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
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…
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.
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…
Central limit theorems under special relativity
McKeague, Ian W.
2015-01-01
Several relativistic extensions of the Maxwell–Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior. PMID:25798020
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.
Local theorems for nonidentically distributed lattice random variables.
NASA Technical Reports Server (NTRS)
Mason, J. D.
1972-01-01
Derivation of local limit theorems for a sequence X sub n of independent integral-valued lattice random variables involving only a finite number of distinct nondegenerate distributions. Given appropriate sequences A sub n and B sub n of constants such that 1/B sub n (X sub 1 +
Randomized central limit theorems: A unified theory
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
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).
Central limit theorem for reducible and irreducible open quantum walks
NASA Astrophysics Data System (ADS)
Sadowski, Przemysław; Pawela, Łukasz
2016-07-01
In this work we aim at proving central limit theorems for open quantum walks on {mathbb {Z}}^d. We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.
Central limit theorem for reducible and irreducible open quantum walks
NASA Astrophysics Data System (ADS)
Sadowski, Przemysław; Pawela, Łukasz
2016-04-01
In this work we aim at proving central limit theorems for open quantum walks on {{Z}}^d . We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.
Some functional limit theorems for compound Cox processes
NASA Astrophysics Data System (ADS)
Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.
2016-06-01
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
From Einstein's theorem to Bell's theorem: a history of quantum non-locality
NASA Astrophysics Data System (ADS)
Wiseman, H. M.
2006-04-01
In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.
Improving Conceptions in Analytical Chemistry: The Central Limit Theorem
ERIC Educational Resources Information Center
Rodriguez-Lopez, Margarita; Carrasquillo, Arnaldo, Jr.
2006-01-01
This article describes the central limit theorem (CLT) and its relation to analytical chemistry. The pedagogic rational, which argues for teaching the CLT in the analytical chemistry classroom, is discussed. Some analytical chemistry concepts that could be improved through an understanding of the CLT are also described. (Contains 2 figures.)
Extremely localized nonorthogonal orbitals by the pairing theorem.
Zoboki, T; Mayer, I
2011-03-01
Using the concepts of Löwdin pairing theorem, a method is developed to calculate extremely localized, but nonorthogonal, sets of molecular orbitals and their strictly localized counterparts. The method is very suitable to study to what extent a given model of bonding in a given molecule can be considered adequate from the point of view of the actual LCAO-MO (Hartree Fock or DFT) wave function and is expected to be useful for doing local approximations of electron correlation. PMID:20941738
FAST TRACK COMMUNICATION: Central limit theorem and deformed exponentials
NASA Astrophysics Data System (ADS)
Vignat, C.; Plastino, A.
2007-11-01
The central limit theorem (CLT) can be ranked among the most important ones in probability theory and statistics and plays an essential role in several basic and applied disciplines, notably in statistical thermodynamics. We show that there exists a natural extension of the CLT from exponentials to so-called deformed exponentials (also denoted as q-Gaussians). Our proposal applies exactly in the usual conditions in which the classical CLT is used.
On the quenched central limit theorem for random dynamical systems
NASA Astrophysics Data System (ADS)
Abdelkader, Mohamed; Aimino, Romain
2016-06-01
We provide a necessary and sufficient condition under which the quenched central limit theorem without random centering holds for one-dimensional random systems that are uniformly expanding. This condition holds in particular when all the maps preserve a common measure. We also give a counter example which shows that this condition is not necessarily satisfied when the maps do not preserve a common measure.
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.
Central Limit Theorems for the Shrinking Target Problem
NASA Astrophysics Data System (ADS)
Haydn, Nicolai; Nicol, Matthew; Vaienti, Sandro; Zhang, Licheng
2013-12-01
Suppose B i := B( p, r i ) are nested balls of radius r i about a point p in a dynamical system ( T, X, μ). The question of whether T i x∈ B i infinitely often (i.o.) for μ a.e. x is often called the shrinking target problem. In many dynamical settings it has been shown that if diverges then there is a quantitative rate of entry and for μ a.e. x∈ X. This is a self-norming type of strong law of large numbers. We establish self-norming central limit theorems (CLT) of the form (in distribution) for a variety of hyperbolic and non-uniformly hyperbolic dynamical systems, the normalization constants are . Dynamical systems to which our results apply include smooth expanding maps of the interval, Rychlik type maps, Gibbs-Markov maps, rational maps and, in higher dimensions, piecewise expanding maps. For such central limit theorems the main difficulty is to prove that the non-stationary variance has a limit in probability.
Central Limit Theorem: New SOCR Applet and Demonstration Activity
Dinov, Ivo D.; Christou, Nicolas; Sanchez, Juana
2011-01-01
Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multifaceted learning environments, which may facilitate student comprehension and information retention. In this manuscript, we describe one such innovative effort of using technological tools for improving student motivation and learning of the theory, practice and usability of the Central Limit Theorem (CLT) in probability and statistics courses. Our approach is based on harnessing the computational libraries developed by the Statistics Online Computational Resource (SOCR) to design a new interactive Java applet and a corresponding demonstration activity that illustrate the meaning and the power of the CLT. The CLT applet and activity have clear common goals; to provide graphical representation of the CLT, to improve student intuition, and to empirically validate and establish the limits of the CLT. The SOCR CLT activity consists of four experiments that demonstrate the assumptions, meaning and implications of the CLT and ties these to specific hands-on simulations. We include a number of examples illustrating the theory and applications of the CLT. Both the SOCR CLT applet and activity are freely available online to the community to test, validate and extend (Applet: http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and Activity: http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem). PMID:21833159
Central Limit Theorem: New SOCR Applet and Demonstration Activity.
Dinov, Ivo D; Christou, Nicolas; Sanchez, Juana
2008-07-01
Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multifaceted learning environments, which may facilitate student comprehension and information retention. In this manuscript, we describe one such innovative effort of using technological tools for improving student motivation and learning of the theory, practice and usability of the Central Limit Theorem (CLT) in probability and statistics courses. Our approach is based on harnessing the computational libraries developed by the Statistics Online Computational Resource (SOCR) to design a new interactive Java applet and a corresponding demonstration activity that illustrate the meaning and the power of the CLT. The CLT applet and activity have clear common goals; to provide graphical representation of the CLT, to improve student intuition, and to empirically validate and establish the limits of the CLT. The SOCR CLT activity consists of four experiments that demonstrate the assumptions, meaning and implications of the CLT and ties these to specific hands-on simulations. We include a number of examples illustrating the theory and applications of the CLT. Both the SOCR CLT applet and activity are freely available online to the community to test, validate and extend (Applet: http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and Activity: http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem). PMID:21833159
Continuous-variable entanglement distillation and noncommutative central limit theorems
NASA Astrophysics Data System (ADS)
Campbell, Earl T.; Genoni, Marco G.; Eisert, Jens
2013-04-01
Entanglement distillation transforms weakly entangled noisy states into highly entangled states, a primitive to be used in quantum repeater schemes and other protocols designed for quantum communication and key distribution. In this work, we present a comprehensive framework for continuous-variable entanglement distillation schemes that convert noisy non-Gaussian states into Gaussian ones in many iterations of the protocol. Instances of these protocols include (a) the recursive-Gaussifier protocol, (b) the temporally reordered recursive-Gaussifier protocol, and (c) the pumping-Gaussifier protocol. The flexibility of these protocols gives rise to several beneficial trade-offs related to success probabilities or memory requirements, which can be adjusted to reflect experimental demands. Despite these protocols involving measurements, we relate the convergence in this protocol to new instances of noncommutative central limit theorems, in a formalism that we lay out in great detail. Implications of the findings for quantum repeater schemes are discussed.
Planetary Accretion, Oxygen Isotopes and the Central Limit Theorem
NASA Technical Reports Server (NTRS)
Nuth, Joseph A., III; Hill, Hugh G. M.; Vondrak, Richard R. (Technical Monitor)
2001-01-01
The accumulation of presolar dust into increasingly larger aggregates (CAIs and Chondrules, Asteroids, Planets) should result in a very drastic reduction in the numerical spread in oxygen isotopic composition between bodies of similar size, in accord with the Central Limit Theorem. Observed variations in oxygen isotopic composition are many orders of magnitude larger than would be predicted by a simple, random accumulation model that begins in a well-mixed nebula - no matter which size-scale objects are used as the beginning or end points of the calculation. This discrepancy implies either that some as yet unspecified process acted on the solids in the Solar Nebula to increase the spread in oxygen isotopic composition during each and every stage of accumulation or that the nebula was heterogeneous and maintained this heterogeneity throughout most of nebular history. Large-scale nebular heterogeneity would have significant consequences for many areas of cosmochemistry, including the application of some well-known isotopic systems to the dating of nebular events or the prediction of bulk compositions of planetary bodies on the basis of a uniform cosmic abundance.
Finiteness theorems for limit cycles: a digest of the revised proof
NASA Astrophysics Data System (ADS)
Ilyashenko, Yu S.
2016-02-01
This is the first paper in a series of two presenting a digest of the proof of the finiteness theorem for limit cycles of a planar polynomial vector field. At the same time we sketch the proof of the following two theorems: an analogous result for analytic vector fields, and a description of the asymptotics of the monodromy transformation for polycycles of such fields.
The Free Will Theorem and Limits on Realistic Theories
NASA Astrophysics Data System (ADS)
Godfrey, Christopher
2010-03-01
The rGRWf model (Tumulka 2006) is a proposed solution of the measurement problem of quantum mechanics involving a stochastic nonlinear wave equation embedded in a relativistic framework. Its primary feature is a mechanism that suppresses superpositions of macroscopically different states for macroscopic systems. However, the Free Will Theorem (FWT) proposed by Conway and Kochen (Conway and Kochen 2007, 2009) purports to prove that no theory that is both non-deterministic and relativistic can reproduce all possible measurement results on a system of two entangled spin-one particles. Here we examine both the rGRWf model and the FWT. It is demonstrated that underlying assumptions in the postulates of the FWT rule out certain classes of realistic physical theories. These underlying assumptions and the characteristics of physical theories permitted by the FWT axioms are discussed.
The Implicit Function Theorem and Non-Existence of Limit of Functions of Several Variables
ERIC Educational Resources Information Center
dos Santos, A. L. C.; da Silva, P. N.
2008-01-01
We use the Implicit Function Theorem to establish a result of non-existence of limit to a certain class of functions of several variables. We consider functions given by quotients such that both the numerator and denominator functions are null at the limit point. We show that the non-existence of the limit of such function is related with the…
Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices
NASA Astrophysics Data System (ADS)
Benaych-Georges, Florent; Guionnet, Alice; Male, Camille
2014-07-01
We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.
Central Limit Theorems and Uniform Laws of Large Numbers for Arrays of Random Fields
Jenish, Nazgul; Prucha, Ingmar R.
2009-01-01
Over the last decades, spatial-interaction models have been increasingly used in economics. However, the development of a sufficiently general asymptotic theory for nonlinear spatial models has been hampered by a lack of relevant central limit theorems (CLTs), uniform laws of large numbers (ULLNs) and pointwise laws of large numbers (LLNs). These limit theorems form the essential building blocks towards developing the asymptotic theory of M-estimators, including maximum likelihood and generalized method of moments estimators. The paper establishes a CLT, ULLN, and LLN for spatial processes or random fields that should be applicable to a broad range of data processes. PMID:20161289
The Power of Doing: A Learning Exercise That Brings the Central Limit Theorem to Life
ERIC Educational Resources Information Center
Price, Barbara A.; Zhang, Xiaolong
2007-01-01
This article demonstrates an active learning technique for teaching the Central Limit Theorem (CLT) in an introductory undergraduate business statistics class. Groups of students carry out one of two experiments in the lab, tossing a die in sets of 5 rolls or tossing a die in sets of 10 rolls. They are asked to calculate the sample average of each…
NASA Astrophysics Data System (ADS)
Biskup, M.; Salvi, M.; Wolff, T.
2014-06-01
Given a resistor network on with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central limit theorem holds. The proof is based on the corrector method and the Martingale Central Limit Theorem; a key integrability condition is furnished by the Meyers estimate. More general domains, boundary conditions and ellipticity contrasts will be addressed in a subsequent paper.
The random-motion theorem in a local cosmology with dark energy
NASA Astrophysics Data System (ADS)
Chernin, A. D.; Dolgachev, V. P.; Domozhilova, L. M.; Teerikorpi, P.; Valtonen, M. Yu.
2010-03-01
It is shown that the random-motion theorem in cosmology proven in the early 1960s can be generalized to take into account the presence of a uniform dark-energy background. The role of the dark energy is substantial: its repulsive force exceeds the gravitational force due to darkmatter and baryons, both on the scale of the Universe as a whole and on local scales of about 1 Mpc. The generalized random-motion theorem has the form of a differential equation relating the kinetic energy of the random motion and the potential energy of the particles due to their own gravitational field and the repulsive dark-energy field. One consequence of the generalized theorem is a virial relation containing the potential energy in the repulsive field.
Zipf's law is not a consequence of the central limit theorem
NASA Astrophysics Data System (ADS)
Troll, G.; Beim Graben, P.
1998-02-01
It has been observed that the rank statistics of string frequencies of many symbolic systems (e.g., word frequencies of natural languages) follows Zipf's law in good approximation. We show that, contrary to claims in the literature, Zipf's law cannot be realized by the central limit theorem(s). The observation that a log-normal distribution of string frequencies yields an approximately Zipf-like rank statistics is actually misleading. Indeed, Zipf's law for the rank statistics is strictly equivalent to a power law distribution of frequencies. There are two natural ways to perform the infinite size limit for the vocabulary. The first one is the method of choice in the literature; it makes the upper word length bound tend to infinity and leads in the case of a multistate Bernoulli process via a central limit theorem to a log-normal frequency distribution. An alternative and for text samples actually better realizable way is to make the lower frequency bound tend to zero. This limit procedure leads to a power law distribution and hence to Zipf's law-at least for Bernoulli processes and to a very good approximation for natural languages where it passes the χ2 test. For the Bernoulli case we will give a heuristic proof.
Limit theorems in the imitative monomer-dimer mean-field model via Stein's method
NASA Astrophysics Data System (ADS)
Chen, Wei-Kuo
2016-08-01
We consider the imitative monomer-dimer model on the complete graph introduced in the work of Alberici et al. [J. Math. Phys. 55, 063301-1-063301-27 (2014)]. It was shown that this model is described by the monomer density and has a phase transition along certain coexistence curve, where the monomer and dimer phases coexist. More recently, it was understood [D. Alberici et al., Commun. Math. Phys. (published online, 2016)] that the monomer density exhibits the central limit theorem away from the coexistence curve and enjoys a non-normal limit theorem at criticality with normalized exponent 3/4. By reverting the model to a weighted Curie-Weiss model with hard core interaction, we establish the complete description of the fluctuation properties of the monomer density on the full parameter space via Stein's method of exchangeable pairs. Our approach recovers what were established in the work of Alberici et al. [Commun. Math. Phys. (published online, 2016)] and furthermore allows to obtain the conditional central limit theorems along the coexistence curve. In all these results, the Berry-Esseen inequalities for the Kolmogorov-Smirnov distance are given.
Day, Troy
2012-04-01
The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century, there have been remarkable advances in the development of theory for this diversification, and the theory's success rests, in part, on the scope of its applicability. A great deal of this theory focuses on a relatively small subset of the space of potential genotypes, chosen largely based on historical or contemporary patterns, and then predicts the evolutionary dynamics within this pre-defined set. To what extent can such an approach be pushed to a broader perspective that accounts for the potential open-endedness of evolutionary diversification? There have been a number of significant theoretical developments along these lines but the question of how far such theory can be pushed has not been addressed. Here a theorem is proven demonstrating that, because of the digital nature of inheritance, there are inherent limits on the kinds of questions that can be answered using such an approach. In particular, even in extremely simple evolutionary systems, a complete theory accounting for the potential open-endedness of evolution is unattainable unless evolution is progressive. The theorem is closely related to Gödel's incompleteness theorem, and to the halting problem from computability theory. PMID:21849390
Day, Troy
2012-01-01
The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century, there have been remarkable advances in the development of theory for this diversification, and the theory's success rests, in part, on the scope of its applicability. A great deal of this theory focuses on a relatively small subset of the space of potential genotypes, chosen largely based on historical or contemporary patterns, and then predicts the evolutionary dynamics within this pre-defined set. To what extent can such an approach be pushed to a broader perspective that accounts for the potential open-endedness of evolutionary diversification? There have been a number of significant theoretical developments along these lines but the question of how far such theory can be pushed has not been addressed. Here a theorem is proven demonstrating that, because of the digital nature of inheritance, there are inherent limits on the kinds of questions that can be answered using such an approach. In particular, even in extremely simple evolutionary systems, a complete theory accounting for the potential open-endedness of evolution is unattainable unless evolution is progressive. The theorem is closely related to Gödel's incompleteness theorem, and to the halting problem from computability theory. PMID:21849390
Non-normalizable densities in strong anomalous diffusion: beyond the central limit theorem.
Rebenshtok, Adi; Denisov, Sergey; Hänggi, Peter; Barkai, Eli
2014-03-21
Strong anomalous diffusion, where ⟨|x(t)|(q)⟩ ∼ tqν(q) with a nonlinear spectrum ν(q) ≠ const, is wide spread and has been found in various nonlinear dynamical systems and experiments on active transport in living cells. Using a stochastic approach we show how this phenomenon is related to infinite covariant densities; i.e., the asymptotic states of these systems are described by non-normalizable distribution functions. Our work shows that the concept of infinite covariant densities plays an important role in the statistical description of open systems exhibiting multifractal anomalous diffusion, as it is complementary to the central limit theorem. PMID:24702341
Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks
NASA Astrophysics Data System (ADS)
Pigeon, Simon; Fusco, Lorenzo; Xuereb, André; De Chiara, Gabriele; Paternostro, Mauro
2016-01-01
We present a general method to undertake a thorough analysis of the thermodynamics of the quantum jump trajectories followed by an arbitrary quantum harmonic network undergoing linear and bilinear dynamics. The approach is based on the phase-space representation of the state of a harmonic network. The large deviation function associated with this system encodes the full counting statistics of exchange and also allows one to deduce fluctuation theorems (FTs) obeyed by the dynamics. We illustrate the method showing the validity of a local FT about the exchange of excitations between a restricted part of the environment (i.e., a local bath) and a harmonic network coupled with different schemes.
Influence of global correlations on central limit theorems and entropic extensivity
NASA Astrophysics Data System (ADS)
Marsh, John A.; Fuentes, Miguel A.; Moyano, Luis G.; Tsallis, Constantino
2006-12-01
We consider probabilistic models of N identical distinguishable, binary random variables. If these variables are strictly or asymptotically independent, then, for N→∞, (i) the attractor in distribution space is, according to the standard central limit theorem, a Gaussian, and (ii) the Boltzmann-Gibbs-Shannon entropy S≡-∑i=1Wpln pi (where W=2 N) is extensive, meaning that S BGS( N)∼ N. If these variables have any nonvanishing global (i.e., not asymptotically independent) correlations, then the attractor deviates from the Gaussian. The entropy appears to be more robust, in the sense that, in some cases, SBGS remains extensive even in the presence of strong global correlations. In other cases, however, even weak global correlations make the entropy deviate from the normal behavior. More precisely, in such cases the entropic form Sq≡{1}/{q-1} (1-∑i=1Wpiq) (with S 1tbnd6 S BGS) can become extensive for some value of q≠1. This scenario is illustrated with several new as well as previously described models. The discussion illuminates recent progress into q-describable nonextensive probabilistic systems, and the conjectured q-Central Limit Theorem ( q-CLT) which posses a q-Gaussian attractor.
Sanov and central limit theorems for output statistics of quantum Markov chains
Horssen, Merlijn van; Guţă, Mădălin
2015-02-15
In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Such higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.
Theorems and Application of Local Activity of CNN with Five State Variables and One Port
Xiong, Gang; Dong, Xisong; Xie, Li; Yang, Thomas
2012-01-01
Coupled nonlinear dynamical systems have been widely studied recently. However, the dynamical properties of these systems are difficult to deal with. The local activity of cellular neural network (CNN) has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice, which is composed of coupled cells. In this paper, the analytical criteria for the local activity in reaction-diffusion CNN with five state variables and one port are presented, which consists of four theorems, including a serial of inequalities involving CNN parameters. These theorems can be used for calculating the bifurcation diagram to determine or analyze the emergence of complex dynamic patterns, such as chaos. As a case study, a reaction-diffusion CNN of hepatitis B Virus (HBV) mutation-selection model is analyzed and simulated, the bifurcation diagram is calculated. Using the diagram, numerical simulations of this CNN model provide reasonable explanations of complex mutant phenomena during therapy. Therefore, it is demonstrated that the local activity of CNN provides a practical tool for the complex dynamics study of some coupled nonlinear systems. PMID:22611440
The Star Forming Main Sequence and its Scatter as Conequences of the Central Limit Theorem
NASA Astrophysics Data System (ADS)
Kelson, Daniel
2015-01-01
Star formation rates of disk galaxies strongly correlate with stellar mass, with a small dispersion in specific star formation rate at fixed mass. With such small scattter this main sequence of star formation has been interpreted as deterministic and fundamental. Here it is demonstrated that it is a simple consequence off he central limit theorem. Treating the star formation histories of galaxies as integrable, non-differentiable functions, where stochastic changes in star formation rate in a galaxy's history are not fully independent of each other, we derive the median specific star formation rate for the flat part of the main sequence from 0
Central limit theorem for a class of globally correlated random variables
NASA Astrophysics Data System (ADS)
Budini, Adrián A.
2016-06-01
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in the presence of strong correlations between the added random contributions. Here, we study this problem for similar interchangeable globally correlated random variables. Under these conditions, a hierarchical set of equations is derived for the conditional transition probabilities. This result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables. Depending on the correlation mechanisms and statistics of the single variables, the corresponding sums are characterized by distinct probability densities. For a class of urn models it is also possible to characterize their domain of attraction, which, as in the standard case, is parametrized by the probability density of each random variable. Symmetric and asymmetric q -Gaussian attractors (q <1 ) arise in a particular two-state case of these urn models.
A central-limit theorem for a single-false match rate
NASA Astrophysics Data System (ADS)
Dietz, Zachariah; Schuckers, Michael E.
2010-04-01
In this paper, we present a central limit theorem (CLT) for the estimation of a false match rate for a single matching system. The false match rate is often a significant factor in an evaluation of such a matching system. To achieve the main result here we utilize the covariance/correlation structure for matching proposed by Schuckers. Along with the main result we present an illustration of the methodology here on biometric authentication data from Ross and Jain. This illustration is from resampling match decisions on three different biometric modalities: hand geometry, fingerprint and facial recognition and shows that as the number of matching pairs grows the sampling distribution for an FMR approaches a Gaussian distribution. These results suggest that statistical inference for a FMR based upon a Gaussian distribution is appropriate.
Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs
NASA Astrophysics Data System (ADS)
Roychoudhuri, Chandrasekhar
2007-09-01
We celebrate the two hundred years of successful use of the Fourier theorem in optics. However, there is a great enigma associated with the Fourier transform integral. It is one of the most pervasively productive and useful tool of physics and optics because its foundation is based on the superposition of harmonic functions and yet we have never declared it as a principle of physics for valid reasons. And, yet there are a good number of situations where we pretend it to be equivalent to the superposition principle of physics, creating epistemological problems of enormous magnitude. The purpose of the paper is to elucidate the problems while underscoring the successes and the elegance of the Fourier theorem, which are not explicitly discussed in the literature. We will make our point by taking six major engineering fields of optics and show in each case why it works and under what restricted conditions by bringing in the relevant physics principles. The fields are (i) optical signal processing, (ii) Fourier transform spectrometry, (iii) classical spectrometry of pulsed light, (iv) coherence theory, (v) laser mode locking and (vi) pulse broadening. We underscore that mathematical Fourier frequencies, not being physical frequencies, cannot generate real physical effects on our detectors. Appreciation of this fundamental issue will open up ways to be innovative in many new optical instrument designs. We underscore the importance of always validating our design platforms based on valid physics principles (actual processes undergoing in nature) captured by an appropriate hypothesis based on diverse observations. This paper is a comprehensive view of the power and limitations of Fourier Transform by summarizing a series of SPIE conference papers presented during 2003-2007.
ERIC Educational Resources Information Center
Yu, Chong Ho; And Others
Central limit theorem (CLT) is considered an important topic in statistics, because it serves as the basis for subsequent learning in other crucial concepts such as hypothesis testing and power analysis. There is an increasing popularity in using dynamic computer software for illustrating CLT. Graphical displays do not necessarily clear up…
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.
ERIC Educational Resources Information Center
Moen, David H.; Powell, John E.
2008-01-01
Using Microsoft® Excel, several interactive, computerized learning modules are developed to illustrate the Central Limit Theorem's appropriateness for comparing the difference between the means of any two populations. These modules are used in the classroom to enhance the comprehension of this theorem as well as the concepts that provide the…
THE LOCAL LIMIT OF GLOBAL GYROKINETIC SIMULATIONS
CANDY J; WALTZ RE; DORLAND W
2003-10-01
OAK-B135 Global gyrokinetic simulations of turbulence include physical effects that are not retained in local flux-tube simulations. nevertheless, in the limit of sufficiently small {rho}* (gyroradius compared to system size) it is expected that a local simulation should agree with a global one (at the local simulation radius) since all effects that are dropped in the local simulations are expected to vanish as {rho}* {yields} 0. In this note, global simulations of a well-established test case are indeed shown to recover the flux-tube limit at each radius.
NASA Astrophysics Data System (ADS)
Salgado-García, R.; Maldonado, Cesar
2013-12-01
We study the diffusion of an ensemble of overdamped particles sliding over a tilted random potential (produced by the interaction of a particle with a random polymer) with long-range correlations. We found that the diffusion properties of such a system are closely related to the correlation function of the corresponding potential. We model the substrate as a symbolic trajectory of a shift space which enables us to obtain a general formula for the diffusion coefficient when normal diffusion occurs. The total time that the particle takes to travel through n monomers can be seen as an ergodic sum to which we can apply the central limit theorem. The latter can be implemented if the correlations decay fast enough in order for the central limit theorem to be valid. On the other hand, we presume that when the central limit theorem breaks down the system give rise to anomalous diffusion. We give two examples exhibiting a transition from normal to anomalous diffusion due to this mechanism. We also give analytical expressions for the diffusion exponents in both cases by assuming convergence to a stable law. Finally we test our predictions by means of numerical simulations.
