-15
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
Central limit theorems under special relativity
McKeague, Ian W.
2015-01-01
Several relativistic extensions of the Maxwell–Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior. PMID:25798020
An investigation of the forward scattering theorem
NASA Technical Reports Server (NTRS)
Karam, M. A.; Fung, A. K.
1987-01-01
The calculation of an EM wave's extinction loss during propagation within an inhomogeneous medium, as in active and passive remote sensing modeling, can be undertaken either through the summation of the scattering and absorption losses or through the use of the forward scattering theorem. Attention is presently given to the similarities and differences of these two approaches as a function of dielectric properties of a spherical scatterer and the incident frequency. Scattering loss is obtainable by integrating the magnitude-squared of the scattered field over a spherical surface surrounding the scatterer; the scattered field and the field within the scatterer are computed according to Mie theory.
Penrose's singularity theorem in a Finsler spacetime
NASA Astrophysics Data System (ADS)
Babak Aazami, Amir; Javaloyes, Miguel Angel
2016-01-01
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting. This activity is supported by the programme 'Young leaders in research' 18942/JLI/13 by Fundación Séneca, Regional Agency for Science and Technology from the Region of Murcia, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
No-cloning theorem on quantum logics
NASA Astrophysics Data System (ADS)
Miyadera, Takayuki; Imai, Hideki
2009-10-01
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
NASA Astrophysics Data System (ADS)
Lampart, Jonas; Lewin, Mathieu
2015-12-01
We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with {0 ≤slant n ≤slant N} particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.
Disentangling theorem and monogamy for entanglement negativity
NASA Astrophysics Data System (ADS)
He, Huan; Vidal, Guifre
2015-01-01
Entanglement negativity is a measure of mixed-state entanglement increasingly used to investigate and characterize emerging quantum many-body phenomena, including quantum criticality and topological order. We present two results for the entanglement negativity: a disentangling theorem, which allows the use of this entanglement measure as a means to detect whether a wave function of three subsystems A ,B , and C factorizes into a product state for parts A B1 and B2C ; and a monogamy relation conjecture based on entanglement negativity, which states that if A is very entangled with B , then A cannot be simultaneously very entangled also with C .
Bayes` theorem and quantitative risk assessment
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.``
Raychaudhuri equation and singularity theorems in Finsler spacetimes
NASA Astrophysics Data System (ADS)
Minguzzi, E.
2015-09-01
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain. Indeed, so do the theorems by Hawking, Penrose, Hawking and Penrose, Geroch, Gannon, Tipler and Kriele, and also the Topological Censorship theorem and so on. It is argued that the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance and geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure, horizons differentiability and conformal transformations are also included.
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.
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.
Meta-analysis and the reversed Theorem of the Means.
Edwardes, Michael D deB
2014-12-01
Conventional meta-analysis estimators are weighted means of study measures, meant to estimate an overall population measure. For measures such as means, mean differences and risk differences, a weighted arithmetic mean is the conventional estimator. When the measures are ratios, such as odds ratios, logarithms of the study measures are most frequently used, and the back-transform is a weighted geometric mean, rather than the arithmetic mean. For numbers needed to treat, a weighted harmonic mean is the back-transform. The Theorem of the Means effectively states that unless all of the studies have an equal result, the arithmetic mean must be greater than the geometric mean, which must be greater than the harmonic mean. When the weights are fixed sampling weights, the inequalities are in the expected direction. However, when the weights are the usual reciprocal variance estimates, the inequalities go in the opposite direction. The use of reciprocal variance weights is therefore questioned as perhaps having a fundamental flaw. An example is shown of a meta-analysis of frequencies of two classes of drug-resistant HIV-1 mutations. PMID:26052955
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.
Bell's theorem, inference, and quantum transactions
NASA Astrophysics Data System (ADS)
Garrett, A. J. M.
1990-04-01
Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, “local”) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's new transactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the “delayed choice” experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theorem reinforces arguments in favor of hidden variables.
Ground-state-energy theorem and the virial theorem of a many-particle system in d dimensions
NASA Technical Reports Server (NTRS)
Iwamoto, N.
1984-01-01
The equivalence of Pauli's ground-state-energy theorem and the virial theorem is demonstrated for a many-particle system interacting with an interparticle potential in d dimensions at zero and finite temperatures. Pauli's theorem has an integral form in which the variable is the coupling constant e-squared, while the virial theorem has a differential form in which the variable has the number density n. The essence of the equivalence proof consists in changing the variable from n to e-squared by noting the dependence of the excess free energy on dimensionless quantities for zero-temperature and classical cases.
Sharp estimates of the Kobayashi metric and Gromov hyperbolicity
NASA Astrophysics Data System (ADS)
Bertrand, Florian
2008-09-01
Let D={[rho]<0} be a smooth relatively compact domain in a four-dimensional almost complex manifold (M,J), where [rho] is a J-plurisubharmonic function on a neighborhood of and strictly J-plurisubharmonic on a neighborhood of [not partial differential]D. We give sharp estimates of the Kobayashi metric. Our approach is based on an asymptotic quantitative description of both the domain D and the almost complex structure J near a boundary point. Following Z.M. Balogh and M. Bonk [Z.M. Balogh, M. Bonk, Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains, Comment. Math. Helv. 75 (2000) 504-533], these sharp estimates provide the Gromov hyperbolicity of the domain D.
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.
Improved Sharp Interface Models in Coastal Aquifers of Finite Dimensions
NASA Astrophysics Data System (ADS)
Christelis, Vasileios; Mantoglou, Aristotelis
2013-04-01
Coastal aquifer management often involves aquifers of finite dimensions where optimal pumping rates must be calculated through a combined simulation-optimization procedure. Variable-density numerical models are considered more exact than sharp interface models as they better describe the governing flow and transport equations. However, such models are not always preferable in pumping optimization studies, due to their complexity and computational burden. On the other hand, sharp interface models are approximate and can lead to large errors if they are not applied properly, particularly when model boundaries are not treated correctly. The present paper proposes improved sharp interface models considering aquifer boundaries in a proper way. Two sharp interface models are investigated based on the single potential formulation and the Ghyben-Herzberg relation. The first model (Strack, 1976) is based on the assumption of a semi-infinite aquifer with a sea-boundary only. The second model (Mantoglou, 2003) is based on an analytical solution developed for coastal aquifers of finite size and accounts for inland and lateral aquifer boundaries. Next, both models are modified using an empirical correction factor (similar to Pool and Carrera, 2011) which accounts for mixing. A simple pumping optimization problem with a single well in a confined coastal aquifer of finite size with four boundaries (sea, inland and lateral impervious boundaries) is employed. The constraint prevents the toe of the interface to reach the well and the optimal pumping rates are calculated for different locations of the pumping well and different combinations of aquifer parameters. Then the results of the sharp interface models are compared to the 'true' results of the corresponding variable-density numerical model in order to evaluate the performance of the sharp interface models. The results indicate that when the location of the well is close to the sea-boundary, the semi-infinite and the finite
Pileup Behavior in Sharp Nanoindentation of AISI 1045 Steel
NASA Astrophysics Data System (ADS)
Zhu, L. N.; Xu, B. S.; Wang, H. D.; Wang, C. B.
Experimental measurements have been used to investigate the pileup behavior during nanoindentation with a sharp indenter. The AISI 1045 steels treated by quenching and annealing were examined. The results show that during sharp nanoindentation process, the amount of pileup is related to the residual stress state, the indentation depth and the work hardening. The quenched steel with compressive residual stress will tend to pile up, and the stress-free annealed steel can decrease the pileup height. It is found that the pileup height gradually increases for the two steels as the indentation depth becomes larger. It is also shown that the low work hardening of the two steels can also result in the pileup deformation.
Sharpness changes of gaussian beams induced by spherically aberrated lenses
NASA Astrophysics Data System (ADS)
Piquero, G.; Mejías, P. M.; Martínez-Herrero, R.
1994-04-01
Sharpness changes of the spatial profile of a gaussian beam induced by spherically aberrated lenses are investigated in terms of the so-called kurtosis parameter. It is shown both theoretically and experimentally that, after a single aberrated lens, it is possible to get flatter and sharper beam intensity distributions than the input gaussian beam depending on the plane where the field is observed. Agreement between analytical and experimental results is discussed.
On the Edge: Haptic Discrimination of Edge Sharpness
Skinner, Andy L.; Kent, Christopher; Rossiter, Jonathan M.; Benton, Christopher P.; Groen, Martin G. M.; Noyes, Jan M.
2013-01-01
The increasing ubiquity of haptic displays (e.g., smart phones and tablets) necessitates a better understanding of the perceptual capabilities of the human haptic system. Haptic displays will soon be capable of locally deforming to create simple 3D shapes. This study investigated the sensitivity of our haptic system to a fundamental component of shapes: edges. A novel set of eight high quality shape stimuli with test edges that varied in sharpness were fabricated in a 3D printer. In a two alternative, forced choice task, blindfolded participants were presented with two of these shapes side by side (one the reference, the other selected randomly from the remaining set of seven) and after actively exploring the test edge of each shape with the tip of their index finger, reported which shape had the sharper edge. We used a model selection approach to fit optimal psychometric functions to performance data, and from these obtained just noticeable differences and Weber fractions. In Experiment 1, participants performed the task with four different references. With sharpness defined as the angle at which one surface meets the horizontal plane, the four JNDs closely followed Weber’s Law, giving a Weber fraction of 0.11. Comparisons to previously reported Weber fractions from other haptic manipulations (e.g. amplitude of vibration) suggests we are sufficiently sensitive to changes in edge sharpness for this to be of potential utility in the design of future haptic displays. In Experiment 2, two groups of participants performed the task with a single reference but different exploration strategies; one was limited to a single touch, the other unconstrained and free to explore as they wished. As predicted, the JND in the free exploration condition was lower than that in the single touch condition, indicating exploration strategy affects sensitivity to edge sharpness. PMID:24023852
Viscoelastic Characterization of Polytetrafluoroethylene (PTFE) Polymer by Sharp Indentation
NASA Astrophysics Data System (ADS)
Stan, Felicia; Munteanu, Ana V.; Fetecau, Catalin
2011-01-01
In this paper, indentation of polytetrafluoroethylene (PTFE) polymer with a sharp indenter is investigated in order to identify the material parameters. The indentation creep, i.e., the relative change of the indentation depth under constant load, is investigated based on a hereditary integral and on a rheological model which describes a viscoelastic plastic response. Experimental data were fitted to the model in order to identify the model parameters.
Legal protection for healthcare workers from sharps injuries.
Ling, Kate
The implementation of the sharps directive is the result of a negotiated agreement at European level between employers' organisations and trade unions. In the UK, NHS Employers, health service unions--including Unison and the Royal College of Nursing--and others have worked with the Health and Safety Executive to try to ensure that the new rules are workable at local level. PMID:23798161
Mimicking Tissue Boundaries by Sharp Multiparameter Matrix Interfaces.
Sapudom, Jiranuwat; Rubner, Stefan; Martin, Steve; Pompe, Tilo
2016-08-01
Engineering interfaces of distinct extracellular compartments mimicking native tissues are key for in-depth in vitro studies on developmental and disease processes in biology and medicine. Sharp interfaces of extracellular matrices are constructed based on fibrillar collagen I networks with a multiparameter control of topology, mechanics, and composition, and their distinct impact on triggering the directionality of cancer cell migration is demonstrated. PMID:27125887
Is there a sharp phase transition for deterministic cellular automata
Wootters, W.K. Los Alamos National Lab., NM Williams Coll., Williamstown, MA . Dept. of Physics); Langton, C.G. )
1990-01-01
Previous work has suggested that there is a kind of phase transition between deterministic automata exhibiting periodic behavior and those exhibiting chaotic behavior. However, unlike the usual phase transitions of physics, this transition takes place over a range of values of the parameter rather than at a specific value. The present paper asks whether the transition can be made sharp, either by taking the limit of an infinitely large rule table, or by changing the parameter in terms of which the space of automata is explored. We find strong evidence that, for the class of automata we consider, the transition does become sharp in the limit of an infinite number of symbols, the size of the neighborhood being held fixed. Our work also suggests an alternative parameter in terms of which it is likely that the transition will become fairly sharp even if one does not increase the number of symbols. In the course of our analysis, we find that mean field theory, which is our main tool, gives surprisingly good predictions of the statistical properties of the class of automata we consider. 18 refs., 6 figs.
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.)
The flat Grothendieck-Riemann-Roch theorem without adiabatic techniques
NASA Astrophysics Data System (ADS)
Ho, Man-Ho
2016-09-01
In this paper we give a simplified proof of the flat Grothendieck-Riemann-Roch theorem. The proof makes use of the local family index theorem and basic computations of the Chern-Simons form. In particular, it does not involve any adiabatic limit computation of the reduced eta-invariant.
Evaluating a Class of Series Using Taylor's Theorem. Classroom Notes
ERIC Educational Resources Information Center
Glaister, P.
2004-01-01
A class of infinite series is evaluated with the aid of Taylor's theorem and a comparison is made with other methods. In a recent note [1] a class of infinite series was shown to be equivalent to a number of definite integrals, and Taylor's theorem was used to establish convergence and to determine the sums of the series and the integrals to any…
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…
Group Theoretical Interpretation of von Neumann's Theorem on Composite Systems.
ERIC Educational Resources Information Center
Bergia, S.; And Others
1979-01-01
Shows that von Neumann's mathematical theorem on composite systems acquires a transparent physical meaning with reference to a suitable physical example; a composite system in a state of definite angular momentum. Gives an outline of the theorem, and the results are restated in Dirac's notation, thus generalizing von Neumann's results which were…
Stimulating Presentation of Theorems Followed by Responsive Proofs.
ERIC Educational Resources Information Center
Movshovitz-Hadar, Nitsa
1988-01-01
Several ways to present two theorems (concerning a square matrix and a property of prime numbers) are demonstrated. One way for each theorem is more stimulating, better setting the stage for the proofs. Several methods of presenting proofs are illustrated, with the outcomes considered from the learner's viewpoint. (MNS)
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2009-02-20
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2008-03-01
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
Leaning on Socrates to Derive the Pythagorean Theorem
ERIC Educational Resources Information Center
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the formula b2 +…
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…
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…
Some Reflections on CAS Assisted Proofs of Theorems
ERIC Educational Resources Information Center
Dana-Picard, Thierry
2005-01-01
A mathematician's work consists of proving theorems, calculating, and making mathematics understandable. An assistant for all three components is a Computer Algebra System. We describe and discuss various CAS-assisted processes for proving theorems, and discuss the constraints which can appear regarding efficiency, confidence in the result and…
Rotation of Axes and the Mean Value Theorem
ERIC Educational Resources Information Center
Price, David
2004-01-01
This article provides a proof of the Mean Value Theorem by rotating a coordinate system through a specified angle. The use of this approach makes it easy to visualize why the Mean Value Theorem is true. An instructor can use the proof as another illustration of the rotation of axis technique in addition to the standard one of simplifying equations…
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.
A most compendious and facile quantum de Finetti theorem
Koenig, Robert; Mitchison, Graeme
2009-01-15
In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's 'exponential' approximation by 'almost-product' states, a theorem which deals with certain triples of representations of the unitary group, and the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choice of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states and leads to some new results, including an exponential theorem for infinite-dimensional systems.
Sampling theorems and compressive sensing on the sphere
NASA Astrophysics Data System (ADS)
McEwen, Jason D.; Puy, Gilles; Thiran, Jean-Philippe; Vandergheynst, Pierre; Van De Ville, Dimitri; Wiaux, Yves
2011-09-01
We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a band-limited signal exactly, this new sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere, such as the canonical Driscoll & Healy sampling theorem. A reduction in the number of samples required to represent a band-limited signal on the sphere has important implications for compressive sensing, both in terms of the dimensionality and sparsity of signals. We illustrate the impact of this property with an inpainting problem on the sphere, where we show superior reconstruction performance when adopting the new sampling theorem.
The virial theorem for the polarizable continuum model
Cammi, R.
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.
The virial theorem for the Polarizable Continuum Model.
Cammi, R
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential. PMID:24588153
A Stochastic Tikhonov Theorem in Infinite Dimensions
Buckdahn, Rainer Guatteri, Giuseppina
2006-03-15
The present paper studies the problem of singular perturbation in the infinite-dimensional framework and gives a Hilbert-space-valued stochastic version of the Tikhonov theorem. We consider a nonlinear system of Hilbert-space-valued equations for a 'slow' and a 'fast' variable; the system is strongly coupled and driven by linear unbounded operators generating a C{sub 0}-semigroup and independent cylindrical Brownian motions. Under well-established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. We avoid differentiability assumptions on the coefficients which would be unnatural in the infinite-dimensional framework.
Extended Ehrenfest theorem with radiative corrections
NASA Astrophysics Data System (ADS)
de la Peña, L.; Cetto, A. M.; Valdés-Hernández, A.
2015-10-01
A set of basic evolution equations for the mean values of dynamical variables is obtained from the Fokker-Planck equation applied to the general problem of a particle subject to a random force. The specific case of stochastic electrodynamics is then considered, in which the random force is due to the zero-point radiation field. Elsewhere it has been shown that when this system reaches a state of energy balance, it becomes controlled by an equation identical to Schrödinger’s, if the radiationless approximation is made. The Fokker-Planck equation was shown to lead to the Ehrenfest theorem under such an approximation. Here we show that when the radiative terms are not neglected, an extended form of the Ehrenfest equation is obtained, from which follow, among others, the correct formulas for the atomic lifetimes and the (nonrelativistic) Lamb shift.
BMS supertranslations and Weinberg's soft graviton theorem
NASA Astrophysics Data System (ADS)
He, Temple; Lysov, Vyacheslav; Mitra, Prahar; Strominger, Andrew
2015-05-01
Recently it was conjectured that a certain infinite-dimensional "diagonal" subgroup of BMS supertranslations acting on past and future null infinity ([InlineMediaObject not available: see fulltext.] and [InlineMediaObject not available: see fulltext.]) is an exact symmetry of the quantum gravity S-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinberg's soft graviton theorem. Along the way we construct the canonical generators of supertranslations at [InlineMediaObject not available: see fulltext.], including the relevant soft graviton contributions. Boundary conditions at the past and future of [InlineMediaObject not available: see fulltext.] and a correspondingly modified Dirac bracket are required. The soft gravitons enter as boundary modes and are manifestly the Goldstone bosons of spontaneously broken supertranslation invariance.
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.
On the Virial Theorem for Interstellar Medium
Ryutov, D
2007-09-24
An attempt has been made to derive a version of the virial integral that would describe average properties of the interstellar medium (ISM). It is suggested to eliminate the (large) contribution of stellar matter by introducing 'exclusion zones' surrounding stars. Such an approach leads to the appearance of several types of additional surface integrals in the general expression. Their contribution depends on the rate of energy and matter exchange between the stars and ISM. If this exchange is weak, one can obtain a desired virial integral for ISM. However, the presence of intermittent large-scale energetic events significantly constrains the applicability of the virial theorem. If valid, the derived virial integral is dominated by cold molecular/atomic clouds, with only minor contribution of the global magnetic field and low-density warm part.
Walking Through the Impulse-Momentum Theorem
NASA Astrophysics Data System (ADS)
Haugland, Ole Anton
2013-02-01
Modern force platforms are handy tools for investigating forces during human motion. Earlier they were very expensive and were mostly used in research laboratories. But now even platforms that can measure in two directions are quite affordable. In this work we used the PASCO 2-Axis Force Platform. The analysis of the data can serve as a nice illustration of qualitative or quantitative use of the impulse-momentum theorem p - p0 = ∫t0t Fdt = I. The most common use of force platforms is to study the force from the base during the push-off period of a vertical jump. I think this is an activity of great value, and I would recommend it. The use of force platforms in teaching is well documented in research literature.1-4
Elementary theorems regarding blue isocurvature perturbations
NASA Astrophysics Data System (ADS)
Chung, Daniel J. H.; Yoo, Hojin
2015-04-01
Blue CDM-photon isocurvature perturbations are attractive in terms of observability and may be typical from the perspective of generic mass relations in supergravity. We present and apply three theorems useful for blue isocurvature perturbations arising from linear spectator scalar fields. In the process, we give a more precise formula for the blue spectrum associated with the axion model of Kasuya and Kawasaki [Axion Isocurvature Fluctuations with Extremely Blue Spectrum, Phys. Rev. D 80, 023516 (2009).], which can in a parametric corner give a factor of O (10 ) correction. We explain how a conserved current associated with Peccei-Quinn symmetry plays a crucial role and explicitly plot several example spectra including the breaks in the spectra. We also resolve a little puzzle arising from a naive multiplication of isocurvature expression that sheds light on the gravitational imprint of the adiabatic perturbations on the fields responsible for blue isocurvature fluctuations.
