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.
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…
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.
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)
''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…
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.
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
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
ERIC Educational Resources Information Center
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…
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.
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)
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
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.
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.
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.
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.)
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.
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…
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.}
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…
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.
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.)
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…
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
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.
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.
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.
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.
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
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.
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 ...
SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN vSHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN SHARP OBLIQUE PERSPECTIVE OF DECK AND APPROACH SPANS ALONG WITH PRINCIPLE CANTILEVER SPAN - Snake River Bridge at Lyons' Ferry, State Route 261 spanning Snake River, Starbuck, Columbia County, WA
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 ...
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…
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…
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.
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…
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.
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…
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).
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.
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
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.
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.
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.
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).
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
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
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
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.
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…
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.
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
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.
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.
[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
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...
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.
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
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.
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.
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.
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.
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.
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.
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
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 ...
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.
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.
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.
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.
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…
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
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.
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.
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.
NASA-Ames Summer High School Apprenticeship Research Program (SHARP)
NASA Technical Reports Server (NTRS)
Powell, P.
1983-01-01
The function of SHARP is to recognize high school juniors who have demonstrated unusually high promise for sucess in mathemtics and science. Twenty academically talented students who will be seniors in high school in September were chosen to participate in SHARP 83. Mentors were selected to provide students with first-hand experiences in a research and development environment in order that each student might try out his or her tentative professional career choice. Some special features of SHARP included field trips to private industries doing similar and related research, special lectures on topics of research here at ARC, individual and group counseling sessions, written research papers and oral reports, and primarily the opportunity to be exposed to the present frontiers in space exploration and research. The long-range goal of SHARP is to contribute to the future recruitment of needed scientists and engineers. This final report is summary of all the phases of the planning and implemenation of the 1983 Summer High School Apprenticeship Research Program (SHARP).
Investigation of micromixing by acoustically oscillated sharp-edges.
Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco
2016-03-01
Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel. PMID:27158292
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.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-01-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571
Aging and nonergodicity beyond the Khinchin theorem
Burov, S.; Metzler, R.; Barkai, E.
2010-01-01
The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin’s theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics. PMID:20624984
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).
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
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 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.
Tests of the lattice index theorem
Jordan, Gerald; Hoellwieser, Roman; Faber, Manfried; Heller, Urs M.
2008-01-01
We investigate the lattice index theorem and the localization of the zero modes for thick classical center vortices. For nonorientable spherical vortices, the index of the overlap Dirac operator differs from the topological charge although the traces of the plaquettes deviate only by a maximum of 1.5% from trivial plaquettes. This may be related to the fact that even in Landau gauge some links of these configuration are close to the nontrivial center elements.
Volume integral theorem for exotic matter
Nandi, Kamal Kanti; Zhang Yuanzhong; Kumar, K.B. Vijaya
2004-12-15
We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well-known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.
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.
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.
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.
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.
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.
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
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.
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,…
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
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.
[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
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
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.
Extending Bell's Theorem: Ruling out Paramater Independent Hidden Variable Theories
NASA Astrophysics Data System (ADS)
Leegwater, G. J.
2016-03-01
Bell's Theorem may well be the best known result in the foundations of quantum mechanics. Here, it is presented as stating that for any hidden variable theory the combination of the conditions Parameter Independence, Outcome Independence, Source Independence and Compatibility with Quantum Theory leads to a contradiction. Based on work by Roger Colbeck and Renato Renner, an extension of Bell's Theorem is considered. In this extension the theorem is strengthened by replacing Outcome Independence by a strictly weaker condition.
A Converse of the Mean Value Theorem Made Easy
ERIC Educational Resources Information Center
Mortici, Cristinel
2011-01-01
The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…
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.
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.
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.
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.
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.``
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.
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 .