Salgado-García, R; Maldonado, Cesar
2013-12-01
We study the diffusion of an ensemble of overdamped particles sliding over a tilted random potential (produced by the interaction of a particle with a random polymer) with long-range correlations. We found that the diffusion properties of such a system are closely related to the correlation function of the corresponding potential. We model the substrate as a symbolic trajectory of a shift space which enables us to obtain a general formula for the diffusion coefficient when normal diffusion occurs. The total time that the particle takes to travel through n monomers can be seen as an ergodic sum to which we can apply the central limit theorem. The latter can be implemented if the correlations decay fast enough in order for the central limit theorem to be valid. On the other hand, we presume that when the central limit theorem breaks down the system give rise to anomalous diffusion. We give two examples exhibiting a transition from normal to anomalous diffusion due to this mechanism. We also give analytical expressions for the diffusion exponents in both cases by assuming convergence to a stable law. Finally we test our predictions by means of numerical simulations. PMID:24483421
The Star-Forming Main Sequence as a Natural Consequence of the Central Limit Theorem
NASA Astrophysics Data System (ADS)
Kelson, Daniel David
2015-08-01
Star-formation rates (SFR) of disk galaxies correlate with stellar mass, with a small dispersion in SSFR at fixed mass, sigma~0.3 dex. With such scatter this star-formation main sequence (SFMS) has been interpreted as deterministic and fundamental. Here I demonstrate that such a correlation arises naturally from the central limit theorem. The derivation begins by approximating in situ stellar mass growth as a stochastic process, much like a random walk, where the expectation of SFR at any time is equal to the SFR at the previous time. The SFRs of real galaxies, however, do not experience wholly random stochastic changes over time, but change in a highly correlated fashion due to the long reach of gravity and the correlation of structure in the universe. We therefore generalize the results for star-formation as a stochastic process that has random correlations over random and potentially infinite timescales. For unbiased samples of (disk) galaxies we derive expectation values for SSFR and its scatter, such that
Occupancy of phase space, extensivity of Sq, and q-generalized central limit theorem
NASA Astrophysics Data System (ADS)
Tsallis, Constantino
2006-06-01
Increasing the number N of elements of a system typically makes the entropy to increase. The question arises on what particular entropic form we have in mind and how it increases with N. Thermodynamically speaking it makes sense to choose an entropy which increases linearly with N for large N, i.e., which is extensive. If the N elements are probabilistically independent (no interactions) or quasi-independent (e.g., short-range interacting), it is known that the entropy which is extensive is that of Boltzmann-Gibbs-Shannon, SBG≡-k∑i=1Wpilnpi. If they are, however, globally correlated (e.g., through long-range interactions), the answer depends on the particular nature of the correlations. There is a large class of correlations (in one way or another related to scale-invariance) for which an appropriate entropy is that on which nonextensive statistical mechanics is based, i.e., Sq≡k(1-∑i=1Wpiq)/q-1 ( S1=SBG), where q is determined by the specific correlations. We briefly review and illustrate these ideas through simple examples of occupation of phase space. A very similar scenario emerges with regard to the central limit theorem (CLT). If the variables that are being summed are independent (or quasi-independent, in the sense that they gradually become independent if N→∞), two basic possibilities exist: if the variance of the random variables that are being composed is finite, the N→∞ attractor in the space of distributions is a Gaussian, whereas if it diverges, it is a Lévy distribution. If the variables that are being summed are however globally correlated, there is no reason to expect the usual CLTs to hold. The N→∞ attractor is expected to depend on the nature of the correlations. That class of correlations (or part of it) that makes Sq to be extensive for q≠1 is expected to have a qe-Gaussian as its N→∞ attractor, where qe depends on q [ qe(q) such that qe(1)=1], and where qe-Gaussians are proportional to [1-(1-qe)β x2] ( β>0; qe<3
NASA Astrophysics Data System (ADS)
Gheorghe, Munteanu Bogdan; Alexei, Leahu; Sergiu, Cataranciuc
2013-09-01
We prove the limit theorem for life time distribution connected with reliability systems when their life time is a Pascal Convolution of independent and identically distributed random variables. We show that, in some conditions, such distributions may be approximated by means of Erlang distributions. As a consequnce, survival functions for such systems may be, respectively, approximated by Erlang survival functions. By using Monte Carlo method we experimantally confirm the theoretical results of our theorem.
The flat Grothendieck-Riemann-Roch theorem without adiabatic techniques
NASA Astrophysics Data System (ADS)
Ho, Man-Ho
2016-09-01
In this paper we give a simplified proof of the flat Grothendieck-Riemann-Roch theorem. The proof makes use of the local family index theorem and basic computations of the Chern-Simons form. In particular, it does not involve any adiabatic limit computation of the reduced eta-invariant.
Resolution limits of ultrafast ultrasound localization microscopy.
Desailly, Yann; Pierre, Juliette; Couture, Olivier; Tanter, Mickael
2015-11-21
As in other imaging methods based on waves, the resolution of ultrasound imaging is limited by the wavelength. However, the diffraction-limit can be overcome by super-localizing single events from isolated sources. In recent years, we developed plane-wave ultrasound allowing frame rates up to 20,000 fps. Ultrafast processes such as rapid movement or disruption of ultrasound contrast agents (UCA) can thus be monitored, providing us with distinct punctual sources that could be localized beyond the diffraction limit. We previously showed experimentally that resolutions beyond λ/10 can be reached in ultrafast ultrasound localization microscopy (uULM) using a 128 transducer matrix in reception. Higher resolutions are theoretically achievable and the aim of this study is to predict the maximum resolution in uULM with respect to acquisition parameters (frequency, transducer geometry, sampling electronics). The accuracy of uULM is the error on the localization of a bubble, considered a point-source in a homogeneous medium. The proposed model consists in two steps: determining the timing accuracy of the microbubble echo in radiofrequency data, then transferring this time accuracy into spatial accuracy. The simplified model predicts a maximum resolution of 40 μm for a 1.75 MHz transducer matrix composed of two rows of 64 elements. Experimental confirmation of the model was performed by flowing microbubbles within a 60 μm microfluidic channel and localizing their blinking under ultrafast imaging (500 Hz frame rate). The experimental resolution, determined as the standard deviation in the positioning of the microbubbles, was predicted within 6 μm (13%) of the theoretical values and followed the analytical relationship with respect to the number of elements and depth. Understanding the underlying physical principles determining the resolution of superlocalization will allow the optimization of the imaging setup for each organ. Ultimately, accuracies better than the size of
Central limit theorem for the solution to the heat equation with moving time
NASA Astrophysics Data System (ADS)
Liu, Junfeng; Tudor, Ciprian A.
2016-03-01
We consider the solution to the stochastic heat equation driven by the time-space white noise and study the asymptotic behavior of its spatial quadratic variations with “moving time”, meaning that the time variable is not fixed and its values are allowed to be very big or very small. We investigate the limit distribution of these variations via Malliavin calculus.
ERIC Educational Resources Information Center
See, Lai-Chu; Huang, Yu-Hsun; Chang, Yi-Hu; Chiu, Yeo-Ju; Chen, Yi-Fen; Napper, Vicki S.
2010-01-01
This study examines the timing using computer-enriched instruction (CEI), before or after a traditional lecture to determine cross-over effect, period effect, and learning effect arising from sequencing of instruction. A 2 x 2 cross-over design was used with CEI to teach central limit theorem (CLT). Two sequences of graduate students in nursing…
Generalised Central Limit Theorems for Growth Rate Distribution of Complex Systems
NASA Astrophysics Data System (ADS)
Takayasu, Misako; Watanabe, Hayafumi; Takayasu, Hideki
2014-04-01
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety of fields can be derived from this basic physical model. Statistical data of growth rates for about 1 million business firms are analysed as a real-world example of randomly growing systems. Not only are the scaling relations consistent with the theoretical solution, but the entire functional form of the growth rate distribution is fitted with a theoretical distribution that has a power-law tail.
Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Wu, Yu-Chun; Wu, Chunfeng; Ye, Xiang-Jun; Żukowski, Marek; Kwek, L C
2015-01-01
We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin's theorem (originally: all pure entangled states violate local realism). Local realism is violated by all mixed states with the above steering property. The new class of states allows one e.g. to perform three party secret sharing with just pairs of entangled qubits, instead of three qubit entanglements (which are currently available with low fidelity). This significantly increases the feasibility of having high performance versions of such protocols. Finally, we discuss some possible applications. PMID:26108704
NASA Astrophysics Data System (ADS)
Lu, Deyu
The adiabatic-connection fluctuation-dissipation theorem (ACFDT) is a formal theoretical framework to treat van der Waals (vdW) dispersion interactions. Under the random phase approximation (RPA), it yields the correct asymptotic behavior at large distances, but the short-range correlation is overestimated. It has been demonstrated that non-local exchange-correlation kernels can systematically correct the errors of RPA for homogenous electron gas. However, direct extension of non-local kernels derived from the electron gas model to inhomogeneous systems raises several issues. In addition to the high computational expense, the non-local kernels worsen the rare gas dimer binding curve as compared to RPA. In this study, we propose a quasi-local approximation of the non-local kernel in order to address these issues. This research used resources of the Center for Functional Nanomaterials, which is a U.S. DOE Office of Science Facility, at Brookhaven National Laboratory under Contract No. DE-SC0012704.
K-means-type algorithms: a generalized convergence theorem and characterization of local optimality.
Selim, S Z; Ismail, M A
1984-01-01
The K-means algorithm is a commonly used technique in cluster analysis. In this paper, several questions about the algorithm are addressed. The clustering problem is first cast as a nonconvex mathematical program. Then, a rigorous proof of the finite convergence of the K-means-type algorithm is given for any metric. It is shown that under certain conditions the algorithm may fail to converge to a local minimum, and that it converges under differentiability conditions to a Kuhn-Tucker point. Finally, a method for obtaining a local-minimum solution is given. PMID:21869168
5 CFR 531.606 - Maximum limits on locality rates.
Code of Federal Regulations, 2010 CFR
2010-01-01
... the pay limitations established in 5 CFR 304.105. (d) A portion of a locality payment that is not... rates. (a) Except as provided by paragraph (b) of this section, a locality rate may not exceed the rate of basic pay payable for level IV of the Executive Schedule. (b)(1) A locality rate for an...
NASA Astrophysics Data System (ADS)
Pluchino, Alessandro; Rapisarda, Andrea; Tsallis, Constantino
2008-05-01
We give a closer look at the Central Limit Theorem (CLT) behavior in quasi-stationary states of the Hamiltonian Mean Field model, a paradigmatic one for long-range-interacting classical many-body systems. We present new calculations which show that, following their time evolution, we can observe and classify three kinds of long-standing quasi-stationary states (QSS) with different correlations. The frequency of occurrence of each class depends on the size of the system. The different microscopic nature of the QSS leads to different dynamical correlations and therefore to different results for the observed CLT behavior.
Kaveh, Kamran; Komarova, Natalia L.; Kohandel, Mohammad
2015-01-01
Evolutionary models on graphs, as an extension of the Moran process, have two major implementations: birth–death (BD) models (or the invasion process) and death–birth (DB) models (or voter models). The isothermal theorem states that the fixation probability of mutants in a large group of graph structures (known as isothermal graphs, which include regular graphs) coincides with that for the mixed population. This result has been proved by Lieberman et al. (2005 Nature 433, 312–316. (doi:10.1038/nature03204)) in the case of BD processes, where mutants differ from the wild-types by their birth rate (and not by their death rate). In this paper, we discuss to what extent the isothermal theorem can be formulated for DB processes, proving that it only holds for mutants that differ from the wild-type by their death rate (and not by their birth rate). For more general BD and DB processes with arbitrary birth and death rates of mutants, we show that the fixation probabilities of mutants are different from those obtained in the mass-action populations. We focus on spatial lattices and show that the difference between BD and DB processes on one- and two-dimensional lattices is non-small even for large population sizes. We support these results with a generating function approach that can be generalized to arbitrary graph structures. Finally, we discuss several biological applications of the results. PMID:26064637
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
Localization and limit laws of a three-state alternate quantum walk on a two-dimensional lattice
NASA Astrophysics Data System (ADS)
Machida, Takuya; Chandrashekar, C. M.
2015-12-01
A two-dimensional discrete-time quantum walk (DTQW) can be realized by alternating a two-state DTQW in one spatial dimension followed by an evolution in the other dimension. This was shown to reproduce a probability distribution for a certain configuration of a four-state DTQW on a two-dimensional lattice. In this work we present a three-state alternate DTQW with a parametrized coin-flip operator and show that it can produce localization that is also observed for a certain other configuration of the four-state DTQW and nonreproducible using the two-state alternate DTQW. We will present two limit theorems for the three-state alternate DTQW. One of the limit theorems describes a long-time limit of a return probability, and the other presents a convergence in distribution for the position of the walker on a rescaled space by time. We find that the spatial entanglement generated by the three-state alternate DTQW is higher than that by the four-state DTQW. Using all our results, we outline the relevance of these walks in three-level physical systems.
A new upper limit to the local population II density.
NASA Technical Reports Server (NTRS)
Weistrop, D.
1972-01-01
An upper limit to the local population II density is derived, in terms of the mass-luminosity ratio, on the basis of U, B, and V photometric observations of several thousand stars with V magnitudes between 12 and 18 in a region near the North Galactic Pole. The photographic and photoelectric photometry and the reduction procedures are discussed. Models of the density distribution and luminosity function of the population II stars are used to predict their distribution in color and apparent magnitude. The derived local density of population II is found to be significantly lower than previous estimates. Possible causes for this discrepancy are considered.
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.; Lumley, J. L.; Abid, R.
1994-01-01
A nonlinear representation for the rapid-pressure correlation appearing in the Reynolds stress equations, consistent with the Taylor-Proudman theorem, is presented. The representation insures that the modeled second-order equations are frame-invariant with respect to rotation when the flow is two-dimensional in planes perpendicular to the axis of rotation. The representation satisfies realizability in a new way: a special ansatz is used to obtain analytically, the values of coefficients valid away from the realizability limit: the model coefficients are functions of the state of the turbulence that are valid for all states of the mechanical turbulence attaining their constant limiting values only when the limit state is achieved. Utilization of all the mathematical constraints are not enough to specify all the coefficients in the model. The unspecified coefficients appear as free parameters which are used to insure that the representation is asymptotically consistent with the known equilibrium states of a homogeneous sheared turbulence. This is done by insuring that the modeled evolution equations have the same fixed points as those obtained from computer and laboratory experiments for the homogeneous shear. Results of computations of the homogeneous shear, with and without rotation, and with stabilizing and destabilizing curvature, are shown. Results are consistently better, in a wide class of flows which the model not been calibrated, than those obtained with other nonlinear models.
NASA Astrophysics Data System (ADS)
Seyed-Aghazadeh, Banafsheh; Modarres-Sadeghi, Yahya
2015-11-01
Vortex-induced vibration (VIV) of a low mass ratio flexible cylinder (m*<1), is studied experimentally. The flexible tension-dominated cylinder was held fixed at both ends and was immersed in the uniform incoming flow. Dynamic response of the system was studied in the reduced velocity range of U* = 2.9 - 14.5 and the Reynolds number range of Re = 315 - 1580. Continuous response of the cylinder was reconstructed from limited number of measurement points based on modal expansion theorem modified using Modal Assurance Criterion (MAC). This reconstruction technique made it possible to properly reconstruct a continuous response along the length of the cylinder, even when the measurement points were localized in a small region of the cylinder. Mono- and multi-frequency excitation responses as well as transition from low mode numbers to higher ones were studied. Also, flow forces acting on the cylinder were calculated and they showed a consistent relation between the regions where the cylinder was being excited by the flow (CLv>0) and the counterclockwise figure-eight trajectories of oscillations in which the phase difference between the inline and crossflow directions were in the range of φxy =[ 0 π].
Magnetic localization limit in TC graded ferromagnetic thin films
NASA Astrophysics Data System (ADS)
Kirby, Brian; Fallarino, Lorenzo; Riego, Patricia; Pancaldi, Matteo; Berger, Andreas; Miller, Casey
We have recently demonstrated that the effective Curie temperature (TC) of a ferromagnetic alloy thin film can be continuously varied as a function of depth via a corresponding compositional gradient. This work showed that the effective TC can be made to vary continuously over tens of nm. However, over a short enough distance, the system must become localized, with exchange coupling dominating the effects of the compositional gradient. Understanding this localization limit is important for potential applications, as it dictates the length-scale below which this technique stops being a viable engineering tool (at least for itinerant ferromagnets and their thermodynamic properties). To determine the localization limit in this class of system, we have fabricated a series of Co[1- x]Cr[ x] alloy alloy films, where x varies sinusoidally between 0.28 (nominal TC ~ 250 K) and 0.22 (TC > 300 K), and have used polarized neutron reflectometry to study samples of differing oscillation wavelength. These measurements confirm the desired sinusoidal pattern was achieved, and reveal the temperature-dependence of the magnetic depth profile. Results will be presented in the context of mean-field simulations.
Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Wu, Yu-Chun; Wu, Chunfeng; Ye, Xiang-Jun; Żukowski, Marek; Kwek, L. C.
2015-01-01
We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin’s theorem (originally: all pure entangled states violate local realism). Local realism is violated by all mixed states with the above steering property. The new class of states allows one e.g. to perform three party secret sharing with just pairs of entangled qubits, instead of three qubit entanglements (which are currently available with low fidelity). This significantly increases the feasibility of having high performance versions of such protocols. Finally, we discuss some possible applications. PMID:26108704
Stephan, Carl N
2014-03-01
By pooling independent study means (x¯), the T-Tables use the central limit theorem and law of large numbers to average out study-specific sampling bias and instrument errors and, in turn, triangulate upon human population means (μ). Since their first publication in 2008, new data from >2660 adults have been collected (c.30% of the original sample) making a review of the T-Table's robustness timely. Updated grand means show that the new data have negligible impact on the previously published statistics: maximum change = 1.7 mm at gonion; and ≤1 mm at 93% of all landmarks measured. This confirms the utility of the 2008 T-Table as a proxy to soft tissue depth population means and, together with updated sample sizes (8851 individuals at pogonion), earmarks the 2013 T-Table as the premier mean facial soft tissue depth standard for craniofacial identification casework. The utility of the T-Table, in comparison with shorths and 75-shormaxes, is also discussed. PMID:24313424
Limits to the quantification of local climate change
NASA Astrophysics Data System (ADS)
Chapman, Sandra C.; Stainforth, David A.; Watkins, Nicholas W.
2015-09-01
We demonstrate how the fundamental timescales of anthropogenic climate change limit the identification of societally relevant aspects of changes in precipitation. We show that it is nevertheless possible to extract, solely from observations, some confident quantified assessments of change at certain thresholds and locations. Maps of such changes, for a variety of hydrologically-relevant, threshold-dependent metrics, are presented. In places in Scotland, for instance, the total precipitation on heavy rainfall days in winter has increased by more than 50%, but only in some locations has this been accompanied by a substantial increase in total seasonal precipitation; an important distinction for water and land management. These results are important for the presentation of scientific data by climate services, as a benchmark requirement for models which are used to provide projections on local scales, and for process-based climate and impacts research to understand local modulation of synoptic and global scale climate. They are a critical foundation for adaptation planning and for the scientific provision of locally relevant information about future climate.
Limits of localized control in extended nonlinear systems
NASA Astrophysics Data System (ADS)
Handel, Andreas
We investigate the limits of localized linear control in spatially extended, nonlinear systems. Spatially extended, nonlinear systems can be found in virtually every field of engineering and science. An important category of such systems are fluid flows. Fluid flows play an important role in many commercial applications, for instance in the chemical, pharmaceutical and food-processing industries. Other important fluid flows include air- or water flows around cars, planes or ships. In all these systems, it is highly desirable to control the flow of the respective fluid. For instance control of the air flow around an airplane or car leads to better fuel-economy and reduced noise production. Usually, it is impossible to apply control everywhere. Consider an airplane: It would not be feasibly to cover the whole body of the plane with control units. Instead, one can place the control units at localized regions, such as points along the edge of the wings, spaced as far apart from each other as possible. These considerations lead to an important question: For a given system, what is the minimum number of localized controllers that still ensures successful control? Too few controllers will not achieve control, while using too many leads to unnecessary expenses and wastes resources. To answer this question, we study localized control in a class of model equations. These model equations are good representations of many real fluid flows. Using these equations, we show how one can design localized control that renders the system stable. We study the properties of the control and derive several expressions that allow us to determine the limits of successful control. We show how the number of controllers that are needed for successful control depends on the size and type of the system, as well as the way control is implemented. We find that especially the nonlinearities and the amount of noise present in the system play a crucial role. This analysis allows us to determine under
Septins localize to microtubules during nutritional limitation in Saccharomyces cerevisiae
Pablo-Hernando, M Evangelina; Arnaiz-Pita, Yolanda; Tachikawa, Hiroyuki; del Rey, Francisco; Neiman, Aaron M; Vázquez de Aldana, Carlos R
2008-01-01
Background In Saccharomyces cerevisiae, nutrient limitation stimulates diploid cells to undergo DNA replication and meiosis, followed by the formation of four haploid spores. Septins are a family of proteins that assemble a ring structure at the mother-daughter neck during vegetative growth, where they control cytokinesis. In sporulating cells, the septin ring disassembles and septins relocalize to the prospore membrane. Results Here, we demonstrate that nutrient limitation triggers a change in the localization of at least two vegetative septins (Cdc10 and Cdc11) from the bud neck to the microtubules. The association of Cdc10 and Cdc11 with microtubules persists into meiosis, and they are found associated with the meiotic spindle until the end of meiosis II. In addition, the meiosis-specific septin Spr28 displays similar behavior, suggesting that this is a common feature of septins. Septin association to microtubules is a consequence of the nutrient limitation signal, since it is also observed when haploid cells are incubated in sporulation medium and when haploid or diploid cells are grown in medium containing non-fermentable carbon sources. Moreover, during meiosis II, when the nascent prospore membrane is formed, septins moved from the microtubules to this membrane. Proper organization of the septins on the membrane requires the sporulation-specific septins Spr3 and Spr28. Conclusion Nutrient limitation in S. cerevisiae triggers the sporulation process, but it also induces the disassembly of the septin bud neck ring and relocalization of the septin subunits to the nucleus. Septins remain associated with microtubules during the meiotic divisions and later, during spore morphogenesis, they are detected associated to the nascent prospore membranes surrounding each nuclear lobe. Septin association to microtubules also occurs during growth in non-fermentable carbon sources. PMID:18826657
Local and Global Limits on Visual Processing in Schizophrenia
Tibber, Marc S.; Anderson, Elaine J.; Bobin, Tracy; Carlin, Patricia; Shergill, Sukhwinder S.; Dakin, Steven C.
2015-01-01
Schizophrenia has been linked to impaired performance on a range of visual processing tasks (e.g. detection of coherent motion and contour detection). It has been proposed that this is due to a general inability to integrate visual information at a global level. To test this theory, we assessed the performance of people with schizophrenia on a battery of tasks designed to probe voluntary averaging in different visual domains. Twenty-three outpatients with schizophrenia (mean age: 40±8 years; 3 female) and 20 age-matched control participants (mean age 39±9 years; 3 female) performed a motion coherence task and three equivalent noise (averaging) tasks, the latter allowing independent quantification of local and global limits on visual processing of motion, orientation and size. All performance measures were indistinguishable between the two groups (ps>0.05, one-way ANCOVAs), with one exception: participants with schizophrenia pooled fewer estimates of local orientation than controls when estimating average orientation (p = 0.01, one-way ANCOVA). These data do not support the notion of a generalised visual integration deficit in schizophrenia. Instead, they suggest that distinct visual dimensions are differentially affected in schizophrenia, with a specific impairment in the integration of visual orientation information. PMID:25689281
OVII and Temperature Limits on the Local Hot Bubble
NASA Astrophysics Data System (ADS)
Pirtle, Robert; Petre, N.; McCammon, D.; Morgan, K.; Sauter, P.; Clavadetscher, K.; Fujimoto, R.; Hagihara, T.; Masui, K.; Mitsuda, K.; Takei, Y.; Wang, Q. D.; Yamasaki, N. Y.; Yao, Y.; Yoshino, T.
2013-01-01
The observed ¼-keV (ROSAT R12 band) X-ray background originates largely in a region of hot ionized gas roughly 100 pc in extent surrounding the Sun known as the Local Hot Bubble (LHB). The observed flux is quite uniform at low latitudes (|b| < 30°), but there a several large areas at intermediate and high latitudes that are enhanced by factors of 2 - 3. Charge exchange between highly charged ions in the Solar wind and interstellar neutral H and He moving through interplanetary space might provide a very roughly isotropic contribution about equal to the low- latitude flux (Koutroumpa et al. 2008), but cannot produce the enhancements. Correlations with the interstellar absorbing column show that some of these bright regions are apparently due to clumps of hot gas in the Galactic halo, while many of them show no correlation and must be due to extensions of the LHB (Kuntz & Snowden 2000, Bellm & Vaillancourt 2005). Global fits of simple plasma emission spectra give temperatures near 1.0 x 106 K for both LHB and halo emission, but the possibility of a substantial contamination by charge exchange could distort this result in unknown ways. Thermal excitation of O VII is strongly temperature dependent in this range, so we have tried to correlate O VII fluxes measured with Suzaku with variations in ¼-keV intensity from the ROSAT R12 band map to determine the temperature. We take eleven O VII intensity measurements from Yoshino et al. (2009), one from Masui et al. (2009), and an additional eighteen from archival Suzaku pointings and correlate these with the R12 band local and halo intensities as separated by Kunzt & Snowden (2000). The lack of detectable correlation in both cases strongly limits any O VII production by the material producing the enhancements, and upper limits to the temperatures are set. This work was supported in part by the National Science Foundation's REU program through NSF Award AST-1004881 and by NASA grant NNX09AF09G. *present address: Department
New Erdős-Kac Type Theorems for Signed Measures on Square-Free Integers
NASA Astrophysics Data System (ADS)
Avdeeva, Maria; Li, Dong; Sinai, Yakov G.
2013-11-01
We consider a family of signed measures supported on the set of square-free numbers. We prove some local limit theorems for the prime divisor counting function ω(n) and establish new Erdős-Kac type results.
Limits on the OVII Emission from the Local Hot Bubble
NASA Astrophysics Data System (ADS)
Jaeckel, Felix T; Li, Yaqiong; Morgan, Kelsey; Petre, Natalia; Sauter, Patrick; McCammon, Dan
2014-06-01
Constraining the properties of the gas in the local hot-bubble (LHB) is important for the understanding of the interstellar medium surrounding the sun. Much information about its energetic state is embedded in the observations of the low-energy diffuse X-ray background. From molecular-cloud shadowing observations (Galeazzi et al. 2006, R. Smith et al. 2007, Henley et al. 2007) it is known that a significant fraction of the 0.57keV OVII X-ray flux originates locally (< ~300 pc).To investigate the origin of this OVII emission, we analyze the correlation between OVII flux (extracted from Suzaku observations cleaned of point sources) against the local fraction of the ROSAT ¼ keV emission (R12 band), as separated from the distant (hot halo/extragalactic) component by Snowden (1998) and Kuntz (2000).Observations were selected to avoid galactic in-plane emission and features of other large-scale ISM structures. After correcting OVII flux for the more distant latitude-dependent emission, we find that it is essentially uncorrelated with the local ¼ keV emission, implying that the local hot bubble is not the source of the observed OVII emission. The lack of OVII emission further precludes temperatures above ~1E6K for the LHB gas (assuming collisional equilibrium models with solar abundance).
Local Area Networks in Education: Overview, Applications, and Current Limitations.
ERIC Educational Resources Information Center
Piele, Philip K.
Local area networks (LAN) are privately owned communication systems that connect multivendor devices at high speed. As microcomputers become more common in schools, user interest in sharing information, software, and peripherals will increase. A basic understanding of the operation of all LAN's can be gained by knowing four elements: media,…
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
Local Revenues for Schools: Limits and Options in California
ERIC Educational Resources Information Center
Perry, Mary; Edwards, Brian
2009-01-01
With K-12 schools representing the single largest expenditure in the state budget, education funding has been a central issue throughout the chaos that has recently characterized California's budget process. School districts throughout California have endured deep cuts in state funding, and more cuts are looming. But state law severely limits the…
Quantization of Chirikov Map and Quantum KAM Theorem.
NASA Astrophysics Data System (ADS)
Shi, Kang-Jie
KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions
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…
Quantum duality, unbounded operators, and inductive limits
Dosi, Anar
2010-06-15
In this paper, we investigate the inductive limits of quantum normed (or operator) spaces. This construction allows us to treat the space of all noncommutative continuous functions over a quantum domain as a quantum (or local operator) space of all matrix continuous linear operators equipped with S-quantum topology. In particular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens-Mackey theorem. Further, the inductive limits of operator spaces are used to introduce locally compact and locally trace class unbounded operators on a quantum domain and prove the dual realization theorem for an abstract quantum space.
Locally Produced IL-10 Limits Cutaneous Vaccinia Virus Spread
Cush, Stephanie S.; Reynoso, Glennys V.; Kamenyeva, Olena; Bennink, Jack R.; Yewdell, Jonathan W.; Hickman, Heather D.
2016-01-01
Skin infection with the poxvirus vaccinia (VV) elicits a powerful, inflammatory cellular response that clears virus infection in a coordinated, spatially organized manner. Given the high concentration of pro-inflammatory effectors at areas of viral infection, it is unclear how tissue pathology is limited while virus-infected cells are being eliminated. To better understand the spatial dynamics of the anti-inflammatory response to a cutaneous viral infection, we first screened cytokine mRNA expression levels after epicutaneous (ec.) VV infection and found a large increase the anti-inflammatory cytokine IL-10. Ex vivo analyses revealed that T cells in the skin were the primary IL-10-producing cells. To understand the distribution of IL-10-producing T cells in vivo, we performed multiphoton intravital microscopy (MPM) of VV-infected mice, assessing the location and dynamic behavior of IL-10 producing cells. Although virus-specific T cells were distributed throughout areas of the inflamed skin lacking overt virus-infection, IL-10+ cells closely associated with large keratinocytic foci of virus replication where they exhibited similar motility patterns to bulk antigen-specific CD8+ T cells. Paradoxically, neutralizing secreted IL-10 in vivo with an anti-IL-10 antibody increased viral lesion size and viral replication. Additional analyses demonstrated that IL-10 antibody administration decreased recruitment of CCR2+ inflammatory monocytes, which were important for reducing viral burden in the infected skin. Based upon these findings, we conclude that spatially concentrated IL-10 production limits cutaneous viral replication and dissemination, likely through modulation of the innate immune repertoire at the site of viral growth. PMID:26991092
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.