Robbing the Bank with a Theorem Prover
NASA Astrophysics Data System (ADS)
Youn, Paul; Adida, Ben; Bond, Mike; Clulow, Jolyon; Herzog, Jonathan; Lin, Amerson; Rivest, Ronald L.; Anderson, Ross
In this work, we present the first automated analysis of security application programming interfaces (security APIs). In particular, we analyze the API of the IBM 4758 CCA, a hardware security module for banking networks. Adapting techniques from formal analyses of security protocols, we model the API purely according its specification and assuming ideal encryption primitives. We then use the automated theorem-prover Otter to analyze this model, combining its standard reasoning strategies with novel techniques of our own (also presented here). In this way, we derive not only all published API-level attacks against the 4758 CCA, but an extension to these attacks as well. Thus, this work represents the first step toward fully-automated, rigorous analyses of security APIs.
Geometry underlying no-hidden-variable theorems
NASA Astrophysics Data System (ADS)
Fivel, Daniel I.
1991-07-01
The set of orientations of a measuring device (e.g., a Stern-Gerlach magnet) produced by the action of a Lie group constitutes a honmogeneous space S (e.g., a sphere). A hidden-variable measure determines a metric D on S, the triangle inequality being Bell's inequality. But identification of S with Hilbert-space projectors induces a locally convex metric d on S. The Einstein-Podolsky-Rosen (EPR) hypotheses imply that D=d2, which is impossible because the square of a locally convex metric cannot be a metric. This proves the Bell-EPR theorem. Classical systems avoid the contradiction by allowing only values d=0,1. The ``watchdog'' effect is shown to result from the form of the quantum-mechanical metric.
Electric-magnetic symmetry and Noether's theorem
NASA Astrophysics Data System (ADS)
Cameron, Robert P.; Barnett, Stephen M.
2012-12-01
In the absence of charges, Maxwell's equations are highly symmetrical. In particular, they place the electric and magnetic fields on equal footing. In light of this electric-magnetic symmetry, we introduce a variational description of the free electromagnetic field that is based upon the acknowledgement of both electric and magnetic potentials. We use our description, together with Noether's theorem, to demonstrate that electric-magnetic symmetry is, in essence, an expression of the conservation of optical helicity. The symmetry associated with the conservation of Lipkin's zilches is also identified. We conclude by considering, with care, the subtle separation of the rotation and boost angular momenta of the field into their ‘spin’ and ‘orbital’ contributions.
Virial Theorem in Nonlocal Newtonian Gravity
NASA Astrophysics Data System (ADS)
Mashhoon, Bahram
2016-05-01
Nonlocal gravity is the recent classical nonlocal generalization of Einstein's theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for "isolated" astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's baryonic diameter---namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time---is predicted to be larger than the effective dark matter fraction times a universal length that is the basic nonlocality length scale of about 3 kpc.
Generalization of Kummer's second theorem with applications
NASA Astrophysics Data System (ADS)
Kim, Yong Sup; Rakha, M. A.; Rathie, A. K.
2010-03-01
The aim of this research paper is to obtain single series expression of e^{ - x/2} _1 F_1 (α ;2α + i;x) for i = 0, ±1, ±2, ±3, ±4, ±5, where 1 F 1(·) is the function of Kummer. For i = 0, we have the well known Kummer second theorem. The results are derived with the help of generalized Gauss second summation theorem obtained earlier by Lavoie et al. In addition to this, explicit expressions of _2 F_1 [ - 2n,α ;2α + i;2]and_2 F_1 [ - 2n - 1,α ;2α + i;2] each for i = 0, ±1, ±2, ±3, ±4, ±5 are also given. For i = 0, we get two interesting and known results recorded in the literature. As an applications of our results, explicit expressions of e^{ - x} _1 F_1 (α ;2α + i;x) × _1 F_1 (α ;2α + j;x) for i, j = 0, ±1, ±2, ±3, ±4, ±5 and (1 - x)^{ - a} _2 F_1 left( {a,b,2b + j; - tfrac{{2x}} {{1 - x}}} right) for j = 0, ±1, ±2, ±3, ±4, ±5 are given. For i = j = 0 and j = 0, we respectively get the well known Preece identity and a well known quadratic transformation formula due to Kummer. The results derived in this paper are simple, interesting, easily established and may be useful in the applicable sciences.
Direct handling of sharp interfacial energy for microstructural evolution
Hernández–Rivera, Efraín; Tikare, Veena; Noirot, Laurence; Wang, Lumin
2014-08-24
In this study, we introduce a simplification to the previously demonstrated hybrid Potts–phase field (hPPF), which relates interfacial energies to microstructural sharp interfaces. The model defines interfacial energy by a Potts-like discrete interface approach of counting unlike neighbors, which we use to compute local curvature. The model is compared to the hPPF by studying interfacial characteristics and grain growth behavior. The models give virtually identical results, while the new model allows the simulator more direct control of interfacial energy.
Sharp nonlinear stability for centrifugal filtration convection in magnetizable media.
Saravanan, S; Brindha, D
2011-11-01
A nonlinear stability theory is adopted to study centrifugal thermal convection in a magnetic-fluid-saturated and differentially heated porous layer placed in a zero-gravity environment. The axis of rotation of the layer is placed within its boundaries that leads to an alternating direction of the centrifugal body force. An analysis through the variational principles is made to find the unconditional and sharp nonlinear limits. The compound matrix method is employed to solve the eigenvalue problems of the nonlinear and corresponding linear theories. The importance of nonlinear theory is established by demonstrating the failure of the linear theory in capturing the physics of the onset of convection. PMID:22181509
Climbing Mt. Sharp: Maximizing Curiosity's Science Over Traversable Terrains
NASA Astrophysics Data System (ADS)
Fraeman, A. A.; Arvidson, R. E.; Bellutta, P.; Sletten, R. S.; Team, M.
2013-12-01
As Curiosity transitions from the plains of Gale Crater to the flanks of Mt. Sharp, the rover will begin to encounter material and terrains that could present greater mobility challenges. These challenges include the presence of significantly steeper slopes and large dunes that have the potential to embed the vehicle. Strategic path planning during this phase of the mission will therefore require carefully selecting a traversable route that is both time-efficient and that will provide access to the most scientifically rewarding targets. We consider possible solutions to this optimization problem by examining multiple orbital data sets in order to locate likely mobility hazards and to select potential science waypoints for future in situ investigation. High resolution HiRISE monochromatic images and digital elevation models show filled craters, rock fields, areas with slopes too steep for the rover to traverse, and other possible mobility obstacles on the northwest flank of Mt. Sharp. Using this context, we review accessibility to scientific targets on Mt. Sharp that have been previously discussed in landing site workshop presentations and peer-reviewed publications. Additionally, we identify new targets using detailed geologic maps combined with oversampled CRISM observations that provide mineralogical information at unprecedented high spatial resolutions (up to 6 m/pixel). For example, the spatially sharpened CRISM spectral data show a localized hematite deposit that is associated with the upper-most stratum of a ridge which is located ~3km from the rover's entry point to Mt. Sharp. This deposit may represent a previously habitable environment and is therefore a high priority target for in situ investigation. In order to study the hematite and also to eventually access the phyllosilicate-bearing trough that is located directly behind the ridge, Curiosity will have to cross this ridge, but the ridge edges are often defined by regions with slopes that are too steep
DSMC Simulations of Shock Interactions About Sharp Double Cones
NASA Technical Reports Server (NTRS)
Moss, James N.
2000-01-01
This paper presents the results of a numerical study of shock interactions resulting from Mach 10 flow about sharp double cones. Computations are made by using the direct simulation Monte Carlo (DSMC) method of Bird. The sensitivity and characteristics of the interactions are examined by varying flow conditions, model size, and configuration. The range of conditions investigated includes those for which experiments have been or will be performed in the ONERA R5Ch low-density wind tunnel and the Calspan-University of Buffalo Research Center (CUBRC) Large Energy National Shock (LENS) tunnel.
Nonlinear electrostatic oscillations in a sharp plasma interface
Haas, F.; Shukla, P. K.
2009-11-10
We revisit a generalized nonlinear Schroedinger equation derived by Stenflo and Gradov, describing electrostatic oscillations in a sharp plasma interface. A Madelung decomposition is used to deduce a Sagdeev potential associated to an autonomous one-dimensional Hamiltonian system, whose solutions are all periodic. A conservation law preventing singularities (under suitable boundary conditions and initial wave profile) is derived. In the particular case where some of the nonlinearities can be neglected, the model is shown to be equivalent to the free-particle Schroedinger equation.
Friedmann's equations in all dimensions and Chebyshev's theorem
Chen, Shouxin; Gibbons, Gary W.; Li, Yijun; Yang, Yisong E-mail: gwg1@damtp.cam.ac.uk E-mail: yisongyang@nyu.edu
2014-12-01
This short but systematic work demonstrates a link between Chebyshev's theorem and the explicit integration in cosmological time t and conformal time η of the Friedmann equations in all dimensions and with an arbitrary cosmological constant Λ. More precisely, it is shown that for spatially flat universes an explicit integration in t may always be carried out, and that, in the non-flat situation and when Λ is zero and the ratio w of the pressure and energy density in the barotropic equation of state of the perfect-fluid universe is rational, an explicit integration may be carried out if and only if the dimension n of space and w obey some specific relations among an infinite family. The situation for explicit integration in η is complementary to that in t. More precisely, it is shown in the flat-universe case with Λ ≠ 0 that an explicit integration in η can be carried out if and only if w and n obey similar relations among a well-defined family which we specify, and that, when Λ = 0, an explicit integration can always be carried out whether the space is flat, closed, or open. We also show that our method may be used to study more realistic cosmological situations when the equation of state is nonlinear.
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
Kohn's theorem, Larmor's equivalence principle and the Newton-Hooke group
Gibbons, G.W.; Pope, C.N.
2011-07-15
Highlights: > We show that non-relativistic electrons moving in a magnetic field with trapping potential admits as relativity group the Newton-Hooke group. > We use this fact to give a group theoretic interpretation of Kohn's theorem and to obtain the spectrum. > We obtain the lightlike lift of the system exhibiting showing it coincides with the Nappi-Witten spacetime. - Abstract: We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a 'relativity group' which is a one-parameter family of deformations of the standard Galilei group to the Newton-Hooke group which is a Wigner-Inoenue contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn's theorem and related results. Larmor's theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the 'Eisenhart' or 'lightlike' lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdicka-Eardley-Nappi-Witten pp-wave solution of Einstein-Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi-Jackiw group.
The Spectral Sharpness Angle of Gamma-ray Bursts
NASA Astrophysics Data System (ADS)
Yu, Hoi-Fung; van Eerten, Hendrik J.; Greiner, Jochen; Sari, Re'em; Bhat, P. Narayana; Kienlin, Andreas von; Paciesas, William S.; Preece, Robert D.
2016-06-01
We explain the results of Yu et al. (2015b) of the novel sharpness angle measurement to a large number of spectra obtained from the Fermi gamma-ray burst monitor. The sharpness angle is compared to the values obtained from various representative emission models: blackbody, single-electron synchrotron, synchrotron emission from a Maxwellian or power-law electron distribution. It is found that more than 91% of the high temporally and spectrally resolved spectra are inconsistent with any kind of optically thin synchrotron emission model alone. It is also found that the limiting case, a single temperature Maxwellian synchrotron function, can only contribute up to 58+23 -18% of the peak flux. These results show that even the sharpest but non-realistic case, the single-electron synchrotron function, cannot explain a large fraction of the observed spectra. Since any combination of physically possible synchrotron spectra added together will always further broaden the spectrum, emission mechanisms other than optically thin synchrotron radiation are likely required in a full explanation of the spectral peaks or breaks of the GRB prompt emission phase.
Single image superresolution based on gradient profile sharpness.
Yan, Qing; Xu, Yi; Yang, Xiaokang; Nguyen, Truong Q
2015-10-01
Single image superresolution is a classic and active image processing problem, which aims to generate a high-resolution (HR) image from a low-resolution input image. Due to the severely under-determined nature of this problem, an effective image prior is necessary to make the problem solvable, and to improve the quality of generated images. In this paper, a novel image superresolution algorithm is proposed based on gradient profile sharpness (GPS). GPS is an edge sharpness metric, which is extracted from two gradient description models, i.e., a triangle model and a Gaussian mixture model for the description of different kinds of gradient profiles. Then, the transformation relationship of GPSs in different image resolutions is studied statistically, and the parameter of the relationship is estimated automatically. Based on the estimated GPS transformation relationship, two gradient profile transformation models are proposed for two profile description models, which can keep profile shape and profile gradient magnitude sum consistent during profile transformation. Finally, the target gradient field of HR image is generated from the transformed gradient profiles, which is added as the image prior in HR image reconstruction model. Extensive experiments are conducted to evaluate the proposed algorithm in subjective visual effect, objective quality, and computation time. The experimental results demonstrate that the proposed approach can generate superior HR images with better visual quality, lower reconstruction error, and acceptable computation efficiency as compared with state-of-the-art works. PMID:25807567
Nematode Chemotaxis: Gradual Turns, Sharp Turns, and Modulated Turn Angles
NASA Astrophysics Data System (ADS)
Patel, Amar; Padmanabhan, Venkat; Rumbaugh, Kendra; Vanapalli, Siva; Blawzdziewicz, Jerzy
2013-03-01
We examine strategies used by the soil-dwelling nematode Caenorhabditis Elegans for chemotaxis in complex environments. The proposed description is based on our recently developed piecewise-harmonic-curvature model of nematode locomotion [PLoS ONE, 7(7) e40121 (2012)], where random harmonic-curvature modes represent elementary locomotory movements. We show that the previously described gradual-turn and sharp-turn chemotaxis strategies can be unified in our model. The gradual-turn mechanism relies on crawling amplitude changes commensurate with the undulation frequency. The sharp-turn mechanism consists in modulation of the frequency of jumps to large-amplitude modes. We hypothesize that there exists a third strategy, where the nematode adjusts the variance of the amplitude distribution. Such adjustments result in a modulation of the magnitude of random turns, with smaller turns performed when the nematode moves toward the increasing chemoatractant concentration. Experiments are proposed to determine if the third strategy is present in the nematode behavior. This work was supported by NSF grant No. CBET 1059745.
Hybridization between Dusky Grouse and Sharp-tailed Grouse
O'Donnell, Ryan P.
2015-01-01
Cache County, Utah, 7 April 2013: rare hybrid combination of grouse noted. Hybridization between Dusky Grouse (Dendragapus obscurus) and Sharp-tailed Grouse (Tympanuchus phasianellus) has been rarely documented in the wild. The only published record was of one collected from Osoyoos, British Columbia, in 1906 (Brooks 1907, Lincoln 1950). There is also one record of this hybrid in captivity (McCarthy 2006)...Although hybridization within genera is more common than between genera, it is perhaps not all too remarkable that these species would hybridize, given that Dendragapus and Tympanuchus are each other’s closest relatives (Drovetski 2002). The ranges of these two species overlap over a broad area ranging roughly from parts of northern Utah and Colorado to Yukon and the Northwest Territories. Given the close relatedness and extent of overlap of their ranges, it is perhaps surprising that there have not been more reports of this hybrid combination in the over-100 years since Brooks (1907) first described one. The species may be segregated by habitat use, as Sharp-tailed prefer open grassland sites for lekking and shrub areas for nesting, and Dusky are often found in more densely forested conifer stands—although Dusky often use more open habitats in the spring.
Consistency relations for sharp features in the primordial spectra
NASA Astrophysics Data System (ADS)
Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris; Soto, Alex
2015-10-01
We study the generation of sharp features in the primordial spectra within the framework of effective field theory of inflation, wherein curvature perturbations are the consequence of the dynamics of a single scalar degree of freedom. We identify two sources in the generation of features: rapid variations of the sound speed cs (at which curvature fluctuations propagate) and rapid variations of the expansion rate H during inflation. With this in mind, we propose a non-trivial relation linking these two quantities that allows us to study the generation of sharp features in realistic scenarios where features are the result of the simultaneous occurrence of these two sources. This relation depends on a single parameter with a value determined by the particular model (and its numerical input) responsible for the rapidly varying background. As a consequence, we find a one-parameter consistency relation between the shape and size of features in the bispectrum and features in the power spectrum. To substantiate this result, we discuss several examples of models for which this one-parameter relation (between cs and H) holds, including models in which features in the spectra are both sudden and resonant.
SHARP simulation of discontinuities in highly convective steady flow
NASA Technical Reports Server (NTRS)
Leonard, B. P.
1987-01-01
For steady multidimesional convection, the Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme has several attractive properties. However, for highly convective simulation of step profiles, QUICK produces unphysical overshoots and a few oscillations, and this may cause serious problems in nonlinear flows. Fortunately, it is possible to modify the convective flux by writing the normalized convected control-volume face value as a function of the normalized adjacent upstream node value, developing criteria for monotonic resolution without sacrificing formal accuracy. This results in a nonlinear functional relationship between the normalized variables, whereas standard methods are all linear in this sense. The resulting Simple High Accuracy Resolution Program (SHARP) can be applied to steady multidimensional flows containing thin shear or mixing layers, shock waves, and other frontal phenomena. This represents a significant advance in modeling highly convective flows of engineering and geophysical importance. SHARP is based on an explicit, conservative, control-volume flux formation, equally applicable to one, two, or three dimensional elliptic, parabolic, hyperbolic, or mixed-flow regimes. Results are given for the bench-mark purely convective first-order results and the nonmonotonic predictions of second- and third-order upwinding.
Federal Register 2010, 2011, 2012, 2013, 2014
2013-07-19
... Availability (NOA) for Sharpe Permit Relinquishment Project Environmental Assessment (EA) Finding of No... Federal Register (78 FR 25258-25259) announcing the publication of the Sharpe Permit Relinquishment... environmental assessment, David Rodriquez, Director, DLA Installation Support, concludes the proposed action...
Central limit theorem for reducible and irreducible open quantum walks
NASA Astrophysics Data System (ADS)
Sadowski, Przemysław; Pawela, Łukasz
2016-07-01
In this work we aim at proving central limit theorems for open quantum walks on {mathbb {Z}}^d. We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.
Central limit theorem for reducible and irreducible open quantum walks
NASA Astrophysics Data System (ADS)
Sadowski, Przemysław; Pawela, Łukasz
2016-04-01
In this work we aim at proving central limit theorems for open quantum walks on {{Z}}^d . We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.
The global Utiyama theorem in Einstein-Cartan theory
NASA Astrophysics Data System (ADS)
Bruzzo, Ugo
1987-09-01
A global formulation of Utiyama's theorem for Einstein-Cartan-type gravitational theories regarded as gauge theories of the group of space-time diffeomorphisms is given. The local conditions for the Lagrangian to be gauge invariant coincide with those found by other authors [A. Pérez-Rendón Collantes, ``Utiyama type theorems,'' in Poincaré Gauge Approach to Gravity. I, Proceedings Journées Relativistes 1984; A. Pérez-Rendón and J. J. Seisdedos, ``Utiyama type theorems in Poincaré gauge approach to gravity. II, '' Preprints de Mathematicas, Universidad de Salamanca, 1986] in Kibble's and Hehl's approaches.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
NASA Astrophysics Data System (ADS)
Stenlund, Mikko
2016-09-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff's ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
Theorems on Positive Data: On the Uniqueness of NMF
Laurberg, Hans; Christensen, Mads Græsbøll; Plumbley, Mark D.; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors. PMID:18497868
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.
Scaling and scale invariance of conservation laws in Reynolds transport theorem framework.
Haltas, Ismail; Ulusoy, Suleyman
2015-07-01
Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework. PMID:26232979
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.
This report presents the results of the verification test of the Sharpe Platinum 2013 high-volume, low-pressure gravity-feed spray gun, hereafter referred to as the Sharpe Platinum, which is designed for use in automotive refinishing. The test coating chosen by Sharpe Manufacturi...
Whitney, Richard
2004-01-01
Columbian Sharp-Tailed Grouse (Tympanuchus phasianellus columbianus) (CSTG) are an important traditional and cultural species to the Colville Confederated Tribes (CCT), Spokane Tribe of Indians (STOI), and other Tribes in the Region. They were once the most abundant upland bird in the Region. Currently, the largest remaining population in Washington State occurs on the CCT Reservation in Okanogan County. Increasing agricultural practices and other land uses has contributed to the decline of sharp-tail habitat and populations putting this species at risk. The decline of this species is not new (Yokum, 1952, Buss and Dziedzic, 1955, Zeigler, 1979, Meints 1991, and Crawford and Snyder 1994). The Tribes (CCT and STOI) are determined to protect, enhance and restore habitat for this species continued existence. When Grand Coulee and Chief Joseph Hydro-projects were constructed, inundated habitat used by this species was lost forever adding to overall decline. To compensate and prevent further habitat loss, the CCT proposed a project with Bonneville Power Administration (BPA) funding to address this species and their habitat requirements. The projects main focus is to address habitat utilized by the current CSTG population and determine ways to protect, restore, and enhance habitats for the conservation of this species over time. The project went through the NPPC Review Process and was funded through FY03 by BPA. This report addresses part of the current CCT effort to address the conservation of this species on the Colville Reservation.
Dynamics of low capillary number interfaces moving through sharp features
NASA Astrophysics Data System (ADS)
Reddy, Shravanthi; Schunk, P. Randall; Bonnecaze, Roger T.