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.
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.
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.
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,…
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.
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
Bradetich, Ryan; Dearien, Jason A; Grussling, Barry Jakob; Remaley, Gavin
2013-11-05
The present disclosure provides systems and methods for remote device management. According to various embodiments, a local intelligent electronic device (IED) may be in communication with a remote IED via a limited bandwidth communication link, such as a serial link. The limited bandwidth communication link may not support traditional remote management interfaces. According to one embodiment, a local IED may present an operator with a management interface for a remote IED by rendering locally stored templates. The local IED may render the locally stored templates using sparse data obtained from the remote IED. According to various embodiments, the management interface may be a web client interface and/or an HTML interface. The bandwidth required to present a remote management interface may be significantly reduced by rendering locally stored templates rather than requesting an entire management interface from the remote IED. According to various embodiments, an IED may comprise an encryption transceiver.
Advances and limits of using population genetics to understand local adaptation.
Tiffin, Peter; Ross-Ibarra, Jeffrey
2014-12-01
Local adaptation shapes species diversity, can be a stepping stone to ecological speciation, and can facilitate species range expansion. Population genetic analyses, which complement organismal approaches in advancing our understanding of local adaptation, have become widespread in recent years. We focus here on using population genetics to address some key questions in local adaptation: what traits are involved? What environmental variables are the most important? Does local adaptation target the same genes in related species? Do loci responsible for local adaptation exhibit trade-offs across environments? After discussing these questions we highlight important limitations to population genetic analyses including challenges with obtaining high-quality data, deciding which loci are targets of selection, and limits to identifying the genetic basis of local adaptation. PMID:25454508
Raychaudhuri equation and singularity theorems in Finsler spacetimes
NASA Astrophysics Data System (ADS)
Minguzzi, E.
2015-09-01
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain. Indeed, so do the theorems by Hawking, Penrose, Hawking and Penrose, Geroch, Gannon, Tipler and Kriele, and also the Topological Censorship theorem and so on. It is argued that the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance and geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure, horizons differentiability and conformal transformations are also included.
NASA Astrophysics Data System (ADS)
Miserev, D. S.
2016-06-01
The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincaré index theorem for these closed trajectories. The VPM equation is also reduced to the nonrelativistic and semiclassical limits. The limit of a small momentum p y of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.
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.
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.
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.
Virial Theorem and Scale Transformations.
ERIC Educational Resources Information Center
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
A Schwinger disentangling theorem
Cross, Daniel J.; Gilmore, Robert
2010-10-15
Baker-Campbell-Hausdorff formulas are exceedingly useful for disentangling operators so that they may be more easily evaluated on particular states. We present such a disentangling theorem for general bilinear and linear combinations of multiple boson creation and annihilation operators. This work generalizes a classical result of Schwinger.
Weinberg, Steven
2008-09-15
It is shown that the generating function for tree graphs in the ''in-in'' formalism may be calculated by solving the classical equations of motion subject to certain constraints. This theorem is illustrated by application to the evolution of a single inflaton field in a Robertson-Walker background.
''CPT Theorem'' for Accelerators
Vladimir Shiltsev
2004-08-05
In this paper we attempt to reveal common features in evolution of various colliders' luminosity over commissioning periods. A simplified formula, ''CPT theorem'' or CP = T, is proposed which relates the time needed for commissioning T, the ''complexity'' of the machine C and performance increase goal P.
ERIC Educational Resources Information Center
Musto, Garrod
2010-01-01
Within his classroom, the author is often confronted by students who fail to see, or accept, the relevance of mathematics both to their lives and the world around them. One topic which is regularly perceived as being disconnected from people's daily lives is that of circle theorems, especially among less motivated students. In this article, the…
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.
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.
ERIC Educational Resources Information Center
Abramovitz, Buma; Berezina, Miryam; Berman, Abraham; Shvartsman, Ludmila
2009-01-01
In this article we describe the process of studying the assumptions and the conclusion of a theorem. We tried to provide the students with exercises and problems where we discuss the following questions: What are the assumptions of a theorem and what are the conclusions? What is the geometrical meaning of a theorem? What happens when one or more…
ERIC Educational Resources Information Center
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
Sampling theorems and compressive sensing on the sphere
NASA Astrophysics Data System (ADS)
McEwen, Jason D.; Puy, Gilles; Thiran, Jean-Philippe; Vandergheynst, Pierre; Van De Ville, Dimitri; Wiaux, Yves
2011-09-01
We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a band-limited signal exactly, this new sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere, such as the canonical Driscoll & Healy sampling theorem. A reduction in the number of samples required to represent a band-limited signal on the sphere has important implications for compressive sensing, both in terms of the dimensionality and sparsity of signals. We illustrate the impact of this property with an inpainting problem on the sphere, where we show superior reconstruction performance when adopting the new sampling theorem.
THE PARKER MAGNETOSTATIC THEOREM
Low, B. C.
2010-08-01
We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly conducting fluid bounded by a pair of rigid plates where each field is anchored, taking the plates perpendicular to the uniform field. Those force-free fields obtainable from the uniform field by continuous magnetic footpoint displacements at the plates have field topologies that are shown to be a restricted subset of the field topologies similarly created without imposing the force-free equilibrium condition. The theorem then follows from the deduction that a continuous nonequilibrium field with a topology not in that subset must find a force-free state containing tangential discontinuities.
NASA Astrophysics Data System (ADS)
Greaves, Hilary; Thomas, Teruji
2014-02-01
We provide a careful development and rigorous proof of the CPT theorem within the framework of mainstream (Lagrangian) quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches in the mainstream approach. We construct the CPT transformation for a general field directly, without appealing to the enumerative classification of representations, and in a manner that is clearly related to the requirements of our proof. Our approach applies equally in Minkowski spacetimes of any dimension at least three, and is in principle neutral between classical and quantum field theories: the quantum CPT theorem has a natural classical analogue. The key mathematical tool is that of complexification; this tool is central to the existing axiomatic proofs, but plays no overt role in the usual mainstream approaches to CPT.
NASA Astrophysics Data System (ADS)
Sarbicki, Gniewomir; Chruściński, Dariusz; Mozrzymas, Marek
2016-07-01
We analyse linear maps of operator algebras {{ B }}H({ H }) mapping the set of rank-k projectors onto the set of rank-l projectors surjectively. A complete characterisation of such maps for prime n={dim} { H } is provided. A particular case corresponding to k=l=1 is well known as Wigner’s theorem. Hence our result may be considered as a generalisation of this celebrated Wigner’s result.
The Steep Nekhoroshev's Theorem
NASA Astrophysics Data System (ADS)
Guzzo, M.; Chierchia, L.; Benettin, G.
2016-03-01
Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be {1/(2nα_1\\cdotsα_{n-2}}) ({α_i}'s being Nekhoroshev's steepness indices and {n ≥ 3} the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.
Factors Associated with Operational Limitations of Training and Visit System at the Local Level.
ERIC Educational Resources Information Center
Navaratnam, K. K.
A study examined the factors associated with operational limitations of the Training and Visit System, an information diffusion method, at the local levels. A personal interview survey was conducted to gather data required for this study from agricultural extension personnel from three predominantly agricultural areas in Sri Lanka. Stepwise…
40 CFR 1400.11 - Limitation on dissemination to State and local government officials.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 34 2013-07-01 2013-07-01 false Limitation on dissemination to State and local government officials. 1400.11 Section 1400.11 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY AND DEPARTMENT OF JUSTICE ACCIDENTAL RELEASE PREVENTION REQUIREMENTS; RISK...
40 CFR 1400.11 - Limitation on dissemination to State and local government officials.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 33 2011-07-01 2011-07-01 false Limitation on dissemination to State and local government officials. 1400.11 Section 1400.11 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY AND DEPARTMENT OF JUSTICE ACCIDENTAL RELEASE PREVENTION REQUIREMENTS; RISK...
40 CFR 1400.11 - Limitation on dissemination to State and local government officials.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 34 2012-07-01 2012-07-01 false Limitation on dissemination to State and local government officials. 1400.11 Section 1400.11 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY AND DEPARTMENT OF JUSTICE ACCIDENTAL RELEASE PREVENTION REQUIREMENTS; RISK...
40 CFR 1400.11 - Limitation on dissemination to State and local government officials.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 33 2014-07-01 2014-07-01 false Limitation on dissemination to State and local government officials. 1400.11 Section 1400.11 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY AND DEPARTMENT OF JUSTICE ACCIDENTAL RELEASE PREVENTION REQUIREMENTS; RISK...
40 CFR 1400.11 - Limitation on dissemination to State and local government officials.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 32 2010-07-01 2010-07-01 false Limitation on dissemination to State and local government officials. 1400.11 Section 1400.11 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY AND DEPARTMENT OF JUSTICE ACCIDENTAL RELEASE PREVENTION REQUIREMENTS; RISK...
Temporal-spatial distribution of atmospheric predictability limit by local dynamical analogues
NASA Astrophysics Data System (ADS)
Li, J. P.; Ding, R. Q.
2012-04-01
To quantify the predictability limit of a chaotic system, the authors recently developed a method using the nonlinear local Lyapunov exponent (NLLE). The NLLE method provides a measure of local predictability limit of chaotic systems and is intended to supplement existing predictability methods. To apply the NLLE in studies of actual atmospheric predictability, an algorithm based on local dynamical analogues is devised to enable the estimation of the NLLE and its derivatives using experimental or observational data. Two examples are given to illustrate the effectiveness of the algorithm, involving the Lorenz63 3-variable model and the Lorenz96 40-variable model; they reveal that the algorithm is applicable in estimating the NLLE of a chaotic system from its experimental time series. On this basis, the NLLE method is used to investigate temporal-spatial distributions of predictability limits of the daily geopotential height and wind fields. The limit of atmospheric predictability varies widely with region, altitude and season. The predictability limits of the daily geopotential height and wind fields are generally less than three weeks in the troposphere, whereas they are approximately one month in the lower stratosphere, revealing a potential predictability source for forecasting weather from the stratosphere. Further work is required to examine broader applications of the NLLE method in predictability studies of the atmosphere, ocean, and other systems.
Building local human resources to implement SLMTA with limited donor funding: The Ghana experience
Nkrumah, Bernard; van der Puije, Beatrice; Bekoe, Veronica; Adukpo, Rowland; Kotey, Nii A.; Yao, Katy; Fonjungo, Peter N.; Luman, Elizabeth T.; Duh, Samuel; Njukeng, Patrick A.; Addo, Nii A.; Khan, Fazle N.; Woodfill, Celia J.I.
2016-01-01
Background In 2009, Ghana adopted the Strengthening Laboratory Management Toward Accreditation (SLMTA) programme in order to improve laboratory quality. The programme was implemented successfully with limited donor funding and local human resources. Objectives To demonstrate how Ghana, which received very limited PEPFAR funding, was able to achieve marked quality improvement using local human resources. Method Local partners led the SLMTA implementation and local mentors were embedded in each laboratory. An in-country training-of-trainers workshop was conducted in order to increase the pool of local SLMTA implementers. Three laboratory cohorts were enrolled in SLMTA in 2011, 2012 and 2013. Participants from each cohort attended in a series of three workshops interspersed with improvement projects and mentorship. Supplemental training on internal audit was provided. Baseline, exit and follow-up audits were conducted using the Stepwise Laboratory Quality Improvement Process Towards Accreditation (SLIPTA) checklist. In November 2013, four laboratories underwent official SLIPTA audits by the African Society for Laboratory Medicine (ASLM). Results The local SLMTA team successfully implemented three cohorts of SLMTA in 15 laboratories. Seven out of the nine laboratories that underwent follow-up audits have reached at least one star. Three out of the four laboratories that underwent official ASLM audits were awarded four stars. Patient satisfaction increased from 25% to 70% and sample rejection rates decreased from 32% to 10%. On average, $40 000 was spent per laboratory to cover mentors' salaries, SLMTA training and improvement project support. Conclusion Building in-country capacity through local partners is a sustainable model for improving service quality in resource-constrained countries such as Ghana. Such models promote country ownership, capacity building and the use of local human resources for the expansion of SLMTA. PMID:26937417
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.
The global Utiyama theorem in Einstein-Cartan theory
NASA Astrophysics Data System (ADS)
Bruzzo, Ugo
1987-09-01
A global formulation of Utiyama's theorem for Einstein-Cartan-type gravitational theories regarded as gauge theories of the group of space-time diffeomorphisms is given. The local conditions for the Lagrangian to be gauge invariant coincide with those found by other authors [A. Pérez-Rendón Collantes, ``Utiyama type theorems,'' in Poincaré Gauge Approach to Gravity. I, Proceedings Journées Relativistes 1984; A. Pérez-Rendón and J. J. Seisdedos, ``Utiyama type theorems in Poincaré gauge approach to gravity. II, '' Preprints de Mathematicas, Universidad de Salamanca, 1986] in Kibble's and Hehl's approaches.
Analysis of Spatially Limited Local Communication for Multi-Robot Foraging
NASA Astrophysics Data System (ADS)
Krannich, Stephan; Maehle, Erik
This work presents a biologically inspired communication model for foraging swarms of cooperative mobile robots. In contrast to conventional, unrestricted local communication the exchange of messages is here spatially restricted to a nest-like area. The performance of the presented communication concept is evaluated using simulation and comparison to common forms of communication. An implementation on hardware robots allows to determine influences from the real world on the model. Results show that spatial limitation of communication to a single nest area can still speed up the performance of foraging swarms whereas further increasing the quantity of conventional local communication is less effective for the process of foraging.
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.
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.
Code of Federal Regulations, 2010 CFR
2010-04-01
... administrative cost limits for States and local areas apply to NFJP grants? No, under 20 CFR 667.210(b), limits... 20 Employees' Benefits 3 2010-04-01 2010-04-01 false Do the WIA administrative cost limits for States and local areas apply to NFJP grants? 669.555 Section 669.555 Employees' Benefits EMPLOYMENT...
Effects of hole localization on limiting p-type conductivity in oxide and nitride semiconductors
Lyons, J. L.; Janotti, A.; Van de Walle, C. G.
2014-01-07
We examine how hole localization limits the effectiveness of substitutional acceptors in oxide and nitride semiconductors and explain why p-type doping of these materials has proven so difficult. Using hybrid density functional calculations, we find that anion-site substitutional impurities in AlN, GaN, InN, and ZnO lead to atomic-like states that localize on the impurity atom itself. Substitution with cation-site impurities, on the other hand, triggers the formation of polarons that become trapped on nearest-neighbor anions, generally leading to large ionization energies for these acceptors. Unlike shallow effective-mass acceptors, these two types of deep acceptors couple strongly with the lattice, significantly affecting the optical properties and severely limiting prospects for achieving p-type conductivity in these wide-band-gap materials.
Probing local order in glasses from limited-volume electron and x-ray diffraction
NASA Astrophysics Data System (ADS)
Liu, A. C. Y.; Tabor, R. F.; Bourgeois, L.; de Jonge, M. D.; Mudie, S. T.; Petersen, T. C.
2016-05-01
It has long been recognised that spatial fluctuations in local order in disordered assemblies of particles can be probed using limited-volume diffraction measurements. These measurements have unique advantages over broad-beam diffraction experiments that isotropically average over many structural configurations and result in one-dimensional intensity curves, requiring modelling to interpret. Despite the advantages of limiting illumination to a low number of particle configurations, obtaining quantitative measurements of local order from such experiments remains a challenge. The effects on the diffraction pattern of changing the beam energy, lateral size, aberrations and coherence and the specimen thickness have only recently been clarified. We review theoretical and experimental efforts in this direction in the fields of both electron and x-ray diffraction and identify promising areas of future development.
Theorems on Positive Data: On the Uniqueness of NMF
Laurberg, Hans; Christensen, Mads Græsbøll; Plumbley, Mark D.; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors. PMID:18497868
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.
Manipulating nutrient limitation using modified local soils: A case study at Lake Taihu (China).
Wang, Lijing; Pan, Gang; Shi, Wenqing; Wang, Zhibin; Zhang, Honggang
2016-09-15
The effect of geo-engineering materials of chitosan modified local soil (MLS) on nutrient limitation was studied in comparable whole ponds in Lake Taihu in October 2013. After 20 kg MLS were sprayed in the whole water pond (400 m(2)), the chlorophyll-a (Chl-a) concentration was decreased from 42 to 18 μg L(-1) within 2 h and remained below 20 μg L(-1) in the following 15 months, while the average Chl-a was 36 μg L(-1) in the control pond throughout the experiment. In situ nutrient addition bioassay experiments indicated that the nutrient limitation was shifted from nitrogen (N) and phosphorus (P) co-limitation to P limitation after MLS treatment from October 2013 to March 2014 compared to the control pond. In the cyanobacterial bloom season of June 2014, N and P co-limitation remained and N was the primary limiting nutrient and P was a secondary one in the control pond where phytoplankton biomass showed significant increase by N addition and further increase by N + P additions, while both N and P became the limiting nutrient for phytoplankton growth where only combined N and P additions showed significant Chl-a stimulation in the treatment pond. In the next summer (June 2014), a cyanobacteria-dominated state still remained in the control pond but chlorophytes, bacillariophytes and cyanophytes distributed equally and submerged vegetation was largely restored in the treatment pond. Meanwhile, the upper limiting concentration of DIN was enhanced from 0.8 to 1.5 mg L(-1) and SRP from 0.1 to 0.3 mg L(-1) compared to the control pond. This study indicates that nutrient limitation can be manipulated by using MLS technology. PMID:27244294
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.
Rossi, Tuomas P. Sakko, Arto; Puska, Martti J.; Lehtola, Susi; Nieminen, Risto M.
2015-03-07
We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semi-core d-electrons that affect their plasmonic response. The basis sets are constructed by augmenting numerical atomic orbital basis sets by truncated Gaussian-type orbitals generated by the completeness-optimization scheme, which is applied to the photoabsorption spectra of homoatomic metal atom dimers. We obtain basis sets of improving accuracy up to the complete basis set limit and demonstrate that the performance of the basis sets transfers to simulations of larger nanoparticles and nanoalloys as well as to calculations with various exchange-correlation functionals. This work promotes the use of the local basis set approach of controllable accuracy in first-principles nanoplasmonics simulations and beyond.
Local adaptation limits lifetime reproductive success of dispersers in a wild salmon metapopulation.
Peterson, Daniel A; Hilborn, Ray; Hauser, Lorenz
2014-01-01
Demographic and evolutionary dynamics in wild metapopulations are critically affected by the balance between dispersal and local adaptation. Where populations are demographically interconnected by migration, gene flow is often assumed to prevent local adaptation. However, reduced fitness of immigrants may limit gene flow between populations adapted to distinct habitat types, although direct quantification of the lifetime reproductive success of immigrants in the wild is lacking. Here, we show that dispersers between stream-spawning populations of sockeye salmon (Oncorhynchus nerka) had similar reproductive success to those that spawned in their natal stream, whereas dispersers from a different habitat (nearby lake beaches) produced half as many offspring. The stream- and beach-spawning ecotypes exhibited striking morphological differences despite their close spatial proximity, yet dispersal from the beach to the streams was more common than dispersal between streams, presenting empirical evidence that variation in immigrant reproductive success is important for the maintenance of intraspecific biodiversity. PMID:24739514
Rossi, Tuomas P; Lehtola, Susi; Sakko, Arto; Puska, Martti J; Nieminen, Risto M
2015-03-01
We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semi-core d-electrons that affect their plasmonic response. The basis sets are constructed by augmenting numerical atomic orbital basis sets by truncated Gaussian-type orbitals generated by the completeness-optimization scheme, which is applied to the photoabsorption spectra of homoatomic metal atom dimers. We obtain basis sets of improving accuracy up to the complete basis set limit and demonstrate that the performance of the basis sets transfers to simulations of larger nanoparticles and nanoalloys as well as to calculations with various exchange-correlation functionals. This work promotes the use of the local basis set approach of controllable accuracy in first-principles nanoplasmonics simulations and beyond. PMID:25747068
Code of Federal Regulations, 2012 CFR
2012-04-01
... the WIA administrative cost limits for States and local areas apply to NFJP grants? No, under 20 CFR... 20 Employees' Benefits 4 2012-04-01 2012-04-01 false Do the WIA administrative cost limits for States and local areas apply to NFJP grants? 669.555 Section 669.555 Employees' Benefits EMPLOYMENT...
Code of Federal Regulations, 2014 CFR
2014-04-01
... the WIA administrative cost limits for States and local areas apply to NFJP grants? No, under 20 CFR... 20 Employees' Benefits 4 2014-04-01 2014-04-01 false Do the WIA administrative cost limits for States and local areas apply to NFJP grants? 669.555 Section 669.555 Employees' Benefits EMPLOYMENT...
Code of Federal Regulations, 2013 CFR
2013-04-01
... the WIA administrative cost limits for States and local areas apply to NFJP grants? No, under 20 CFR... 20 Employees' Benefits 4 2013-04-01 2013-04-01 false Do the WIA administrative cost limits for States and local areas apply to NFJP grants? 669.555 Section 669.555 Employees' Benefits EMPLOYMENT...
Phase space localization for anti-de Sitter quantum mechanics and its zero curvature limit
NASA Technical Reports Server (NTRS)
Elgradechi, Amine M.
1993-01-01
Using techniques of geometric quantization and SO(sub 0)(3,2)-coherent states, a notion of optimal localization on phase space is defined for the quantum theory of a massive and spinning particle in anti-de Sitter space time. It is shown that this notion disappears in the zero curvature limit, providing one with a concrete example of the regularizing character of the constant (nonzero) curvature of the anti-de Sitter space time. As a byproduct a geometric characterization of masslessness is obtained.
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.
Code of Federal Regulations, 2011 CFR
2011-01-01
... Local Television Broadcast Signals. 2201.9 Section 2201.9 Agriculture Regulations of the Department of... REGULATIONS General § 2201.9 Limitation on the applicability of the definition of Local Television Broadcast Signals. Notwithstanding the definition of Local Television Broadcast Signals provided in § 2201.1 of...
Code of Federal Regulations, 2013 CFR
2013-01-01
... Local Television Broadcast Signals. 2201.9 Section 2201.9 Agriculture Regulations of the Department of... REGULATIONS General § 2201.9 Limitation on the applicability of the definition of Local Television Broadcast Signals. Notwithstanding the definition of Local Television Broadcast Signals provided in § 2201.1 of...
Code of Federal Regulations, 2010 CFR
2010-01-01
... Local Television Broadcast Signals. 2201.9 Section 2201.9 Agriculture Regulations of the Department of... REGULATIONS General § 2201.9 Limitation on the applicability of the definition of Local Television Broadcast Signals. Notwithstanding the definition of Local Television Broadcast Signals provided in § 2201.1 of...
Code of Federal Regulations, 2012 CFR
2012-01-01
... Local Television Broadcast Signals. 2201.9 Section 2201.9 Agriculture Regulations of the Department of... REGULATIONS General § 2201.9 Limitation on the applicability of the definition of Local Television Broadcast Signals. Notwithstanding the definition of Local Television Broadcast Signals provided in § 2201.1 of...
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.
Crop response to localized organic amendment in soils with limiting physical properties
NASA Astrophysics Data System (ADS)
Lordan, Joan; Pascual, Miquel; Fonseca, Francisco; Villar, Josep Maria; Montilla, Victor; Papió, Josep; Rufat, Josep
2013-04-01
This 2-year study evaluated the use of rice husk as a localized organic amendment in a soil with limiting physical properties. The research was conducted in a commercial peach orchard planted in 2011 using a ridge planting system. Six soil and water management treatments were evaluated in 18 experimental units, which were set up in the field using a randomized complete block design. The treatments were compared both in terms of soil physical properties and crop response. Soil amendment with rice husk was the most effective technique. It improved soil conditions (soil infiltration and soil porosity), providing a better soil environment for root activity and thereby resulted in better crop performance. Concerning growth parameters, the amended treatment presented the highest overall values without negatively affecting crop water status. These techniques were suitable for mitigating the effects of soils with limiting physical conditions. Localized applications of amendments, as proposed in this work, imply an important reduction in application rates. It is important to consider an efficient use of by-products since there is a growing interest in industrial and agronomical exploitations.
Cohen, S.A.; Hosea, J.C.; Timberlake, J.R.
1984-10-19
A limiter with a specially contoured front face is provided. The front face of the limiter (the plasma-side face) is flat with a central indentation. In addition, the limiter shape is cylindrically symmetric so that the limiter can be rotated for greater heat distribution. This limiter shape accommodates the various power scrape-off distances lambda p, which depend on the parallel velocity, V/sub parallel/, of the impacting particles.
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
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.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
NASA Astrophysics Data System (ADS)
Woolgar, Eric; Wylie, William
2016-02-01
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-Émery" N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (-∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (-∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
NASA Astrophysics Data System (ADS)
Kushner, Paul J.; Shepherd, Theodore G.
1995-05-01
A study of the semi-geostrophic (SG) geophysical fluid dynamics is presented. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. An invariant for the semi-geostrophic equations is derived and use it to obtain: (1) a linear stability theorem analogous to Arnold's first theorem; and (2) a small-amplitude local conservation law for invariant, obeying the group-velocity in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number.
Cohen, Samuel A.; Hosea, Joel C.; Timberlake, John R.
1986-01-01
A limiter with a specially contoured front face accommodates the various power scrape-off distances .lambda..sub.p, which depend on the parallel velocity, V.sub..parallel., of the impacting particles. The front face of the limiter (the plasma-side face) is flat with a central indentation. In addition, the limiter shape is cylindrically symmetric so that the limiter can be rotated for greater heat distribution.
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.
Spatial resolution limits for the localization of noise sources using direct sound mapping
NASA Astrophysics Data System (ADS)
Fernandez Comesaña, D.; Holland, K. R.; Fernandez-Grande, E.
2016-08-01
One of the main challenges arising from noise and vibration problems is how to identify the areas of a device, machine or structure that produce significant acoustic excitation, i.e. the localization of main noise sources. The direct visualization of sound, in particular sound intensity, has extensively been used for many years to locate sound sources. However, it is not yet well defined when two sources should be regarded as resolved by means of direct sound mapping. This paper derives the limits of the direct representation of sound pressure, particle velocity and sound intensity by exploring the relationship between spatial resolution, noise level and geometry. The proposed expressions are validated via simulations and experiments. It is shown that particle velocity mapping yields better results for identifying closely spaced sound sources than sound pressure or sound intensity, especially in the acoustic near-field.
Avoiding the local-minimum problem in multi-agent systems with limited sensing and communication
NASA Astrophysics Data System (ADS)
Okamoto, Makiko; Akella, Maruthi R.
2016-06-01
In this paper, we consider a control problem for nonholonomic multi-agent systems in which agents and obstacles operate within a circular-shaped work area. We assume that agents only have limited sensing and communication ranges. We propose a novel control scheme using potential functions that drives agents from the initial to the goal configuration while avoiding collision with other agents, obstacles, and the boundary of the work area. The control scheme employs an avoidance strategy that ensures that the agents are never trapped at local minima that are typically encountered with most potential function-based approaches. A numerical simulation is presented to demonstrate the validity and effectiveness of the proposed control scheme.
Multi Sensor Fusion Framework for Indoor-Outdoor Localization of Limited Resource Mobile Robots
Marín, Leonardo; Vallés, Marina; Soriano, Ángel; Valera, Ángel; Albertos, Pedro
2013-01-01
This paper presents a sensor fusion framework that improves the localization of mobile robots with limited computational resources. It employs an event based Kalman Filter to combine the measurements of a global sensor and an inertial measurement unit (IMU) on an event based schedule, using fewer resources (execution time and bandwidth) but with similar performance when compared to the traditional methods. The event is defined to reflect the necessity of the global information, when the estimation error covariance exceeds a predefined limit. The proposed experimental platforms are based on the LEGO Mindstorm NXT, and consist of a differential wheel mobile robot navigating indoors with a zenithal camera as global sensor, and an Ackermann steering mobile robot navigating outdoors with a SBG Systems GPS accessed through an IGEP board that also serves as datalogger. The IMU in both robots is built using the NXT motor encoders along with one gyroscope, one compass and two accelerometers from Hitecnic, placed according to a particle based dynamic model of the robots. The tests performed reflect the correct performance and low execution time of the proposed framework. The robustness and stability is observed during a long walk test in both indoors and outdoors environments. PMID:24152933
Multi sensor fusion framework for indoor-outdoor localization of limited resource mobile robots.
Marín, Leonardo; Vallés, Marina; Soriano, Ángel; Valera, Ángel; Albertos, Pedro
2013-01-01
This paper presents a sensor fusion framework that improves the localization of mobile robots with limited computational resources. It employs an event based Kalman Filter to combine the measurements of a global sensor and an inertial measurement unit (IMU) on an event based schedule, using fewer resources (execution time and bandwidth) but with similar performance when compared to the traditional methods. The event is defined to reflect the necessity of the global information, when the estimation error covariance exceeds a predefined limit. The proposed experimental platforms are based on the LEGO Mindstorm NXT, and consist of a differential wheel mobile robot navigating indoors with a zenithal camera as global sensor, and an Ackermann steering mobile robot navigating outdoors with a SBG Systems GPS accessed through an IGEP board that also serves as datalogger. The IMU in both robots is built using the NXT motor encoders along with one gyroscope, one compass and two accelerometers from Hitecnic, placed according to a particle based dynamic model of the robots. The tests performed reflect the correct performance and low execution time of the proposed framework. The robustness and stability is observed during a long walk test in both indoors and outdoors environments. PMID:24152933
NASA Astrophysics Data System (ADS)
Cartin, Daniel
2015-10-01
At this point in time, there is very little empirical evidence on the likelihood of a space-faring species originating in the biosphere of a habitable world. However, there is a tension between the expectation that such a probability is relatively high (given our own origins on Earth), and the lack of any basis for believing the Solar System has ever been visited by an extraterrestrial colonization effort. From the latter observational fact, this paper seeks to place upper limits on the probability of an interstellar civilization arising on a habitable planet in its stellar system, using a percolation model to simulate the progress of such a hypothetical civilization's colonization efforts in the local Solar neighbourhood. To be as realistic as possible, the actual physical positions and characteristics of all stars within 40 parsecs of the Solar System are used as possible colony sites in the percolation process. If an interstellar civilization is very likely to have such colonization programmes, and they can travel over large distances, then the upper bound on the likelihood of such a species arising per habitable world is of the order of 10-3 on the other hand, if civilizations are not prone to colonize their neighbours, or do not travel very far, then the upper limiting probability is much larger, even of order one.
Tau leaping of stiff stochastic chemical systems via local central limit approximation
Yang, Yushu; Rathinam, Muruhan
2013-06-01
Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-stepping method to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods have shortcomings in this regard. The implicit tau method is far more stable than the trapezoidal tau method but underestimates the asymptotic variance. On the other hand, the trapezoidal tau method which estimates the asymptotic variance exactly for linear systems suffers from the fact that the transients of the method do not decay fast enough in the context of very stiff systems. We propose a tau leaping method that possesses the same stability properties as the implicit method while it also captures the asymptotic variance with reasonable accuracy at least for the test system S{sub 1}↔S{sub 2}. The proposed method uses a central limit approximation (CLA) locally over the tau leaping interval and is referred to as the LCLA-τ. The CLA predicts the mean and covariance as solutions of certain differential equations (ODEs) and for efficiency we solve these using a single time step of a suitable low order method. We perform a mean/covariance stability analysis of various possible low order schemes to determine the best scheme. Numerical experiments presented show that LCLA-τ performs favorably for stiff systems and that the LCLA-τ is also able to capture bimodal distributions unlike the CLA itself. The proposed LCLA-τ method uses a split implicit step to compute the mean update. We also prove that any tau leaping method employing a split implicit step converges in the fluid limit to the implicit Euler method as applied to the fluid limit differential equation.
Tau leaping of stiff stochastic chemical systems via local central limit approximation
NASA Astrophysics Data System (ADS)
Yang, Yushu; Rathinam, Muruhan
2013-06-01
Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-stepping method to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods have shortcomings in this regard. The implicit tau method is far more stable than the trapezoidal tau method but underestimates the asymptotic variance. On the other hand, the trapezoidal tau method which estimates the asymptotic variance exactly for linear systems suffers from the fact that the transients of the method do not decay fast enough in the context of very stiff systems. We propose a tau leaping method that possesses the same stability properties as the implicit method while it also captures the asymptotic variance with reasonable accuracy at least for the test system S1↔S2. The proposed method uses a central limit approximation (CLA) locally over the tau leaping interval and is referred to as the LCLA-τ. The CLA predicts the mean and covariance as solutions of certain differential equations (ODEs) and for efficiency we solve these using a single time step of a suitable low order method. We perform a mean/covariance stability analysis of various possible low order schemes to determine the best scheme. Numerical experiments presented show that LCLA-τ performs favorably for stiff systems and that the LCLA-τ is also able to capture bimodal distributions unlike the CLA itself. The proposed LCLA-τ method uses a split implicit step to compute the mean update. We also prove that any tau leaping method employing a split implicit step converges in the fluid limit to the implicit Euler method as applied to the fluid limit differential equation.
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.
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.
The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project
ERIC Educational Resources Information Center
Robiette, Alan G.
1975-01-01
Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)
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.
Experimentally testing Bell's theorem based on Hardy's nonlocal ladder proofs
NASA Astrophysics Data System (ADS)
Guo, WeiJie; Fan, DaiHe; Wei, LianFu
2015-02-01
Bell's theorem argues the existence of quantum nonlocality which goes basically against the hidden variable theory (HVT). Many experiments have been done via testing the violations of Bell's inequalities to statistically verify the Bell's theorem. Alternatively, by testing the Hardy's ladder proofs we experimentally demonstrate the deterministic violation of HVT and thus confirm the quantum nonlocality. Our tests are implemented with non-maximal entangled photon pairs generated by spontaneous parametric down conversions (SPDCs). We show that the degree freedom of photon entanglement could be significantly enhanced by using interference filters. As a consequence, the Hardy's ladder proofs could be tested and Bell's theorem is verified robustly. The probability of violating the locality reach to 41.9%, which is close to the expectably ideal value 46.4% for the photon pairs with degree of entanglement ɛ = 0.93. The higher violating probability is possible by further optimizing the experimental parameters.
Towards a novel no-hair theorem for black holes
Hertog, Thomas
2006-10-15
We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four-dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.
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.
Geometry underlying no-hidden-variable theorems
NASA Astrophysics Data System (ADS)
Fivel, Daniel I.
1991-07-01
The set of orientations of a measuring device (e.g., a Stern-Gerlach magnet) produced by the action of a Lie group constitutes a honmogeneous space S (e.g., a sphere). A hidden-variable measure determines a metric D on S, the triangle inequality being Bell's inequality. But identification of S with Hilbert-space projectors induces a locally convex metric d on S. The Einstein-Podolsky-Rosen (EPR) hypotheses imply that D=d2, which is impossible because the square of a locally convex metric cannot be a metric. This proves the Bell-EPR theorem. Classical systems avoid the contradiction by allowing only values d=0,1. The ``watchdog'' effect is shown to result from the form of the quantum-mechanical metric.
NASA Astrophysics Data System (ADS)
Ivanov, Martin; Kotlarski, Sven; Schär, Christoph
2015-04-01
The Swiss CH2011 scenarios provide a portfolio of climate change scenarios for the region of Switzerland, specifically tailored for use in climate impact research. Although widely applied by a variety of end-users, these scenarios are subject to several limitations related to the underlying delta change methodology. Examples are difficulties to appropriately account for changes in the spatio-temporal variability of meteorological fields and for changes in extreme events. The recently launched ELAPSE project (Enhancing local and regional climate change projections for Switzerland) is connected to the EU COST Action VALUE (www.value-cost.eu) and aims at complementing CH2011 by further scenario products, including a bias-corrected version of daily scenarios at the site scale. For this purpose the well-established empirical quantile mapping (QM) methodology is employed. Here, daily temperature and precipitation output of 15 GCM-RCM model chains of the ENSEMBLES project is downscaled and bias-corrected to match observations at weather stations in Switzerland. We consider established QM techniques based on all empirical quantiles or linear interpolation between the empirical percentiles. In an attempt to improve the downscaling of extreme precipitation events, we also apply a parametric approximation of the daily precipitation distribution by a dynamically weighted mixture of a Gamma distribution for the bulk and a Pareto distribution for the right tail for the first time in the context of QM. All techniques are evaluated and intercompared in a cross-validation framework. The statistical downscaling substantially improves virtually all considered distributional and temporal characteristics as well as their spatial distribution. The empirical methods have in general very similar performances. The parametric method does not show an improvement over the empirical ones. Critical sites and seasons are highlighted and discussed. Special emphasis is placed on investigating the
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,…
Generalized Pump-restriction Theorem
Sinitsyn, Nikolai A; Chernyak, Vladimir Y
2008-01-01
We formulate conditions under which periodic modulations of parameters on a finite graph with stochastic transitions among its nodes do not lead to overall pump currents through any given link. Our theorem unifies previously known results with the new ones and provides a universal approach to explore futher restrictions on stochastic pump effect in non-adiabatically driven systems with detailed balance.
Equivalence theorem and infrared divergences
Torma, T.
1996-08-01
We look at the equivalence theorem as a statement about the absence of polynomial infrared divergences when {ital m}{sub {ital W}}{r_arrow}0. We prove their absence in a truncated toy model and conjecture that, if they exist at all, they are due to couplings between light particles. {copyright} {ital 1996 The American Physical Society.}
Angle Defect and Descartes' Theorem
ERIC Educational Resources Information Center
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
An implicit sampling theorem for bounded bandlimited functions
NASA Technical Reports Server (NTRS)
Bar-David, I.
1974-01-01
A rigorous proof of the 'strong bias tone' scheme is embodied in the implicit sampling theorem. The representation of signals that are sample functions of possible nonstationary random processes being of principal interest, the proof could not directly invoke results from classical analysis, which depend on the existence of the Fourier transform of the function under consideration; rather, it is based on Zakai's (1965) theorem on the series expansion of functions, band-limited under a suitably extended definition. A practical circuit that restores an approximate version of the signal from its sine-wave-crossings is presented and possible improvements to it are discussed.
Extension of Euler's theorem to n-dimensional spaces
NASA Technical Reports Server (NTRS)
Bar-Itzhack, Itzhack Y.
1989-01-01
Euler's theorem states that any sequence of finite rotations of a rigid body can be described as a single rotation of the body about a fixed axis in three-dimensional Euclidean space. The usual statement of the theorem in the literature cannot be extended to Euclidean spaces of other dimensions. Equivalent formulations of the theorem are given and proved in a way which does not limit them to the three-dimensional Euclidean space. Thus, the equivalent theorems hold in other dimensions. The proof of one formulation presents an algorithm which shows how to compute an angular-difference matrix that represents a single rotation which is equivalent to the sequence of rotations that have generated the final n-D orientation. This algorithm results also in a constant angular velocity which, when applied to the initial orientation, eventually yields the final orientation regardless of what angular velocity generated the latter. The extension of the theorem is demonstrated in a four-dimensional numerical example.
Extension to Eulers's theorem to n-dimensional spaces
NASA Technical Reports Server (NTRS)
Bar-Itzhack, Itzhack Y.
1989-01-01
Euler's theorem states that any sequence of finite rotations of a rigid body can be described as a single rotation of the body about a fixed axis in three-dimensional Euclidean space. The usual statement of the theorem in the literature cannot be extended to Euclidean spaces of other dimensions. Equivalent formulations of the theorem are given in this paper and proven in a way which does not limit them to the three-dimensional Euclidean space. Thus, the equivalent theorems hold in other dimensions. The proof of one formulation presents an algorithm which shows how to compute an angular-difference matrix that represents a single rotation which is equivalent to the sequence of rotations that have generated the final n-D orientation. This algorithm results also in a constant angular-velocity which, when applied to the initial orientation, yields eventually the final orientation regardless of what angular velocity generated the latter. Finally, the extension of the theorem is demonstrated in a four-dimensional numerical example.
Analytical proof of Gisin's theorem for three qubits
Choudhary, Sujit K.; Ghosh, Sibasish; Kar, Guruprasad; Rahaman, Ramij
2010-04-15
Gisin's theorem assures that for any pure bipartite entangled state, there is violation of the inequality of Bell and of Clauser, Horne, Shimony, and Holt, revealing its contradiction with local realistic model. Whether a similar result holds for three-qubit pure entangled states remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy's nonlocality argument.
A Fundamental Theorem on Particle Acceleration
Xie, Ming
2003-05-01
A fundamental theorem on particle acceleration is derived from the reciprocity principle of electromagnetism and a rigorous proof of the theorem is presented. The theorem establishes a relation between acceleration and radiation, which is particularly useful for insightful understanding of and practical calculation about the first order acceleration in which energy gain of the accelerated particle is linearly proportional to the accelerating field.
Investigating the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Johnson, Heather L.
2010-01-01
The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were…
Generalizations of Ptolemy and Brahmagupta Theorems
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
Pythagorean Theorem Proofs: Connecting Interactive Websites
ERIC Educational Resources Information Center
Lin, Cheng-Yao
2007-01-01
There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)
Bell's theorem, inference, and quantum transactions
NASA Astrophysics Data System (ADS)
Garrett, A. J. M.
1990-04-01
Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, “local”) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's new transactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the “delayed choice” experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theorem reinforces arguments in favor of hidden variables.
Local Accountability in Vocational Education: A Theoretical Model and Its Limitations in Practice.
ERIC Educational Resources Information Center
Stecher, Brian M.; Hanser, Lawrence M.
A study sought to determine the extent to which local accountability systems exist in vocational education and to describe the nature of the underlying relationships between such programs and their constituents. Data were collected through interviews from two local vocational education programs in each of five states (California, Florida,…
McGarry, Conor K.; Bokrantz, Rasmus; O’Sullivan, Joe M.; Hounsell, Alan R.
2014-10-01
Efficacy of inverse planning is becoming increasingly important for advanced radiotherapy techniques. This study’s aims were to validate multicriteria optimization (MCO) in RayStation (v2.4, RaySearch Laboratories, Sweden) against standard intensity-modulated radiation therapy (IMRT) optimization in Oncentra (v4.1, Nucletron BV, the Netherlands) and characterize dose differences due to conversion of navigated MCO plans into deliverable multileaf collimator apertures. Step-and-shoot IMRT plans were created for 10 patients with localized prostate cancer using both standard optimization and MCO. Acceptable standard IMRT plans with minimal average rectal dose were chosen for comparison with deliverable MCO plans. The trade-off was, for the MCO plans, managed through a user interface that permits continuous navigation between fluence-based plans. Navigated MCO plans were made deliverable at incremental steps along a trajectory between maximal target homogeneity and maximal rectal sparing. Dosimetric differences between navigated and deliverable MCO plans were also quantified. MCO plans, chosen as acceptable under navigated and deliverable conditions resulted in similar rectal sparing compared with standard optimization (33.7 ± 1.8 Gy vs 35.5 ± 4.2 Gy, p = 0.117). The dose differences between navigated and deliverable MCO plans increased as higher priority was placed on rectal avoidance. If the best possible deliverable MCO was chosen, a significant reduction in rectal dose was observed in comparison with standard optimization (30.6 ± 1.4 Gy vs 35.5 ± 4.2 Gy, p = 0.047). Improvements were, however, to some extent, at the expense of less conformal dose distributions, which resulted in significantly higher doses to the bladder for 2 of the 3 tolerance levels. In conclusion, similar IMRT plans can be created for patients with prostate cancer using MCO compared with standard optimization. Limitations exist within MCO regarding conversion of navigated plans to
Mitaim, Sanya; Kosko, Bart
2014-11-01
We show that the main forbidden interval theorems of stochastic resonance hold for a correlation performance measure. Earlier theorems held only for performance measures based on mutual information or the probability of error detection. Forbidden interval theorems ensure that a threshold signal detector benefits from deliberately added noise if the average noise does not lie in an interval that depends on the threshold value. We first show that this result holds for correlation for all finite-variance noise and for all forms of infinite-variance stable noise. A second forbidden-interval theorem gives necessary and sufficient conditions for a local noise benefit in a bipolar signal system when the noise comes from a location-scale family. A third theorem gives a general condition for a local noise benefit for arbitrary signals with finite second moments and for location-scale noise. This result also extends forbidden intervals to forbidden bands of parameters. A fourth theorem gives necessary and sufficient conditions for a local noise benefit when both the independent signal and noise are normal. A final theorem derives necessary and sufficient conditions for forbidden bands when using arrays of threshold detectors for arbitrary signals and location-scale noise. PMID:25493756
Code of Federal Regulations, 2011 CFR
2011-04-01
... 20 Employees' Benefits 3 2011-04-01 2011-04-01 false Do the WIA administrative cost limits for States and local areas apply to NFJP grants? 669.555 Section 669.555 Employees' Benefits EMPLOYMENT AND TRAINING ADMINISTRATION, DEPARTMENT OF LABOR NATIONAL FARMWORKER JOBS PROGRAM UNDER TITLE I OF THE WORKFORCE INVESTMENT ACT...
Code of Federal Regulations, 2014 CFR
2014-04-01
... 20 Employees' Benefits 4 2014-04-01 2014-04-01 false Under what limited conditions may a Local Board directly be a provider of core services, intensive services, or training services, or act as a One-Stop Operator? 661.310 Section 661.310 Employees' Benefits EMPLOYMENT AND TRAINING...
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
NASA Astrophysics Data System (ADS)
Miles, J. A.; Das, Diptaranjan; Simmons, Z. J.; Yavuz, D. D.
2015-09-01
We experimentally demonstrate the localization of excitation between hyperfine ground states of 87Rb atoms to as small as λ /13 -wide spatial regions. We use ultracold atoms trapped in a dipole trap and utilize electromagnetically induced transparency (EIT) for the atomic excitation. The localization is achieved by combining a spatially varying coupling laser (standing wave) with the intensity dependence of EIT. The excitation is fast (150 ns laser pulses) and the dark-state fidelity can be made higher than 94% throughout the standing wave. Because the width of the localized regions is much smaller than the wavelength of the driving light, traditional optical imaging techniques cannot resolve the localized features. Therefore, to measure the excitation profile, we use an autocorrelation-like method where we perform two EIT sequences separated by a time delay, during which we move the standing wave.
Krasilnikov, M. B. Kudryavtsev, A. A.; Kapustin, K. D.
2014-12-15
It is shown that the local approximation for computing the electron distribution function depends both on the ratio between the energy relaxation length and a characteristic plasma length and on the ratio between heating and ambipolar electric fields. In particular, the local approximation is not valid at the discharge periphery even at high pressure due to the fact that the ambipolar electric field practically always is larger than the heating electric field.
Subotnik, Joseph E; Sodt, Alex; Head-Gordon, Martin
2008-01-21
Local coupled-cluster theory provides an algorithm for measuring electronic correlation quickly, using only the spatial locality of localized electronic orbitals. Previously, we showed [J. Subotnik et al., J. Chem. Phys. 125, 074116 (2006)] that one may construct a local coupled-cluster singles-doubles theory which (i) yields smooth potential energy surfaces and (ii) achieves near linear scaling. That theory selected which orbitals to correlate based only on the distances between the centers of different, localized orbitals, and the approximate potential energy surfaces were characterized as smooth using only visual identification. This paper now extends our previous algorithm in three important ways. First, locality is now based on both the distances between the centers of orbitals as well as the spatial extent of the orbitals. We find that, by accounting for the spatial extent of a delocalized orbital, one can account for electronic correlation in systems with some electronic delocalization using fast correlation methods designed around orbital locality. Second, we now enforce locality on not just the amplitudes (which measure the exact electron-electron correlation), but also on the two-electron integrals themselves (which measure the bare electron-electron interaction). Our conclusion is that we can bump integrals as well as amplitudes, thereby gaining a tremendous increase in speed and paradoxically increasing the accuracy of our LCCSD approach. Third and finally, we now make a rigorous definition of chemical smoothness as requiring that potential energy surfaces not support artificial maxima, minima, or inflection points. By looking at first and second derivatives from finite difference techniques, we demonstrate complete chemical smoothness of our potential energy surfaces (bumping both amplitudes and integrals). These results are significant both from a theoretical and from a computationally practical point of view. PMID:18205484
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)).
A global conformal extension theorem for perfect fluid Bianchi space-times
Luebbe, Christian Tod, Paul
2008-12-15
A global extension theorem is established for isotropic singularities in polytropic perfect fluid Bianchi space-times. When an extension is possible, the limiting behaviour of the physical space-time near the singularity is analysed.
Isothermal-sweep theorems for ultracold quantum gases in a canonical ensemble
NASA Astrophysics Data System (ADS)
Iskin, M.
2011-03-01
After deriving the isothermal Hellmann-Feynman theorem (IHFT) that is suitable for mixed states in a canonical ensemble, we use this theorem to obtain the isothermal magnetic-field sweep theorems for the free, average, and trapping energies and for the entropy, specific heat, pressure, and atomic compressibility of strongly correlated ultracold quantum gases. In particular, we apply the sweep theorems to two-component Fermi gases in the weakly interacting Bardeen-Cooper-Schrieffer and Bose-Einstein condensate limits, showing that the temperature dependence of the contact parameter can be determined by varying either the entropy or specific heat with respect to the scattering length. We also use the IHFT to obtain the virial theorem in a canonical ensemble and discuss its implications for quantum gases.
Numerous strategies but limited implementation guidance in US local adaptation plans
NASA Astrophysics Data System (ADS)
Woodruff, Sierra C.; Stults, Missy
2016-08-01
Adaptation planning offers a promising approach for identifying and devising solutions to address local climate change impacts. Yet there is little empirical understanding of the content and quality of these plans. We use content analysis to evaluate 44 local adaptation plans in the United States and multivariate regression to examine how plan quality varies across communities. We find that plans draw on multiple data sources to analyse future climate impacts and include a breadth of strategies. Most plans, however, fail to prioritize impacts and strategies or provide detailed implementation processes, raising concerns about whether adaptation plans will translate into on-the-ground reductions in vulnerability. Our analysis also finds that plans authored by the planning department and those that engaged elected officials in the planning process were of higher quality. The results provide important insights for practitioners, policymakers and scientists wanting to improve local climate adaptation planning and action.
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.
Hijacked organic, limited local, faulty fair trade: what's a radical to eat?
Engler, Mark
2012-01-01
Organic farming has been hijacked by big business. Local food can have a larger carbon footprint than products shipped in from overseas. Fair trade doesn't address the real concerns of farmers in the global South. As the food movement has moved from the countercultural fringe to become a mainstream phenomenon, organic, local, and fair trade advocates have been beset by criticism from overt foes and erstwhile allies alike. Now that Starbucks advertises fair trade coffee and Kraft owns Boca soy burgers, it's fair to ask, "What's a radical to eat?" PMID:22834045
Multifluorophore localization as a percolation problem: limits to density and precision.
Small, Alex
2016-07-01
We show that the maximum desirable density of activated fluorophores in a superresolution experiment can be determined by treating the overlapping point spread functions as a problem in percolation theory. We derive a bound on the density of activated fluorophores, taking into account the desired localization accuracy and precision, as well as the number of photons emitted. Our bound on density is close to that reported in experimental work, suggesting that further increases in the density of imaged fluorophores will come at the expense of localization accuracy and precision. PMID:27409704
49 CFR 172.822 - Limitation on actions by states, local governments, and Indian tribes.
Code of Federal Regulations, 2010 CFR
2010-10-01
... state, political subdivision of a state, or an Indian tribe that designates, limits, or prohibits the use of a rail line (other than a rail line owned by a state, political subdivision of a state, or...
Limits on Einstein’s Equivalence Principle from the First Localized Fast Radio Burst FRB 150418
NASA Astrophysics Data System (ADS)
Tingay, S. J.; Kaplan, D. L.
2016-04-01
Fast radio bursts (FRBs) have recently been used to place limits on Einstein's Equivalence Principle via observations of time delays between photons of different radio frequencies by Wei et al. These limits on differential post-Newtonian parameters ({{Δ }}γ \\lt 2.52× {10}-8) are the best yet achieved, but they still rely on uncertain assumptions, namely the relative contributions of dispersion and gravitational delays to the observed time delays and the distances to FRBs. Also, very recently, the first FRB host galaxy has likely been identified, providing the first redshift-based distance estimate to FRB 150418. Moreover, consistency between the {{{Ω }}}{{IGM}} estimate from FRB 150418 and {{{Ω }}}{{IGM}}, expected from ΛCDM models and WMAP observations, leads one to conclude that the observed time delay for FRB 150418 is highly dominated by dispersion, with any gravitational delays being small contributors. This points to even tighter limits on Δγ. In this paper, the technique of Wei et al. is applied to FRB 150418 to produce a limit of Δγ < 1-2 × 10-9, approximately an order of magnitude better than previous limits and in line with expectations by Wei et al. for what could be achieved if the dispersive delay is separated from other effects. Future substantial improvements in such limits will depend on accurately determining the contribution of individual ionized components to the total observed time delays for FRBs.
No-go theorems for generalized chameleon field theories.
Wang, Junpu; Hui, Lam; Khoury, Justin
2012-12-14
The chameleon, or generalizations thereof, is a light scalar that couples to matter with gravitational strength, but whose manifestation depends on the ambient matter density. A key feature is that the screening mechanism suppressing its effects in high-density environments is determined by the local scalar field value. Under very general conditions, we prove two theorems limiting its cosmological impact: (i) the Compton wavelength of such a scalar can be at most ~/= 1 MPc at the present cosmic density, which restricts its impact to nonlinear scales; and (ii) the conformal factor relating Einstein- and Jordan-frame scale factors is essentially constant over the last Hubble time, which precludes the possibility of self-acceleration. These results imply that chameleonlike scalar fields have a negligible effect on the linear-scale growth history; theories that invoke a chameleonlike scalar to explain cosmic acceleration rely on a form of dark energy rather than a genuine modified gravity effect. Our analysis applies to a broad class of chameleon, symmetron, and dilaton theories. PMID:23368302
Implementation of a workplace smoking ban in bars: The limits of local discretion
Montini, Theresa; Bero, Lisa A
2008-01-01
Background In January 1998, the California state legislature extended a workplace smoking ban to bars. The purpose of this study was to explore the conditions that facilitate or hinder compliance with a smoking ban in bars. Methods We studied the implementation of the smoking ban in bars by interviewing three sets of policy participants: bar employers responsible for complying with the law; local government officials responsible for enforcing the law; and tobacco control activists who facilitated implementation. We transcribed the interviews and did a qualitative analysis of the text. Results The conditions that facilitated bar owners' compliance with a smoking ban in bars included: if the cost to comply was minimal; if the bars with which they were in competition were in compliance with the smoking ban; and if there was authoritative, consistent, coordinated, and uniform enforcement. Conversely, the conditions that hindered compliance included: if the law had minimal sanctions; if competing bars in the area allowed smoking; and if enforcement was delayed or inadequate. Conclusion Many local enforcers wished to forfeit their local discretion and believed the workplace smoking ban in bars would be best implemented by a state agency. The potential implication of this study is that, given the complex nature of local politics, smoking bans in bars are best implemented at a broader provincial or national level. PMID:19063716
Localization of type I interferon receptor limits interferon-induced TLR-3 in epithelial cells
This study aimed to expand on the role of type I IFNs in the influenza-induced upregulation of TLR3 and determine whether and how the localization of the IFN-alpha/beta receptor (IFNAR) in respiratory epithelial cells could modify IFN-induced responses. Using differentiated prima...
Limitations of a localized surface plasmon resonance sensor on Salmonella detection
Technology Transfer Automated Retrieval System (TEKTRAN)
We have designed a localized surface plasmon resonance (LSPR) biosensor to perform the whole cell detection of Salmonella using gold nanoparticls fabricated by oblique angle deposition technique. The LSPR sensor showed a plasmon peak shift due to the Salmonella antigen and anti-Salmonella antibody r...
Taking account of local culture: limits to the development of a professional ethos.
Goopy, Suzanne E
2005-06-01
The need to extend the discussion of culture in the study of nursing, combined with an enthusiasm for the possibility of viewing nursing from a new perspective, provides the impetus for this study. Based on fieldwork undertaken in the intensive care unit (RICU) of a major public hospital in Rome (Italy), this paper explores some of the key aspects of the social relations and local staff culture of one particular group of Italian nurses. In a climate of globalization, where the deployment of dominant Anglo-American ideas is difficult to counter, the RICU presents as a setting which challenges the widespread assumptions of universal standards of nursing practice. By building a picture of the working world of these particular nurses, we are assisted in our understanding of nursing practice as a local cultural activity. In exploring the significance of local culture this paper brings into question the universality of the current paradigm of professionalism and professional identity, and emphasizes the value of acknowledging local culture. PMID:15892730
The value, limitations, and challenges of employing local experts in conservation research.