2005-12-01
The success of any nanoimprint process depends upon its ability to exactly reproduce the template pattern. Thus, complete filling of recessed features in the template is an important issue that is controlled by the dynamics of the flow through these sharp structures. At these small scales, capillary forces are large and must be included in the fluid flow model. The mechanism of interface advancement at low capillary number through sharp rectangular features is useful for understanding how and why features fill or trap air. In this study we present a two-dimensional simulation of this feature filling to capture the details of the process, including the viscous and capillary effects. Fluid is injected into the channel between the template and substrate, where the fluid-air interface soon encounters a rectangular feature with some height greater than the channel gap. As the fluid advances through the channel, the shape of the interface is a circular arc due to the strong capillary forces. The interface maintains this circular arc as it negotiates the first sharp corner of the feature; the upper contact line effectively pins to the initial corner of the feature as it moves around this corner, during which time the lower contact line continues to advance forward along the substrate surface, causing the interface to stretch. For sufficiently wide or shallow features, once the upper contact line has negotiated the first corner and has moved vertically up the inner wall of the feature, it must move through the top corner of the feature. At this point the interface undergoes a rapid reconfiguration from a high surface area circular arc to a lower surface area circular arc inside the feature. Alternatively, for narrow or high features, the stretched interface can catch on the far, final corner of the feature, trapping air inside the feature and preventing filling. The conditions for filling are studied parametrically for a variety of wetting contact angles and feature
The sharpness of gamma-ray burst prompt emission spectra
NASA Astrophysics Data System (ADS)
Yu, Hoi-Fung; van Eerten, Hendrik J.; Greiner, Jochen; Sari, Re'em; Narayana Bhat, P.; von Kienlin, Andreas; Paciesas, William S.; Preece, Robert D.
2015-11-01
Context. We study the sharpness of the time-resolved prompt emission spectra of gamma-ray bursts (GRBs) observed by the Gamma-ray Burst Monitor (GBM) on board the Fermi Gamma-ray Space Telescope. Aims: We aim to obtain a measure of the curvature of time-resolved spectra that can be compared directly to theory. This tests the ability of models such as synchrotron emission to explain the peaks or breaks of GBM prompt emission spectra. Methods: We take the burst sample from the official Fermi GBM GRB time-resolved spectral catalog. We re-fit all spectra with a measured peak or break energy in the catalog best-fit models in various energy ranges, which cover the curvature around the spectral peak or break, resulting in a total of 1113 spectra being analyzed. We compute the sharpness angles under the peak or break of the triangle constructed under the model fit curves and compare them to the values obtained from various representative emission models: blackbody, single-electron synchrotron, synchrotron emission from a Maxwellian or power-law electron distribution. Results: We find that 35% of the time-resolved spectra are inconsistent with the single-electron synchrotron function, and 91% are inconsistent with the Maxwellian synchrotron function. The single temperature, single emission time, and location blackbody function is found to be sharper than all the spectra. No general evolutionary trend of the sharpness angle is observed, neither per burst nor for the whole population. It is found that the limiting case, a single temperature Maxwellian synchrotron function, can only contribute up to % of the peak flux. Conclusions: Our results show that even the sharpest but non-realistic case, the single-electron synchrotron function, cannot explain a large fraction of the observed GRB prompt spectra. Because any combination of physically possible synchrotron spectra added together will always further broaden the spectrum, emission mechanisms other than optically thin
Equipartition theorem in glasses and liquids
NASA Astrophysics Data System (ADS)
Levashov, Valentin A.; Egami, Takeshi; Aga, Rachel S.; Morris, James R.
2008-03-01
In glasses and liquids phonons have very short life-time, whereas the total potential energy is not linear with temperature, but follows the T**(3/5) law. Thus it may appear that atomic vibrations in liquids cannot be described by the harmonic oscillator model that follows the equipartition theorem for the kinetic energy and potential energy. We show that the description of the nearest neighbor oscillation in terms of the atomic level stresses indeed provide such a description. The model was tested for various pair-wise potentials, including the Lennard-Jones potential, the Johnson potentials, and only the repulsive part of the Johnson potential. In all cases each of the local elastic energies of the six independent components of the stress tensor is equal to kT/4, thus the total potential energy is equal to (3/2)kT. Thus this model provides the basis for discussing the thermodynamic properties of glasses and liquids based on atomistic excitations. An example of this model leading to the description of the glass transition temperature in metallic glasses is discussed [1]. [1] T. Egami, et al., Phys. Rev. B 76, 024203 (2007).
New Fermionic Soft Theorems for Supergravity Amplitudes.
Chen, Wei-Ming; Huang, Yu-Tin; Wen, Congkao
2015-07-10
Soft limits of a massless S matrix are known to reflect the symmetries of the theory. In particular, for theories with Goldstone bosons, the double-soft limit of scalars reveals the coset structure of the vacuum manifold. In this Letter, we propose that such universal double-soft behavior is not only true for scalars, but also for spin-1/2 particles in four dimensions and fermions in three dimensions. We first consider the Akulov-Volkov theory and demonstrate that the double-soft limit of Goldstinos yields the supersymmetry algebra. More surprisingly, we also find that amplitudes in 4≤N≤8 supergravity theories in four dimensions as well as N=16 supergravity in three dimensions behave universally in the double-soft-fermion limit, analogous to the scalar ones. The validity of the new soft theorems at loop level is also studied. The results for supergravity are beyond what is implied by supersymmetry Ward identities and may impose nontrivial constraints on the possible counterterms for supergravity theories. PMID:26207460
Analysing nature's experiment: Fisher's inductive theorem of natural selection.
Edwards, A W F
2016-06-01
The paper by Ewens and Lessard (2015) adds to the progress that has been made in exploring the discrete-generation analytical version of Fisher's Fundamental Theorem of Natural Selection introduced by Ewens (1989). Fisher's continuous-time theorem differs from the version described by Ewens and Lessard by using a different concept of fitness. Ewens and Lessard use the conventional 'viability' concept whereas for Fisher the fitness of a genotype was its relative rate of increase or decrease in the population. The sole purpose of the present paper is to emphasize the alternative inductive nature of Fisher's theorem, as presented by him in 1930, by placing it in the context of his contemporary development of the analysis of variance in agricultural experiments. It is not a general discussion of the theorem itself. PMID:26581894
Two time physics and Hamiltonian Noether theorem for gauge systems
Nieto, J. A.; Ruiz, L.; Silvas, J.; Villanueva, V. M.
2006-09-25
Motivated by two time physics theory we revisited the Noether theorem for Hamiltonian constrained systems. Our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints.
Oscillation theorems for second order nonlinear forced differential equations.
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. PMID:25077054
Extension of the Blasius force theorem to subsonic speeds
NASA Astrophysics Data System (ADS)
Barsony-Nagy, A.
1985-11-01
The theorem considered by Blasius (1910) represents a well-known method for calculating the force on a body situated in an incompressible, inviscid two-dimensional flow. The efficiency of the Blasius theorem is due to its quality of expressing the forces with the aid of contour integrals of analytic functions of complex variables. The present note has the objective to deduce an analog of Blasius theorem for the aerodynamic forces in subsonic flow. It is assumed that an approximate velocity potential of the subsonic flow has been calculated by using the Imai-Lamla method. It is pointed out that this method is a variant specially suited for the two-dimensionally flows of the Janzen-Rayleigh expansion method. The derived formula expresses the aerodynamic forces with the aid of contour integrals of analytic complex functions. It can be regarded as the Blasius theorem with first-order compressibility correction for the subsonic speed regime.
Bernoulli theorem generalized to rheologically complex viscous fluid flow
NASA Astrophysics Data System (ADS)
Brutyan, M. A.; Krapivskii, P. L.
1992-08-01
The Bernoulli theorem is generalized to two-dimensional and axisymmetric micropolar incompressible fluid flows. It is shown that the approach developed is also applicable to magnetohydrodynamic flows of a viscous Newtonian fluid.
An Epistemological Criticism to the Bell-Kochen-Specker Theorem
NASA Astrophysics Data System (ADS)
Garola, Claudio
2009-03-01
The Bell-Kochen-Specker theorem is criticized from an epistemological point of view, showing that its proofs rest on an implicit epistemological assumption which does not fit in with the operational and antimetaphysical attitude of orthodox quantum mechanics.
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.
On an order reduction theorem in the Lagrangian formalism
NASA Astrophysics Data System (ADS)
Grigore, D. R.
1996-11-01
We provide a new proof of a important theorem in the Lagrangian formalism about necessary and sufficient conditions for a second-order variational system of equations to follow from a first-order Lagrangian.
Fluctuation theorem in driven nonthermal systems with quenched disorder
Reichhardt, Charles; Reichhardt, C J; Drocco, J A
2009-01-01
We demonstrate that the fluctuation theorem of Evans and Searles can be used to characterize the class of dynamics that arises in nonthermal systems of collectively interacting particles driven over random quenched disorder. By observing the frequency of entropy-destroying trajectories, we show that there are specific dynamical regimes near depinning in which this theorem holds. Hence the fluctuation theorem can be used to characterize a significantly wider class of non-equilibrium systems than previously considered. We discuss how the fluctuation theorem could be tested in specific systems where noisy dynamics appear at the transition from a pinned to a moving phase such as in vortices in type-II superconductors, magnetic domain walls, and dislocation dynamics.
On the generalized virial theorem for systems with variable mass
NASA Astrophysics Data System (ADS)
Ganghoffer, Jean-François; Rahouadj, Rachid
2016-03-01
We presently extend the virial theorem for both discrete and continuous systems of material points with variable mass, relying on developments presented in Ganghoffer (Int J Solids Struct 47:1209-1220, 2010). The developed framework is applicable to describe physical systems at very different scales, from the evolution of a population of biological cells accounting for growth to mass ejection phenomena occurring within a collection of gravitating objects at the very large astrophysical scales. As a starting basis, the field equations in continuum mechanics are written to account for a mass source and a mass flux, leading to a formulation of the virial theorem accounting for non-constant mass within the considered system. The scalar and tensorial forms of the virial theorem are then written successively in both Lagrangian and Eulerian formats, incorporating the mass flux. As an illustration, the averaged stress tensor in accreting gravitating solid bodies is evaluated based on the generalized virial theorem.
Biological fitness and the fundamental theorem of natural selection.
Grafen, Alan
2015-07-01
Fisher's fundamental theorem of natural selection is proved satisfactorily for the first time, resolving confusions in the literature about the nature of reproductive value and fitness. Reproductive value is defined following Fisher, without reference to genetic variation, and fitness is the proportional rate of increase in an individual's contribution to the demographic population size. The mean value of fitness is the same in each age class, and it also equals the population's Malthusian parameter. The statement and derivation are regarded as settled here, and so the general biological significance of the fundamental theorem can be debated. The main purpose of the theorem is to find a quantitative measure of the effect of natural selection in a Mendelian system, thus founding Darwinism on Mendelism and identifying the design criterion for biological adaptation, embodied in Fisher's ingenious definition of fitness. The relevance of the newly understood theorem to five current research areas is discussed. PMID:26098334
Amplitude estimation of a sine function based on confidence intervals and Bayes' theorem
NASA Astrophysics Data System (ADS)
Eversmann, D.; Pretz, J.; Rosenthal, M.
2016-05-01
This paper discusses the amplitude estimation using data originating from a sine-like function as probability density function. If a simple least squares fit is used, a significant bias is observed if the amplitude is small compared to its error. It is shown that a proper treatment using the Feldman-Cousins algorithm of likelihood ratios allows one to construct improved confidence intervals. Using Bayes' theorem a probability density function is derived for the amplitude. It is used in an application to show that it leads to better estimates compared to a simple least squares fit.
Awake hippocampal sharp-wave ripples support spatial memory.
Jadhav, Shantanu P; Kemere, Caleb; German, P Walter; Frank, Loren M
2012-06-15
The hippocampus is critical for spatial learning and memory. Hippocampal neurons in awake animals exhibit place field activity that encodes current location, as well as sharp-wave ripple (SWR) activity during which representations based on past experiences are often replayed. The relationship between these patterns of activity and the memory functions of the hippocampus is poorly understood. We interrupted awake SWRs in animals learning a spatial alternation task. We observed a specific learning and performance deficit that persisted throughout training. This deficit was associated with awake SWR activity, as SWR interruption left place field activity and post-experience SWR reactivation intact. These results provide a link between awake SWRs and hippocampal memory processes, which suggests that awake replay of memory-related information during SWRs supports learning and memory-guided decision-making. PMID:22555434
Diagenetic Crystal Clusters and Dendrites, Lower Mount Sharp, Gale Crater
NASA Technical Reports Server (NTRS)
Kah, L. C.; Kronyak, R.; Van Beek, J.; Nachon, M.; Mangold, N.; Thompson, L.; Wiens, R.; Grotzinger, J.; Farmer, J.; Minitti, M.; Shieber, J.; Oehler, D.
2015-01-01
Since approximately Sol 753 (to sol 840+) the Mars Science Laboratory Curiosity rover has been investigating the Pahrump locality. Mapping of HiRise images suggests that the Pahrup locality represents the first occurrence of strata associated with basal Mount Sharp. Considerable efforts have been made to document the Pahrump locality in detail, in order to constrain both depositional and diagenetic facies. The Pahrump succession consists of approximately 13 meters of recessive-weathering mudstone interbedded with thin (decimeter-scale) intervals of more erosionally resistant mudstone, and crossbedded sandstone in the upper stratigraphic levels. Mudstone textures vary from massive, to poorly laminated, to well-laminated. Here we investigate the distribution and structure of unusual diagenetic features that occur in the lowermost portion of the Pahrump section. These diagenetic features consist of three dimensional crystal clusters and dendrites that are erosionally resistant with respect to the host rock.
Origin of the first sharp diffraction peak in glasses
NASA Astrophysics Data System (ADS)
Crupi, Cristina; Carini, Giuseppe; González, Miguel; D'Angelo, Giovanna
2015-10-01
Although glasses have been largely used for a wide variety of technological applications, much of their underlying structure and dynamical properties remain puzzling. We present a detailed investigation of the intermediate-range structure of a series of alkaline borate glasses carried out by performing neutron diffraction measurements. We propose that the first sharp diffraction peak of glasses arises from the periodicity of the boundaries of voids in a random network and explain its compositional and pressure dependence. In this framework, the planar section of a void is an n -membered ring of all-side vertex sharing basic structural units. Furthermore, we suggest that thermally activated relaxations responsible for the ultrasonic absorption in borate glasses stem from transverse motions of atoms bridging structural units confining voids.
The inviscid stability of supersonic flow past a sharp cone
NASA Technical Reports Server (NTRS)
Duck, Peter W.; Shaw, Stephen J.
1990-01-01
The effects of lateral curvature on the development of supersonic laminar inviscid boundary-layer flow on a sharp cone with adiabatic wall conditions are investigated analytically, with a focus on the linear temporal inviscid stability properties. The derivation of the governing equations and of a 'triply generalized' inflexion condition is outlined, and numerical results for freestream Mach number 3.8 are presented in extensive graphs and characterized in detail. A third instability mode related to the viscous mode observed by Duck and Hall (1990) using triple-deck theory is detected and shown to be more unstable and to have larger growth rates than the second mode in some cases. It is found that the 'sonic' neutral mode is affected by the lateral curvature and becomes a supersonic neutral mode.
Numerical investigation of shedding partial cavities over a sharp wedge
NASA Astrophysics Data System (ADS)
Budich, B.; Neuner, S.; Schmidt, S. J.; Adams, N. A.
2015-12-01
In this contribution, we examine transient dynamics and cavitation patterns of periodically shedding partial cavities by numerical simulations. The investigation reproduces reference experiments of the cavitating flow over a sharp wedge. Utilizing a homogeneous mixture model, full compressibility of the two-phase flow of water and water vapor is taken into account by the numerical method. We focus on inertia-dominated mechanisms, thus modeling the flow as inviscid. Based on the assumptions of thermodynamic equilibrium and barotropic flow, the thermodynamic properties are computed from closed-form analytical relations. Emphasis is put on a validation of the employed numerical approach. We demonstrate that computed shedding dynamics are in agreement with the references. Complex flow features observed in the experiments, including cavitating hairpin and horse-shoe vortices, are also predicted by the simulations. Furthermore, a condensation discontinuity occurring during the collapse phase at the trailing portion of the partial cavity is equally obtained.
Space charge limited current emission for a sharp tip
Zhu, Y. B. Ang, L. K.
2015-05-15
In this paper, we formulate a self-consistent model to study the space charge limited current emission from a sharp tip in a dc gap. The tip is assumed to have a radius in the order of 10s nanometer. The electrons are emitted from the tip due to field emission process. It is found that the localized current density J at the apex of the tip can be much higher than the classical Child Langmuir law (flat surface). A scaling of J ∝ V{sub g}{sup 3/2}/D{sup m}, where V{sub g} is the gap bias, D is the gap size, and m = 1.1–1.2 (depending on the emission area or radius) is proposed. The effects of non-uniform emission and the spatial dependence of work function are presented.
A sharp upper bound for departure from normality
Lee, S.L.
1993-08-01
The departure from normality of a matrix is a real scalar that is impractical to compute if a matrix is large and its eigenvalues are unknown. A simple formula is presented for computing an upper bound for departure from normality in the Frobenius norm. This new upper bound is cheaper to compute than the upper bound derived by Henrici. Moreover, the new bound is sharp for Hermitian matrices, skew-Hermitian matrices and, in general, any matrix with eigenvalues that are horizontally or vertically aligned in the complex plane. In terms of applications, the new bound can be used in computing bounds for the spectral norm of matrix functions or bounds for the sensitivity of eigenvalues to matrix perturbations.
Sharp monotonic resolution of discontinuities without clipping of narrow extrema
NASA Technical Reports Server (NTRS)
Leonard, B. P.; Niknafs, H. S.
1991-01-01
A strategy is presented for accurately simulating highly convective flows containing discontinuities such as density fronts or shock waves, without distorting smooth profiles or clipping narrow local extrema. The convection algorithm is based on non-artificially-diffusive third-order upwinding in smooth regions, with automatic adaptive stencil expansion to (in principle, arbitrarily) higher order upwinding locally, in regions of rapidly changing gradients. This is highly cost-effective because the wider stencil is used only where needed - in isolated narrow regions. A recently developed universal limiter assures sharp monotonic resolution of discontinuities without introducing artificial diffusion or numerical compression. An adaptive discriminator is constructed to distinguish between spurious overshoots and physical peaks; this automatically relaxes the limiter near local turning points, thereby avoiding loss of resolution in narrow extrema. Examples are given for one-dimensional pure convection of scalar profiles at constant velocity.
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
Ultrathin 90-degree sharp bends for spoof surface plasmon polaritons.
Yang, Yihao; Chen, Hongsheng; Xiao, Sanshui; Mortensen, N Asger; Zhang, Jingjing
2015-07-27
At low frequencies outside the plasmonic range, strongly confined surface waves can be achieved on periodically structured metal surfaces, thereby allowing for the design of compact electromagnetic guiding devices. Here, we propose an approach to realize highly efficient transmission of spoof surface plasmons around 90-degree sharp bends on ultrathin metallic films in the microwave regime. We demonstrate that by judiciously engineering the structure, the dispersion relation can be designed to reduce the scattering. Furthermore, the reflection can be suppressed by proper structural decoration at the bending corner. A one-dimensional scattering theory is employed to understand and verify the transmission properties of our waveguide bend structure. Our design scheme is not restricted to the specific structure we propose here but can be applied to other guiding components built up on two dimensional metal surfaces. PMID:26367570
Triomicrus Sharp of Eastern China (Coleoptera: Staphylinidae: Pselaphinae).
Shen, Jia-Wei; Yin, Zi-Wei; Li, Li-Zhen
2015-01-01
Twelve species of the genus Triomicrus Sharp are here recognized in eastern China, with eleven of them described as new: T. Inaequalis Shen & Yin, sp. n. and T. mirus Shen & Yin, sp. n. from Anhui, T. abhorridus Shen & Yin, sp. n., T. aculeus Shen & Yin, sp. n., T. damingensis Shen & Yin, sp. n., T. frondosus Shen & Yin, sp. n., T. gutianensis Shen & Yin, sp. n. and T. tibialis Shen & Yin, sp. n. from Zhejiang, T. anfractus Shen & Yin, sp. n. from Anhui and Zhejiang, T. Hamus Shen & Yin, sp. n. from Jiangxi, and T. contus Shen & Yin, sp. n. from Jiangxi and Zhejiang. New distributional data for T. rougemonti Löbl, Kurbatov &Nomura is given. A key for the identification of the Triomicrus species in eastern China is presented. PMID:26623829
Does the Sharpness of the Gutenberg Discontinuity Require Melt?
NASA Astrophysics Data System (ADS)
Bagley, B.; Revenaugh, J.