Elbroch, Mark; Mwampamba, Tuyeni H; Santos, Maria J; Zylberberg, Maxine; Liebenberg, Louis; Minye, James; Mosser, Christopher; Reddy, Erin
2011-12-01
Evidence suggests that the involvement of local people in conservation work increases a project's chances of success. Involving citizen scientists in research, however, raises questions about data quality. As a tool to better assess potential participants for conservation projects, we developed a knowledge gradient, K, along which community members occupy different positions on the basis of their experience with and knowledge of a research subject. This gradient can be used to refine the citizen-science concept and allow researchers to differentiate between community members with expert knowledge and those with little knowledge. We propose that work would benefit from the inclusion of select local experts because it would allow researchers to harness the benefits of local involvement while maintaining or improving data quality. We used a case study from the DeHoop Nature Preserve, South Africa, in which we conducted multiple interviews, identified and employed a local expert animal tracker, evaluated the expert's knowledge, and analyzed the data collected by the expert. The expert animal tracker J.J. created his own sampling design and gathered data on mammals. He patrolled 4653 km in 214 days and recorded 4684 mammals. He worked from a central location, and his patrols formed overlapping loops; however, his data proved neither spatially nor temporally autocorrelated. The distinctive data collected by J.J. are consistent with the notion that involving local experts can produce reliable data. We developed a conceptual model to help identify the appropriate participants for a given project on the basis of research budget, knowledge or skills needed, technical literacy requirements, and scope of the project. PMID:21966985
Maximum precision closed-form solution for localizing diffraction-limited spots in noisy images
Larkin, Joshua D.; Cook, Peter R.
2012-01-01
Super-resolution techniques like PALM and STORM require accurate localization of single fluorophores detected using a CCD. Popular localization algorithms inefficiently assume each photon registered by a pixel can only come from an area in the specimen corresponding to that pixel (not from neighboring areas), before iteratively (slowly) fitting a Gaussian to pixel intensity; they fail with noisy images. We present an alternative; a probability distribution extending over many pixels is assigned to each photon, and independent distributions are joined to describe emitter location. We compare algorithms, and recommend which serves best under different conditions. At low signal-to-noise ratios, ours is 2-fold more precise than others, and 2 orders of magnitude faster; at high ratios, it closely approximates the maximum likelihood estimate. PMID:23038398
Neutrophil Recruitment to Lymph Nodes Limits Local Humoral Response to Staphylococcus aureus
Kamenyeva, Olena; Boularan, Cedric; Kabat, Juraj; Cheung, Gordon Y. C.; Cicala, Claudia; Yeh, Anthony J.; Chan, June L.; Periasamy, Saravanan; Otto, Michael; Kehrl, John H.
2015-01-01
Neutrophils form the first line of host defense against bacterial pathogens. They are rapidly mobilized to sites of infection where they help marshal host defenses and remove bacteria by phagocytosis. While splenic neutrophils promote marginal zone B cell antibody production in response to administered T cell independent antigens, whether neutrophils shape humoral immunity in other lymphoid organs is controversial. Here we investigate the neutrophil influx following the local injection of Staphylococcus aureus adjacent to the inguinal lymph node and determine neutrophil impact on the lymph node humoral response. Using intravital microscopy we show that local immunization or infection recruits neutrophils from the blood to lymph nodes in waves. The second wave occurs temporally with neutrophils mobilized from the bone marrow. Within lymph nodes neutrophils infiltrate the medulla and interfollicular areas, but avoid crossing follicle borders. In vivo neutrophils form transient and long-lived interactions with B cells and plasma cells, and their depletion augments production of antigen-specific IgG and IgM in the lymph node. In vitro activated neutrophils establish synapse- and nanotube-like interactions with B cells and reduce B cell IgM production in a TGF- β1 dependent manner. Our data reveal that neutrophils mobilized from the bone marrow in response to a local bacterial challenge dampen the early humoral response in the lymph node. PMID:25884622
New pulsar limit on local Lorentz invariance violation of gravity in the standard-model extension
NASA Astrophysics Data System (ADS)
Shao, Lijing
2014-12-01
In the pure-gravity sector of the minimal standard-model extension, nine Lorentz-violating coefficients of a vacuum-condensed tensor field describe dominant observable deviations from general relativity, out of which eight were already severely constrained by precision experiments with lunar laser ranging, atom interferometry, and pulsars. However, the time-time component of the tensor field, s¯TT, dose not enter into these experiments, and was only very recently constrained by Gravity Probe B. Here we propose a novel idea of using the Lorentz boost between different frames to mix different components of the tensor field, and thereby obtain a stringent limit of s¯TT from binary pulsars. We perform various tests with the state-of-the-art white dwarf optical spectroscopy and pulsar radio timing observations, in order to get new robust limits of s¯TT. With the isotropic cosmic microwave background as a preferred frame, we get |s¯ TT|<1.6 ×10-5 (95% C.L.), and without assuming the existence of a preferred frame, we get |s¯ TT|<2.8 ×10-4 (95% C.L.). These two limits are respectively about 500 times and 30 times better than the current best limit.
The Effect of Local Limitations on General State Aid in Illinois.
ERIC Educational Resources Information Center
Bush, Erik
2002-01-01
Study to determine if a substantive relationship exits between the progression of a federal Tax Increment Financing (TIF) district, the long-term effects of the state Property Tax Extension Limitation Law (PTELL), and the General State Aid funding of school districts in Illinois. Finds that both TIF and PTELL lead to an increase in General State…
New Fermionic Soft Theorems for Supergravity Amplitudes.
Chen, Wei-Ming; Huang, Yu-Tin; Wen, Congkao
2015-07-10
Soft limits of a massless S matrix are known to reflect the symmetries of the theory. In particular, for theories with Goldstone bosons, the double-soft limit of scalars reveals the coset structure of the vacuum manifold. In this Letter, we propose that such universal double-soft behavior is not only true for scalars, but also for spin-1/2 particles in four dimensions and fermions in three dimensions. We first consider the Akulov-Volkov theory and demonstrate that the double-soft limit of Goldstinos yields the supersymmetry algebra. More surprisingly, we also find that amplitudes in 4≤N≤8 supergravity theories in four dimensions as well as N=16 supergravity in three dimensions behave universally in the double-soft-fermion limit, analogous to the scalar ones. The validity of the new soft theorems at loop level is also studied. The results for supergravity are beyond what is implied by supersymmetry Ward identities and may impose nontrivial constraints on the possible counterterms for supergravity theories. PMID:26207460
NASA Astrophysics Data System (ADS)
Adams, R. J.; Wang, G.; Canning, F. X.; Davis, B. A.
2006-12-01
A procedure is outlined for determining compressed representations of the plane wave response matrix (P matrix) for transverse magnetic scattering with respect to the z axis from convex cylinders. The method is based on the determination of band-limited spectral modes that excite spatially localized solutions to the wave equation and satisfy global boundary conditions. Numerical examples indicate that the proposed method provides a representation of the P matrix with reduced computational complexity.
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.
Moon, Sojin; Bannen, Ryan M; Rutkoski, Thomas J; Phillips, George N; Bae, Euiyoung
2014-10-01
Local structural entropy (LSE) is a descriptor for the extent of conformational heterogeneity in short protein sequences that is computed from structural information derived from the Protein Data Bank. Reducing the LSE of a protein sequence by introducing amino acid mutations can result in fewer conformational states and thus a more stable structure, indicating that LSE optimization can be used as a protein stabilization method. Here, we describe a series of LSE optimization experiments designed to stabilize mesophilic and thermophilic adenylate kinases (AKs) and report crystal structures of LSE-optimized AK variants. In the mesophilic AK, thermal stabilization by LSE reduction was effective but limited. Structural analyses of the LSE-optimized mesophilic AK variants revealed a strong correlation between LSE and the apolar buried surface area. Additional mutations designed to introduce noncovalent interactions between distant regions of the polypeptide resulted in further stabilization. Unexpectedly, optimizing the LSE of the thermophilic AK resulted in a decrease in thermal stability. This destabilization was reduced when charged residues were excluded from the possible substitutions during LSE optimization. These observations suggest that stabilization by LSE reduction may result from the optimization of local hydrophobic contacts. The limitations of this process are likely due to ignorance of other interactions that bridge distant regions in a given amino acid sequence. Our results illustrate the effectiveness and limitations of LSE optimization as a protein stabilization strategy and highlight the importance and complementarity of local conformational stability and global interactions in protein thermal stability. PMID:24931334
Non-local rheological properties of granular flows near a jamming limit.
Aranson, I. S.; Tsimring, L. S.; Malloggi, F.; Clement, E.; Materials Science Division; Univ. of California at San Diego; CNRS-ESPCI Univ.
2008-01-01
We study the rheology of sheared granular flows close to a jamming transition. We use the approach of partially fluidized theory (PFT) with a full set of equations extending the thin layer approximation derived previously for the description of the granular avalanches phenomenology. This theory provides a picture compatible with a local rheology at large shear rates [G. D. R. Midi, Eur. Phys. J. E 14, 341 (2004)] and it works in the vicinity of the jamming transition, where a description in terms of a simple local rheology comes short. We investigate two situations displaying important deviations from local rheology. The first one is based on a set of numerical simulations of sheared soft two-dimensional circular grains. The next case describes previous experimental results obtained on avalanches of sandy material flowing down an incline. Both cases display, close to jamming, significant deviations from the now standard Pouliquen's flow rule [O. Pouliquen, Phys. Fluids 11, 542 (1999); 11, 1956 (1999)]. This discrepancy is the hallmark of a strongly nonlocal rheology and in both cases, we relate the empirical results and the outcomes of PFT. The numerical simulations show a characteristic constitutive structure for the fluid part of the stress involving the confining pressure and the material stiffness that appear in the form of an additional dimensionless parameter. This constitutive relation is then used to describe the case of sandy flows. We show a quantitative agreement as far as the effective flow rules are concerned. A fundamental feature is identified in PFT as the existence of a jammed layer developing in the vicinity of the flow arrest that corroborates the experimental findings. Finally, we study the case of solitary erosive granular avalanches and relate the outcome with the PFT analysis.
NASA Astrophysics Data System (ADS)
Ebrahimi, F.; Blackman, E. G.
2016-06-01
For cylindrical differentially rotating plasmas, we study large-scale magnetic field generation from finite amplitude non-axisymmetric perturbations by comparing numerical simulations with quasi-linear analytic theory. When initiated with a vertical magnetic field of either zero or finite net flux, our global cylindrical simulations exhibit the magnetorotational instability (MRI) and large-scale dynamo growth of radially alternating mean fields, averaged over height and azimuth. This dynamo growth is explained by our analytic calculations of a non-axisymmetric fluctuation-induced electromotive force that is sustained by azimuthal shear of the fluctuating fields. The standard `Ω effect' (shear of the mean field by differential rotation) is unimportant. For the MRI case, we express the large-scale dynamo field as a function of differential rotation. The resulting radially alternating large-scale fields may have implications for angular momentum transport in discs and corona. To connect with previous work on large-scale dynamos with local linear shear and identify the minimum conditions needed for large-scale field growth, we also solve our equations in local Cartesian coordinates. We find that large-scale dynamo growth in a linear shear flow without rotation can be sustained by shear plus non-axisymmetric fluctuations - even if not helical, a seemingly previously unidentified distinction. The linear shear flow dynamo emerges as a more restricted version of our more general new global cylindrical calculations.
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.
Strong converse theorems using Rényi entropies
NASA Astrophysics Data System (ADS)
Leditzky, Felix; Wilde, Mark M.; Datta, Nilanjana
2016-08-01
We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint arXiv:1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.
Feedback localization of freely diffusing fluorescent particles near the optical shot-noise limit
NASA Astrophysics Data System (ADS)
Berglund, Andrew J.; McHale, Kevin; Mabuchi, Hideo
2007-01-01
We report near-optimal tracking of freely diffusing fluorescent particles in a quasi-two-dimensional geometry via photon counting and real-time feedback. We present a quantitative statistical model of our feedback network and find excellent agreement with the experiment. We monitor the motion of a single fluorescent particle with a sensitivity of 15 nm/sqrt Hz while collecting fewer than 5000 fluorescence photons/s. Fluorescent microspheres (diffusion coefficient 1.3 μm2/s) are tracked with a root-mean-square tracking error of 170 nm, within a factor of 2 of the theoretical limit set by photon counting shot noise.
Experiments with central-limit properties of spatial samples from locally covariant random fields
Barringer, T.H.; Smith, T.E.
1992-01-01
When spatial samples are statistically dependent, the classical estimator of sample-mean standard deviation is well known to be inconsistent. For locally dependent samples, however, consistent estimators of sample-mean standard deviation can be constructed. The present paper investigates the sampling properties of one such estimator, designated as the tau estimator of sample-mean standard deviation. In particular, the asymptotic normality properties of standardized sample means based on tau estimators are studied in terms of computer experiments with simulated sample-mean distributions. The effects of both sample size and dependency levels among samples are examined for various value of tau (denoting the size of the spatial kernel for the estimator). The results suggest that even for small degrees of spatial dependency, the tau estimator exhibits significantly stronger normality properties than does the classical estimator of standardized sample means. ?? 1992.
Cosacov, Andrea; Nattero, Julieta; Cocucci, Andrea A.
2008-01-01
Background and Aims Few studies have examined the dynamics of specialist plant–pollinator interactions at a geographical scale. This knowledge is crucial for a more general evolutionary and ecological understanding of specialized plant–pollinator systems. In the present study, variations in pollinator activity, assemblage composition and pollen limitation were explored in the oil-producing species Nierembergia linariifolia (Solanaceae). Methods Pollen limitation in fruit and seed production was analysed by supplementary hand pollination in five wild populations. Pollinator activity and identity were recorded while carrying out supplementary pollination to assess the effect of pollinators on the degree of pollen limitation. In two populations, pollen limitation was discriminated into quantitative and qualitative components by comparing supplementation and hand cross-pollination in fruit set and seed set. The effect of flower number per plant on the number of flowers pollinated per visitor per visit to a plant was examined in one of these populations as a possible cause of low-quality pollination by increasing geitonogamy. Results and Conclusions Although pollen limitation was evident along time and space, differences in magnitude were detected among populations and years that were greatly explained by pollinator activity, which was significantly different across populations. Floral display size had a significant effect on the visitation rate per flower. Limitation by quality clearly affected one population presumably due to a high proportion of geitonogamous pollen. The great inter-population variation in plant–pollinator interaction (both in pollinator assemblages composition and pollinator activity) and fitness consequences, suggests that this system should be viewed as a mosaic of locally selective processes and locally specialized interactions. PMID:18765440
F. Cui; F.J. Presuel-Moreno; R.G. Kelly
2005-10-13
The ability of a SS316L surface wetted with a thin electrolyte layer to serve as an effective cathode for an active localized corrosion site was studied computationally. The dependence of the total net cathodic current, I{sub net}, supplied at the repassivation potential E{sub rp} (of the anodic crevice) on relevant physical parameters including water layer thickness (WL), chloride concentration ([Cl{sup -}]) and length of cathode (Lc) were investigated using a three-level, full factorial design. The effects of kinetic parameters including the exchange current density (i{sub o,c}) and Tafel slope ({beta}{sub c}) of oxygen reduction, the anodic passive current density (i{sub p}) (on the cathodic surface), and E{sub rp} were studied as well using three-level full factorial designs of [Cl{sup -}] and Lc with a fixed WL of 25 {micro}m. The study found that all the three parameters WL, [Cl{sup -}] and Lc as well as the interactions of Lc x WL and Lc x [Cl{sup -}] had significant impact on I{sub net}. A five-factor regression equation was obtained which fits the computation results reasonably well, but demonstrated that interactions are more complicated than can be explained with a simple linear model. Significant effects on I{sub net} were found upon varying either i{sub o,c}, {beta}{sub c}, or E{sub rp}, whereas i{sub p} in the studied range was found to have little impact. It was observed that I{sub net} asymptotically approached maximum values (I{sub max}) when Lc increased to critical minimum values. I{sub max} can be used to determine the stability of coupled localized corrosion and the critical Lc provides important information for experimental design and corrosion protection.
Yaroshchuk, Andriy
2012-11-15
The problem is considered theoretically of dynamics of current-induced concentration polarization of interfaces between ideally perm-selective and non-ideally perm-selective ("leaky") ion-exchange media in binary electrolyte solutions under galvanostatic conditions and at negligible volume flow. In contrast to the previous studies, the analysis is systematically carried out in terms of local thermodynamic equilibrium in the approximation of local electric neutrality in virtual solution. For macroscopically homogeneous media, this enables one to obtain model-independent results in quadratures for the stationary state as well as an approximate scaling-form solution for the transient response to the step-wise increase in electric-current density. These results are formulated in terms of such phenomenological properties of the "leaky" medium as ion transport numbers, diffusion permeability to salt and specific chemical capacity. An easy-to-solve numerically 1D PDE is also formulated in the same terms. A systematic parametric study is carried out within the scope of fine-pore model of "leaky" medium in terms of such properties as volumetric concentration of fixed electric charges and diffusivities of ions of symmetrical electrolyte. While previous studies paid principal attention to the shape and propagation rate of the so-called deionization "shocks", we also consider in detail the time evolution of voltage drop and interface salt concentration. Our analysis confirms the previously predicted pattern of propagating deionization "shocks" within the "leaky" medium but also reveals several novel features. In particular, we demonstrate that the deionization-shock pattern is really pronounced only at intermediate ratios of fixed-charge concentration to the initial salt concentration and at quite high steady-state voltages where the model used in this and previous studies is applicable only at relatively early stages of concentration-polarization process. PMID:22947188
Maheshwari, Anurag; Janssens, Kris; Bogie, Jeroen; Van Den Haute, Chris; Struys, Tom; Lambrichts, Ivo; Baekelandt, Veerle; Stinissen, Piet; Hendriks, Jerome J A; Slaets, Helena; Hellings, Niels
2013-01-01
Demyelination is one of the pathological hallmarks of multiple sclerosis (MS). To date, no therapy is available which directly potentiates endogenous remyelination. Interleukin-11 (IL-11), a member of the gp130 family of cytokines, is upregulated in MS lesions. Systemic IL-11 treatment was shown to ameliorate clinical symptoms in experimental autoimmune encephalomyelitis (EAE), an animal model of MS. IL-11 modulates immune cells and protects oligodendrocytes in vitro. In this study, the cuprizone-induced demyelination mouse model was used to elucidate effects of IL-11 on de- and remyelination, independent of the immune response. Prophylactic-lentiviral- (LV-) mediated overexpression of IL-11 in mouse brain significantly limited acute demyelination, which was accompanied with the preservation of CC1(+) mature oligodendrocytes (OLs) and a decrease in microglial activation (Mac-2(+)). We further demonstrated that IL-11 directly reduces myelin phagocytosis in vitro. When IL-11 expressing LV was therapeutically applied in animals with extensive demyelination, a significant enhancement of remyelination was observed as demonstrated by Luxol Fast Blue staining and electron microscopy imaging. Our results indicate that IL-11 promotes maturation of NG2(+) OPCs into myelinating CC1(+) OLs and may thus explain the enhanced remyelination. Overall, we demonstrate that IL-11 is of therapeutic interest for MS and other demyelinating diseases by limiting demyelination and promoting remyelination. PMID:23818742
Maheshwari, Anurag; Janssens, Kris; Bogie, Jeroen; Van Den Haute, Chris; Struys, Tom; Lambrichts, Ivo; Baekelandt, Veerle; Stinissen, Piet; Hendriks, Jerome J. A.; Hellings, Niels
2013-01-01
Demyelination is one of the pathological hallmarks of multiple sclerosis (MS). To date, no therapy is available which directly potentiates endogenous remyelination. Interleukin-11 (IL-11), a member of the gp130 family of cytokines, is upregulated in MS lesions. Systemic IL-11 treatment was shown to ameliorate clinical symptoms in experimental autoimmune encephalomyelitis (EAE), an animal model of MS. IL-11 modulates immune cells and protects oligodendrocytes in vitro. In this study, the cuprizone-induced demyelination mouse model was used to elucidate effects of IL-11 on de- and remyelination, independent of the immune response. Prophylactic-lentiviral- (LV-) mediated overexpression of IL-11 in mouse brain significantly limited acute demyelination, which was accompanied with the preservation of CC1+ mature oligodendrocytes (OLs) and a decrease in microglial activation (Mac-2+). We further demonstrated that IL-11 directly reduces myelin phagocytosis in vitro. When IL-11 expressing LV was therapeutically applied in animals with extensive demyelination, a significant enhancement of remyelination was observed as demonstrated by Luxol Fast Blue staining and electron microscopy imaging. Our results indicate that IL-11 promotes maturation of NG2+ OPCs into myelinating CC1+ OLs and may thus explain the enhanced remyelination. Overall, we demonstrate that IL-11 is of therapeutic interest for MS and other demyelinating diseases by limiting demyelination and promoting remyelination. PMID:23818742
Artinianness of local cohomology modules
NASA Astrophysics Data System (ADS)
Aghapournahr, Moharram; Melkersson, Leif
2014-04-01
Some uniform theorems on the artinianness of certain local cohomology modules are proven in a general situation. They generalize and imply previous results about the artinianness of some special local cohomology modules in the graded case.
Differentiable Cohomology on Locally Compact Groups
Whyburn, Kenneth
1970-01-01
In this paper the notions of vector field and differential form are extended to locally compact groups which are the inverse limit of Lie groups. This is done using Bruhat's definition of [unk]c∞ functions on such a group. Vector fields are defined as derivations on the [unk]c∞ functions. Then tangent vectors at a point are defined as elements of the inverse limit of the tangent spaces of the Lie groups. Tangent vectors then are put together to form vector fields, corresponding to a bundle definition, and the two notions are shown to be equivalent. Differential forms are defined using a bundle type definition from continuous linear functional on the tangent space. An existence and uniqueness theorem is proven for the exterior differential. Then an analog of the Poincaré lemma leads to the de Rham theorem relating the Cech cohomology with real coefficients to the cohomology of the differential forms. PMID:16591866
Differentiable cohomology on locally compact groups.
Whyburn, K
1970-09-01
In this paper the notions of vector field and differential form are extended to locally compact groups which are the inverse limit of Lie groups. This is done using Bruhat's definition of [unk](c) (infinity) functions on such a group. Vector fields are defined as derivations on the [unk](c) (infinity) functions. Then tangent vectors at a point are defined as elements of the inverse limit of the tangent spaces of the Lie groups. Tangent vectors then are put together to form vector fields, corresponding to a bundle definition, and the two notions are shown to be equivalent. Differential forms are defined using a bundle type definition from continuous linear functional on the tangent space. An existence and uniqueness theorem is proven for the exterior differential. Then an analog of the Poincaré lemma leads to the de Rham theorem relating the Cech cohomology with real coefficients to the cohomology of the differential forms. PMID:16591866
NASA Astrophysics Data System (ADS)
Borghi, Riccardo
2014-03-01
In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.
General Theorems about Homogeneous Ellipsoidal Inclusions
ERIC Educational Resources Information Center
Korringa, J.; And Others
1978-01-01
Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)
Bring the Pythagorean Theorem "Full Circle"
ERIC Educational Resources Information Center
Benson, Christine C.; Malm, Cheryl G.
2011-01-01
Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…
The Classical Version of Stokes' Theorem Revisited
ERIC Educational Resources Information Center
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
A Generalization of the Prime Number Theorem
ERIC Educational Resources Information Center
Bruckman, Paul S.
2008-01-01
In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiable…
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.
Walters, R W; Grunst, T; Bergelson, J M; Finberg, R W; Welsh, M J; Zabner, J
1999-04-01
Recent identification of two receptors for the adenovirus fiber protein, coxsackie B and adenovirus type 2 and 5 receptor (CAR), and the major histocompatibility complex (MHC) Class I alpha-2 domain allows the molecular basis of adenoviral infection to be investigated. Earlier work has shown that human airway epithelia are resistant to infection by adenovirus. Therefore, we examined the expression and localization of CAR and MHC Class I in an in vitro model of well differentiated, ciliated human airway epithelia. We found that airway epithelia express CAR and MHC Class I. However, neither receptor was present in the apical membrane; instead, both were polarized to the basolateral membrane. These findings explain the relative resistance to adenovirus infection from the apical surface. In contrast, when the virus was applied to the basolateral surface, gene transfer was much more efficient because of an interaction of adenovirus fiber with its receptors. In addition, when the integrity of the tight junctions was transiently disrupted, apically applied adenovirus gained access to the basolateral surface and enhanced gene transfer. These data suggest that the receptors required for efficient infection are not available on the apical surface, and interventions that allow access to the basolateral space where fiber receptors are located increase gene transfer efficiency. PMID:10187807
NASA Astrophysics Data System (ADS)
Briggs, M. A.; Day-Lewis, F. D.; Ong, J. B.; Lane, J. W.; Curtis, G. P.
2012-12-01
In the presence of rate-limited mass transfer (RLMT), conventional chemical sampling of the subsurface preferentially pulls pore water from the mobile domain. Therefore, the characteristics of the immobile domain must be inferred from the mobile tracer signal, which is modified with transport and immobile exchange over a representative length. Because conventional chemical data are not directly sensitive to the immobile zone, this representative length must be sufficient to allow enough exchange between the two domains to inform immobile parameter estimation (e.g., optimal Damkohler range). Flowpath "averaged" RLMT parameters may not well describe the true field variability in the immobile domain size and exchange coefficient, parameters which control the retention and subsequent long-term release of contaminants. In contrast, bulk electrical conductivity is sensitive to the volume-weighted ionic tracer concentration in both the mobile and immobile domains. When co-located bulk conductivity and fluid conductivity are analyzed concurrently, estimates can be obtained for (1) effective RLMT parameters averaged along the upgradient flowpath and (2) local-scale RLMT parameters for the volume from which chemical samples and electrical measurements are taken. Here, we use electrical resistivity tomography (ERT), for the first time, to discriminate and identify effective flowpath and local-scale RLMT parameters, informing the true spatial variability in mass transfer. We apply this technique at the field scale at a uranium contamination site in Naturita, Colorado, USA. Inverse modeling was used to optimize parameter estimates to best simulate both the observed bulk and fluid conductivity, and objectively determine parameter sensitivity, correlation, and confidence. Local RLMT parameters were found to be most sensitive to changes in bulk conductivity, while effective flowpath parameters were most sensitive to changes in fluid conductivity. Observed non-linear hysteresis
Optimized Local Infarct Restraint Improves Left Ventricular Function and Limits Remodeling
Koomalsingh, Kevin J.; Witschey, Walter R.T.; McGarvey, Jeremy R.; Shuto, Takashi; Kondo, Norihiro; Xu, Chun; Jackson, Benjamin M.; Gorman, Joseph H.; Gorman, Robert C.; Pilla, James J.
2013-01-01
Background Preventing expansion and dyskinetic movement of a myocardial infarction (MI) can limit left ventricular (LV) remodeling. Using a device designed to produce variable alteration of infarct stiffness and geometry, we sought to understand how these parameters affect LV function and remodeling early after MI. Methods Ten pigs had posterolateral infarctions. An unexpanded device was placed in 5 animals at the time of infarction, and 5 animals served as untreated controls. One week after MI animals underwent MRI to assess LV size and regional function. In the treatment group, after initial imaging, the device was expanded with 2ml, 4ml, 6ml, 8ml and 10ml of saline. The optimal degree of inflation was defined as that which maximized stroke volume (SV). The device was left optimally inflated in the treatment animals for three additional weeks. Results One week after MI, device inflation to ≥6ml significantly (p<0.05) decreased endsystolic volume (ESV) (0ml:59.9ml±3.8, 6ml:54.0ml≥±3.1, 8ml:50.5ml±4.8, 10ml:46.1ml±2.2) and increased ejection fraction (EF) (0ml:34.6%±1.6, 6ml:39.7%±0.9, 8ml:43.1%±2.7, 10ml:44.1%±0.9). SV significantly (p<0.05) improved for the 6ml and 8ml volumes (0ml: 31.2ml±2.6, 6ml: 35.7ml±2.0, 8ml: 37.5ml±1.9) but trended downward for 10ml (36.6ml±2.8). At four-weeks after MI, end-diastolic volume and ESV were unchanged from one-week values in the treatment group while the control group continued to dilate. SV (38.2±4.4ml vs. 34.0.1±4.8ml, p=0.08) and EF (36.0±2.6% vs. 27.6±1.4%, p=0.04) were also better in the treatment animals. Conclusions Optimized isolated infarct restraint can limit adverse LV remodeling after MI. The tested device affords the potential for a patient-specific therapy to preserve cardiac function after MI. PMID:23146279
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).
Yan, Dongmei; Zhang, Yong; Zhu, Shuangli; Chen, Na; Li, Xiaolei; Wang, Dongyan; Ma, Xiaozhen; Zhu, Hui; Tong, Wenbin; Xu, Wenbo
2014-07-01
From August 2011 to February 2012, an outbreak caused by type 2 circulating vaccine-derived poliovirus (cVDPV) occurred in Aba County, Sichuan, China. During the outbreak, four type 2 VDPVs (≥0.6% nucleotide divergence in the VP1 region relative to the Sabin 2 strain) were isolated from 3 patients with acute flaccid paralysis (AFP) and one close contact. In addition, a type 2 pre-VDPV (0.3% to 0.5% divergence from Sabin 2) that was genetically related to these type 2 VDPVs was isolated from another AFP patient. These 4 patients were all unimmunized children 0.7 to 1.1 years old. Nucleotide sequencing revealed that the 4 VDPV isolates differed from Sabin 2 by 0.7% to 1.2% in nucleotides in the VP1 region and shared 5 nucleotide substitutions with the pre-VDPV. All 5 isolates were closely related, and all were S2/S3/S2/S3 recombinants sharing common recombination crossover sites. Although the two major determinants of attenuation and temperature sensitivity phenotype of Sabin 2 (A481 in the 5' untranslated region and Ile143 in the VP1 protein) had reverted in all 5 isolates, one VDPV (strain CHN16017) still retained the temperature sensitivity phenotype. Phylogenetic analysis of the third coding position of the complete P1 coding region suggested that the cVDPVs circulated locally for about 7 months following the initiating oral poliovirus vaccine (OPV) dose. Our findings reinforce the point that cVDPVs can emerge and spread in isolated communities with immunity gaps and highlight the emergence risks of type 2 cVDPVs accompanying the trivalent OPV used. To solve this issue, it is recommended that type 2 OPV be removed from the trivalent OPV or that inactivated polio vaccine (IPV) be used instead. PMID:24850620
Localization of tissue plasminogen activator in the endothelium of a limited number of vessels.
Levin, E. G.; del Zoppo, G. J.
1994-01-01
The immunolocalization of tissue plasminogen activator (tPA) was assessed in vessels of various sizes from baboons. Femoral artery and vein, carotid artery, aorta, and sections from basal ganglia and cerebral cortex were stained for tPA and CD31, an endothelial cell-specific surface antigen. In each case, the endothelium of the large vessel stained positively for anti-CD31 but not for tPA. However, vascular structures in the adventitia corresponding to the vasa vasorum were found to be associated with tPA antigen. In situ hybridization of femoral artery with 35S-labeled cRNA probes detected tPA mRNA in the vasa vasorum but not the large vessel endothelium. Analysis of the microvasculature of the basal ganglia and cerebral cortex showed limited immunohistochemical staining for tPA; only 3% of the vessels measuring 4 to 100 mu were positive. Even so, tPA was mostly distributed within a narrow range of vessel size; 90% of the positive vessels were classified as precapillary arterioles and postcapillary venules (7.5 to 30.0 mu), whereas only 3% of the capillaries were positive, despite accounting for 40% of all vessels. Thus, tPA-containing endothelium are distributed mainly in smaller vessels, excluding the capillaries. Images Figure 1 Figure 2 Figure 3 PMID:8178936
Kelkar, Manasi; Martin, Sophie G.
2015-01-01
Cells couple growth with division and regulate size in response to nutrient availability. In rod-shaped fission yeast, cell-size control occurs at mitotic commitment. An important regulator is the DYRK-family kinase Pom1, which forms gradients from cell poles and inhibits the mitotic activator Cdr2, itself localized at the medial cortex. Where and when Pom1 modulates Cdr2 activity is unclear as Pom1 medial cortical levels remain constant during cell elongation. Here we show that Pom1 re-localizes to cell sides upon environmental glucose limitation, where it strongly delays mitosis. This re-localization is caused by severe microtubule destabilization upon glucose starvation, with microtubules undergoing catastrophe and depositing the Pom1 gradient nucleator Tea4 at cell sides. Microtubule destabilization requires PKA/Pka1 activity, which negatively regulates the microtubule rescue factor CLASP/Cls1/Peg1, reducing CLASP's ability to stabilize microtubules. Thus, PKA signalling tunes CLASP's activity to promote Pom1 cell side localization and buffer cell size upon glucose starvation. PMID:26443240
Evidence for a fluctuation theorem in an atmospheric circulation model.
Schalge, B; Blender, R; Wouters, J; Fraedrich, K; Lunkeit, F
2013-05-01
An investigation of the distribution of finite time trajectory divergence is performed on an atmospheric global circulation model. The distribution of the largest local Lyapunov exponent shows a significant probability for negative values over time spans up to 10 days. This effect is present for resolutions up to wave numbers ℓ=42 (≈250 km). The probability for a negative local largest Lyapunov exponent decreases over time, similarly to the predictions of the fluctuation theorem for entropy production. The model used is hydrostatic with variable numbers of vertical levels and different horizontal resolutions. PMID:23767493
Evidence for a fluctuation theorem in an atmospheric circulation model
NASA Astrophysics Data System (ADS)
Schalge, B.; Blender, R.; Wouters, J.; Fraedrich, K.; Lunkeit, F.
2013-05-01
An investigation of the distribution of finite time trajectory divergence is performed on an atmospheric global circulation model. The distribution of the largest local Lyapunov exponent shows a significant probability for negative values over time spans up to 10 days. This effect is present for resolutions up to wave numbers ℓ=42 (≈250 km). The probability for a negative local largest Lyapunov exponent decreases over time, similarly to the predictions of the fluctuation theorem for entropy production. The model used is hydrostatic with variable numbers of vertical levels and different horizontal resolutions.
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
Quantum macrostates, equivalence of ensembles, and an H-theorem
NASA Astrophysics Data System (ADS)
De Roeck, Wojciech; Maes, Christian; Netočný, Karel
2006-07-01
Before the thermodynamic limit, macroscopic averages need not commute for a quantum system. As a consequence, aspects of macroscopic fluctuations or of constrained equilibrium require a careful analysis, when dealing with several observables. We propose an implementation of ideas that go back to John von Neumann's writing about the macroscopic measurement. We apply our scheme to the relation between macroscopic autonomy and an H-theorem, and to the problem of equivalence of ensembles. In particular, we show how the latter is related to the asymptotic equipartition theorem. The main point of departure is an expression of a law of large numbers for a sequence of states that start to concentrate, as the size of the system gets larger, on the macroscopic values for the different macroscopic observables. Deviations from that law are governed by the entropy.
Testability of the Pusey-Barrett-Rudolph Theorem
NASA Astrophysics Data System (ADS)
Halataei, Seyyed Mohammad Hassan
2014-03-01
Pusey, Barrett, and Rudolph (PBR) proved a mathematically neat theorem which assesses the reality of the quantum state. They proposed a test such that if any pair of quantum states could pass it, then for small deviation in the probabilities of measurement outcomes, ɛ, from the predicted quantum probabilities, one can conclude that the physical state λ ``is normally closely associated with only one of the two quantum states.'' While the mathematics of their theorem is correct, the physical conclusion is incomplete. In this talk, I present an argument which greatly limits the conclusion one can draw from even a successful PBR test. Specifically, I show that the physical state can be associated with several quantum states and, thus, the reality of quantum states cannot be deduced. This work was supported by the MacArthur Professorship endowed by the John D. and Catherine T. MacArthur Foundation at the University of Illinois.
Sampling Theorem in Terms of the Bandwidth and Sampling Interval
NASA Technical Reports Server (NTRS)
Dean, Bruce H.
2011-01-01
An approach has been developed for interpolating non-uniformly sampled data, with applications in signal and image reconstruction. This innovation generalizes the Whittaker-Shannon sampling theorem by emphasizing two assumptions explicitly (definition of a band-limited function and construction by periodic extension). The Whittaker- Shannon sampling theorem is thus expressed in terms of two fundamental length scales that are derived from these assumptions. The result is more general than what is usually reported, and contains the Whittaker- Shannon form as a special case corresponding to Nyquist-sampled data. The approach also shows that the preferred basis set for interpolation is found by varying the frequency component of the basis functions in an optimal way.
Sano, Nobuyuki
2015-12-28
The impurity-limited resistance and the effect of the phase interference among localized multiple impurities in the quasi-one dimensional (quasi-1D) nanowire structures are systematically investigated under the framework of the scattering theory. We derive theoretical expressions of the impurity-limited resistance in the nanowire under the linear response regime from the Landauer formula and from the Boltzmann transport equation (BTE) with the relaxation time approximation. We show that the formula from the BTE exactly coincides with that from the Landauer approach with the weak-scattering limit when the energy spectrum of the in-coming electrons from the reservoirs is narrow and, thus, point out a possibility that the distinction of the impurity-limited resistances derived from the Landauer formula and that of the BTE could be made clear. The derived formulas are applied to the quasi-1D nanowires doped with multiple localized impurities with short-range scattering potential and the validity of various approximations on the resistance are discussed. It is shown that impurity scattering becomes so strong under the nanowire structures that the weak-scattering limit breaks down in most cases. Thus, both phase interference and phase randomization simultaneously play a crucial role in determining the impurity-limited resistance even under the fully coherent framework. When the impurity separation along the wire axis direction is small, the constructive phase interference dominates and the resistance is much greater than the average resistance. As the separation becomes larger, however, it approaches the series resistance of the single-impurity resistance due to the phase randomization. Furthermore, under the uniform configuration of impurities, the space-average resistance of multiple impurities at room temperature is very close to the series resistance of the single-impurity resistance, and thus, each impurity could be regarded as an independent scattering center. The
NASA Astrophysics Data System (ADS)
Sano, Nobuyuki
2015-12-01
The impurity-limited resistance and the effect of the phase interference among localized multiple impurities in the quasi-one dimensional (quasi-1D) nanowire structures are systematically investigated under the framework of the scattering theory. We derive theoretical expressions of the impurity-limited resistance in the nanowire under the linear response regime from the Landauer formula and from the Boltzmann transport equation (BTE) with the relaxation time approximation. We show that the formula from the BTE exactly coincides with that from the Landauer approach with the weak-scattering limit when the energy spectrum of the in-coming electrons from the reservoirs is narrow and, thus, point out a possibility that the distinction of the impurity-limited resistances derived from the Landauer formula and that of the BTE could be made clear. The derived formulas are applied to the quasi-1D nanowires doped with multiple localized impurities with short-range scattering potential and the validity of various approximations on the resistance are discussed. It is shown that impurity scattering becomes so strong under the nanowire structures that the weak-scattering limit breaks down in most cases. Thus, both phase interference and phase randomization simultaneously play a crucial role in determining the impurity-limited resistance even under the fully coherent framework. When the impurity separation along the wire axis direction is small, the constructive phase interference dominates and the resistance is much greater than the average resistance. As the separation becomes larger, however, it approaches the series resistance of the single-impurity resistance due to the phase randomization. Furthermore, under the uniform configuration of impurities, the space-average resistance of multiple impurities at room temperature is very close to the series resistance of the single-impurity resistance, and thus, each impurity could be regarded as an independent scattering center. The
Coster, Stephanie S; Babbitt, Kimberly J; Cooper, Andrew; Kovach, Adrienne I
2015-02-01
Dispersal and gene flow within animal populations are influenced by the composition and configuration of the landscape. In this study, we evaluated hypotheses about the impact of natural and anthropogenic factors on genetic differentiation in two amphibian species, the spotted salamander (Ambystoma maculatum) and the wood frog (Lithobates sylvaticus) in a commercial forest in central Maine. We conducted this analysis at two scales: a local level, focused on factors measured at each breeding pond, and a landscape level, focused on factors measured between ponds. We investigated the effects of a number of environmental factors in six categories including Productivity, Physical, Land Composition, Land Configuration, Isolation and Location. Embryos were sampled from 56 spotted salamander breeding ponds and 39 wood frog breeding ponds. We used a hierarchical Bayesian approach in the program GESTE at each breeding pond and a random forest algorithm in conjunction with a network analysis between the ponds. We found overall high genetic connectivity across distances up to 17 km for both species and a limited effect of natural and anthropogenic factors on gene flow. We found the null models best explained patterns of genetic differentiation at a local level and found several factors at the landscape level that weakly influenced gene flow. This research indicates multiscale investigations that incorporate local and landscape factors are valuable for understanding patterns of gene flow. Our findings suggest that dispersal rates in this system are high enough to minimize genetic structuring and that current forestry practices do not significantly impede dispersal. PMID:25580642
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.
Equipartition theorem in glasses and liquids
NASA Astrophysics Data System (ADS)
Levashov, Valentin A.; Egami, Takeshi; Aga, Rachel S.; Morris, James R.
2008-03-01
In glasses and liquids phonons have very short life-time, whereas the total potential energy is not linear with temperature, but follows the T**(3/5) law. Thus it may appear that atomic vibrations in liquids cannot be described by the harmonic oscillator model that follows the equipartition theorem for the kinetic energy and potential energy. We show that the description of the nearest neighbor oscillation in terms of the atomic level stresses indeed provide such a description. The model was tested for various pair-wise potentials, including the Lennard-Jones potential, the Johnson potentials, and only the repulsive part of the Johnson potential. In all cases each of the local elastic energies of the six independent components of the stress tensor is equal to kT/4, thus the total potential energy is equal to (3/2)kT. Thus this model provides the basis for discussing the thermodynamic properties of glasses and liquids based on atomistic excitations. An example of this model leading to the description of the glass transition temperature in metallic glasses is discussed [1]. [1] T. Egami, et al., Phys. Rev. B 76, 024203 (2007).
Deacon, Nicholas John; Cavender-Bares, Jeannine
2015-01-01
Background Quercus oleoides Cham. and Schlect., tropical live oak, is a species of conservation importance in its southern range limit of northwestern Costa Rica. It occurs in high-density stands across a fragmented landscape spanning a contrasting elevation and precipitation gradient. We examined genetic diversity and spatial genetic structure in this geographically isolated and genetically distinct population. We characterized population genetic diversity at 11 nuclear microsatellite loci in 260 individuals from 13 sites. We monitored flowering time at 10 sites, and characterized the local environment in order to compare observed spatial genetic structure to hypotheses of isolation-by-distance and isolation-by-environment. Finally, we quantified pollen dispersal distances and tested for local adaptation through a reciprocal transplant experiment in order to experimentally address these hypotheses. Results High genetic diversity is maintained in the population and the genetic variation is significantly structured among sampled sites. We identified 5 distinct genetic clusters and average pollen dispersal predominately occurred over short distances. Differences among sites in flowering phenology and environmental factors, however, were not strictly associated with genetic differentiation. Growth and survival of upland and lowland progeny in their native and foreign environments was expected to exhibit evidence of local adaptation due to the more extreme dry season in the lowlands. Seedlings planted in the lowland garden experienced much higher mortality than seedlings in the upland garden, but we did not identify evidence for local adaptation. Conclusion Overall, this study indicates that the Costa Rican Q. oleoides population has a rich population genetic history. Despite environmental heterogeneity and habitat fragmentation, isolation-by-distance and isolation-by-environment alone do not explain spatial genetic structure. These results add to studies of genetic
On soft theorems and form factors in N=4 SYM theory
NASA Astrophysics Data System (ADS)
Bork, L. V.; Onishchenko, A. I.
2015-12-01
Soft theorems for the form factors of 1/2-BPS and Konishi operator super-multiplets are derived at tree level in N=4 SYM theory. They have a form identical to the one in the amplitude case. For MHV sectors of stress tensor and Konishi operator supermultiplets loop corrections to soft theorems are considered at one loop level. They also appear to have universal form in the soft limit. Possible generalization of the on-shell diagrams to the form factors based on leading soft behavior is suggested. Finally, we give some comments on inverse soft limit and integrability of form factors in the limit q 2 → 0.
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?).
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
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.
A Converse of Fermat's Little Theorem
ERIC Educational Resources Information Center
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
No-hair theorem for the Galileon.
Hui, Lam; Nicolis, Alberto
2013-06-14
We consider a Galileon field coupled to gravity. The standard no-hair theorems do not apply because of the Galileon's peculiar derivative interactions. We prove that, nonetheless, static spherically symmetric black holes cannot sustain nontrivial Galileon profiles. Our theorem holds for trivial boundary conditions and for cosmological ones, and regardless of whether there are nonminimal couplings between the Galileon and gravity of the covariant Galileon type. PMID:25165906
Noether's second theorem for BRST symmetries
Bashkirov, D.; Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2005-05-01
We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles Y{yields}X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.
The matrix Euler-Fermat theorem
NASA Astrophysics Data System (ADS)
Arnol'd, Vladimir I.
2004-12-01
We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem.
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.
Patsha, Avinash E-mail: dhara@igcar.gov.in; Dhara, Sandip; Tyagi, A. K.
2015-09-21
The localized effect of impurities in single GaN nanowires in the sub-diffraction limit is reported using the study of lattice vibrational modes in the evanescent field of Au nanoparticle assisted tip enhanced Raman spectroscopy (TERS). GaN nanowires with the O impurity and the Mg dopants were grown by the chemical vapor deposition technique in the catalyst assisted vapor-liquid-solid process. Symmetry allowed Raman modes of wurtzite GaN are observed for undoped and doped nanowires. Unusually very strong intensity of the non-zone center zone boundary mode is observed for the TERS studies of both the undoped and the Mg doped GaN single nanowires. Surface optical mode of A{sub 1} symmetry is also observed for both the undoped and the Mg doped GaN samples. A strong coupling of longitudinal optical (LO) phonons with free electrons, however, is reported only in the O rich single nanowires with the asymmetric A{sub 1}(LO) mode. Study of the local vibration mode shows the presence of Mg as dopant in the single GaN nanowires.
Wang, Gordon; Smith, Stephen J.
2012-01-01
Photon diffraction limits the resolution of conventional light microscopy at the lateral focal plane to 0.61λ/NA (λ = wavelength of light, NA = numerical aperture of the objective) and at the axial plane to 1.4nλ/NA2 (n = refractive index of the imaging medium, 1.51 for oil immersion), which with visible wavelengths and a 1.4NA oil immersion objective is ∼220 nm and ∼600 nm in the lateral plane and axial plane respectively. This volumetric resolution is too large for the proper localization of protein clustering in subcellular structures. Here we combine the newly developed proteomic imaging technique, Array Tomography (AT), with its native 50–100 nm axial resolution achieved by physical sectioning of resin embedded tissue, and a 2D maximum likelihood deconvolution method, based on Bayes' rule, which significantly improves the resolution of protein puncta in the lateral plane to allow accurate and fast computational segmentation and analysis of labeled proteins. The physical sectioning of AT allows tissue specimens to be imaged at the physical optimum of modern high NA plan-apochormatic objectives. This translates to images that have little out of focus light, minimal aberrations and wave-front distortions. Thus, AT is able to provide images with truly invariant point spread functions (PSF), a property critical for accurate deconvolution. We show that AT with deconvolution increases the volumetric analytical fidelity of protein localization by significantly improving the modulation of high spatial frequencies up to and potentially beyond the spatial frequency cut-off of the objective. Moreover, we are able to achieve this improvement with no noticeable introduction of noise or artifacts and arrive at object segmentation and localization accuracies on par with image volumes captured using commercial implementations of super-resolution microscopes. PMID:22956902
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.
Code of Federal Regulations, 2012 CFR
2012-04-01
... EMPLOYMENT AND TRAINING ADMINISTRATION, DEPARTMENT OF LABOR (CONTINUED) INDIAN AND NATIVE AMERICAN PROGRAMS... administrative cost limit for States and local areas apply to section 166 grants? No, under 20 CFR...
Code of Federal Regulations, 2014 CFR
2014-04-01
... EMPLOYMENT AND TRAINING ADMINISTRATION, DEPARTMENT OF LABOR (CONTINUED) INDIAN AND NATIVE AMERICAN PROGRAMS... administrative cost limit for States and local areas apply to section 166 grants? No, under 20 CFR...
Code of Federal Regulations, 2013 CFR
2013-04-01
... EMPLOYMENT AND TRAINING ADMINISTRATION, DEPARTMENT OF LABOR (CONTINUED) INDIAN AND NATIVE AMERICAN PROGRAMS... administrative cost limit for States and local areas apply to section 166 grants? No, under 20 CFR...
ERIC Educational Resources Information Center
Kallemeyn, Leanne M.; DeStefano, Lizanne
2009-01-01
Using concepts from the evaluation literature, this case study describes the instrumental, conceptual, and political influence of the Head Start National Reporting System (NRS) and on-going child assessments in a local Head Start program. This study found that a local program intentionally aimed to limit the influence of the NRS. The NRS validated…
Pedagogical Simulation of Sampling Distributions and the Central Limit Theorem
ERIC Educational Resources Information Center
Hagtvedt, Reidar; Jones, Gregory Todd; Jones, Kari
2007-01-01
Students often find the fact that a sample statistic is a random variable very hard to grasp. Even more mysterious is why a sample mean should become ever more Normal as the sample size increases. This simulation tool is meant to illustrate the process, thereby giving students some intuitive grasp of the relationship between a parent population…
Central Limit Theorem: New SOCR Applet and Demonstration Activity
ERIC Educational Resources Information Center
Dinov, Ivo D.; Christou, Nicholas; Sanchez, Juana
2008-01-01
Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multi-faceted learning environments, which may facilitate student comprehension and information…
Goldstone's Theorem on a Light-Like Plane
NASA Astrophysics Data System (ADS)
Beane, Silas R.
2015-09-01
I review various aspects of chiral symmetry and its spontaneous breaking on null planes, including the interesting manner in which Goldstone's theorem is realized and the constraints that chiral symmetry imposes on the null-plane Hamiltonians. Specializing to QCD with N massless flavors, I show that there is an interesting limit in which the chiral constraints on the null-plane Hamiltonians can be solved to give the spin-flavor algebra SU(2 N), recovering a result originally found by Weinberg using different methods.
Generalized parametric down conversion, many particle interferometry, and Bell's theorem
NASA Technical Reports Server (NTRS)
Choi, Hyung Sup
1992-01-01
A new field of multi-particle interferometry is introduced using a nonlinear optical spontaneous parametric down conversion (SPDC) of a photon into more than two photons. The study of SPDC using a realistic Hamiltonian in a multi-mode shows that at least a low conversion rate limit is possible. The down converted field exhibits many stronger nonclassical phenomena than the usual two photon parametric down conversion. Application of the multi-particle interferometry to a recently proposed many particle Bell's theorem on the Einstein-Podolsky-Rosen problem is given.
Double soft theorems and shift symmetry in nonlinear sigma models
NASA Astrophysics Data System (ADS)
Low, Ian
2016-02-01
We show that both the leading and subleading double soft theorems of the nonlinear sigma model follow from a shift symmetry enforcing Adler's zero condition in the presence of an unbroken global symmetry. They do not depend on the underlying coset G /H and are universal infrared behaviors of Nambu-Goldstone bosons. Although nonlinear sigma models contain an infinite number of interaction vertices, the double soft limit is determined entirely by a single four-point interaction, together with the existence of Adler's zeros.
A Program Certification Assistant Based on Fully Automated Theorem Provers
NASA Technical Reports Server (NTRS)
Denney, Ewen; Fischer, Bernd
2005-01-01
We describe a certification assistant to support formal safety proofs for programs. It is based on a graphical user interface that hides the low-level details of first-order automated theorem provers while supporting limited interactivity: it allows users to customize and control the proof process on a high level, manages the auxiliary artifacts produced during this process, and provides traceability between the proof obligations and the relevant parts of the program. The certification assistant is part of a larger program synthesis system and is intended to support the deployment of automatically generated code in safety-critical applications.
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
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.
Jorgensen, Christopher F.; Powell, Larkin A.; Lusk, Jeffery J.; Bishop, Andrew A.; Fontaine, Joseph J.
2014-01-01
Landscapes in agricultural systems continue to undergo significant change, and the loss of biodiversity is an ever-increasing threat. Although habitat restoration is beneficial, management actions do not always result in the desired outcome. Managers must understand why management actions fail; yet, past studies have focused on assessing habitat attributes at a single spatial scale, and often fail to consider the importance of ecological mechanisms that act across spatial scales. We located survey sites across southern Nebraska, USA and conducted point counts to estimate Ring-necked Pheasant abundance, an economically important species to the region, while simultaneously quantifying landscape effects using a geographic information system. To identify suitable areas for allocating limited management resources, we assessed land cover relationships to our counts using a Bayesian binomial-Poisson hierarchical model to construct predictive Species Distribution Models of relative abundance. Our results indicated that landscape scale land cover variables severely constrained or, alternatively, facilitated the positive effects of local land management for Ring-necked Pheasants. PMID:24918779
Jorgensen, Christopher F; Powell, Larkin A; Lusk, Jeffery J; Bishop, Andrew A; Fontaine, Joseph J
2014-01-01
Landscapes in agricultural systems continue to undergo significant change, and the loss of biodiversity is an ever-increasing threat. Although habitat restoration is beneficial, management actions do not always result in the desired outcome. Managers must understand why management actions fail; yet, past studies have focused on assessing habitat attributes at a single spatial scale, and often fail to consider the importance of ecological mechanisms that act across spatial scales. We located survey sites across southern Nebraska, USA and conducted point counts to estimate Ring-necked Pheasant abundance, an economically important species to the region, while simultaneously quantifying landscape effects using a geographic information system. To identify suitable areas for allocating limited management resources, we assessed land cover relationships to our counts using a Bayesian binomial-Poisson hierarchical model to construct predictive Species Distribution Models of relative abundance. Our results indicated that landscape scale land cover variables severely constrained or, alternatively, facilitated the positive effects of local land management for Ring-necked Pheasants. PMID:24918779
Rellich’s theorem and N-body Schrödinger operators
NASA Astrophysics Data System (ADS)
Ito, K.; Skibsted, E.
2016-07-01
We show an optimal version of Rellich’s theorem for generalized N-body Schrödinger operators. It applies to singular potentials, in particular, to a model for atoms and molecules with infinite mass and finite extent nuclei. Our proof relies on a Mourre estimate [10] and a functional calculus localization technique.
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.
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.
Majdak, Piotr; Walder, Thomas; Laback, Bernhard
2013-09-01
Sound localization in the sagittal planes, including the ability to distinguish front from back, relies on spectral features caused by the filtering effects of the head, pinna, and torso. It is assumed that important spatial cues are encoded in the frequency range between 4 and 16 kHz. In this study, in a double-blind design and using audio-visual training covering the full 3-D space, normal-hearing listeners were trained 2 h per day over three weeks to localize sounds which were either band limited up to 8.5 kHz or spectrally warped from the range between 2.8 and 16 kHz to the range between 2.8 and 8.5 kHz. The training effect for the warped condition exceeded that for procedural task learning, suggesting a stable auditory recalibration due to the training. After the training, performance with band-limited sounds was better than that with warped ones. The results show that training can improve sound localization in cases where spectral cues have been reduced by band-limiting or remapped by warping. This suggests that hearing-impaired listeners, who have limited access to high frequencies, might also improve their localization ability when provided with spectrally warped or band-limited sounds and adequately trained on sound localization. PMID:23967945
Kochen-Specker theorem as a precondition for secure quantum key distribution
Nagata, Koji
2005-07-15
We show that (1) the violation of the Ekert 1991 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 1992 (BBM92) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each quantum key distribution protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two key distribution processes into the no-hidden-variables theorem and into witness on distillable entanglement. We also discuss the explicit difference between the KS realism and Bell's local realism in the Hilbert space formalism of quantum theory.
Moving mirrors and the fluctuation-dissipation theorem
NASA Astrophysics Data System (ADS)
Stargen, D. Jaffino; Kothawala, Dawood; Sriramkumar, L.
2016-07-01
We investigate the random motion of a mirror in (1 +1 )-dimensions that is immersed in a thermal bath of massless scalar particles which are interacting with the mirror through a boundary condition. Imposing the Dirichlet or the Neumann boundary conditions on the moving mirror, we evaluate the mean radiation reaction force on the mirror and the correlation function describing the fluctuations in the force about the mean value. From the correlation function thus obtained, we explicitly establish the fluctuation-dissipation theorem governing the moving mirror. Using the fluctuation-dissipation theorem, we compute the mean-squared displacement of the mirror at finite and zero temperature. We clarify a few points concerning the various limiting behavior of the mean-squared displacement of the mirror. While we recover the standard result at finite temperature, we find that the mirror diffuses logarithmically at zero temperature, confirming similar conclusions that have been arrived at earlier in this context. We also comment on a subtlety concerning the comparison between zero temperature limit of the finite temperature result and the exact zero temperature result.