2008-12-01
A low-velocity zone (LVZ) underlying the fast seismic lid has been recognized since Gutenberg (1959). While, strictly speaking, the asthenosphere and the LVZ are defined by different properties, their upper boundaries are functionally equivalent in the oceanic setting. The Gutenberg (G) discontinuity marks the seismically sharp upper boundary of the lid-low-velocity transition beneath oceans and is characterized by an abrupt shear wave impedance decrease of roughly 9%. Explanations for the low seismic velocities include a contrast in volatile content, structurally bound water, and the effects of temperature and grain size. Partial melt, which once enjoyed the status of an obvious cause, has fallen from favor, primarily because of the difficulty of retaining a connecting fluid phase in the LVZ. But recent results demonstrate large velocity decrements for very small grain boundary melt fractions that could remain unconnected and trapped in the LVZ (Faul and Jackson, 2007). In order to provide better constraints on the structure of the low-velocity zone, we have examined the G discontinuity beneath a large portion of the central and western Pacific. Our focus is on the sharpness of the G reflector and the impedance decrease across it. Using multiple ScS reverberations we sampled the G discontinuity along a series of oceanic paths. We obtain impedance decreases between 4.7 and 14.2%, averaging 9.1%, assuming a first-order discontinuity. Our data do not, however, require the change in impedance to be sharp and can easily tolerate an extended transition of 10 to 15 km with little change in the estimated impedance contrast. However, extending the transition further requires a greater net impedance decrease across the interval. This provides an important constraint on the thickness of the transition interval. Preliminary results that consider acceptable net impedance contrasts (obtained from surface wave and turning wave constraints on LVZ severity) impose a conservative
Hypersonic Flows About a 25 degree Sharp Cone
NASA Technical Reports Server (NTRS)
Moss, James N.
2001-01-01
This paper presents the results of a numerical study that examines the surface heating discrepancies observed between computed and measured values along a sharp cone. With Mach numbers of an order of 10 and the freestream length Reynolds number of an order of 10 000, the present computations have been made with the direct simulation Monte Carlo (DSMC) method by using the G2 code of Bird. The flow conditions are those specified for two experiments conducted in the Veridian 48-inch Hypersonic Shock Tunnel. Axisymmetric simulations are made since the test model was assumed to be at zero incidence. Details of the current calculations are presented, along with comparisons between the experimental data, for surface heating and pressure distributions. Results of the comparisons show major differences in measured and calculated results for heating distributions, with differences in excess of 25 percent for the two cases examined.
Strong no-go theorem for Gaussian quantum bit commitment
Magnin, Loieck; Magniez, Frederic; Leverrier, Anthony
2010-01-15
Unconditionally secure bit commitment is forbidden by quantum mechanics. We extend this no-go theorem to continuous-variable protocols where both players are restricted to use Gaussian states and operations, which is a reasonable assumption in current-state optical implementations. Our Gaussian no-go theorem also provides a natural counter-example to a conjecture that quantum mechanics can be rederived from the assumption that key distribution is allowed while bit commitment is forbidden in Nature.
Note on soft graviton theorem by KLT relation
NASA Astrophysics Data System (ADS)
Du, Yi-Jian; Feng, Bo; Fu, Chih-Hao; Wang, Yihong
2014-11-01
Recently, new soft graviton theorem proposed by Cachazo and Strominger has inspired a lot of works. In this note, we use the KLT-formula to investigate the theorem. We have shown how the soft behavior of color ordered Yang-Mills amplitudes can be combined with KLT relation to give the soft behavior of gravity amplitudes. As a byproduct, we find two nontrivial identities of the KLT momentum kernel must hold.
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.
A study on arithmetical functions and the prime number theorem
NASA Astrophysics Data System (ADS)
Imm, Yeoh Saw
2014-06-01
In this paper, Leibniz triangle and suitable binomial coefficients were used to get the bounds of ψ (x) . Using the generalized convolution and the differentiation on generalized convolution of arithmetical functions, we get to prove Tatuzawa-Izeki identity. Selberg's asymptotic formula is included as a special case, which is the beginning of certain elementary proofs of the Prime Number Theorem. Integration is used on some related inequalities to provide a smoother elementary proof of the Prime Number Theorem.
Sharp Interface Tracking in Rotating Microflows of Solvent Extraction
Glimm, James; Almeida, Valmor de; Jiao, Xiangmin; Sims, Brett; Li, Xaiolin
2013-01-08
The objective of this project is to develop a specialized sharp interface tracking simulation capability for predicting interaction of micron-sized drops and bubbles in rotating flows relevant to optimized design of contactor devices used in solvent extraction processes of spent nuclear fuel reprocessing. The primary outcomes of this project include the capability to resolve drops and bubbles micro-hydrodynamics in solvent extraction contactors, determining from first principles continuum fluid mechanics how micro-drops and bubbles interact with each other and the surrounding shearing fluid for realistic flows. In the near term, this effort will play a central role in providing parameters and insight into the flow dynamics of models that average over coarser scales, say at the millimeter unit length. In the longer term, it will prove to be the platform to conduct full-device, detailed simulations as parallel computing power reaches the exaflop level. The team will develop an accurate simulation tool for flows containing interacting droplets and bubbles with sharp interfaces under conditions that mimic those found in realistic contactor operations. The main objective is to create an off-line simulation capability to model drop and bubble interactions in a domain representative of the averaged length scale. The technical approach is to combine robust interface tracking software, subgrid modeling, validation quality experiments, powerful computational hardware, and a team with simulation modeling, physical modeling and technology integration experience. Simulations will then fully resolve the microflow of drops and bubbles at the microsecond time scale. This approach is computationally intensive but very accurate in treating important coupled physical phenomena in the vicinity of interfaces. The method makes it possible to resolve spatial scales smaller than the typical distance between bubbles and to model some non-equilibrium thermodynamic features such as finite
On a variational theorem in acousto-elastodynamics
NASA Astrophysics Data System (ADS)
Thompson, B. S.
1982-08-01
A variational theorem is presented which may be used as a basis for developing the equations of motion and the boundary conditions appropriate for studying the vibrational behavior of flexible bodied systems and the surrounding acoustic medium. The theorem is a generalization of two theorems which are both based on the principle of virtual work; the first governs the elastodynamics of the mechanical system and the second governs the behavior of the fluid medium. Lagrange multipliers are used in the development of the two basic theorems and they are also employed to incorporate the constraints at the solid-fluid interface within the functional for the acousto-elastodynamic theorem. When independent arbitrary variations of the system parameters are permitted, this theorem yields as characteristic equations the equations of motion for each member of the mechanical system, the acoustic wave equation, the compatibility conditions at the mechanical joints, the compatibility conditions at the interface and also the mixed boundary conditions for the complete system. As an illustrative example, the derivation of the problem statement for a flexible slider crank mechanism operating in a perfect gas is presented in which it is assumed that the flexural motion of the links is governed by the Timoshenko beam theory.
NASA Astrophysics Data System (ADS)
Stojanović, Vladimir M.; Vanević, Mihajlo; Demler, Eugene; Tian, Lin
2014-04-01
We propose an analog superconducting quantum simulator for a one-dimensional model featuring momentum-dependent (nonlocal) electron-phonon couplings of Su-Schrieffer-Heeger and "breathing-mode" types. Because its corresponding coupling vertex function depends on both the electron and phonon quasimomenta, this model does not belong to the realm of validity of the Gerlach-Löwen theorem that rules out any nonanalyticities in single-particle properties. The superconducting circuit behind the proposed simulator entails an array of transmon qubits and microwave resonators. By applying microwave driving fields to the qubits, a small-polaron Bloch state with an arbitrary quasimomentum can be prepared in this system within times several orders of magnitude shorter than the typical qubit decoherence times. We demonstrate that—by varying the externally tunable parameters—one can readily reach the critical coupling strength required for observing the sharp transition from a nondegenerate (single-particle) ground state corresponding to zero quasimomentum (Kgs=0) to a twofold-degenerate small-polaron ground state at nonzero quasimomenta Kgs and -Kgs. Through exact numerical diagonalization of our effective Hamiltonian, we show how this nonanalyticity is reflected in the relevant single-particle properties (ground-state energy, quasiparticle residue, average number of phonons). We also show that the proposed setup provides an ideal testbed for studying the nonequilibrium dynamics of small-polaron formation in the presence of strongly momentum-dependent electron-phonon interactions.
[Health care systems and impossibility theorems].
Penchas, Shmuel
2004-02-01
results are Kurt Godel's seminal paper in 1931: "Ueber formal unentscheidbare Saetze der Principia Mathematica and verwandter System I" and Arrow's Nobel Prize winning "Impossibility Theorem" (Social Choice and Individual Values, 1951). Godel showed, unequivocally, that there is an enormous gap between what is being perceived as truth and what in fact can be proven as such. Arrow showed that the translation of individual preferences into a social order is impossible--except in a dictatorship. The unsolved controversies concerning the desirable or ideal structure of health care systems are impinged upon by these findings generally, and, in the case of the impossibility theorem, also directly. There is the impossibility of aggregating preferences and, at a deeper level, the impossibility of defining certain fundamental values, coupled with the problematic use of certain words, the absence of the possibility of creating, on a logically defined base, a complex system, complete and comprehensive in its own right. This is added to the fact that according to the elaboration by Stephen Wolfram in "A New Kind of Science", it is not easy to reduce complicated systems to simple components and to predict the continuation of their development even from simple basic laws without complicated calculations. All of these factors impede the construction of satisfying health care systems and leave obvious problems which overshadow the structure and the operation of health care systems. PMID:15143703
Subexponential estimates in Shirshov's theorem on height
Belov, Aleksei Ya; Kharitonov, Mikhail I
2012-04-30
Suppose that F{sub 2,m} is a free 2-generated associative ring with the identity x{sup m}=0. In 1993 Zelmanov put the following question: is it true that the nilpotency degree of F{sub 2,m} has exponential growth? We give the definitive answer to Zelmanov's question by showing that the nilpotency class of an l-generated associative algebra with the identity x{sup d}=0 is smaller than {Psi}(d,d,l), where {Psi}(n,d,l)=2{sup 18}l(nd){sup 3log}{sub 3}{sup (nd)+13}d{sup 2}. This result is a consequence of the following fact based on combinatorics of words. Let l, n and d{>=}n be positive integers. Then all words over an alphabet of cardinality l whose length is not less than {Psi}(n,d,l) are either n-divisible or contain x{sup d}; a word W is n-divisible if it can be represented in the form W=W{sub 0}W{sub 1} Horizontal-Ellipsis W{sub n} so that W{sub 1},...,W{sub n} are placed in lexicographically decreasing order. Our proof uses Dilworth's theorem (according to V.N. Latyshev's idea). We show that the set of not n-divisible words over an alphabet of cardinality l has height h<{Phi}(n,l) over the set of words of degree {<=}n-1, where {Phi}(n,l)=2{sup 87}l{center_dot}n{sup 12log}{sub 3}{sup n+48}. Bibliography: 40 titles.
Testing the no-hair theorem with black hole ringdowns using TIGER
NASA Astrophysics Data System (ADS)
Meidam, J.; Agathos, M.; Van Den Broeck, C.; Veitch, J.; Sathyaprakash, B. S.
2014-09-01
The Einstein Telescope, a proposed third-generation gravitational-wave observatory, would enable tests of the no-hair theorem by looking at the characteristic frequencies and damping times of black hole ringdown signals. In previous work it was shown that with a single 500-1000 M⊙ black hole at a distance ≲6 Gpc (or redshift z ≲1), deviations of a few percent in the frequencies and damping times of dominant and subdominant modes would be within the range of detectability. Given that such sources may be relatively rare, it is of interest to see how well the no-hair theorem can be tested with events at much larger distances and with smaller signal-to-noise ratios, thus accessing a far bigger volume of space and a larger number of sources. We employ a model-selection scheme called TIGER (Test Infrastructure for GEneral Relativity), which was originally developed to test general relativity with weak binary coalescence signals that will be seen in second-generation detectors, such as Advanced LIGO and Advanced Virgo. TIGER is well suited for the regime of low signal-to-noise ratios, and information from a population of sources can be combined so as to arrive at a stronger test. By performing a range of simulations using the expected noise power spectral density of the Einstein Telescope, we show that with TIGER, similar deviations from the no-hair theorem (such as those considered in previous works) will be detectable with great confidence using O(10) sources distributed uniformly in a comoving volume out to 50 Gpc (z≲5).
Residue theorem and summing over Kaluza-Klein excitations
Feng Taifu; Chen Jianbin; Gao Tiejun; Sun Kesheng
2011-11-01
Applying the equations of motion together with corresponding boundary conditions of bulk profiles at infrared and ultraviolet branes, we verify some lemmas on the eigenvalues of Kaluza-Klein modes in extension of the standard model with a warped extra dimension and the custodial symmetry SU(3){sub c}xSU(2){sub L}xSU(2){sub R}xU(1){sub X}xP{sub LR}. Using the lemmas and performing properly analytic extensions of bulk profiles, we present the sufficient condition for a convergent series of Kaluza-Klein excitations and sum over the series through the residue theorem. The method can also be applied to sum over the infinite series of Kaluza-Klein excitations in a universal extra dimension. Furthermore, we analyze the possible connection between the propagators in five-dimensional full theory and the product of bulk profiles with corresponding propagators of exciting Kaluza-Klein modes in four-dimensional effective theory, and recover some relations presented in the literature for warped and universal extra dimensions, respectively. As an example, we present the correction from new physics to the branching ratio of B{yields}X{sub s{gamma}} to the order O({mu}{sub EW}{sup 2}/{Lambda}{sub KK}{sup 2}) in extension of the standard model with a warped extra dimension and the custodial symmetry, where {Lambda}{sub KK} denotes the energy scale of low-lying Kaluza-Klein excitations and {mu}{sub EW} denotes the electroweak energy scale.
Sharp Wave Ripples during Visual Exploration in the Primate Hippocampus
Leonard, Timothy K.; Mikkila, Jonathan M.; Eskandar, Emad N.; Gerrard, Jason L.; Kaping, Daniel; Patel, Shaun R.; Womelsdorf, Thilo
2015-01-01
Hippocampal sharp-wave ripples (SWRs) are highly synchronous oscillatory field potentials that are thought to facilitate memory consolidation. SWRs typically occur during quiescent states, when neural activity reflecting recent experience is replayed. In rodents, SWRs also occur during brief locomotor pauses in maze exploration, where they appear to support learning during experience. In this study, we detected SWRs that occurred during quiescent states, but also during goal-directed visual exploration in nonhuman primates (Macaca mulatta). The exploratory SWRs showed peak frequency bands similar to those of quiescent SWRs, and both types were inhibited at the onset of their respective behavioral epochs. In apparent contrast to rodent SWRs, these exploratory SWRs occurred during active periods of exploration, e.g., while animals searched for a target object in a scene. SWRs were associated with smaller saccades and longer fixations. Also, when they coincided with target-object fixations during search, detection was more likely than when these events were decoupled. Although we observed high gamma-band field potentials of similar frequency to SWRs, only the SWRs accompanied greater spiking synchrony in neural populations. These results reveal that SWRs are not limited to off-line states as conventionally defined; rather, they occur during active and informative performance windows. The exploratory SWR in primates is an infrequent occurrence associated with active, attentive performance, which may indicate a new, extended role of SWRs during exploration in primates. SIGNIFICANCE STATEMENT Sharp-wave ripples (SWRs) are high-frequency oscillations that generate highly synchronized activity in neural populations. Their prevalence in sleep and quiet wakefulness, and the memory deficits that result from their interruption, suggest that SWRs contribute to memory consolidation during rest. Here, we report that SWRs from the monkey hippocampus occur not only during
Overview and Major Findings of the Study of Houston Atmospheric Radical Precursors (SHARP) Campaign
NASA Astrophysics Data System (ADS)
Lefer, B. L.; Brune, W. H.; Collins, D. R.; Dibb, J. E.; Griffin, R. J.; Herndon, S. C.; Huey, L. G.; Jobson, B. T.; Luke, W. T.; Mellqvist, J.; Morris, G. A.; Mount, G. H.; North, S. W.; Olaguer, E. P.; Rappenglueck, B.; Ren, X.; Stutz, J.; Yu, X.; Zhang, R.
2010-12-01
Despite recent improvements in Houston’s air quality, particularly in the reduction of the number of days with ozone mixing ratios with a 1-hr average of 125 ppbv or greater, the Houston-Galveston-Brazoria (HGB) metropolitan area still has approximately 30 days where 8-hr ozone levels exceed the 75 ppbv standard. More than a third of these high ozone episodes typically occur during the Springtime. Based on the 2006 TexAQS-II and TRAMP findings highlighting the importance of HONO, HCHO, and potentially ClNO2 as radical sources in the Houston atmosphere, the Study of Houston Atmospheric Radical Precursors (SHARP) 2009 project was designed to address the following goals: (1) determine the contribution of direct emissions of OH radical precursors HCHO and HONO from flares and other point and mobile sources; (2) detect the important urban formation pathways of HONO (day/night, surface, heterogeneous, homogeneous); (3) quantify the impact of soot (fresh and coated) on chemistry and radiation, (4) measure the ambient levels of ClNO2 in Houston and determine its’ potential as a radical source; (5) perform an intercomparison of ambient HONO measurement techniques in a urban environment; (6) identify the relative importance of springtime ozone formation mechanisms in Houston. The overall purpose of pursuing these objectives was to reduce the uncertainties surrounding these processes with the aim of improve our ability to model radicals and ozone formation in Houston and other coastal cities with petrochemical operations. The majority of the time the meteorological and chemical conditions during the 2009 SHARP campaign resulted in clean southerly flow from the Gulf of Mexico. This southerly flow was interrupted at least 4 times by cold front passages during the campaign. Each frontal passage resulted in an 8-hr ozone exceedance one to three days later. Significant findings from the SHARP project from 15 April to 30 May 2009 include: (a) measurements of HCHO emitted
Ji, Laixi; Wang, Haijun; Cao, Yuxia; Yan, Ping; Jin, Xiaofei; Nie, Peirui; Wang, Chaojian; Li, Rangqian; Zhang, Chunlong; Yang, Mingxiao; Yang, Jie
2015-01-01
The Feng Gou Zhen (sharp-hook acupuncture) as a traditional form of ancient acupuncture is said to be particularly effective for managing periarthritis of shoulder. We conducted this randomized controlled trial to evaluate the effectiveness of Feng Gou Zhen as an add-on compared to conventional analgesics for patients with PAS. 132 patients were randomly assigned in a 1 : 1 ratio to either a acupuncture group receiving sharp-hook acupuncture plus acupoint injection with conventional analgesics or a control group. Patients from both groups were evaluated at week 0 (baseline), week 1, and week 4. The primary outcome measure was the change from baseline shoulder pain, measured by Visual Analogue Scale at 7 days after treatment. Secondary outcome measures include the (i) function of shoulder joint and (ii) McGill pain questionnaire. The results showed that patients in acupuncture group had better pain relief and function recovery compared with control group (P < 0.05) at 1 week after treatment. Moreover, there were statistical differences between two groups in VAS and shoulder joint function and McGill pain questionnaire at 4 weeks after treatment (P < 0.05). Therefore, the sharp-hook acupuncture helps to relieve the pain and restore the shoulder function for patients with periarthritis of shoulder. PMID:26640496
Moldovan, N.; Divan, R.; Zeng, H.; Carlisle, J. A.; Advanced Diamond Tech.
2009-12-07
Ultrasharp diamond tips make excellent atomic force microscopy probes, field emitters, and abrasive articles due to diamond's outstanding physical properties, i.e., hardness, low friction coefficient, low work function, and toughness. Sharp diamond tips are currently fabricated as individual tips or arrays by three principal methods: (1) focused ion beam milling and gluing onto a cantilever of individual diamond tips, (2) coating silicon tips with diamond films, or (3) molding diamond into grooves etched in a sacrificial substrate, bonding the sacrificial substrate to another substrate or electrodepositing of a handling chip, followed by dissolution of the sacrificial substrate. The first method is tedious and serial in nature but does produce very sharp tips, the second method results in tips whose radius is limited by the thickness of the diamond coating, while the third method involves a costly bonding and release process and difficulties in thoroughly filling the high aspect ratio apex of molding grooves with diamond at the nanoscale. To overcome the difficulties with these existing methods, this article reports on the feasibility of the fabrication of sharp diamond tips by direct etching of ultrananocrystalline diamond (UNCD{reg_sign}) as a starting and structural material. The UNCD is reactive ion etched using a cap-precursor-mask scheme. An optimized etching recipe demonstrates the formation of ultrasharp diamond tips ({approx} 10 nm tip radius) with etch rates of 650 nm/min.
An investigation into a micro-sized droplet impinging on a surface with sharp wettability contrast
NASA Astrophysics Data System (ADS)
Lim, C. Y.; Lam, Y. C.
2014-10-01
An experimental investigation was conducted into a micro-sized droplet jetted onto a surface with sharp wettability contrast. The dynamics of micro-sized droplet impingement on a sharp wettability contrast surface, which is critical in inkjet printing technology, has not been investigated in the literature. Hydrophilic lines with line widths ranging from 27 to 53 µm, and contact angle ranging from 17° to 77°, were patterned on a hydrophobic surface with a contact angle of 107°. Water droplets with a diameter of 81 µm were impinged at various offset distances from the centre of the hydrophilic line. The evolution of the droplet upon impingement can be divided into three distinct phases, namely the kinematic phase, the translating phase where the droplet moves towards the centre of the hydrophilic line, and the conforming phase where the droplet spreads along the line. The key parameters affecting the conformability of the droplet to the hydrophilic line pattern are the ratio of the line width to the initial droplet diameter and the contact angle of the hydrophilic line. The droplet will only conform completely to the hydrophilic pattern if the line width is not overly small relative to the droplet and the contact angle of the hydrophilic line is sufficiently low. The impact offset distance does not affect the final shape and final location of the droplet, as long as part of the droplet touches the hydrophilic line upon impingement. This process has a significant impact on inkjet printing technology as high accuracy of inkjet droplet deposition and shape control can be achieved through wettability patterning.