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.
Tennis Rackets and the Parallel Axis Theorem
NASA Astrophysics Data System (ADS)
Christie, Derek
2014-04-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
Student Research Project: Goursat's Other Theorem
ERIC Educational Resources Information Center
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
Abel's Theorem Simplifies Reduction of Order
ERIC Educational Resources Information Center
Green, William R.
2011-01-01
We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.
Student Thinking Strategies in Reconstructing Theorems
ERIC Educational Resources Information Center
Siswono, Tatag Yuli Eko
2005-01-01
A mathematics university student as a future mathematician should have the ability to find "new" mathematics structures or construct theorems based on particular axioms. That ability can be created by using problem posing tasks. To do the tasks, students with different abilities will use different thinking strategies. To understand them exactly,…
Tennis Rackets and the Parallel Axis Theorem
ERIC Educational Resources Information Center
Christie, Derek
2014-01-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
On Viviani's Theorem and Its Extensions
ERIC Educational Resources Information Center
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
An Elementary Proof of Pick's Theorem.
ERIC Educational Resources Information Center
Pullman, Howard W.
1979-01-01
Pick's Theorem, a statement of the relationship between the area of a polygonal region on a lattice and its interior and boundary lattice points, is familiar to those whose students have participated in activities and discovery lessons using the geoboard. The proof presented, although rather long, is well within the grasp of the average geometry…
Areas and the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Vajiac, A.; Vajiac, B.
2008-01-01
We present a concise, yet self-contained module for teaching the notion of area and the Fundamental Theorem of Calculus for different groups of students. This module contains two different levels of rigour, depending on the class it used for. It also incorporates a technological component. (Contains 6 figures.)
The Pythagorean Theorem and the Solid State
ERIC Educational Resources Information Center
Kelly, Brenda S.; Splittgerber, Allan G.
2005-01-01
Packing efficiency and crystal density can be calculated from basic geometric principles employing the Pythagorean theorem, if the unit-cell structure is known. The procedures illustrated have applicability in courses such as general chemistry, intermediate and advanced inorganic, materials science, and solid-state physics.
The Binomial Theorem Tastes the Rainbow.
ERIC Educational Resources Information Center
Cuff, Carolyn K.
1998-01-01
Discusses the commercial for Skittles candies and asks the question "How many flavor combinations can you find?" Focuses on the modeling for a Skittles exercise which includes a brief outline of the mathematical modeling process. Guides students in the use of the binomial theorem and Pascal's triangle in this activity. (ASK)
Special ergodic theorems and dynamical large deviations
NASA Astrophysics Data System (ADS)
Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav
2012-11-01
Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.
Ptolemy's Theorem and Familiar Trigonometric Identities.
ERIC Educational Resources Information Center
Bidwell, James K.
1993-01-01
Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)
Fundamental Theorems of Algebra for the Perplexes
ERIC Educational Resources Information Center
Poodiak, Robert; LeClair, Kevin
2009-01-01
The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…
Codimension- p Paley-Wiener theorems
NASA Astrophysics Data System (ADS)
Yang, Yan; Qian, Tao; Sommen, Frank
2007-04-01
We obtain the generalized codimension- p Cauchy-Kovalevsky extension of the exponential function e^{i
An Ordinary but Surprisingly Powerful Theorem
ERIC Educational Resources Information Center
Sultan, Alan
2009-01-01
Being a mathematician, the author started to wonder if there are any theorems in mathematics that seem very ordinary on the outside, but when applied, have surprisingly far reaching consequences. The author thought about this and came up with the following unlikely candidate which follows immediately from the definition of the area of a rectangle…
Reflection theorem for Lorentz-Minkowski spaces
NASA Astrophysics Data System (ADS)
Lee, Nam-Hoon
2016-07-01
We generalize the reflection theorem of the Lorentz-Minkowski plane to that of the Lorentz-Minkowski spaces of higher dimensions. As a result, we show that an isometry of the Lorentz-Minkowski spacetime is a composition of at most 5 reflections.
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…
Invisibility and cloaking structures as weak or strong solutions of Devaney-Wolf theorem.
Labate, Giuseppe; Matekovits, Ladislau
2016-08-22
Inspired by a general theorem on non-radiating sources demonstrated by Devaney and Wolf, a unified theory for invisible and cloaking structures is here proposed. By solving Devaney-Wolf theorem in the quasi-static limit, a weak solution is obtained, demonstrating the existence of Anapole modes, Mantle Cloaking and Plasmonic Cloaking. Beyond the quasi-static regime, a strong solution of Devaney-Wolf theorem can be formulated, predicting general non-scattering devices based on directional invisibility, Transformation Optics, neutral inclusions and refractive index continuity. Both weak and strong solutions are analytically demonstrated to depend on the concept of contrast, mathematically defined as a normalized difference between constitutive parameters (or wave-impedance property) of a material and its surrounding background. PMID:27557204
Sparse image reconstruction on the sphere: implications of a new sampling theorem.
McEwen, Jason D; Puy, Gilles; Thiran, Jean-Philippe; Vandergheynst, Pierre; Van De Ville, Dimitri; Wiaux, Yves
2013-06-01
We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result, we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations, we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem. PMID:23475360
NASA Astrophysics Data System (ADS)
Hollen, S. M.; Fernandes, G. E.; Xu, J. M.; Valles, J. M.
2014-10-01
A Bose insulator composed of a low density of strongly localized Cooper pairs develops at the two-dimensional superconductor to insulator transition (SIT) in a number of thin film systems. Investigations of ultrathin amorphous PbBi films far from the SIT described here provide evidence that the Bose insulator gives way to a second insulating phase with decreasing film thickness. At a critical film thickness dc the magnetoresistance changes sign from positive, as expected for boson transport, to negative, as expected for fermion transport, signs of local Cooper-pair phase coherence effects on transport vanish, and the transport activation energy exhibits a kink. Below dc pairing fluctuation effects remain visible in the high-temperature transport while the activation energy continues to rise. These features show that Cooper pairing persists and suggest that the localized unpaired electron states involved in transport are interspersed among regions of strongly localized Cooper pairs in this strongly localized, low Cooper-pair density phase.
Quantum Stratonovich calculus and the quantum Wong-Zakai theorem
Gough, John
2006-11-15
We extend the Ito(bar sign)-to-Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes. Working within the framework of quantum stochastic calculus, we define Stratonovich calculus as an algebraic modification of the Ito(bar sign) one and give conditions for the existence of Stratonovich time-ordered exponentials. We show that conversion formula for the coefficients has a striking resemblance to Green's function formulas from standard perturbation theory. We show that the calculus conveniently describes the Markov limit of regular open quantum dynamical systems in much the same way as in the Wong-Zakai approximation theorems of classical stochastic analysis. We extend previous limit results to multiple-dimensions with a proof that makes use of diagrammatic conventions.
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.
Bevan, Kirk H; Zhu, Wenguang; Stocks, George Malcolm; Guo, Hong; Zhang, Zhenyu
2012-01-01
Utilizing first-principles quantum transport calculations, we investigate the role of local fields in conductor surface electromigration. A nanometer-thick Ag(100) thin film is adopted as our prototypical conductor, where we demonstrate the existence of intense local electric fields at atomic surface defects under an external bias. It is shown that such local fields can play an important role in driving surface electromigration and electrical breakdown. The intense fields originate from the relatively short (atomic-scale) screening lengths common to most elemental metals. This general short-range screening trend is established self-consistently within an intuitive picture of linear response electrostatics. The findings shed new light on the underlying physical origins of surface electromigration and point to the possibility of harnessing local fields to engineer electromigration at the nanoscale.
Relativistic Momentum and Manifestly Covariant Equipartition Theorem Revisited
Chacon-Acosta, Guillermo; Dagdug, Leonardo; Morales-Tecotl, Hugo A.
2010-07-12
Recently the discussion about the right relativistic generalization of thermodynamics has been revived. In particular the case of temperature has been investigated by alluding to a form of relativistic equipartition theorem. Now from the kinetic theory point of view a covariant equipartition involves necessarily the relativistic momentum of the system, which is given by an integral of the energy-momentum tensor over a spacelike hypersurface. Some authors have even proposed to trade the spacelike hypersurfaces entering in there by lightlike ones to accommodate Lorentz covariance. In this work we argue that a well defined momentum for a diluted gas can be given by making use of the velocity of the gas as whole and thereby selecting a hypersurface; this being in direct analogy with the case of an extended classical electron model and which turned out to solve the Abraham-Lorentz controversy codified in the wrong non-relativistic limit. We also discuss the effect of such choices on the equipartition theorem calculated through the covariant form of the Juettner distribution function.
Aging and nonergodicity beyond the Khinchin theorem
Burov, S.; Metzler, R.; Barkai, E.
2010-01-01
The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin’s theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics. PMID:20624984
Aging and nonergodicity beyond the Khinchin theorem.
Burov, S; Metzler, R; Barkai, E
2010-07-27
The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin's theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics. PMID:20624984
An analogue of a theorem of Kurzweil
NASA Astrophysics Data System (ADS)
Simmons, David
2015-05-01
A theorem of Kurzweil ('55) on inhomogeneous Diophantine approximation states that if θ is an irrational number, then the following are equivalent: (A) for every decreasing positive function ψ such that \\sumq = 1^∞ \\psi(q) = ∞ , and for almost every s\\in R , there exist infinitely many q\\in N such that ‖qθ - s‖ < ψ(q), and (B) θ is badly approximable. This theorem is not true if one adds to condition (A) the hypothesis that the function q ↦ qψ(q) is decreasing. In this paper we find a condition on the continued fraction expansion of θ which is equivalent to the modified version of condition (A). This expands on a recent paper of Kim (2014 Nonlinearity 27 1985-97).
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-01-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571
A torus bifurcation theorem with symmetry
NASA Technical Reports Server (NTRS)
Vangils, S. A.; Golubitsky, M.
1989-01-01
Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.
A 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.
Construction of momentum theorem using cross moments
NASA Astrophysics Data System (ADS)
Hahm, T. S.; Wang, Lu; Diamond, P. H.
2009-11-01
Charney-Drazin theorem has been extended to Hasegawa Wakatani system for zonal flow problem in magnetic fusion [P.H. Diamond, et al., Plasma Phys. Control. Fusion 50, 124018 (2008)]. For this model, the guiding center density is the potential vorticity and zonal flow is influenced by the particle flux. In this work we construct momentum theorems in terms of a hierarchy of cross moments
Volume integral theorem for exotic matter
Nandi, Kamal Kanti; Zhang Yuanzhong; Kumar, K.B. Vijaya
2004-12-15
We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well-known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.
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.
NASA Astrophysics Data System (ADS)
Spirig, Christoph; Neftel, Albrecht; Kleinman, Lawrence I.; Hjorth, Jens
2002-11-01
We characterize the local O3 production at an urban and a rural site in the northern part of the Po valley (Italy) during the Pianura Padana Produzione di Ozono experiment (PIPAPO). A steady state calculation based on observations is performed to determine the local O3 production rate, P(O3), and its sensitivity to precursor concentrations. The urban site exhibited a strongly VOC sensitive O3 production rate, while both VOC and NOx sensitive conditions were observed at the rural site. In addition to the local steady state analysis, we performed one-dimensional Lagrangian model calculations that simulate conditions in the Po valley. These calculations show that the P(O3) at the surface tends to be more VOC sensitive than the average in the mixed layer. The Lagrangian calculations are also used to determine the response of O3 concentration to an emissions change. We compare emission control information with information on sensitivities from the local analysis. It is concluded that a local analysis of P(O3) within the mixing layer offers useful qualitative information but tends to overestimate VOC sensitivity as judged by a comparison with an emissions-based Lagrangian model.
Joint probability distributions and fluctuation theorems
NASA Astrophysics Data System (ADS)
García-García, Reinaldo; Lecomte, Vivien; Kolton, Alejandro B.; Domínguez, Daniel
2012-02-01
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation-dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators.
Theorem Proving In Higher Order Logics
NASA Technical Reports Server (NTRS)
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Code of Federal Regulations, 2010 CFR
2010-04-01
... Board directly be a provider of core services, intensive services, or training services, or act as a One... Board directly be a provider of core services, intensive services, or training services, or act as a One-Stop Operator? (a) A Local Board may not directly provide core services, or intensive services, or...
Chandra, Vishal; Choi, Yong-Bock; Hwang, Hai-Li; Lee, Jeong-Hwa; Park, Seong-Yeol; Kim, Hyun-Kyoung; Poojan, Shiv; Koh, Jae-Soo; Kim, Han-Seong; Hong, Kyeong-Man
2015-09-01
We have shown both LLC1 expression in the lung epithelium by in situ hybridization and its inactivation in lung cancer by epigenetic modification. However, LLC1 protein's cellular localization or its role in normal lung or cancer tissues has not yet been evaluated. In the present study, a monoclonal antibody against recombinant LLC1 was produced, and immunohistochemical staining was performed on arrays including various human tissues, normal lung and non-small cell lung cancer (NSCLC) tissues for LLC1 localization. The immunohistochemical results showed LLC1 expression in the cilia of normal-airway epithelial cells and in the cytoplasm of type II pneumocytes in bronchiectatic patients, but no expression in most of the NSCLC tissues, which is consistent with our previous report positing LLC1 as a tumor suppressor. However, LLC1 over-expression in NSCLC cell lines NCI-H1299 and NCI-H23 did not show any change in proliferation or migration, which does not indicate any LLC1 tumor-suppressor role. As for the other human tissues, LLC1 was localized in renal tubular cells, pancreatic acinar cells, and epithelial cells of the stomach, duodenum, and gallbladder. In summary, our findings suggest that LLC1 is not a tumor suppressor, and that it is localized in the cilia of the normal lung epithelium but is absent in most NSCLC cases, probably due to the loss of cilia during lung carcinogenesis. PMID:25786037
ERIC Educational Resources Information Center
Cliburn, Jill
1999-01-01
Geographic information systems (GIS) provide a computer-based system for organizing, tracking, and using practically any kind of information that has a geographic component. Partnerships between rural electric cooperatives and local governments in Minnesota and Missouri make GIS data available for various uses by electric cooperatives, county and…
James, Peter; Ito, Kate; Banay, Rachel F.; Buonocore, Jonathan J.; Wood, Benjamin; Arcaya, Mariana C.
2014-01-01
Decreasing traffic speeds increases the amount of time drivers have to react to road hazards, potentially averting collisions, and makes crashes that do happen less severe. Boston’s regional planning agency, the Metropolitan Area Planning Council (MAPC), in partnership with the Massachusetts Department of Public Health (MDPH), conducted a Health Impact Assessment (HIA) that examined the potential health impacts of a proposed bill in the state legislature to lower the default speed limits on local roads from 30 miles per hour (mph) to 25 mph. The aim was to reduce vehicle speeds on local roads to a limit that is safer for pedestrians, cyclists, and children. The passage of this proposed legislation could have had far-reaching and potentially important public health impacts. Lower default speed limits may prevent around 18 fatalities and 1200 serious injuries to motorists, cyclists and pedestrians each year, as well as promote active transportation by making local roads feel more hospitable to cyclists and pedestrians. While a lower speed limit would increase congestion and slightly worsen air quality, the benefits outweigh the costs from both a health and economic perspective and would save the state approximately $62 million annually from prevented fatalities and injuries. PMID:25279544
James, Peter; Ito, Kate; Banay, Rachel F; Buonocore, Jonathan J; Wood, Benjamin; Arcaya, Mariana C
2014-01-01
Decreasing traffic speeds increases the amount of time drivers have to react to road hazards, potentially averting collisions, and makes crashes that do happen less severe. Boston's regional planning agency, the Metropolitan Area Planning Council (MAPC), in partnership with the Massachusetts Department of Public Health (MDPH), conducted a Health Impact Assessment (HIA) that examined the potential health impacts of a proposed bill in the state legislature to lower the default speed limits on local roads from 30 miles per hour (mph) to 25 mph. The aim was to reduce vehicle speeds on local roads to a limit that is safer for pedestrians, cyclists, and children. The passage of this proposed legislation could have had far-reaching and potentially important public health impacts. Lower default speed limits may prevent around 18 fatalities and 1200 serious injuries to motorists, cyclists and pedestrians each year, as well as promote active transportation by making local roads feel more hospitable to cyclists and pedestrians. While a lower speed limit would increase congestion and slightly worsen air quality, the benefits outweigh the costs from both a health and economic perspective and would save the state approximately $62 million annually from prevented fatalities and injuries. PMID:25279544
A problem with the stress theorem commonly used in DFT codes
NASA Astrophysics Data System (ADS)
Nicholson, Donald
2015-03-01
The change in energy when an affine transformation (strain) is applied to a lattice of ions can be obtained by evaluating the algebraic derivative of the DFT energy (in practice a local or other approximation) of an electron density that has been similarly strained. Because the DFT energy is stationary in the density, it is only required that the strained density reduces to the exact density at zero strain; it does. The algebraic derivatives of the Hartree and exchange energies are straightforward. The derivative with respect to strain of the non-interacting kinetic energy depends on two assumptions: 1) the modulus squared of the strained orbitals equals the strained electron density, and 2) the strained orbitals minimize the non-interacting kinetic energy. The first assumption is correct. I find that the second assumption applies only in special cases. The limitations and possible modifications of the stress theorem are discussed. Work at the University of North Carolina Asheville and Oak Ridge National Laboratory was supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Materials Science and Engineering Division.
NASA Astrophysics Data System (ADS)
Phartiyal, P.; Field, P.; Kansal, T.
2014-12-01
Scientific information on, and regulatory oversight of, the U.S. oil and gas extraction have been outpaced by the scale and extent of development, particularly in states like Pennsylvania. Through recent convenings and focus groups with local officials from municipalities and counties facing such development, we asked how scientific information can be gathered and communicated to help policymakers make decisions on whether to proceed with development and, if so, what regulatory and non-regulatory approaches to consider to manage the risks from such activity. We found that the highly technical nature of unconventional oil and gas development can make conveying information difficult and public conversations harder. And, although there is scientific agreement on areas of greater risk, such as air, water, and socioeconomics effects, communities vary widely in their perceptions and concerns about these. Local leaders expressed concerns about the availability and accessibility of information: much of it is scattered, sourced from a variety of sources and viewpoints, and is viewed with confusion, skepticism, or disbelief among various stakeholders. In order to generate independent and trusted information, baseline testing, monitoring and enforcement, and data sharing are needed - but the specifics of who would do the studies, who would fund them, and how much data one would need before decisions can be made remain largely unclear. One reason for this uncertainty is the patchwork and contested nature of regulation between local, state, tribal, and federal authorities. Another is the fragmented operations disbursed across the landscape, numerous kinds and scales of operators, and the host of actors involved in land access, well development, production, and piping, lead to disjointed sources of studies, data, and communication. Another reason is that the impacts of oil and gas development activities are nested and complex, each affecting the other at varied levels, local to
The Ultrathin Limit and Dead-layer Effects in Local Polarization Switching of BiFeO3
Maksymovych, Petro; Huijben, Mark; Pan, Minghu; Jesse, Stephen; Balke, Nina; Chang, Hye Jung; Borisevich, Albina Y; Baddorf, Arthur P; Rijnders, Guus; Blank, Dave H. A.; Ramesh, R.; Kalinin, Sergei V
2012-01-01
Using piezoresponse force microscopy in ultra-high vacuum, polarization switching has been detected and quantified in epitaxial BiFeO3 films from 200 down to ~ 4 unit cells. Local remnant piezoresponse was used to infer the applied electric field inside the ferroelectric volume, and account for the elusive effect of dead-layers in ultrathin films. The dead-layer manifested itself in the slower than anticipated decrease of the switching bias with film thickness, yielding apparent Kay-Dunn scaling of the switching field, while the statistical analysis of hysteresis loops revealed lateral variation of the dead-layer with sub-10 nm resolution.
Near distance approximation in astrodynamical applications of Lambert's theorem
NASA Astrophysics Data System (ADS)
Rauh, Alexander; Parisi, Jürgen
2014-01-01
The smallness parameter of the approximation method is defined in terms of the non-dimensional initial distance between target and chaser satellite. In the case of a circular target orbit, compact analytical expressions are obtained for the interception travel time up to third order. For eccentric target orbits, an explicit result is worked out to first order, and the tools are prepared for numerical evaluation of higher order contributions. The possible transfer orbits are examined within Lambert's theorem. For an eventual rendezvous it is assumed that the directions of the angular momenta of the two orbits enclose an acute angle. This assumption, together with the property that the travel time should vanish with vanishing initial distance, leads to a condition on the admissible initial positions of the chaser satellite. The condition is worked out explicitly in the general case of an eccentric target orbit and a non-coplanar transfer orbit. The condition is local. However, since during a rendezvous maneuver, the chaser eventually passes through the local space, the condition propagates to non-local initial distances. As to quantitative accuracy, the third order approximation reproduces the elements of Mars, in the historical problem treated by Gauss, to seven decimals accuracy, and in the case of the International Space Station, the method predicts an encounter error of about 12 m for an initial distance of 70 km.
Extending Bell's Theorem: Ruling out Paramater Independent Hidden Variable Theories
NASA Astrophysics Data System (ADS)
Leegwater, G. J.
2016-03-01
Bell's Theorem may well be the best known result in the foundations of quantum mechanics. Here, it is presented as stating that for any hidden variable theory the combination of the conditions Parameter Independence, Outcome Independence, Source Independence and Compatibility with Quantum Theory leads to a contradiction. Based on work by Roger Colbeck and Renato Renner, an extension of Bell's Theorem is considered. In this extension the theorem is strengthened by replacing Outcome Independence by a strictly weaker condition.
A unified optical theorem for scalar and vectorial wave fields.
Wapenaar, Kees; Douma, Huub
2012-05-01
The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers. PMID:22559339
Fatou type theorems for series in Mittag-Leffler functions
NASA Astrophysics Data System (ADS)
Paneva-Konovska, Jordanka
2012-11-01
In studying the behaviour of series, defined by means of the Mittag-Leffler functions, on the boundary of its domain of convergence in the complex plane, we give analogues of the classical theorems for the power series like Cauchy-Hadamard, Abel, as well as Fatou theorems. The asymptotic formulae for the Mittag-Leffler functions in the cases of "large" values of indices that are used in the proofs of the convergence theorems for the considered series are also provided.
A Converse of the Mean Value Theorem Made Easy
ERIC Educational Resources Information Center
Mortici, Cristinel
2011-01-01
The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…
Index Theorem for Topological Excitations on R^3 \\times S^1 and Chern-Simons Theory
Poppitz, Erich; Unsal, Mithat
2008-12-12
We derive an index theorem for the Dirac operator in the background of various topological excitations on an R{sup 3} x S{sup 1} geometry. The index theorem provides more refined data than the APS index for an instanton on R{sup 4} and reproduces it in decompactification limit. In the R{sup 3} limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the {eta}-invariant associated with the boundary Dirac operator. Neither topological charge nor {eta}-invariant is typically an integer, however, the non-integer parts cancel to give an integer-valued index. Our derivation is based on axial current non-conservation--an exact operator identity valid on any four-manifold--and on the existence of a center symmetric, or approximately center symmetric, boundary holonomy (Wilson line). We expect the index theorem to usefully apply to many physical systems of interest, such as low temperature (large S{sup 1}, confined) phases of gauge theories, center stabilized Yang-Mills theories with vector-like or chiral matter (at S{sup 1} of any size), and supersymmetric gauge theories with supersymmetry-preserving boundary conditions (also at any S{sup 1}). In QCD-like and chiral gauge theories, the index theorem should shed light into the nature of topological excitations responsible for chiral symmetry breaking and the generation of mass gap in the gauge sector. We also show that imposing chirally-twisted boundary condition in gauge theories with fermions induces a Chern-Simons term in the infrared. This suggests that some QCD-like gauge theories should possess components with a topological Chern-Simons phase in the small S{sup 1} regime.
Kelly, V.A.; Beach, J.A.; Statham, W.H.; Pickens, J.F.
1993-02-19
The Savannah River Site (SRS) is a Department of Energy (DOE) facility located near Aiken, South Carolina which is currently operated and managed by Westinghouse Savannah River Company (WSRC). The Sanitary Landfill (Sanitary Landfill) at the SRS is located approximately 2,000 feet Northwest of Upper Three Runs Creek (UTRC) on an approximately 70 acre site located south of Road C between the SRS B-Area and UTRC. The Sanitary Landfill has been receiving wastes since 1974 and operates as an unlined trench and fill operation. The original landfill site was 32 acres. This area reached its capacity around 1987 and a Northern Expansion of 16 acres and a Southern Expansion of 22 acres were added in 1987. The Northern Expansion has not been used for waste disposal to date and the Southern Expansion is expected to reach capacity in 1992 or 1993. The waste received at the Sanitary Landfill is predominantly paper, plastics, rubber, wood, metal, cardboard, rags saturated with degreasing solvents, pesticide bags, empty cans, and asbestos in bags. The landfill is not supposed to receive any radioactive wastes. However, tritium has been detected in the groundwater at the site. Gross alpha and gross beta are also evaluated at the landfill. The objectives of this modeling study are twofold: (1) to create a local scale Sanitary Landfill flow model to study hydraulic effects resulting from capping the Sanitary Landfill; and (2) to create a Sanitary Landfill local scale transport model to support ACL Demonstrations for a RCRA Part B Permit Renewal.
Delayed plastic relaxation limit in SiGe islands grown by Ge diffusion from a local source
Vanacore, G. M.; Zani, M.; Tagliaferri, A.; Nicotra, G.; Bollani, M.; Bonera, E.; Montalenti, F.; Picco, A.; Boioli, F.; Capellini, G.; Isella, G.; Osmond, J.
2015-03-14
The hetero-epitaxial strain relaxation in nano-scale systems plays a fundamental role in shaping their properties. Here, the elastic and plastic relaxation of self-assembled SiGe islands grown by surface-thermal-diffusion from a local Ge solid source on Si(100) are studied by atomic force and transmission electron microscopies, enabling the simultaneous investigation of the strain relaxation in different dynamical regimes. Islands grown by this technique remain dislocation-free and preserve a structural coherence with the substrate for a base width as large as 350 nm. The results indicate that a delay of the plastic relaxation is promoted by an enhanced Si-Ge intermixing, induced by the surface-thermal-diffusion, which takes place already in the SiGe overlayer before the formation of a critical nucleus. The local entropy of mixing dominates, leading the system toward a thermodynamic equilibrium, where non-dislocated, shallow islands with a low residual stress are energetically stable. These findings elucidate the role of the interface dynamics in modulating the lattice distortion at the nano-scale, and highlight the potential use of our growth strategy to create composition and strain-controlled nano-structures for new-generation devices.
Delayed plastic relaxation limit in SiGe islands grown by Ge diffusion from a local source
NASA Astrophysics Data System (ADS)
Vanacore, G. M.; Nicotra, G.; Zani, M.; Bollani, M.; Bonera, E.; Montalenti, F.; Capellini, G.; Isella, G.; Osmond, J.; Picco, A.; Boioli, F.; Tagliaferri, A.
2015-03-01
The hetero-epitaxial strain relaxation in nano-scale systems plays a fundamental role in shaping their properties. Here, the elastic and plastic relaxation of self-assembled SiGe islands grown by surface-thermal-diffusion from a local Ge solid source on Si(100) are studied by atomic force and transmission electron microscopies, enabling the simultaneous investigation of the strain relaxation in different dynamical regimes. Islands grown by this technique remain dislocation-free and preserve a structural coherence with the substrate for a base width as large as 350 nm. The results indicate that a delay of the plastic relaxation is promoted by an enhanced Si-Ge intermixing, induced by the surface-thermal-diffusion, which takes place already in the SiGe overlayer before the formation of a critical nucleus. The local entropy of mixing dominates, leading the system toward a thermodynamic equilibrium, where non-dislocated, shallow islands with a low residual stress are energetically stable. These findings elucidate the role of the interface dynamics in modulating the lattice distortion at the nano-scale, and highlight the potential use of our growth strategy to create composition and strain-controlled nano-structures for new-generation devices.
Generalized acceleration theorem for spatiotemporal Bloch waves
Arlinghaus, Stephan; Holthaus, Martin
2011-08-01
A representation is put forward for wave functions of quantum particles in periodic lattice potentials subjected to homogeneous time-periodic forcing, based on an expansion with respect to Bloch-like states which embody both the spatial and the temporal periodicity. It is shown that there exists a generalization of Bloch's famous acceleration theorem which grows out of this representation and captures the effect of a weak probe force applied in addition to a strong dressing force. Taken together, these elements point at a ''dressing and probing'' strategy for coherent wave-packet manipulation, which could be implemented in present experiments with optical lattices.