Sharps Injuries and Other Blood and Body Fluid Exposures Among Home Health Care Nurses and Aides
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
Energy boost in laser wakefield accelerators using sharp density transitions
NASA Astrophysics Data System (ADS)
Döpp, A.; Guillaume, E.; Thaury, C.; Lifschitz, A.; Ta Phuoc, K.; Malka, V.
2016-05-01
The energy gain in laser wakefield accelerators is limited by dephasing between the driving laser pulse and the highly relativistic electrons in its wake. Since this phase depends on both the driver and the cavity length, the effects of dephasing can be mitigated with appropriate tailoring of the plasma density along propagation. Preceding studies have discussed the prospects of continuous phase-locking in the linear wakefield regime. However, most experiments are performed in the highly non-linear regime and rely on self-guiding of the laser pulse. Due to the complexity of the driver evolution in this regime, it is much more difficult to achieve phase locking. As an alternative, we study the scenario of rapid rephasing in sharp density transitions, as was recently demonstrated experimentally. Starting from a phenomenological model, we deduce expressions for the electron energy gain in such density profiles. The results are in accordance with particle-in-cell simulations, and we present gain estimations for single and multiple stages of rephasing.
The inviscid stability of supersonic flow past a sharp cone
NASA Technical Reports Server (NTRS)
Duck, Peter W.; Shaw, Stephen J.
1990-01-01
The laminar boundary layer which forms on a sharp cone in a supersonic freestream, where lateral curvature plays a key role in the physics of the problem is considered. This flow is then analyzed from the point of view of linear, temporal, inviscid stability. The basic, non-axisymmetric disturbance equations are derived for general flows of this class, and a so called triply generalized inflexion condition is found for the existence of subsonic neutral modes of instability. This condition is analogous to the well-known generalized inflexion condition found in planar flows, although in the present case the condition depends on both axial and aximuthal wavenumbers. Extensive numerical results are presented for the stability problem at a freestream Mach number of 3.8, for a range of streamwise locations. These results reveal that a new mode of instability may occur, peculiar to flows of this type involving curvature. Additionally, asymptotic analyses valid close to the tip of the cone, far downstream of the cone are presented, and these give a partial (asymptotic) description of this additional mode of instability.
Sharp-Interface Nematic-Isotropic Phase Transformations With Flow
NASA Astrophysics Data System (ADS)
Fried, Eliot
2008-11-01
We develop a sharp-interface theory for phase transformations between the isotropic and uniaxial nematic phases of a flowing liquid crystal. Aside from conventional evolution equations for the bulk phases and corresponding interface conditions, the theory includes a supplemental interface condition expressing the balance of configurational momentum. As an idealized illustrative application of the theory, we consider the problem of an evolving spherical droplet of the isotropic phase surrounded by the nematic phase in a radially-oriented state. For this problem, the bulk and interfacial equations collapse to a single nonlinear second-order ordinary differential equation for the radius of the droplet—an equation which, in essence, expresses the balance of configurational momentum on the interface. This droplet evolution equation, which closely resembles a previously derived and extensively studied equation for the expansion of contraction of a spherical gas bubble in an incompressible viscous liquid, includes terms accounting for the curvature elasticity and viscosity of the nematic phase, interfacial energy, interfacial viscosity, and the ordering kinetics of the phase transformation. We determine the equilibria of this equation and study their stability. Additionally, we find that motion of the interface generates a backflow, without director reorientation, in the nematic phase. Our analysis indicates that a backflow measurement has the potential to provide an independent means to determine the density difference between the isotropic and uniaxial nematic phases.
Effectiveness of steam sterilization on the contents of sharps containers.
Palenik, C J; Riggen, S D; Celis, L J; Sheldrake, M A; Miller, C H
1992-01-01
The purpose of this study was to evaluate the killing effect that treatment in gravity or high-vacuum steam autoclaves had on endospores present on strips or applied to dental needles within 10 types of small sharps containers. Spore strips containing Bacillus stearothermophilus endospores were used, while needles were soiled with an equal number of spores or with spores mixed with blood. Needles were tested capped and uncapped. Strips and needles were autoclaved in empty and 3/4 filled containers placed in several orientations (vents open or closed, upward or on-side). If sterilization was not accomplished within the initial period, additional exposure time was added up to a one hour maximum. Major findings for gravity autoclaves were: 1) strips and needles present in empty containers could, in most cases, be sterilized within 15 minutes when the vents were left open and the containers were placed on-side; 2) spore- and spore plus blood-soiled needles were more difficult to sterilize then were commercial spore strips; 3) capping of needles and the presence of blood did not decrease sterilization efficiency; 4) sterilization in the presence of fill material required additional exposure times and 5) larger containers (greater than 500 ml volume) were more difficult to sterilize than were the smaller (250 ml) ones. All type of open-vented, filled containers could be sterilized within 10 minutes in a high-vacuum autoclave. PMID:1499239
Evaluation of a standardized hourly rounding process (SHaRP).
Krepper, Rebecca; Vallejo, Beryl; Smith, Claudia; Lindy, Cheryl; Fullmer, Cheryl; Messimer, Sharon; Xing, Yun; Myers, Karen
2014-01-01
Current research suggests that hourly rounds on hospitalized patients may be associated with improvements in care delivery and in the patients' perception of care, as well as a reduction in patient safety events. Implementing an hourly rounding protocol involves a major change in nursing staff workflow and a substantial training and education program to ensure the success of the program. This quasi-experimental study aimed to determine if a standardized hourly rounding process (SHaRP), implemented through a formal education program, would result in improved efficiency, quality, safety, and patient satisfaction metrics when compared to a less standardized process introduced through the traditional train-the-trainer method. Data were collected over a 6-month period and results were trended for an additional 6 months later to determine if significant gains were sustained over time. Significant reductions in call light use during the study period (p = .001) and the number of steps taken by the day-shift staff (p = .02) were seen on the intervention unit. Differences in the number of patient falls, 30-day readmission rates, and patients' perception of care were not statistically significant. PMID:23237186
Sharp knee phenomenon of primary cosmic ray energy spectrum
NASA Astrophysics Data System (ADS)
Ter-Antonyan, Samvel
2014-06-01
Primary energy spectral models are tested in the energy range of 1-200 PeV using standardized extensive air shower responses from BASJE-MAS, Tibet, GAMMA and KASCADE scintillation shower arrays. Results point toward the two-component origin of observed cosmic ray energy spectra in the knee region consisting of a pulsar component superimposed upon rigidity-dependent power law diffuse Galactic flux. The two-component energy spectral model accounts for both the sharp knee shower spectral phenomenon and observed irregularity of all-particle energy spectrum in the region of 50-100 PeV. Alternatively, tested multipopulation primary energy spectra predicted by nonlinear diffusive shock acceleration models describe observed shower spectra in the knee region provided that the cutoff magnetic rigidities of accelerating particles are 6±0.3 and 45±2 PV for the first two populations, respectively. Both tested spectral models confirm the predominant H-He primary nuclei origin of observed shower spectral knee. The parameters of tested energy spectra are evaluated using solutions of the inverse problem on the basis of the corresponding parameterizations of energy spectra for primary H, He, O-like and Fe-like nuclei, standardized shower size spectral responses in the 550-1085 g/cm2 atmospheric slant depth range and near vertical muon truncated size spectra detected by the GAMMA array.
A Theorem for Two Nucleon Transfer
NASA Astrophysics Data System (ADS)
Zamick, Larry; Mekjian, Aram
2004-05-01
We use the short notation for a unitary 9j symbol U9j(Ja,Jb)=<(jj)Ja(jj)Ja|(jj)Jb(jj)Jb>I=0 The wave fcn of a state of 44Ti with ang momentum I can be written as sum D(Jp,Jn) [(jj)Jp (jj)Jn]I. For the I=0 ground stae Jp=Jn. We found a new relationship SumJp U9j(Jp,Jx) D(Jp,Jp)= 1/2 D(Jx,Jx) for T=0 and =-D(Jx,Jx) for T=2. We could explain this by regarding U9j for even Jp,Jx as a square matrix hamiltonian, which, when diagonalized has eigenvalues of 1/2(triply degenerate) and -1(singly degenerate) corresponding to T=0 and T=2 respectively.*This theorem is useful,in the context of 2 nucleon transfer, for counting the number of pairs of particles in 44Ti with even Jx.The expressions simplifies to 3|D(Jx,Jx|^2,thus eliminating a complex 9jsymbol A deeper understanding of this result arises if we consider the strange interplay of angular momentum and isospin. Consider the interaction 1/4-t(1).t(2),which is unity for T=0 states and zero for T=1. For n nucleons with isospin T the eigenvalues are n^2/8+n/4-T(T+1)/2 But if we evaluate this with the usual Racah algebra then we note that in the single j shell the interaction can also be written as <(jj)Ia V (jj)Ia>= (1-(-1)^Ia)/2 i.e. the interaction acts only in odd J states since they have isospin T=0.In 44Ti the matrix element of the hamiltonian is [2+2U9j(Jp,Jx)].Connecting this with the isospin expression gives us the eigenvalues above for U9j. * L.Zamick, E. Moya de Guerra,P.Sarriguren,A.Raduta and A. Escuderos, preprint.
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.
Dielectric theorem within the Hartree-Fock-Bogoliubov framework
Capelli, Luigi; Colo, Gianluca; Li, Jun
2009-05-15
Excitation spectra usually reveal important features of the many-body systems. The vibrational excitations can be studied through the well-known linear response theory. This theory is realized, in the nuclear case, by means of the random-phase approximation (RPA); the generalization in the case in which one deals with open shells, and the pairing force is active, is the quasiparticle RPA (QRPA). It is useful to have at one's disposal theorems that provide information on, e.g., the sum rules and mean excitation energies associated with given external operators acting on the system. This article focuses on such theorems in the case of self-consistent QRPA based on Hartree-Fock-Bogoliubov (HFB). In particular, the so-called dielectric theorem that provides the value of the inverse-energy-weighted sum rule based on the simple knowledge of the ground state is demonstrated. This theorem is applied to the case of constrained calculations of the average excitation energy of the monopole resonance combined with the Thouless theorem. The pairing correlations are shown to have the effect of increasing the polarizability m{sub -1}. The detailed analysis of the profile of the strength functions by mean of QRPA reveals that the decrease of the average monopole excitation energies in some isotopes is associated with neutron states that emerge at an energy that is lower than the main giant resonance peak.
Extension of Euler's theorem to n-dimensional spaces
NASA Technical Reports Server (NTRS)
Bar-Itzhack, Itzhack Y.
1989-01-01
Euler's theorem states that any sequence of finite rotations of a rigid body can be described as a single rotation of the body about a fixed axis in three-dimensional Euclidean space. The usual statement of the theorem in the literature cannot be extended to Euclidean spaces of other dimensions. Equivalent formulations of the theorem are given and proved in a way which does not limit them to the three-dimensional Euclidean space. Thus, the equivalent theorems hold in other dimensions. The proof of one formulation presents an algorithm which shows how to compute an angular-difference matrix that represents a single rotation which is equivalent to the sequence of rotations that have generated the final n-D orientation. This algorithm results also in a constant angular velocity which, when applied to the initial orientation, eventually yields the final orientation regardless of what angular velocity generated the latter. The extension of the theorem is demonstrated in a four-dimensional numerical example.
Extension to Eulers's theorem to n-dimensional spaces
NASA Technical Reports Server (NTRS)
Bar-Itzhack, Itzhack Y.
1989-01-01
Euler's theorem states that any sequence of finite rotations of a rigid body can be described as a single rotation of the body about a fixed axis in three-dimensional Euclidean space. The usual statement of the theorem in the literature cannot be extended to Euclidean spaces of other dimensions. Equivalent formulations of the theorem are given in this paper and proven in a way which does not limit them to the three-dimensional Euclidean space. Thus, the equivalent theorems hold in other dimensions. The proof of one formulation presents an algorithm which shows how to compute an angular-difference matrix that represents a single rotation which is equivalent to the sequence of rotations that have generated the final n-D orientation. This algorithm results also in a constant angular-velocity which, when applied to the initial orientation, yields eventually the final orientation regardless of what angular velocity generated the latter. Finally, the extension of the theorem is demonstrated in a four-dimensional numerical example.
Mechanisms of sharp wave initiation and ripple generation.
Schlingloff, Dániel; Káli, Szabolcs; Freund, Tamás F; Hájos, Norbert; Gulyás, Attila I
2014-08-20
Replay of neuronal activity during hippocampal sharp wave-ripples (SWRs) is essential in memory formation. To understand the mechanisms underlying the initiation of irregularly occurring SWRs and the generation of periodic ripples, we selectively manipulated different components of the CA3 network in mouse hippocampal slices. We recorded EPSCs and IPSCs to examine the buildup of neuronal activity preceding SWRs and analyzed the distribution of time intervals between subsequent SWR events. Our results suggest that SWRs are initiated through a combined refractory and stochastic mechanism. SWRs initiate when firing in a set of spontaneously active pyramidal cells triggers a gradual, exponential buildup of activity in the recurrent CA3 network. We showed that this tonic excitatory envelope drives reciprocally connected parvalbumin-positive basket cells, which start ripple-frequency spiking that is phase-locked through reciprocal inhibition. The synchronized GABA(A) receptor-mediated currents give rise to a major component of the ripple-frequency oscillation in the local field potential and organize the phase-locked spiking of pyramidal cells. Optogenetic stimulation of parvalbumin-positive cells evoked full SWRs and EPSC sequences in pyramidal cells. Even with excitation blocked, tonic driving of parvalbumin-positive cells evoked ripple oscillations. Conversely, optogenetic silencing of parvalbumin-positive cells interrupted the SWRs or inhibited their occurrence. Local drug applications and modeling experiments confirmed that the activity of parvalbumin-positive perisomatic inhibitory neurons is both necessary and sufficient for ripple-frequency current and rhythm generation. These interneurons are thus essential in organizing pyramidal cell activity not only during gamma oscillation, but, in a different configuration, during SWRs. PMID:25143618
Keeping the Edges Sharp II: Honing Simulations of Narrow Rings
NASA Astrophysics Data System (ADS)
Rimlinger, Thomas; Hamilton, Douglas; Hahn, Joseph M.
2016-05-01
It has long been believed that shepherd satellites are necessary to keep narrow rings confined. While a pair of nearby satellites brackets Saturn’s F ring and Uranus’ Epsilon ring, dozens of other ringlets observed around the outer three planets seem to be unattended. Hamilton et al. (this meeting) have argued analytically that eccentric or inclined rings can maintain their sharp edges for millions or even billions of years despite continually dissipating energy. Here, we present numerical integrations showing isolated eccentric ringlets that do not spread; our model includes only the gravity from an oblate planet, ring self-gravity, and viscosity. We use the symplectic integrator epi_int written by Hahn & Spitale (2013).For narrow rings, the weak perturbation forces that we study act on secular rather than orbital timescales. Therefore, we find that we can use an unusually long timestep, in which these weak forces are applied once every ~30 orbits, with good energy and angular momentum conservation. Long timesteps allow us to run simulations that might otherwise take hours or even days in a matter of minutes. We present comparisons between simulations with identical initial conditions but varying timesteps to show that our approach is appropriate for this class of problems. This technique of speeding up numerical integrations works for any symplectic integrator, requiring only that the forces be weak and that the timescale of interest be long. Problems well suited to this approach (those with only secular and drag forces) include tidally-damped exoplanets and dust grains subject to radiation pressure and Poynting-Robertson drag.
Intercomparison of Nitrous Acid (HONO) Measurement Techniques during SHARP
NASA Astrophysics Data System (ADS)
Pinto, J. P.; Meng, Q.; Dibb, J. E.; Lefer, B. L.; Rappenglueck, B.; Ren, X.; Stutz, J.; Zhang, R.
2010-12-01
HONO is regarded as a potentially important radical precursor in a number of diverse environments ranging from polar to semi-tropical. As part of the SHARP (Study of Houston Atmospheric Radical Precursors), time series of HONO were obtained by five different measurement techniques. Techniques used were long path differential optical absorption spectroscopy (DOAS), long-path absorption photometry (LoPAP), mist chamber (MC), quantum cascade laser and ionization detection-chemical ionization mass spectrometry. Various combinations of techniques were in operation during the whole period from 15 April through 31 May 2009 with a common measurement period extending from 16 to 28 May. All instruments recorded a similar diurnal pattern of HONO concentrations with higher mean values from the in-situ techniques than either the low- or mid-path DOAS. The largest differences among techniques were found during the afternoon with measurements from the in-situ techniques higher than either the low- or mid-path DOAS. Principal components analysis using measurements of trace species was used to identify possible sources of interference in the chemical measurements. Two major components were identified: one associated with primary, mainly traffic related pollutants and the other with photochemical species. The afternoon differences between DOAS and MC and the U Miami LoPAP were found to be most strongly associated with the photochemical component. The results for comparison between DOAS and MC are in accord with those found previously during August-September 2006. All instruments showed some association between measurement differences and the primary component. Further details and associations with air coming from different areas of the Houston airshed will also be presented.
Serotonin dependent masking of hippocampal sharp wave ripples.
ul Haq, Rizwan; Anderson, Marlene L; Hollnagel, Jan-Oliver; Worschech, Franziska; Sherkheli, Muhammad Azahr; Behrens, Christoph J; Heinemann, Uwe
2016-02-01
Sharp wave ripples (SPW-Rs) are thought to play an important role in memory consolidation. By rapid replay of previously stored information during slow wave sleep and consummatory behavior, they result from the formation of neural ensembles during a learning period. Serotonin (5-HT), suggested to be able to modify SPW-Rs, can affect many neurons simultaneously by volume transmission and alter network functions in an orchestrated fashion. In acute slices from dorsal hippocampus, SPW-Rs can be induced by repeated high frequency stimulation that induces long-lasting LTP. We used this model to study SPW-R appearance and modulation by 5-HT. Although stimulation in presence of 5-HT permitted LTP induction, SPW-Rs were "masked"--but appeared after 5-HT wash-out. This SPW-R masking was dose dependent with 100 nM 5-HT being sufficient--if the 5-HT re-uptake inhibitor citalopram was present. Fenfluramine, a serotonin releaser, could also mask SPW-Rs. Masking was due to 5-HT1A and 5-HT2A/C receptor activation. Neither membrane potential nor membrane conductance changes in pyramidal cells caused SPW-R blockade since both remained unaffected by combining 5-HT and citalopram. Moreover, 10 and 30 μM 5-HT mediated SPW-R masking preceded neuronal hyperpolarization and involved reduced presynaptic transmitter release. 5-HT, as well as a 5-HT1A agonist, augmented paired pulse facilitation and affected the coefficient of variance. Spontaneous SPW-Rs in mice hippocampal slices were also masked by 5-HT and fenfluramine. While neuronal ensembles can acquire long lasting LTP during higher 5-HT levels, lower 5-HT levels enable neural ensembles to replay previously stored information and thereby permit memory consolidation memory. PMID:26409781
A Sharp Edge of the Cratonic Lithosphere of North America
NASA Astrophysics Data System (ADS)
Harper, T. B.; Skryzalin, P. A.; Menke, W. H.; Levin, V. L.; Darbyshire, F. A.
2015-12-01
Using teleseismic travel time delays, we develop a tomographic model of the lithosphere beneath northeastern North America, from the shore of James Bay in Quebec to the Atlantic coast of New England and to a depth of 300 km. Three major terranes lie within this cratonic margin: the 2.7 Ga Superior province, the 1 Ga Grenville orogenic belt and the 0.3-0.4 Ga Appalachian terranes, which are bounded by the Grenville Front (GF) and Appalachian Front (AF), respectively. Additionally, the 0.8 Ga Avalon terrain was accreted to coastal New England by strike-skip faulting during the Appalachian orogeny. Our tomographic model uses earthquake seismograms recorded by permanent US and Canadian stations, the Transportable Array and the temporary QMIII deployment. All data were corrected for instrument response and record sections were examined visually to identify gross errors in response and timing. Differential arrival times of P and PKP waves were determined by cross-correlation and have a maximum amplitude of about ±1 second. In our model, lithospheric boundaries do not correlate well with geological boundaries, nor do they strike parallel to them. The seismically-fast (by 5% relative to AK135) cratonic lithosphere of North America is much thicker than that of the younger terranes, extending to 200 km or more depth but with a sharp east-dipping eastern edge located (at Moho depths) 100-250 km northwest of the GF. The lithosphere beneath the Grenville and Appalachian terranes, which were affected by subduction during the Grenville and Appalachian orogenies, is slower (by 4%). A sliver of seismically-fast lithosphere, extending to ~150 km depth, occurs along the Atlantic coast and is interpreted as the Avalonian lithosphere.
Experimentally testing Bell's theorem based on Hardy's nonlocal ladder proofs
NASA Astrophysics Data System (ADS)
Guo, WeiJie; Fan, DaiHe; Wei, LianFu
2015-02-01
Bell's theorem argues the existence of quantum nonlocality which goes basically against the hidden variable theory (HVT). Many experiments have been done via testing the violations of Bell's inequalities to statistically verify the Bell's theorem. Alternatively, by testing the Hardy's ladder proofs we experimentally demonstrate the deterministic violation of HVT and thus confirm the quantum nonlocality. Our tests are implemented with non-maximal entangled photon pairs generated by spontaneous parametric down conversions (SPDCs). We show that the degree freedom of photon entanglement could be significantly enhanced by using interference filters. As a consequence, the Hardy's ladder proofs could be tested and Bell's theorem is verified robustly. The probability of violating the locality reach to 41.9%, which is close to the expectably ideal value 46.4% for the photon pairs with degree of entanglement ɛ = 0.93. The higher violating probability is possible by further optimizing the experimental parameters.
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.
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.
Noether's second theorem and Ward identities for gauge symmetries
NASA Astrophysics Data System (ADS)
Avery, Steven G.; Schwab, Burkhard U. W.
2016-02-01
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 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 second theorem and known results in the recent literature. Our approach suggests a novel point of view with important physical consequences.
Quantum de Finetti theorem in phase-space representation
Leverrier, Anthony; Cerf, Nicolas J.
2009-07-15
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form {sigma}{sup xn}. Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states)
Formulation of Liouville's theorem for grand ensemble molecular simulations
NASA Astrophysics Data System (ADS)
Delle Site, Luigi
2016-02-01
Liouville's theorem in a grand ensemble, that is for situations where a system is in equilibrium with a reservoir of energy and particles, is a subject that, to our knowledge, has not been explicitly treated in literature related to molecular simulation. Instead, Liouville's theorem, a central concept for the correct employment of molecular simulation techniques, is implicitly considered only within the framework of systems where the total number of particles is fixed. However, the pressing demand of applied science in treating open systems leads to the question of the existence and possible exact formulation of Liouville's theorem when the number of particles changes during the dynamical evolution of the system. The intention of this paper is to stimulate a debate about this crucial issue for molecular simulation.
Noncommutative topology and the world’s simplest index theorem
van Erp, Erik
2010-01-01
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool for proving results in classical analysis and geometry. PMID:20418506
Towards a novel no-hair theorem for black holes
Hertog, Thomas
2006-10-15
We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four-dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.
Canonical Approaches to Applications of the Virial Theorem.
Walton, Jay R; Rivera-Rivera, Luis A; Lucchese, Robert R; Bevan, John W
2016-02-11
Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem. PMID:26788937
Note on identities inspired by new soft theorems
NASA Astrophysics Data System (ADS)
Rao, Junjie; Feng, Bo
2016-04-01
The new soft theorems, for both gravity and gauge amplitudes, have inspired a number of works, including the discovery of new identities related to amplitudes. In this note, we present the proof and discussion for two sets of identities. The first set includes an identity involving the half-soft function which had been used in the soft theorem for one-loop rational gravity amplitudes, and another simpler identity as its byproduct. The second set includes two identities involving the KLT momentum kernel, as the consistency conditions of the KLT relation plus soft theorems for both gravity and gauge amplitudes. We use the CHY formulation to prove the first identity, and transform the second one into a convenient form for future discussion.
Measuring grinding surface roughness based on the sharpness evaluation of colour images
NASA Astrophysics Data System (ADS)
Huaian, Y. I.; Jian, L. I. U.; Enhui, L. U.; Peng, A. O.
2016-02-01
Current machine vision-based detection methods for metal surface roughness mainly use the grey values of images for statistical analysis but do not make full use of the colour information and ignore the subjective judgment of the human vision system. To address these problems, this paper proposes a method to measure surface roughness through the sharpness evaluation of colour images. Based on the difference in sharpness of virtual images of colour blocks that are formed on grinding surfaces with different roughness, an algorithm for evaluating the sharpness of colour images that is based on the difference of the RGB colour space was used to develop a correlation model between the sharpness and the surface roughness. The correlation model was analysed under two conditions: constant illumination and varying illumination. The effect of the surface textures of the grinding samples on the image sharpness was also considered, demonstrating the feasibility of the detection method. The results show that the sharpness is strongly correlated with the surface roughness; when the illumination and the surface texture have the same orientation, the sharpness clearly decreases with increasing surface roughness. Under varying illumination, this correlation between the sharpness and surface roughness was highly robust, and the sharpness of each virtual image increased linearly with the illumination. Relative to the detection method for surface roughness using gray level co-occurrence matrix or artificial neural network, the proposed method is convenient, highly accurate and has a wide measurement range.
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.
Levinson theorem for the Dirac equation in D+1 dimensions
Gu Xiaoyan; Ma Zhongqi; Dong Shihai
2003-06-01
In terms of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation with a spherically symmetric potential in D+1 dimensions is uniformly established as a relation between the total number of bound states and the sum of the phase shifts of the scattering states at E={+-}M with a given angular momentum. The critical case, where the Dirac equation has a half bound state, is analyzed in detail. A half bound state is a zero-momentum solution if its wave function is finite but does not decay fast enough at infinity to be square integrable.
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.
Distributed Online Judge System for Interactive Theorem Provers
NASA Astrophysics Data System (ADS)
Mizuno, Takahisa; Nishizaki, Shin-ya
2014-03-01
In this paper, we propose a new software design of an online judge system for interactive theorem proving. The distinctive feature of this architecture is that our online judge system is distributed on the network and especially involves volunteer computing. In volunteers' computers, network bots (software robots) are executed and donate computational resources to the central host of the online judge system. Our proposed design improves fault tolerance and security. We gave an implementation to two different styles of interactive theorem prover, Coq and ACL2, and evaluated our proposed architecture. From the experiment on the implementation, we concluded that our architecture is efficient enough to be used practically.
An implicit sampling theorem for bounded bandlimited functions
NASA Technical Reports Server (NTRS)
Bar-David, I.
1974-01-01
A rigorous proof of the 'strong bias tone' scheme is embodied in the implicit sampling theorem. The representation of signals that are sample functions of possible nonstationary random processes being of principal interest, the proof could not directly invoke results from classical analysis, which depend on the existence of the Fourier transform of the function under consideration; rather, it is based on Zakai's (1965) theorem on the series expansion of functions, band-limited under a suitably extended definition. A practical circuit that restores an approximate version of the signal from its sine-wave-crossings is presented and possible improvements to it are discussed.
General self-tuning solutions and no-go theorem
Förste, Stefan; Kim, Jihn E.; Lee, Hyun Min E-mail: jihnekim@gmail.com
2013-03-01
We consider brane world models with one extra dimension. In the bulk there is in addition to gravity a three form gauge potential or equivalently a scalar (by generalisation of electric magnetic duality). We find classical solutions for which the 4d effective cosmological constant is adjusted by choice of integration constants. No go theorems for such self-tuning mechanism are circumvented by unorthodox Lagrangians for the three form respectively the scalar. It is argued that the corresponding effective 4d theory always includes tachyonic Kaluza-Klein excitations or ghosts. Known no go theorems are extended to a general class of models with unorthodox Lagrangians.
Strength of Butt and Sharp-Cornered Joints
REEDY JR.,EARL DAVID
2000-08-21
There has been considerable progress in recent years towards developing a stress intensity factor-based method for predicting crack initiation at a sharp, bimaterial comer. There is now a comprehensive understanding of the nature of multi-material, two-dimensional, linear-elastic, wedge-tip stress fields. In general, the asymptotic stress state at the apex of dissimilar bonded elastic wedges (i.e. at an interface comer) can have one or more power-law singularities of differing strength and with exponents that can be real or complex. There are, however; many configurations of practical importance, (e.g. adhesively bonded butt joints, hi-material beams, etc.) where interface-comer stresses are described by one, real-valued power-law singularity. In such cases, one can reasonably hypothesize that failure occurs at a critical value of the stress intensity factor: when K{sub a}=K{sub ac}.This approach is completely analogous to LEFM except that the critical stress intensity factor is associated with a discontinuity other than a crack. To apply the K{sub ac} criterion, one must be able to accurately calculate K{sub a} for arbitrary geometries. There are several well-established methods for calculating K{sub a}. These include matching asymptotic and detailed finite element results, evaluation of a path-independent contour integral, and general finite element methods for calculating K. for complex geometries. A rapidly expanding catalog of K{sub a} calibrations is now available for a number of geometries of practical interest. These calibrations provide convenient formulas that can be used in a failure analysis without recourse to a detailed numerical analysis. The K{sub ac} criterion has been applied with some notable successes. For example, the variation in strength of adhesively bonded butt joints with bond thickness and the dependence of this relationship on adhered stiffness is readily explained. No other one-parameter fracture criterion is able to make this sort of
Granular flow behavior at sharp changes in slope
NASA Astrophysics Data System (ADS)
Crosta, Giovanni; De Blasio, Fabio; Locatelli, Michele
2015-04-01
This study extends some recent experiments and analyses performed by the authors to examine the behavior of granular flows along path characterised by sharp changes in slope. In particular, various series of experiments along a bi-linear broken slope (an inclined initial sector followed by a horizontal one) have been completed using a uniform (Hostun, 0.32 mm) sand and a uniform fine gravel (2 mm grains). 60 new have been performed by releasing different volumes (1.5, 2.1 and 5.1 L) on surfaces characterized by different slope angles (35-60°), type of materials (wood and plexiglass), with or without an erodible layer (sand), or in presence of a shallow water pond (0.5 cm). These geometrical features are typical of many large rock and snow avalanches, rock falls and of chalk flows. The latter are usually typical of coastal cliffs where a shallow water environment is typical. The evolution of the flow has been monitored through a laser profilometer at 120 Hz sampling frequency and high speed camera, and in this way it has been possible to follow the evolution of the flow and deposition, and to analyse the change in deposition mode at varying the slope angle, the material and the basal friction. This is an extremely interesting development in the study of the evolution of the deposition and of the final morphology typical of such phenomena, and can support the testing of numerical models. Propagation and deposition occur forward or backward accordingly to the slope angle and the basal friction. Forward movement and deposition occur at high slope angles and with low basal friction. The opposite is true for the backward deposition. The internal "layering" within the deposit is also strongly controlled by the combination of such parameters. The time evolution of the flow allowed to determine the velocity of flow and the mode of deposition through the analysis of the change in thickness, position of the front and of the flow tail. Presence of water reduces the runout of
Derivation of a sphere theorem for the Stokes flow following Imai's procedure
NASA Astrophysics Data System (ADS)
Hasimoto, Hidenori
2007-07-01
A sphere theorem for general three-dimensional Stokes flow is shown to be derived by the use of Imai's procedure for solving the Stokes equation for spherical boundary in terms of one vector harmonic function and Kelvin's inversion theorem.
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…
Establishing Appropriate Conditions: Students Learning to Apply a Theorem
ERIC Educational Resources Information Center
Scataglini-Belghitar, Giovanna; Mason, John
2012-01-01
During a sequence of tutorials conducted by the first author, it became evident that students were not seeing how to apply the theorem concerning a continuous function on a closed and bounded interval attaining its extreme values in situations in which it is necessary first to construct the closed and bounded interval by reasoning about properties…
A fixed point theorem for certain operator valued maps
NASA Technical Reports Server (NTRS)
Brown, D. R.; Omalley, M. J.
1978-01-01
In this paper, we develop a family of Neuberger-like results to find points z epsilon H satisfying L(z)z = z and P(z) = z. This family includes Neuberger's theorem and has the additional property that most of the sequences q sub n converge to idempotent elements of B sub 1(H).
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…
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…
Local theorems for nonidentically distributed lattice random variables.
NASA Technical Reports Server (NTRS)
Mason, J. D.
1972-01-01
Derivation of local limit theorems for a sequence X sub n of independent integral-valued lattice random variables involving only a finite number of distinct nondegenerate distributions. Given appropriate sequences A sub n and B sub n of constants such that 1/B sub n (X sub 1 +
On the Positive Mass Theorem for Manifolds with Corners
NASA Astrophysics Data System (ADS)
McFeron, Donovan; Székelyhidi, Gábor
2012-07-01
We study the positive mass theorem for certain non-smooth metrics following P. Miao's work. Our approach is to smooth the metric using the Ricci flow. As well as improving some previous results on the behaviour of the ADM mass under the Ricci flow, we extend the analysis of the zero mass case to higher dimensions.
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.…
Discovering and Experiencing the Fundamental Theorem of Calculus.
ERIC Educational Resources Information Center
Rosenthal, Bill
1992-01-01
Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…
Start the Year Right-Discover Pick's Theorem.
ERIC Educational Resources Information Center
Wilcock, Douglas
1992-01-01
Describes a problem to challenge students as they come back from summer vacation. Working in small groups, students discover Pick's Theorem, the formula to calculate the area of a polygon constructed on a geoboard. A writing assignment evaluates the students' efforts. (MDH)
Proof by Analogy: The Case of the Pythagorean Theorem.
ERIC Educational Resources Information Center
Levine, Deborah R.
1983-01-01
The proof is given that, if three equilateral triangles are constructed on the sides of a right triangle, then the sum of the areas on the sides equals the area on the hypotenuse. This is based on one of the hundreds of proofs that exist for the Pythogorean theorem. (MP)
A decoupling theorem for the BPHZL-scheme
Aschenbrenner, M.
1996-09-01
Conditions are stated, which are sufficient for the heavy-mass-suppression of BPHZL-subtracted Feynman-integrals containing propagators of {open_quote}{open_quote}heavy fields{close_quote}{close_quote}. This result generalizes the Decoupling Theorems of Ambjo/rn, Manoukian and Landsman to cases, where massless fields (e.g., gauge fields) are present. {copyright} 1996 Academic Press, Inc.
A representation theorem of infimum of bounded quantum observables
Liu Weihua; Wu Junde
2008-07-15
In 2006, Gudder introduced a logic order on the bounded quantum observable set S(H). In 2007, Pulmannova and Vincekova proved that for each subset D of S(H), the infimum of D exists with respect to this logic order. In this paper, we present a representation theorem for the infimum of D.
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.
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…
Ambarzumyan's theorem for the quasi-periodic boundary conditions
NASA Astrophysics Data System (ADS)
Kıraç, Alp Arslan
2015-10-01
We obtain the classical Ambarzumyan's theorem for the Sturm-Liouville operators Lt(q) with qin L1[0,1] and quasi-periodic boundary conditions, tin [0,2π ) , when there is not any additional condition on the potential q.
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.
On the Fundamental Theorem of Calculus for Fractal Sets
NASA Astrophysics Data System (ADS)
Bongiorno, Donatella; Corrao, Giuseppa
2015-04-01
The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock-Kurzweil type is introduced.
A strengthening of a theorem of Bourgain and Kontorovich. III
NASA Astrophysics Data System (ADS)
Kan, I. D.
2015-04-01
We prove that the set of positive integers contains a positive proportion of denominators of the finite continued fractions all of whose partial quotients belong to the alphabet \\{1,2,3,4,10\\}. The corresponding theorem was previousy known only for the alphabet \\{1,2,3,4,5\\} and for alphabets of larger cardinality.
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…
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.
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…
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.)
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.
Solving open questions with an automated theorem-proving program
Wos, L.
1982-01-01
The primary objective of this paper is to demonstrate the feasibility of using an automated theorem-proving program as an automated reasoning assistant. Such usage is not merely a matter of conjecture. As evidence, we cite a number of open questions which were solved with the aid of a theorem-proving program. The open questions are taken from studies of ternary boolean algebra, finite semigroups, equivalential calculus, and the design of digital circuits. Despite the variety of successes, no doubt there still exists many who are very skeptical of the value of automating any form of deep reasoning. It is the nature of this skepticism which brings us to the second objective of the paper. The secondary objective is that of dispelling, at least in part, some of the resistance to such automation. To do this, we discuss two myths which form the basis for the inaccurate evaluation of both the usefulness and the potential of automated theorem proving. Rejection of the two myths removes an important obstacle to assigning to an automated theorem-proving program its proper role - the role of colleague and assistant.
On exponential sums of digital sums related to Gelfond's theorem
NASA Astrophysics Data System (ADS)
Okada, Tatsuya; Kobayashi, Zenji; Sekiguchi, Takeshi; Shiota, Yasunobu
2008-01-01
In this paper, we first give explicit formulas of exponential sums of sum of digits related to Gelfond's theorem. As an application of these formulas, we obtain a simple expression of Newman-Coquet type summation formula related to the number of binary digits in a multiple of a prime number.
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…
Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED.
Fodor, Z; Hoelbling, C; Krieg, S; Lellouch, L; Lippert, Th; Portelli, A; Sastre, A; Szabo, K K; Varnhorst, L
2016-08-19
In a previous Letter [Borsanyi et al., Phys. Rev. Lett. 111, 252001 (2013)] we determined the isospin mass splittings of the baryon octet from a lattice calculation based on N_{f}=2+1 QCD simulations to which QED effects have been added in a partially quenched setup. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. Our ensembles include 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. For the parameter which quantifies violations to Dashen's theorem, we obtain ϵ=0.73(2)(5)(17), where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, m_{u}=2.27(6)(5)(4) and m_{d}=4.67(6)(5)(4) MeV in the modified minimal subtraction scheme at 2 GeV and the isospin breaking ratios m_{u}/m_{d}=0.485(11)(8)(14), R=38.2(1.1)(0.8)(1.4), and Q=23.4(0.4)(0.3)(0.4). Our results exclude the m_{u}=0 solution to the strong CP problem by more than 24 standard deviations. PMID:27588847
Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED
NASA Astrophysics Data System (ADS)
Fodor, Z.; Hoelbling, C.; Krieg, S.; Lellouch, L.; Lippert, Th.; Portelli, A.; Sastre, A.; Szabo, K. K.; Varnhorst, L.; Budapest-Marseille-Wuppertal Collaboration
2016-08-01
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 Nf=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 ɛ =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, mu=2.27 (6 )(5 )(4 ) and md=4.67 (6 )(5 )(4 ) MeV in the modified minimal subtraction scheme at 2 G e V and the isospin breaking ratios mu/md=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 mu=0 solution to the strong C P problem by more than 24 standard deviations.
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
Maintaining knife sharpness in industrial meat cutting: A matter of knife or meat cutter ability.
Karltun, J; Vogel, K; Bergstrand, M; Eklund, J
2016-09-01
Knife sharpness is imperative in meat cutting. The aim of this study was to compare the impact of knife blade steel quality with meat cutters' individual ability to maintain the cutting edge sharp in an industrial production setting. Twelve meat cutters in two different companies using three different knives during normal production were studied in this quasi-experimental study. Methods included were measuring knife cutting force before and after knife use, time knives were used, ratings of sharpness and discomfort and interviews. Results showed that the meat cutters' skill of maintaining sharpness during work had a much larger effect on knife sharpness during work than the knife steel differences. The ability was also related to feelings of discomfort and to physical exertion. It was found that meat cutters using more knives were more likely to suffer from discomfort in the upper limbs, which is a risk for developing MSD. PMID:27184316
Measurements of system sharpness for two digital breast tomosynthesis systems.
Marshall, N W; Bosmans, H
2012-11-21
The aim of this work was to propose system sharpness parameters for digital breast tomosynthesis (DBT) systems that include the influence of focus size and focus motion for use in quality assurance protocols. X-ray focus size was measured using a multiple pinhole test object, while detector presampling modulation transfer function (MTF) was measured from projection images of a 10 cm × 10 cm, 1 mm thick steel edge, for the Siemens Inspiration and Hologic Selenia Dimensions DBT systems. The height of the edge above the table was then varied from 1 to 78 mm. The MTF expected from theory for the projection images was calculated from the measured detector MTF, focus size MTF and focus motion MTF and was compared against measured curves. Two methods were used to measure the in-plane MTF in the DBT volume: a tungsten wire of diameter 25 µm and an Al edge 0.2 mm thick, both imaged with a 15 mm thick poly(methyl methacrylate) (PMMA) plate. The in-depth point spread function (PSF) was measured using an angled tungsten wire. The full 3D MTF was estimated with a 0.5 mm diameter aluminium bead held in a 45 mm thick PMMA phantom, with the bead 15 and 65 mm above the table. Inspiration DBT projection images are saved at native detector resolution (85 µm), while the Dimensions re-bins projections to 140 µm pixels (2 × 2 binning); both systems used 2 × 2 binning of projection data before reconstruction. The 50% point for the MTF (MTF(0.50)) measured in the DBT projection images for the tube-travel direction fell as a function of height above the table from 3.60 to 0.90 mm(-1) for the Inspiration system and from 2.50 to 1.20 mm(-1) for the Dimensions unit. The maximum deviation of measured MTF(0.50) from the calculated value was 13%. MTF(0.50) measured in-plane (tube-travel direction) fell as a function of height above the table from 1.66 to 0.97 mm(-1) for the Inspiration system and from 2.21 to 1.31 mm(-1) for the Dimensions system. The full-width half-maximum for the in
Measurements of system sharpness for two digital breast tomosynthesis systems
NASA Astrophysics Data System (ADS)
Marshall, N. W.; Bosmans, H.
2012-11-01
The aim of this work was to propose system sharpness parameters for digital breast tomosynthesis (DBT) systems that include the influence of focus size and focus motion for use in quality assurance protocols. X-ray focus size was measured using a multiple pinhole test object, while detector presampling modulation transfer function (MTF) was measured from projection images of a 10 cm × 10 cm, 1 mm thick steel edge, for the Siemens Inspiration and Hologic Selenia Dimensions DBT systems. The height of the edge above the table was then varied from 1 to 78 mm. The MTF expected from theory for the projection images was calculated from the measured detector MTF, focus size MTF and focus motion MTF and was compared against measured curves. Two methods were used to measure the in-plane MTF in the DBT volume: a tungsten wire of diameter 25 µm and an Al edge 0.2 mm thick, both imaged with a 15 mm thick poly(methyl methacrylate) (PMMA) plate. The in-depth point spread function (PSF) was measured using an angled tungsten wire. The full 3D MTF was estimated with a 0.5 mm diameter aluminium bead held in a 45 mm thick PMMA phantom, with the bead 15 and 65 mm above the table. Inspiration DBT projection images are saved at native detector resolution (85 µm), while the Dimensions re-bins projections to 140 µm pixels (2 × 2 binning); both systems used 2 × 2 binning of projection data before reconstruction. The 50% point for the MTF (MTF0.50) measured in the DBT projection images for the tube-travel direction fell as a function of height above the table from 3.60 to 0.90 mm-1 for the Inspiration system and from 2.50 to 1.20 mm-1 for the Dimensions unit. The maximum deviation of measured MTF0.50 from the calculated value was 13%. MTF0.50 measured in-plane (tube-travel direction) fell as a function of height above the table from 1.66 to 0.97 mm-1 for the Inspiration system and from 2.21 to 1.31 mm-1 for the Dimensions system. The full-width half-maximum for the in-depth PSF was 3
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.
The Fundamental Theorem of Prevision. Technical Report No. 506. November 1987.
ERIC Educational Resources Information Center
Lad, F. R.; And Others
B. De Finetti's "Fundamental Theorem of Probability" is reformulated as a computable linear programming problem. The theorem is substantially extended, and shown to have fundamental implications for the theory and practice of statistics. It supports an operational meaning for the partial assertion of prevision via asserted bounds. The theorem is…
Isotopic Ratio, Isotonic Ratio, Isobaric Ratio and Shannon Information Uncertainty
NASA Astrophysics Data System (ADS)
Ma, Chun-Wang; Wei, Hui-Ling
2014-11-01
The isoscaling and the isobaric yield ratio difference (IBD) probes, both of which are constructed by yield ratio of fragment, provide cancelation of parameters. The information entropy theory is introduced to explain the physical meaning of the isoscaling and IBD probes. The similarity between the isoscaling and IBD results is found, i.e., the information uncertainty determined by the IBD method equals to β - α determined by the isoscaling (α (β) is the parameter fitted from the isotopic (isotonic) yield ratio).
Chemical Composition of lower Mount Sharp at Gale Crater, Mars, as measured by the APXS
NASA Astrophysics Data System (ADS)
Gellert, R.; Boyd, N.; Campbell, J. L.; VanBommel, S.; Perrett, G. M.; Desouza, E.; Thompson, L. M.; Yen, A. S.; Berger, J. A.
2015-12-01
From sol 810 through to 950 the MSL Curiosity Rover carried out detailed investigations at Pahrump, which likely represents the lowest strata of Mount Sharp. The bulk chemistry is very different compared to previously encountered formations like Sheepbed at Yellowknifebay, which resembled an average Mars composition. The bedrock is significantly depleted in Mg and Ca, elevated in Al and Si and enriched in Zn (~2000 ppm), Se (~50 ppm) and Pb(~100 ppm). The composition varies only slightly over the ~10 meter elevation explored at Pahrump and is chemically homogenous on a 10 cm scale. However, some clear trends uphill are present. Zn and Se decrease with elevation, the Fe/Mn ratio, a possible indicator for the Fe3+ content, increases from 50 to 100. Elevated 2.5% P2O5 were encountered at higher elevations. SO3 ranges from 5 to 8% in the drill samples, higher abundances were found in Ca-sulfate veins and diagenetic features that contain ~15% (Mg,Ni)-sulfates. The Pahrump bedrock may be traced ~500m to the north and south. Bonanza King (sol 755, Hidden Valley) and Spokane (sol 989) share the same major chemistry, including similar trends in minor and trace elements. Most recently the rover approached a contact between Pahrump-like bedrock and an overlying, more resistant unit identified from orbit at Marias Pass. High SiO2, ranging from 63 to 72%, was found close to the contact, above which the sandstone composition changes abruptly to that of average Mars. Increased Si is correlated with elevated P and Ti, lower Al and Fe, and a dramatic decrease in Zn, Ni and Cr to very low values of a few 100 ppm and less. The elevated silica and associated elemental trends observed at Marias Pass share characteristics with the high silica bedrock examined at HomePlate in Gusev Crater, where acidic leaching or silica mobilization has been proposed. The stratigraphy together with data from 4 drill samples for SAM and Chemin might shed light on the formation history of this extensive
Super-Sharp Radio "Vision" Measures Galaxy's Motion in Space
NASA Astrophysics Data System (ADS)
2005-03-01
Astronomers using the National Science Foundation's Very Long Baseline Array (VLBA) have measured the motion across the sky of a galaxy nearly 2.4 million light-years from Earth. While scientists have been measuring the motion of galaxies directly toward or away from Earth for decades, this is the first time that the transverse motion (called proper motion by astronomers) has been measured for a galaxy that is not a satellite of our own Milky Way Galaxy. M33 Radio/Optical Image of M33 CREDIT: NRAO/AUI/NSF, NOAO/AURA/NSF (Click on image for more files) An international scientific team analyzed VLBA observations made over two and a half years to detect minuscule shifts in the sky position of the spiral galaxy M33. Combined with previous measurements of the galaxy's motion toward Earth, the new data allowed the astronomers to calculate M33's movement in three dimensions for the first time. "A snail crawling on Mars would appear to be moving across the surface more than 100 times faster than the motion we measured for this galaxy," said Mark Reid, of the Harvard-Smithsonian Center for Astrophysics in Cambridge, MA. M33 is a satellite of the larger galaxy M31, the well-known Andromeda Galaxy that is the most distant object visible to the naked eye. Both are part of the Local Group of galaxies that includes the Milky Way. In addition to measuring the motion of M33 as a whole, the astronomers also were able to make a direct measurement of the spiral galaxy's rotation. Both measurements were made by observing the changes in position of giant clouds of molecules inside the galaxy. The water vapor in these clouds acts as a natural maser, strengthening, or amplifying, radio emission the same way that lasers amplify light emission. The natural masers acted as bright radio beacons whose movement could be tracked by the ultra-sharp radio "vision" of the VLBA. Reid and his colleagues plan to continue measuring M33's motion and also to make similar measurements of M31's motion
Super-Sharp Radio 'Eye' Remeasuring the Universe
NASA Astrophysics Data System (ADS)
2011-02-01
Using the super-sharp radio "vision" of astronomy's most precise telescope, scientists have extended a directly-measured "yardstick" three times farther into the cosmos than ever before, an achievement with important implications for numerous areas of astrophysics, including determining the nature of Dark Energy, which constitutes 70 percent of the Universe. The continent-wide Very Long Baseline Array (VLBA) also is redrawing the map of our home Galaxy and is poised to yield tantalizing new information about extrasolar planets, among many other cutting-edge research projects. The VLBA provides the greatest ability to see fine detail, called resolving power, of any telescope in the world. It can produce images hundreds of times more detailed than those from the Hubble Space Telescope -- power equivalent to sitting in New York and reading a newspaper in Los Angeles. This power allows astronomers to make precise cosmic measurements with far-ranging implications for research within our own Galaxy and far beyond. New measurements with the VLBA have placed a galaxy called NGC 6264 at a distance of 450 million light-years from Earth, with an uncertainty of no more than 9 percent. This is the farthest distance ever directly measured, surpassing a measurement of 160 million light-years to another galaxy in 2009. Previously, distances beyond our own Galaxy have been estimated through indirect methods. "Our direct, geometric measurements are independent of the assumptions and complications inherent in other techniques," said James Braatz, of the National Radio Astronomy Observatory (NRAO), who worked with Cheng-Yu Kuo, of the University of Virginia and NRAO. Fine-tuning the measurement of ever-greater distances is vital to determining the expansion rate of the Universe, which helps theorists narrow down possible explanations for the nature of Dark Energy. Different models of Dark Energy predict different values for the expansion rate, known as the Hubble Constant. "Solving
Super-Sharp Radio "Vision" Measures Galaxy's Motion in Space
NASA Astrophysics Data System (ADS)
2005-03-01
Astronomers using the National Science Foundation's Very Long Baseline Array (VLBA) have measured the motion across the sky of a galaxy nearly 2.4 million light-years from Earth. While scientists have been measuring the motion of galaxies directly toward or away from Earth for decades, this is the first time that the transverse motion (called proper motion by astronomers) has been measured for a galaxy that is not a satellite of our own Milky Way Galaxy. M33 Radio/Optical Image of M33 CREDIT: NRAO/AUI/NSF, NOAO/AURA/NSF (Click on image for more files) An international scientific team analyzed VLBA observations made over two and a half years to detect minuscule shifts in the sky position of the spiral galaxy M33. Combined with previous measurements of the galaxy's motion toward Earth, the new data allowed the astronomers to calculate M33's movement in three dimensions for the first time. "A snail crawling on Mars would appear to be moving across the surface more than 100 times faster than the motion we measured for this galaxy," said Mark Reid, of the Harvard-Smithsonian Center for Astrophysics in Cambridge, MA. M33 is a satellite of the larger galaxy M31, the well-known Andromeda Galaxy that is the most distant object visible to the naked eye. Both are part of the Local Group of galaxies that includes the Milky Way. In addition to measuring the motion of M33 as a whole, the astronomers also were able to make a direct measurement of the spiral galaxy's rotation. Both measurements were made by observing the changes in position of giant clouds of molecules inside the galaxy. The water vapor in these clouds acts as a natural maser, strengthening, or amplifying, radio emission the same way that lasers amplify light emission. The natural masers acted as bright radio beacons whose movement could be tracked by the ultra-sharp radio "vision" of the VLBA. Reid and his colleagues plan to continue measuring M33's motion and also to make similar measurements of M31's motion
Unsteady flow past wings having sharp-edge separation
NASA Technical Reports Server (NTRS)
Atta, E. H.; Kandil, O. A.; Mook, D. T.; Nayfeh, A. H.
1976-01-01
A vortex-lattice technique is developed to model unsteady, incompressible flow past thin wings. This technique predicts the shape of the wake as a function of time; thus, it is not restricted by planform, aspect ratio, or angle of attack as long as vortex bursting does not occur and the flow does not separate from the wing surface. Moreover, the technique can be applied to wings of arbitrary curvature undergoing general motion; thus, it can treat rigid-body motion, arbitrary wing deformation, gusts in the freestream, and periodic motions. Numerical results are presented for low-aspect rectangular wings undergoing a constant-rate, rigid-body rotation about the trailing edge. The results for the unsteady motion are compared with those predicted by assuming quasi-steady motion. The present results exhibit hysteretic behavior.
Women in Surgery: Bright, Sharp, Brave, and Temperate
McLemore, Elisabeth C; Ramamoorthy, Sonia; Peterson, Carrie Y; Bass, Barbara L
2012-01-01
Women make up an increasing proportion of students entering the medical profession. Before 1970, women represented 6% or less of the medical student population. In drastic contrast, nearly half of first-time applicants to medical schools in 2011 were women. However, the ratio of women to men is less balanced among graduates from surgical residencies and among leadership positions in surgery. Less than 20% of full professor, tenured faculty, and departmental head positions are currently held by women. However, this disparity may resolve with time as more women who entered the field in the 1980s emerge as mature surgeons and leaders. The aim of this article is to review the history of women in surgery and to highlight individual and institutional creative modifications that can promote the advancement of women in surgery. A secondary aim of the article is to add some levity to the discussion with personal anecdotes representing the primary author's (ECM) personal opinions, biases, and reflections. PMID:23012600
NASA Astrophysics Data System (ADS)
Vermeulen, B.; Hoitink, A. J. F.; Berkum, S. W.; Hidayat, H.
2014-07-01
Autogenic scouring in sharp river bends has received ample attention in laboratory and modeling studies. These studies have significantly advanced our understanding of how flow processes are influenced by strong curvature and how they affect the bathymetry. Here we present a 300 km reach of the Mahakam River in Indonesia, which features several sharp bends (W/R > 0.5), providing a unique field data set to validate existing knowledge on sharp bends. Scour depths were found to strongly exceed what can be expected based on existing understanding of sharp bends and are highly correlated with curvature. A comprehensive stream reconnaissance was carried out to compare the occurrence of sharp bends and deep scours with lateral bank migration. Histograms of the occurrence of erosive, stable, advancing, and bar-type banks as a function of curvature quantify the switch from a mildly curved bend regime to a sharp bend regime. In mild bends, outer banks erode and inner banks advance. In sharp bends the erosion pattern inverts. Outer banks stabilize or advance, while inner banks erode. In sharply curved river bends, bars occur near the outer banks that become less erosive for higher curvatures. Inner banks become more erosive for higher curvatures but nevertheless accommodate the larger portion of exposed bars. No relation was found between the land cover adjacent to the river and the occurrence of sharp bends. Soil processes may play a crucial role in the formation of sharp bends, which is inferred from iron and manganese concretions observed in the riverbanks, indicating ferric horizons and early stages of the formation of plinthic horizons. Historical topographic maps show the planform activity of the river is low, which may relate to the scour holes slowing down planimetric development.
George Sudarshan, No-Go theorems and the exclusion principle
NASA Astrophysics Data System (ADS)
Han, M. Y.
2009-11-01
We review two areas of my work that were directly and indirectly initiated and inspired by George. One is the proofs of no-go theorems in combining the spacetime and internal symmetries in non-trivial ways and the other is how Georges firm conviction on the fundamentality of the spin-statistics theorem helped to expand the domain of applicability of the spin-statistics theorem into the arena of quarks and gluons, going far beyond the original application of the exclusion principle in atomic physics. In order to provide deeper understanding of mass differences of particles belonging to spin-degenerate multiplets, attempts have been made to see if some non-trivial way of embedding the Lorentz group and internal symmetry groups such as SU(2) and SU(3) into a larger group. When a hint of no-go theorem (that such non-trivial embedding cannot be achieved) first appeared, George went to work and led many of us, including myself, into this area of research. A series of proofs of no-go theorems by George, myself and others eventually led to the definitive proof by Lochlainn O'Raifeartaigh that came to be known as the ORaifeartaigh theorem. Lochlainn also joined George at Syracuse at the same time I went there. The second area in which George had significant influence on my work is his fervent belief in the fundamental importance of the spin-statistics relationship. First postulated by Worlfgang Pauli to explain the periodic table of elements, the relationship the exclusion principle has exceeded far beyond its original domain of validity. The relationship has been upheld across the scale molecular, atomic, and nuclear structures. What is less known is the fact the relationship continues to remain valid in scales smaller than nucleons. The spin-statistics relationship was one of the compelling reasons for Nambu and I to introduce a new set of then undiscovered degrees freedom for quarks inside nucleons. This new degrees of freedom came to be called the color charges of
Slimani, S; Sahraoui, M; Bennadji, A; Ladjouze-Rezig, A
2014-08-01
Paraneoplastic syndromes commonly occur in malignancies and often precede the first symptoms of the tumor. By definition, paraneoplastic syndromes are only associated with malignancies although some exceptions have been reported, occurring with benign tumors. We report a patient presenting with a clinical and serological Sharp syndrome, followed a few months later by a cervical schwannoma. Curative surgical resection of the mass resulted in a clinical and serological healing from the Sharp syndrome. To our knowledge, this is the first report of a benign schwannoma complicated by a possible paraneoplastic Sharp syndrome. PMID:24951380
The escalating threat of Rhizoctonia cerealis, the causal agent of sharp eyespot in wheat.
Hamada, Mohamed Sobhy; Yin, Yanni; Chen, Huaigu; Ma, Zhonghua
2011-11-01
Rhizoctonia cerealis, the causal agent of sharp eyespot on wheat, was not considered to be an important pathogen for many years. Recently, the disease has become endemic in many countries except for South America. The disease has created a new threat to world wheat production because the damage of wheat sharp eyespot has become increasingly severe. In this paper, previous studies on this pathogen, including the disease geographical distribution, pathogen identification, life cycle, symptoms, favourable environmental conditions, effects on wheat yield and control strategy, are reviewed. Such information will be helpful in management of sharp eyespot. PMID:21726039
User friendly web site a winner. San Diego's Sharp HealthCare provides wealth of information.
Rees, Tom
2003-01-01
The Sharp HealthCare, San Diego, web site, a winner of the 2002 Medicine on the Net Web Excellence Award, provides a wealth of information without wasting space or confusing the visitor. The web site, www.sharp.com, can be viewed in both English and Spanish, a valuable consideration for those living in the California-Mexico border area served by Sharp. The integrated health network operates seven hospitals and three medical group practices. It has 2,541 physicians on medical staffs and more than 11,000 employees. PMID:12807120
Examples of probabilistic semantics of the basic coding theorem for uncertainty spaces
Diduk, N.N.
1995-03-01
The basic coding theorem for discrete uncertainty spaces is so far the central result of the developing uncertainty theory. The theorem was first published in and its proof in. A refinement of the basic coding theorem with a new proof was subsequently published. The theoretical value of the basic coding theorem is in that it essentially made possible the development of a general theoretical apparatus covering various types of uncertainty. But this theorem should not be regarded as a purely theoretical result, because it also has a clear applied meaning. Indeed, the theorem deals with what can and cannot be accomplished by encoding elements of uncertainty spaces. Such questions are of considerable practical importance, because problems of finding good information encoding techniques are encountered in many spheres of human activity. Moreover, possible applications of the theorem are not restricted to coding problems: we know that prefix coding is analogous to construction of successful search strategies. Search problems therefore constitute another potential application of the proposed theorem. It is thus useful to consider the practical aspects of the basic coding theorem. The basis for the application of the theorem is its semantics, i.e., the system of possible meaningful interpretations. The present paper examines examples of particular cases of the basic coding theorem which admit a probabilistic interpretation. The choice of the topic is motivated by the fact that uncertainty situations that have a probabilistic meaning are undoubtedly of exceptional interest from both theoretical and applied considerations.
NASA Astrophysics Data System (ADS)
Qiu, Zhiping; Wang, Xiaojun
2005-04-01
Generalized eigenvalue problems from the modal analysis are often converted to the standard eigenvalue problems. In this paper, it evaluates the upper and lower bounds on the eigenvalues of the standard eigenvalue problem of structures subject to severely deficient information about the structural parameters. Here, we focus on non-probabilistic interval analysis models of uncertainty, which are adapted to the case of severe lack of information on uncertainty. Non-probabilistic, interval analysis method in which uncertainties are defined by interval numbers appears as an alternative to the classical probabilistic models. For the standard eigenvalue problem of structures with uncertain-but-bounded parameters, the vertex solution theorem, the positive semi-definite solution theorem and the parameter decomposition solution theorem for the standard eigenvalue problem are presented, and compared with Deif's solution theorem in numerical examples. It is shown that, for the upper and lower bounds on the eigenvalues of the standard eigenvalue problem with uncertain-but-bounded parameters, the presented vertex solution theorem is unconditional, and the positive semi-definite solution theorem and the parameter decomposition solution theorem have less limitary conditions compared with Deif's solution theorem. The effectiveness of the vertex solution theorem, the positive semi-definite solution theorem and the parameter decomposition solution theorem are illustrated by numerical examples
Sharp Eccentric Rings in Planetless Hydrodynamical Models of Debris Disks
NASA Technical Reports Server (NTRS)
Lyra, W.; Kuchner, M. J.
2013-01-01
Exoplanets are often associated with disks of dust and debris, analogs of the Kuiper Belt in our solar system. These "debris disks" show a variety of non-trivial structures attributed to planetary perturbations and utilized to constrain the properties of the planets. However, analyses of these systems have largely ignored the fact that, increasingly, debris disks are found to contain small quantities of gas, a component all debris disks should contain at some level. Several debris disks have been measured with a dust-to-gas ratio around unity where the effect of hydrodynamics on the structure of the disk cannot be ignored. Here we report that dust-gas interactions can produce some of the key patterns seen in debris disks that were previously attributed to planets. Through linear and nonlinear modeling of the hydrodynamical problem, we find that a robust clumping instability exists in this configuration, organizing the dust into narrow, eccentric rings, similar to the Fomalhaut debris disk. The hypothesis that these disks might contain planets, though thrilling, is not necessarily required to explain these systems.
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.
Boltzmann's H theorem for systems with frictional dissipation.
Bizarro, João P S
2011-03-01
By use of Boltzmann's equation to describe an ensemble of particles under the influence of a friction force, Boltzmann's H theorem is refined to explicitly include frictional dissipation, the accompanying fluctuations being modeled via an added diffusive, Fokker-Planck term. If the friction force per particle mass is proportional to velocity, as is the case with viscous drag with a friction coefficient γ, Boltzmann's H theorem for the time rate of change of the quantity H reads dH/dt ≤ γ. The classical formulation stating that H can never increase is thus replaced by the statement that H cannot increase at a rate higher than γ, a general result but of particular relevance when fluctuations are negligible and the system is far from equilibrium. When the particles are not far from thermal equilibrium, an alternative, more suitable expression emerges which can be written in the form of a Clausius inequality. PMID:21517545
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.
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]).
Quantum macrostates, equivalence of ensembles, and an H-theorem
NASA Astrophysics Data System (ADS)
De Roeck, Wojciech; Maes, Christian; Netočný, Karel
2006-07-01
Before the thermodynamic limit, macroscopic averages need not commute for a quantum system. As a consequence, aspects of macroscopic fluctuations or of constrained equilibrium require a careful analysis, when dealing with several observables. We propose an implementation of ideas that go back to John von Neumann's writing about the macroscopic measurement. We apply our scheme to the relation between macroscopic autonomy and an H-theorem, and to the problem of equivalence of ensembles. In particular, we show how the latter is related to the asymptotic equipartition theorem. The main point of departure is an expression of a law of large numbers for a sequence of states that start to concentrate, as the size of the system gets larger, on the macroscopic values for the different macroscopic observables. Deviations from that law are governed by the entropy.
Levinson theorem for the Dirac equation in one dimension
Ma Zhongqi; Dong Shihai; Wang Luya
2006-07-15
The Levinson theorem for the (1+1)-dimensional Dirac equation with a symmetric potential is proved with the Sturm-Liouville theorem. The half-bound states at the energies E={+-}M, whose wave function is finite but does not decay at infinity fast enough to be square integrable, are discussed. The number n{sub {+-}} of bound states is equal to the sum of the phase shifts at the energies E={+-}M:{delta}{sub {+-}}(M)+{delta}{sub {+-}}(-M)=(n{sub {+-}}+a){pi}, where the subscript {+-} denotes the parity and the constant a is equal to -1/2 when no half-bound state occurs, to 0 when one half-bound state occurs at E=M or at E=-M, and to 1/2 when two half-bound states occur at both E={+-}M.
Testability of the Pusey-Barrett-Rudolph Theorem
NASA Astrophysics Data System (ADS)
Halataei, Seyyed Mohammad Hassan
2014-03-01
Pusey, Barrett, and Rudolph (PBR) proved a mathematically neat theorem which assesses the reality of the quantum state. They proposed a test such that if any pair of quantum states could pass it, then for small deviation in the probabilities of measurement outcomes, ɛ, from the predicted quantum probabilities, one can conclude that the physical state λ ``is normally closely associated with only one of the two quantum states.'' While the mathematics of their theorem is correct, the physical conclusion is incomplete. In this talk, I present an argument which greatly limits the conclusion one can draw from even a successful PBR test. Specifically, I show that the physical state can be associated with several quantum states and, thus, the reality of quantum states cannot be deduced. This work was supported by the MacArthur Professorship endowed by the John D. and Catherine T. MacArthur Foundation at the University of Illinois.
Bell's Theorem and the Issue of Determinism and Indeterminism
NASA Astrophysics Data System (ADS)
Esfeld, Michael
2015-05-01
The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell's theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for the derivation of Bell's theorem. Determinism as such does not undermine that independence (unless there are particular initial conditions of the universe that would amount to conspiracy). Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave-function can go together with effective wave-functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave-functions are sufficient for the mentioned independence premise to hold.
Sampling Theorem in Terms of the Bandwidth and Sampling Interval
NASA Technical Reports Server (NTRS)
Dean, Bruce H.
2011-01-01
An approach has been developed for interpolating non-uniformly sampled data, with applications in signal and image reconstruction. This innovation generalizes the Whittaker-Shannon sampling theorem by emphasizing two assumptions explicitly (definition of a band-limited function and construction by periodic extension). The Whittaker- Shannon sampling theorem is thus expressed in terms of two fundamental length scales that are derived from these assumptions. The result is more general than what is usually reported, and contains the Whittaker- Shannon form as a special case corresponding to Nyquist-sampled data. The approach also shows that the preferred basis set for interpolation is found by varying the frequency component of the basis functions in an optimal way.
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.
FAST TRACK COMMUNICATION: Central limit theorem and deformed exponentials
NASA Astrophysics Data System (ADS)
Vignat, C.; Plastino, A.
2007-11-01
The central limit theorem (CLT) can be ranked among the most important ones in probability theory and statistics and plays an essential role in several basic and applied disciplines, notably in statistical thermodynamics. We show that there exists a natural extension of the CLT from exponentials to so-called deformed exponentials (also denoted as q-Gaussians). Our proposal applies exactly in the usual conditions in which the classical CLT is used.
Opposites attract: a theorem about the Casimir Force.
Kenneth, Oded; Klich, Israel
2006-10-20
We consider the Casimir interaction between (nonmagnetic) dielectric bodies or conductors. Our main result is a proof that the Casimir force between two bodies related by reflection is always attractive, independent of the exact form of the bodies or dielectric properties. Apart from being a fundamental property of fields, the theorem and its corollaries also rule out a class of suggestions to obtain repulsive forces, such as the two hemisphere repulsion suggestion and its relatives. PMID:17155375
Watson's theorem and the N Δ (1232 ) axial transition
NASA Astrophysics Data System (ADS)
Alvarez-Ruso, L.; Hernández, E.; Nieves, J.; Vacas, M. J. Vicente
2016-01-01
We present a new determination of the N Δ axial form factors from neutrino induced pion production data. For this purpose, the model of Hernandez et al. [Phys. Rev. D 76, 033005 (2007)] is improved by partially restoring unitarity. This is accomplished by imposing Watson's theorem on the dominant vector and axial multipoles. As a consequence, a larger C5A(0 ), in good agreement with the prediction from the off-diagonal Goldberger-Treiman relation, is now obtained.
Applications of Noether conservation theorem to Hamiltonian systems
NASA Astrophysics Data System (ADS)
Mouchet, Amaury
2016-09-01
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether's approach is illustrated on several examples, including classical field theory and quantum dynamics.
A notion of graph likelihood and an infinite monkey theorem
NASA Astrophysics Data System (ADS)
Banerji, Christopher R. S.; Mansour, Toufik; Severini, Simone
2014-01-01
We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.
A proof of van Aubel's theorem using orthogonal vectors
NASA Astrophysics Data System (ADS)
Glaister, P.
2016-04-01
We show how two linearly independent vectors can be used to construct two orthogonal vectors of equal magnitude in a simple way. The proof that the constructed vectors are orthogonal and of equal magnitude is a good exercise for students studying properties of scalar and vector triple products. We then show how this result can be used to prove van Aubel's theorem that relates the two line segments joining the centres of squares on opposite sides of a plane quadrilateral.
Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces.
Kim, Jong Kyu; Pathak, Ramesh Prasad; Dashputre, Samir; Diwan, Shailesh Dhar; Gupta, Rajlaxmi
2016-01-01
In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditions. Our results are the extension and improvements of the recent well-known results announced in the current literature. PMID:27386356
Analytical proof of Gisin's theorem for three qubits
Choudhary, Sujit K.; Ghosh, Sibasish; Kar, Guruprasad; Rahaman, Ramij
2010-04-15
Gisin's theorem assures that for any pure bipartite entangled state, there is violation of the inequality of Bell and of Clauser, Horne, Shimony, and Holt, revealing its contradiction with local realistic model. Whether a similar result holds for three-qubit pure entangled states remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy's nonlocality argument.
On the quenched central limit theorem for random dynamical systems
NASA Astrophysics Data System (ADS)
Abdelkader, Mohamed; Aimino, Romain
2016-06-01
We provide a necessary and sufficient condition under which the quenched central limit theorem without random centering holds for one-dimensional random systems that are uniformly expanding. This condition holds in particular when all the maps preserve a common measure. We also give a counter example which shows that this condition is not necessarily satisfied when the maps do not preserve a common measure.
Klein's theorem and the proof of E0 = mc2
NASA Astrophysics Data System (ADS)
Ohanian, Hans C.
2012-12-01
Despite repeated attempts, Einstein failed to give us a general and rigorous proof of his E0=mc2 relation. A completely general proof emerged in 1918 from a theorem on the four-vector character of energy-momentum of extended systems by the mathematician Felix Klein, but this proof is not well known, rarely seen in textbooks, and sometimes misunderstood. A simple version of this proof is presented here, with discussion of the crucial role of the energy-momentum tensor.
Black holes, information, and the universal coefficient theorem
NASA Astrophysics Data System (ADS)
Patrascu, Andrei T.
2016-07-01
General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article, I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by the demanding invariance of the laws of physics to the change of coefficient structures in cohomology.
Extremely localized nonorthogonal orbitals by the pairing theorem.
Zoboki, T; Mayer, I
2011-03-01
Using the concepts of Löwdin pairing theorem, a method is developed to calculate extremely localized, but nonorthogonal, sets of molecular orbitals and their strictly localized counterparts. The method is very suitable to study to what extent a given model of bonding in a given molecule can be considered adequate from the point of view of the actual LCAO-MO (Hartree Fock or DFT) wave function and is expected to be useful for doing local approximations of electron correlation. PMID:20941738
SharpViSu: integrated analysis and segmentation of super-resolution microscopy data
Andronov, Leonid; Lutz, Yves; Vonesch, Jean-Luc; Klaholz, Bruno P.
2016-01-01
Summary: We introduce SharpViSu, an interactive open-source software with a graphical user interface, which allows performing processing steps for localization data in an integrated manner. This includes common features and new tools such as correction of chromatic aberrations, drift correction based on iterative cross-correlation calculations, selection of localization events, reconstruction of 2D and 3D datasets in different representations, estimation of resolution by Fourier ring correlation, clustering analysis based on Voronoi diagrams and Ripley’s functions. SharpViSu is optimized to work with eventlist tables exported from most popular localization software. We show applications of these on single and double-labelled super-resolution data. Availability and implementation: SharpViSu is available as open source code and as compiled stand-alone application under https://github.com/andronovl/SharpViSu. Contact: klaholz@igbmc.fr Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27153691
NASA Technical Reports Server (NTRS)
Limanskiy, A. V.; Timoshenko, V. I.
1986-01-01
Numerical results on the hypersonic gas flow in viscous interaction regime past sharp circular cones with thermally destructible Teflon surface are presented. Characteristics of the mutual influence between the thermochemical decomposition of the surface and the viscous interaction are revealed.
Needles and Other Sharps (Safe Disposal Outside of Health Care Settings)
... are generally available through pharmacies, medical supply companies, health care providers and online. These containers are made of ... proper disposal methods for sharps used outside of health care settings visit this website or call (800) 643- ...
Ultrasonic trapping of small particles by sharp edges vibrating in a flexural mode
NASA Astrophysics Data System (ADS)
Hu, Junhui; Yang, Jianbo; Xu, Jun
2004-12-01
Ultrasonic trapping of small particles by sharp edges vibrating in a flexural mode is reported. Two rectangular metal plates with a sharp edge are mechanically excited to vibrate in a flexural mode by the piezoelectric rings which are pressed between them by a bolt structure. Small particles such as mint seeds and flying color seeds can be attracted to the sharp edges of the plates. Relationship between input power applied to the piezoelectric rings and the number of trapped particles is experimentally investigated for mint seeds and flying color seeds in water and air. The result shows that for a given type of particle, there exists an input power at which the number of trapped particles is a maximum. Mechanism analysis shows that nodes or antinodes of acoustic pressure of the sound field near the sharp edges are responsible for the trapping.
Method of improving image sharpness for annular-illumination scanning electron microscopes
NASA Astrophysics Data System (ADS)
Enyama, Momoyo; Hamada, Koichi; Fukuda, Muneyuki; Kazumi, Hideyuki
2016-06-01
Annular illumination is effective in enhancing the depth of focus for scanning electron microscopes (SEMs). However, owing to high side lobes of the point-spread function (PSF), annular illumination results in poor image sharpness. The conventional deconvolution method, which converts the PSF to a delta function, can improve image sharpness, but results in artifacts due to noise amplification. In this paper, we propose an image processing method that can reduce the deterioration of image sharpness. With this method, the PSF under annular illumination is converted to that under standard illumination. Through simulations, we verified that the image sharpness of SEM images under annular illumination with the proposed method can be improved without noise amplification.
Derivation of the Direct-Interaction Approximation Using Novikov's Theorem
NASA Astrophysics Data System (ADS)
Krommes, J. A.
2015-11-01
The direct-interaction approximation (DIA) is a crucially important statistical closure for both neutral fluids and plasmas. Kraichnan's original derivation proceeded in k space and assumed a large number N of interacting Fourier modes. That is problematic; the DIA can be formulated even for N = 3 . In the present work an alternate x-space procedure based on Novikov's theorem is described. That theorem is a statement about the correlations of certain Gaussian functionals. Turbulence cannot be Gaussian due to nonlinearity, but Novikov's theorem can be used to formulate self-consistent equations for a Gaussian component of the turbulence. The DIA emerges under the assumption that certain higher-order correlations are small. In essence, this procedure is merely a restatement of Kraichnan's arguments, but it adds additional perspective because the assumption of large N is not required. Details can be found in a lengthy set of tutorial Lecture Notes. Work supported by U.S.D.o.E. Contract DE-AC02-09CH11466.
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.
Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields
Pan, Xiao-Yin; Sahni, Viraht
2015-11-07
The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momenta. The proofs differ from the original HK proof and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function. A Percus-Levy-Lieb constrained-search proof expanding the domain of validity to N-representable functions, and to degenerate states, again for fixed electron number and angular momentum, is also provided.
Manifestly covariant Jüttner distribution and equipartition theorem
NASA Astrophysics Data System (ADS)
Chacón-Acosta, Guillermo; Dagdug, Leonardo; Morales-Técotl, Hugo A.
2010-02-01
The relativistic equilibrium velocity distribution plays a key role in describing several high-energy and astrophysical effects. Recently, computer simulations favored Jüttner’s as the relativistic generalization of Maxwell’s distribution for d=1,2,3 spatial dimensions and pointed to an invariant temperature. In this work, we argue an invariant temperature naturally follows from manifest covariance. We present a derivation of the manifestly covariant Jüttner’s distribution and equipartition theorem. The standard procedure to get the equilibrium distribution as a solution of the relativistic Boltzmann’s equation, which holds for dilute gases, is here adopted. However, contrary to previous analysis, we use Cartesian coordinates in d+1 momentum space, with d spatial components. The use of the multiplication theorem of Bessel functions turns crucial to regain the known invariant form of Jüttner’s distribution. Since equilibrium kinetic-theory results should agree with thermodynamics in the comoving frame to the gas the covariant pseudonorm of a vector entering the distribution can be identified with the reciprocal of temperature in such comoving frame. Then by combining the covariant statistical moments of Jüttner’s distribution a form of the equipartition theorem is advanced which also accommodates the invariant comoving temperature and it contains, as a particular case, a previous not manifestly covariant form.
Sharp-front wave of strong magnetic field diffusion in solid metal
NASA Astrophysics Data System (ADS)
Xiao, Bo; Gu, Zhuo-wei; Kan, Ming-xian; Wang, Gang-hua; Zhao, Jian-heng
2016-08-01
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.
Transient global amnesia with post-hyperventilation temporal sharp waves--a case report.
Jeong, Hye Seon; Moon, Jeong Soo; Baek, In Chul; Lee, Ae Young; Kim, Jae Moon
2010-11-01
We report a 55-year-old woman, who presented with transient amnesia for 7h following underwater swimming. There was no evidence of neurological disturbance except global amnesia. Sharp waves in both temporal regions were registered during the initial EEG recording, which was accentuated by hyperventilation. Right hippocampal high signal intensity was observed in DWI performed 56 h after symptom onset. The sharp waves were all disappeared on follow-up EEG recordings. PMID:20951337
Noble gases in the Bells (C2) and Sharps (H3) chondrites
NASA Astrophysics Data System (ADS)
Zadnik, M. G.
1985-06-01
The Bells and Sharps chondrites are of uncertain classification in virtue of their mineralogical and chemical peculiarities, prompting the present elemental and isotopic measurements of the noble gases in them, together with such quantities derivable from them as cosmogenic exposure and gas retention ages, as well as primordial gas contents. The radiogenic and, above all, the cosmogenic gases link Bells to the C2 group, while Sharps is found to lie in the second largest peak of the H-chondrite distribution.
CD-SEM tool stability and tool-to-tool matching management using image sharpness monitor
NASA Astrophysics Data System (ADS)
Abe, Hideaki; Ishibashi, Yasuhiko; Yamazaki, Yuichiro; Kono, Akemi; Maeda, Tatsuya; Miura, Akihiro; Koshihara, Shunsuke; Hibino, Daisuke
2009-03-01
As device feature size reduction continues, requirements for Critical Dimension (CD) metrology tools are becoming stricter. For sub-32 nm node, it is important to establish a CD-SEM tool management system with higher sensitivity for tool fluctuation and short Turn around Time (TAT). We have developed a new image sharpness monitoring method, PG monitor. The key feature of this monitoring method is the quantification of tool-induced image sharpness deterioration. The image sharpness index is calculated by a convolution method of image sharpness deterioration function caused by SEM optics feature. The sensitivity of this methodology was tested by the alteration of the beam diameter using astigmatism. PG monitor result can be related to the beam diameter variation that causes CD variation through image sharpness. PG monitor can detect the slight image sharpness change that cannot be noticed by engineer's visual check. Furthermore, PG monitor was applied to tool matching and long-term stability monitoring for multiple tools. As a result, PG monitor was found to have sufficient sensitivity to CD variation in tool matching and long-term stability assessment. The investigation showed that PG monitor can detect CD variation equivalent to ~ 0.1 nm. The CD-SEM tool management system using PG monitor is effective for CD metrology in production.
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.
Code of Federal Regulations, 2013 CFR
2013-01-01
... children that by reason of their functional purpose necessarily present the hazard of sharp metal or glass... sharp metal or glass edge in toys and other articles intended for use by children under 8 years of age... intended for use by children under 8 years of age. (a) Objective. The sharp edge test method prescribed...
Code of Federal Regulations, 2011 CFR
2011-01-01
... children that by reason of their functional purpose necessarily present the hazard of sharp metal or glass... sharp metal or glass edge in toys and other articles intended for use by children under 8 years of age... intended for use by children under 8 years of age. (a) Objective. The sharp edge test method prescribed...
Code of Federal Regulations, 2014 CFR
2014-01-01
... children that by reason of their functional purpose necessarily present the hazard of sharp metal or glass... sharp metal or glass edge in toys and other articles intended for use by children under 8 years of age... intended for use by children under 8 years of age. (a) Objective. The sharp edge test method prescribed...
Code of Federal Regulations, 2010 CFR
2010-01-01
... children that by reason of their functional purpose necessarily present the hazard of sharp metal or glass... sharp metal or glass edge in toys and other articles intended for use by children under 8 years of age... intended for use by children under 8 years of age. (a) Objective. The sharp edge test method prescribed...
77 FR 52061 - Notice of Proposed Exemption Involving Sharp HealthCare Located in San Diego, CA
Federal Register 2010, 2011, 2012, 2013, 2014
2012-08-28
... Benefits Security Administration Notice of Proposed Exemption Involving Sharp HealthCare Located in San... involve the Sharp HealthCare Health and Dental Plan (the Plan). The proposed exemption, if granted, would... does not reflect the views of the Department. 1. Background Sharp is an integrated health care...
Sharp Contradiction for Local-Hidden-State Model in Quantum Steering.
Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar
2016-01-01
In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell's nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR's original scenario is "steering", i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox. PMID:27562658
Sharp Contradiction for Local-Hidden-State Model in Quantum Steering
Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar
2016-01-01
In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell’s nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR’s original scenario is “steering”, i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox. PMID:27562658
Simulating sharp geometric features in six degrees-of-freedom haptic rendering.
Yu, Ge; Wang, Dangxiao; Zhang, Yuru; Xiao, Jing
2015-01-01
It is a challenging problem to achieve six degree-of-freedom (DoF) haptic simulation of subtle force feelings caused by contacts at sharp geometric features in multi-region contact scenarios. We design a novel sphere-tree model for objects with sharp features and use a configuration-based optimization method to compute feedback force and torque. Given a triangle mesh of an object, a sphere-tree model is created based on dihedral angles between pairs of adjacent triangles. The model consists of a hierarchical sphere-tree for global shape and a linked-list of spheres for local areas with sharp features. In each local area with a sharp edge, we first identify those spheres with radii greater than an upper limit determined by the dihedral angle of the edge. Those spheres are further divided into a linear list of smaller spheres by a splitting method. The experiment results from a cylinder-cube interaction validate that the proposed method can simulate subtle force direction changes when an object slides across sharp edges. Perception-based experiments and a haptic-to-vision shape matching task are also used to compare the performance between our proposed method and other rendering methods. The comparison results show that our method is more effective in simulating sharp features both in terms of measured force signals and human subjective evaluation. Non-penetration among objects is maintained for multi-region contact scenarios. The haptic rendering rate is about 1 kHz, and the subtle force feeling of sliding along sharp features can be stably simulated. PMID:25532133