Flory Theorem for Structurally Asymmetric Mixtures
NASA Astrophysics Data System (ADS)
Dobrynin, Andrey; Sun, Frank; Shirvanyants, David; Rubinstein, Gregory; Rubinstein, Michael; Sheiko, Sergei; Lee, Hyung-Il; Matyjaszewski, Krzysztof
2008-03-01
The generalization of the Flory theorem for structurally asymmetric mixtures was derived and tested by direct visualization of conformational transformations of brushlike macromolecules embedded in a melt of linear chains. Swelling of a brush molecule was shown to be controlled not only by the degree of polymerization of the surrounding linear chains, NB, but also by the degree of polymerization of the brush's side chains, N, which determines the structural asymmetry of the mixed species. The boundaries of the swelling region were established by scaling analysis as N^2
Flory Theorem for Structurally Asymmetric Mixtures
NASA Astrophysics Data System (ADS)
Sun, Frank C.; Dobrynin, Andrey V.; Shirvanyants, David; Lee, Hyung-Il; Matyjaszewski, Krzysztof; Rubinstein, Gregory J.; Rubinstein, Michael; Sheiko, Sergei S.
2007-09-01
The generalization of the Flory theorem for structurally asymmetric mixtures was derived and tested by direct visualization of conformational transformations of brushlike macromolecules embedded in a melt of linear chains. Swelling of a brush molecule was shown to be controlled not only by the degree of polymerization (DP) of the surrounding linear chains, NB, but also by the DP of the brush’s side chains, N, which determines the structural asymmetry of the mixed species. The boundaries of the swelling region were established by scaling analysis as N2
Generating Test Templates via Automated Theorem Proving
NASA Technical Reports Server (NTRS)
Kancherla, Mani Prasad
1997-01-01
Testing can be used during the software development process to maintain fidelity between evolving specifications, program designs, and code implementations. We use a form of specification-based testing that employs the use of an automated theorem prover to generate test templates. A similar approach was developed using a model checker on state-intensive systems. This method applies to systems with functional rather than state-based behaviors. This approach allows for the use of incomplete specifications to aid in generation of tests for potential failure cases. We illustrate the technique on the cannonical triangle testing problem and discuss its use on analysis of a spacecraft scheduling system.
No-cloning theorem on quantum logics
Miyadera, Takayuki; Imai, Hideki
2009-10-15
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
An investigation of the forward scattering theorem
NASA Technical Reports Server (NTRS)
Karam, M. A.; Fung, A. K.
1987-01-01
The calculation of an EM wave's extinction loss during propagation within an inhomogeneous medium, as in active and passive remote sensing modeling, can be undertaken either through the summation of the scattering and absorption losses or through the use of the forward scattering theorem. Attention is presently given to the similarities and differences of these two approaches as a function of dielectric properties of a spherical scatterer and the incident frequency. Scattering loss is obtainable by integrating the magnitude-squared of the scattered field over a spherical surface surrounding the scatterer; the scattered field and the field within the scatterer are computed according to Mie theory.
Penrose's singularity theorem in a Finsler spacetime
NASA Astrophysics Data System (ADS)
Babak Aazami, Amir; Javaloyes, Miguel Angel
2016-01-01
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting. This activity is supported by the programme 'Young leaders in research' 18942/JLI/13 by Fundación Séneca, Regional Agency for Science and Technology from the Region of Murcia, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
No-cloning theorem on quantum logics
NASA Astrophysics Data System (ADS)
Miyadera, Takayuki; Imai, Hideki
2009-10-01
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
Disentangling theorem and monogamy for entanglement negativity
NASA Astrophysics Data System (ADS)
He, Huan; Vidal, Guifre
2015-01-01
Entanglement negativity is a measure of mixed-state entanglement increasingly used to investigate and characterize emerging quantum many-body phenomena, including quantum criticality and topological order. We present two results for the entanglement negativity: a disentangling theorem, which allows the use of this entanglement measure as a means to detect whether a wave function of three subsystems A ,B , and C factorizes into a product state for parts A B1 and B2C ; and a monogamy relation conjecture based on entanglement negativity, which states that if A is very entangled with B , then A cannot be simultaneously very entangled also with C .
Bayes` theorem and quantitative risk assessment
Kaplan, S.
1994-12-31
This paper argues that for a quantitative risk analysis (QRA) to be useful for public and private decision making, and for rallying the support necessary to implement those decisions, it is necessary that the QRA results be ``trustable.`` Trustable means that the results are based solidly and logically on all the relevant evidence available. This, in turn, means that the quantitative results must be derived from the evidence using Bayes` theorem. Thus, it argues that one should strive to make their QRAs more clearly and explicitly Bayesian, and in this way make them more ``evidence dependent`` than ``personality dependent.``
Fluctuation theorems and work relations for single polymer rheology
NASA Astrophysics Data System (ADS)
Latinwo, Folarin Babajide
Synthetic and biological polymeric materials are ubiquitous in nature and modern technology. The emergent properties afforded by these materials allows for wide a array of applications as found in adhesives, coatings, and synthetic polymers for plastics. Importantly, the molecular properties of polymeric systems ultimately determine their bulk macroscopic response and behavior in equilibrium and highly nonequilibrium conditions. As a result, the field of single polymer rheology can play a key role in establishing a molecular level understanding of polymeric systems by investigating the dynamics of single chains. Single polymer rheology is now a well-established approach to study polymer dynamics from experimental and computational perspectives. In general, this approach allows for the determination of molecular subpopulations, relaxation, and polymer chain dynamics in a wide variety of flows. Despite recent progress, current methods in single polymer rheology do not allow for the determination of equilibrium and nonequilibrium thermodynamic properties of polymeric systems. Moreover, it is challenging to connect backbone dynamics to key macroscopic rheological phenomena. In this context, the impact of single polymer rheology has remained limited for the past two decades. In this thesis, we address these challenges by developing and applying fluctuation theorems and nonequilibrium work relations to the field of single polymer rheology. The discovery of thermodynamic identities known as nonequilibrium work relations (NWRs) and fluctuation theorems (FTs) has catalyzed recent advances in statistical mechanics. In general, work relations provide an unprecedented route to extract fundamental materials properties of equilibrium and nonequilibrium systems. Furthermore, these identities have uncovered a broad range of unexpected and remarkable thermodynamic phenomena, including molecular level violations to the second law of thermodynamics. In the context of rheology and
Ground-state-energy theorem and the virial theorem of a many-particle system in d dimensions
NASA Technical Reports Server (NTRS)
Iwamoto, N.
1984-01-01
The equivalence of Pauli's ground-state-energy theorem and the virial theorem is demonstrated for a many-particle system interacting with an interparticle potential in d dimensions at zero and finite temperatures. Pauli's theorem has an integral form in which the variable is the coupling constant e-squared, while the virial theorem has a differential form in which the variable has the number density n. The essence of the equivalence proof consists in changing the variable from n to e-squared by noting the dependence of the excess free energy on dimensionless quantities for zero-temperature and classical cases.
On the Limits of Measuring the Bulge and Disk Properties of Local and High-redshift Massive Galaxies
NASA Astrophysics Data System (ADS)
Davari, Roozbeh; Ho, Luis C.; Peng, Chien Y.
2016-06-01
A considerable fraction of the massive quiescent galaxies at z ≈ 2, which are known to be much more compact than galaxies of comparable mass today, appear to have a disk. How well can we measure the bulge and disk properties of these systems? We simulate two-component model galaxies in order to systematically quantify the effects of non-homology in structures and the methods employed. We employ empirical scaling relations to produce realistic-looking local galaxies with a uniform and wide range of bulge-to-total ratios (B/T), and then rescale them to mimic the signal-to-noise ratios and sizes of observed galaxies at z ≈ 2. This provides the most complete set of simulations to date for which we can examine the robustness of two-component decomposition of compact disk galaxies at different B/T. We confirm that the size of these massive, compact galaxies can be measured robustly using a single Sérsic fit. We can measure B/T accurately without imposing any constraints on the light profile shape of the bulge, but, due to the small angular sizes of bulges at high redshift, their detailed properties can only be recovered for galaxies with B/T ≳ 0.2. The disk component, by contrast, can be measured with little difficulty.
Determination of the fractal dimension for the epitaxial n-GaAs surface in the local limit
Torkhov, N. A. Bozhkova, V. G.; Ivonin, I. V.; Novikov, V. A.
2009-01-15
Atomic-force microscopy studies of epitaxial n-GaAs surfaces prepared to deposit barrier contacts showed that major relief for such surfaces is characterized by a roughness within 3-15 nm, although 'surges' up to 30-70 nm are observed. Using three independent methods for determining the spatial dimension of the surface, based on the fractal analysis for the surface (triangulation method), its section contours in the horizontal plane, and the vertical section (surface profile), it was shown that the active surface for epitaxial n-GaAs obeys all main features of behavior for fractal Brownian surfaces and, in the local approximation, can be characterized by the fractal dimension D{sub f} slightly differing for various measuring scales. The most accurate triangulation method showed that the fractal dimensions for the studied surface of epitaxial n-GaAs for measurement scales from 0.692 to 0.0186 {mu}m are in the range D{sub f} = 2.490-2.664. The real surface area S{sub real} for n-GaAs epitaxial layers was estimated using a graphical method in the approximation {delta} {sup {yields}} 0 {delta} is the measurement scale parameter). It was shown that the real surface area for epitaxial n-GaAs can significantly (ten times and more) exceed the area of the visible contact window.
Weaver, Daniel M.; Coghlan Jr., Stephen M.; Zydlewski, Joseph
2016-01-01
Resource flows from adjacent ecosystems are critical in maintaining structure and function of freshwater food webs. Migrating sea lamprey (Petromyzon marinus) deliver a pulsed marine-derived nutrient subsidy to rivers in spring when the metabolic demand of producers and consumers are increasing. However, the spatial and temporal dynamics of these nutrient subsidies are not well characterized. We used sea lamprey carcass additions in a small stream to examine changes in nutrients, primary productivity, and nutrient assimilation among consumers. Algal biomass increased 57%–71% immediately adjacent to carcasses; however, broader spatial changes from multiple-site carcass addition may have been influenced by canopy cover. We detected assimilation of nutrients (via δ13C and δ15N) among several macroinvertebrate families including Heptageniidae, Hydropsychidae, and Perlidae. Our research suggests that subsidies may evoke localized patch-scale effects on food webs, and the pathways of assimilation in streams are likely coupled to adjacent terrestrial systems. This research underscores the importance of connectivity in streams, which may influence sea lamprey spawning and elicit varying food web responses from carcass subsidies due to fine-scale habitat variables.
Harris, Robin E; Setiawan, Linda; Saul, Josh; Hariharan, Iswar K
2016-01-01
Many organisms lose the capacity to regenerate damaged tissues as they mature. Damaged Drosophila imaginal discs regenerate efficiently early in the third larval instar (L3) but progressively lose this ability. This correlates with reduced damage-responsive expression of multiple genes, including the WNT genes wingless (wg) and Wnt6. We demonstrate that damage-responsive expression of both genes requires a bipartite enhancer whose activity declines during L3. Within this enhancer, a damage-responsive module stays active throughout L3, while an adjacent silencing element nucleates increasing levels of epigenetic silencing restricted to this enhancer. Cas9-mediated deletion of the silencing element alleviates WNT repression, but is, in itself, insufficient to promote regeneration. However, directing Myc expression to the blastema overcomes repression of multiple genes, including wg, and restores cellular responses necessary for regeneration. Localized epigenetic silencing of damage-responsive enhancers can therefore restrict regenerative capacity in maturing organisms without compromising gene functions regulated by developmental signals. DOI: http://dx.doi.org/10.7554/eLife.11588.001 PMID:26840050
Bradshaw, Debbie; Daniels, Johann; Zinyakatira, Nesbert; Matzopoulos, Richard; Bourne, David; Shaikh, Najma; Naledi, Tracey
2010-01-01
Abstract Objective To identify the leading causes of mortality and premature mortality in Cape Town, South Africa, and its subdistricts, and to compare levels of mortality between subdistricts. Methods Cape Town mortality data for the period 2001–2006 were analysed by age, cause of death and sex. Cause-of-death codes were aggregated into three main cause groups: (i) pre-transitional causes (e.g. communicable diseases, maternal causes, perinatal conditions and nutritional deficiencies), (ii) noncommunicable diseases and (iii) injuries. Premature mortality was calculated in years of life lost (YLLs). Population estimates for the Cape Town Metro district were used to calculate age-specific rates per 100 000 population, which were then age-standardized and compared across subdistricts. Findings The pattern of mortality in Cape Town reflects the quadruple burden of disease observed in the national cause-of-death profile, with HIV/AIDS, other infectious diseases, injuries and noncommunicable diseases all accounting for a significant proportion of deaths. HIV/AIDS has replaced homicide as the leading cause of death. HIV/AIDS, homicide, tuberculosis and road traffic injuries accounted for 44% of all premature mortality. Khayelitsha, the poorest subdistrict, had the highest levels of mortality for all main cause groups. Conclusion Local mortality surveillance highlights the differential needs of the population of Cape Town and provides a wealth of data to inform planning and implementation of targeted interventions. Multisectoral interventions will be required to reduce the burden of disease. PMID:20539858
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
Random numbers certified by Bell's theorem.
Pironio, S; Acín, A; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C
2010-04-15
Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based and device-independent quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory. PMID:20393558
Panettieri, Vanessa; Ruben, Jeremy D.; Senthi, Sashendra
2016-01-01
Background Intensity modulated radiotherapy (IMRT) is routinely utilized in the treatment of locally advanced non-small cell lung cancer (NSCLC). RTOG 0617 found that overall survival was impacted by increased low (5 Gy) and intermediate (30 Gy) cardiac doses. We evaluated the impact of esophageal-sparing IMRT on cardiac doses with and without the heart considered in the planning process and predicted toxicity compared to 3D-conventional radiotherapy (3DCRT). Methods Ten consecutive patients with N2 Stage III NSCLC treated to 60 Gy in 30 fractions, between February 2012 and September 2014, were evaluated. For each patient, 3DCRT and esophageal-sparing IMRT plans were generated. IMRT plans were then created with and without the heart considered in the optimization process. To compare plans, the dose delivered to 95% and 99% of the target (D95% and D99%), and doses to the esophagus, lung and heart were compared by determining the volume receiving X dose (VXGy) and the normal tissue complication probability (NTCP) calculated. Results IMRT reduced maximum esophagus dose to below 60 Gy in all patients and produced significant reductions to V50Gy, V40Gy and esophageal NTCP. The cost of this reduction was a non-statistically, non-clinically significant increase in low dose (5 Gy) lung exposure that did not worsen lung NTCP. IMRT plans produced significant cardiac sparing, with the amount of improvement correlating to the amount of heart overlapping with the target. When included in plan optimization, for selected patients further sparing of the heart and improvement in heart NTCP was possible. Conclusions Esophageal-sparing IMRT can significantly spare the heart even if it is not considered in the optimization process. Further sparing can be achieved if plan optimization constrains low and intermediate heart doses, without compromising lung doses. PMID:27162670
Kostrov, S.V.; Chernovskaya, T.V.; Khodova, O.M.; Borukhov, S.I.; Ryzhavskaya, A.S.; Izotova, L.S.; Strongin, A.Ya.
1986-05-20
Large peptide fragments of human leukocyte interferon-..cap alpha..2 (INF-..cap alpha..2) were produced by limited proteolysis with trypsin, pepsin, thermolysin, and Bacillus amyloliquefaciens serine proteinase, and the ability of the fragments to react with murine monoclonal antibodies NK2, directed toward INF-..cap alpha..2, was studied by the immunoblotting technique. The region of the sequence 110-149 is the most sensitive to proteinase attack and evidently is exposed on the surface of the INF-..cap alpha..2 molecule. The INF-..cap alpha..2 fragments 1-139, 1-147, and 1-149 react with antibodies, whereas the fragments 1-109 and 1-112 do not bind NK2 antibodies. A comparison of the primary structure of the families of human leukocyte and murine leukocyte INF in the region of the sequence 110-139 and an analysis of the ability of human INF differing in amino acid sequence to interact with NK2 antibodies suggested that the antigenic determinant that binds monoclonal antibodies NK2 is the sequence Glu/sub 114/-Asp/sub 115/-Ser/sub 116/-He/sub 117/ of the INF-..cap alpha..2 molecule.
Markey, Kathryn L.; Abdo, Dave A.; Evans, Scott N.; Bosserelle, Cyprien
2016-01-01
In 2011 the first recorded bleaching event for the high latitude Houtman Abrolhos Islands (HAI) coral communities was documented. This bleaching event highlighted the question of whether a supply of ‘heat tolerant’ coral recruits from the tropical north would be sufficient to provide a level of resistance for these reefs to future warming events. Using Lagrangian modelling we showed that due to its regional isolation, large-scale larval input from potential tropical northern source populations to the HAI is unlikely, despite the southward flowing Leeuwin current. Successful recruitment to artificial substrates was recorded following the bleaching event. However, this was negligible (0.4 ± 0.1 recruits per tile) compared to 2013 post impact recruitment (128.8 ± 15.8 recruits per tile). Our data therefore provides preliminary evidence suggesting that the connectivity of the HAI with coral communities in the north is limited, and population maintenance and recovery is likely driven primarily by self-recruitment. Given the low thermal tolerance of the HAI coral communities, the dominance of Acropora, and the apparent reliance on self-recruitment, an increased frequency of thermally anomalous conditions at the HAI (such as experienced in 2011) has the potential to reduce the long-term stability of the HAI coral populations and species that depend upon them. PMID:26812259
Markey, Kathryn L; Abdo, Dave A; Evans, Scott N; Bosserelle, Cyprien
2016-01-01
In 2011 the first recorded bleaching event for the high latitude Houtman Abrolhos Islands (HAI) coral communities was documented. This bleaching event highlighted the question of whether a supply of 'heat tolerant' coral recruits from the tropical north would be sufficient to provide a level of resistance for these reefs to future warming events. Using Lagrangian modelling we showed that due to its regional isolation, large-scale larval input from potential tropical northern source populations to the HAI is unlikely, despite the southward flowing Leeuwin current. Successful recruitment to artificial substrates was recorded following the bleaching event. However, this was negligible (0.4 ± 0.1 recruits per tile) compared to 2013 post impact recruitment (128.8 ± 15.8 recruits per tile). Our data therefore provides preliminary evidence suggesting that the connectivity of the HAI with coral communities in the north is limited, and population maintenance and recovery is likely driven primarily by self-recruitment. Given the low thermal tolerance of the HAI coral communities, the dominance of Acropora, and the apparent reliance on self-recruitment, an increased frequency of thermally anomalous conditions at the HAI (such as experienced in 2011) has the potential to reduce the long-term stability of the HAI coral populations and species that depend upon them. PMID:26812259
Non-equilibrium spin-boson model: counting statistics and the heat exchange fluctuation theorem.
Nicolin, Lena; Segal, Dvira
2011-10-28
We focus on the non-equilibrium two-bath spin-boson model, a toy model for examining quantum thermal transport in many-body open systems. Describing the dynamics within the noninteracting-blip approximation equations, applicable, e.g., in the strong system-bath coupling limit and/or at high temperatures, we derive expressions for the cumulant generating function in both the Markovian and non-Markovian limits by energy-resolving the quantum master equation of the subsystem. For a Markovian bath, we readily demonstrate the validity of a steady-state heat exchange fluctuation theorem. In the non-Markovian limit a "weaker" symmetry relation generally holds, a general outcome of microreversibility. We discuss the reduction of this symmetry relation to the universal steady-state fluctuation theorem. Using the cumulant generating function, an analytic expression for the heat current is obtained. Our results establish the validity of the steady-state heat exchange fluctuation theorem in quantum systems with strong system-bath interactions. From the practical point of view, this study provides tools for exploring transport characteristics of the two-bath spin-boson model, a prototype for a nonlinear thermal conductor. PMID:22047227
Computer Algebra Systems and Theorems on Real Roots of Polynomials
ERIC Educational Resources Information Center
Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.
2010-01-01
A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)
Evaluating a Class of Series Using Taylor's Theorem. Classroom Notes
ERIC Educational Resources Information Center
Glaister, P.
2004-01-01
A class of infinite series is evaluated with the aid of Taylor's theorem and a comparison is made with other methods. In a recent note [1] a class of infinite series was shown to be equivalent to a number of definite integrals, and Taylor's theorem was used to establish convergence and to determine the sums of the series and the integrals to any…
Systematic Approaches to Experimentation: The Case of Pick's Theorem
ERIC Educational Resources Information Center
Papadopoulos, Ioannis; Iatridou, Maria
2010-01-01
In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…
Group Theoretical Interpretation of von Neumann's Theorem on Composite Systems.
ERIC Educational Resources Information Center
Bergia, S.; And Others
1979-01-01
Shows that von Neumann's mathematical theorem on composite systems acquires a transparent physical meaning with reference to a suitable physical example; a composite system in a state of definite angular momentum. Gives an outline of the theorem, and the results are restated in Dirac's notation, thus generalizing von Neumann's results which were…
Stimulating Presentation of Theorems Followed by Responsive Proofs.
ERIC Educational Resources Information Center
Movshovitz-Hadar, Nitsa
1988-01-01
Several ways to present two theorems (concerning a square matrix and a property of prime numbers) are demonstrated. One way for each theorem is more stimulating, better setting the stage for the proofs. Several methods of presenting proofs are illustrated, with the outcomes considered from the learner's viewpoint. (MNS)
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2009-02-20
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2008-03-01
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
Leaning on Socrates to Derive the Pythagorean Theorem
ERIC Educational Resources Information Center
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the formula b2 +…
Discovering Theorems in Abstract Algebra Using the Software "GAP"
ERIC Educational Resources Information Center
Blyth, Russell D.; Rainbolt, Julianne G.
2010-01-01
A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…
When 95% Accurate Isn't: Exploring Bayes's Theorem
ERIC Educational Resources Information Center
CadwalladerOlsker, Todd D.
2011-01-01
Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…
Some Reflections on CAS Assisted Proofs of Theorems
ERIC Educational Resources Information Center
Dana-Picard, Thierry
2005-01-01
A mathematician's work consists of proving theorems, calculating, and making mathematics understandable. An assistant for all three components is a Computer Algebra System. We describe and discuss various CAS-assisted processes for proving theorems, and discuss the constraints which can appear regarding efficiency, confidence in the result and…
Rotation of Axes and the Mean Value Theorem
ERIC Educational Resources Information Center
Price, David
2004-01-01
This article provides a proof of the Mean Value Theorem by rotating a coordinate system through a specified angle. The use of this approach makes it easy to visualize why the Mean Value Theorem is true. An instructor can use the proof as another illustration of the rotation of axis technique in addition to the standard one of simplifying equations…
Three Lectures on Theorem-proving and Program Verification
NASA Technical Reports Server (NTRS)
Moore, J. S.
1983-01-01
Topics concerning theorem proving and program verification are discussed with particlar emphasis on the Boyer/Moore theorem prover, and approaches to program verification such as the functional and interpreter methods and the inductive assertion approach. A history of the discipline and specific program examples are included.
A most compendious and facile quantum de Finetti theorem
Koenig, Robert; Mitchison, Graeme
2009-01-15
In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's 'exponential' approximation by 'almost-product' states, a theorem which deals with certain triples of representations of the unitary group, and the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choice of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states and leads to some new results, including an exponential theorem for infinite-dimensional systems.
The virial theorem for the polarizable continuum model
Cammi, R.
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.
The virial theorem for the Polarizable Continuum Model.
Cammi, R
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential. PMID:24588153
Adler-Bardeen theorem and manifest anomaly cancellation to all orders in gauge theories
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2014-10-01
We reconsider the Adler-Bardeen theorem for the cancellation of gauge anomalies to all orders, when they vanish at one loop. Using the Batalin-Vilkovisky formalism and combining the dimensional-regularization technique with the higher-derivative gauge invariant regularization, we prove the theorem in the most general perturbatively unitary renormalizable gauge theories coupled to matter in four dimensions, and identify the subtraction scheme where anomaly cancellation to all orders is manifest, namely no subtractions of finite local counterterms are required from two loops onwards. Our approach is based on an order-by-order analysis of renormalization, and, differently from most derivations existing in the literature, does not make use of arguments based on the properties of the renormalization group. As a consequence, the proof we give also applies to conformal field theories and finite theories.
A Stochastic Tikhonov Theorem in Infinite Dimensions
Buckdahn, Rainer Guatteri, Giuseppina
2006-03-15
The present paper studies the problem of singular perturbation in the infinite-dimensional framework and gives a Hilbert-space-valued stochastic version of the Tikhonov theorem. We consider a nonlinear system of Hilbert-space-valued equations for a 'slow' and a 'fast' variable; the system is strongly coupled and driven by linear unbounded operators generating a C{sub 0}-semigroup and independent cylindrical Brownian motions. Under well-established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. We avoid differentiability assumptions on the coefficients which would be unnatural in the infinite-dimensional framework.
Extended Ehrenfest theorem with radiative corrections
NASA Astrophysics Data System (ADS)
de la Peña, L.; Cetto, A. M.; Valdés-Hernández, A.
2015-10-01
A set of basic evolution equations for the mean values of dynamical variables is obtained from the Fokker-Planck equation applied to the general problem of a particle subject to a random force. The specific case of stochastic electrodynamics is then considered, in which the random force is due to the zero-point radiation field. Elsewhere it has been shown that when this system reaches a state of energy balance, it becomes controlled by an equation identical to Schrödinger’s, if the radiationless approximation is made. The Fokker-Planck equation was shown to lead to the Ehrenfest theorem under such an approximation. Here we show that when the radiative terms are not neglected, an extended form of the Ehrenfest equation is obtained, from which follow, among others, the correct formulas for the atomic lifetimes and the (nonrelativistic) Lamb shift.
BMS supertranslations and Weinberg's soft graviton theorem
NASA Astrophysics Data System (ADS)
He, Temple; Lysov, Vyacheslav; Mitra, Prahar; Strominger, Andrew
2015-05-01
Recently it was conjectured that a certain infinite-dimensional "diagonal" subgroup of BMS supertranslations acting on past and future null infinity ([InlineMediaObject not available: see fulltext.] and [InlineMediaObject not available: see fulltext.]) is an exact symmetry of the quantum gravity S-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinberg's soft graviton theorem. Along the way we construct the canonical generators of supertranslations at [InlineMediaObject not available: see fulltext.], including the relevant soft graviton contributions. Boundary conditions at the past and future of [InlineMediaObject not available: see fulltext.] and a correspondingly modified Dirac bracket are required. The soft gravitons enter as boundary modes and are manifestly the Goldstone bosons of spontaneously broken supertranslation invariance.
Theorem Proving in Intel Hardware Design
NASA Technical Reports Server (NTRS)
O'Leary, John
2009-01-01
For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.
On the Virial Theorem for Interstellar Medium
Ryutov, D
2007-09-24
An attempt has been made to derive a version of the virial integral that would describe average properties of the interstellar medium (ISM). It is suggested to eliminate the (large) contribution of stellar matter by introducing 'exclusion zones' surrounding stars. Such an approach leads to the appearance of several types of additional surface integrals in the general expression. Their contribution depends on the rate of energy and matter exchange between the stars and ISM. If this exchange is weak, one can obtain a desired virial integral for ISM. However, the presence of intermittent large-scale energetic events significantly constrains the applicability of the virial theorem. If valid, the derived virial integral is dominated by cold molecular/atomic clouds, with only minor contribution of the global magnetic field and low-density warm part.
Walking Through the Impulse-Momentum Theorem
NASA Astrophysics Data System (ADS)
Haugland, Ole Anton
2013-02-01
Modern force platforms are handy tools for investigating forces during human motion. Earlier they were very expensive and were mostly used in research laboratories. But now even platforms that can measure in two directions are quite affordable. In this work we used the PASCO 2-Axis Force Platform. The analysis of the data can serve as a nice illustration of qualitative or quantitative use of the impulse-momentum theorem p - p0 = ∫t0t Fdt = I. The most common use of force platforms is to study the force from the base during the push-off period of a vertical jump. I think this is an activity of great value, and I would recommend it. The use of force platforms in teaching is well documented in research literature.1-4
Elementary theorems regarding blue isocurvature perturbations
NASA Astrophysics Data System (ADS)
Chung, Daniel J. H.; Yoo, Hojin
2015-04-01
Blue CDM-photon isocurvature perturbations are attractive in terms of observability and may be typical from the perspective of generic mass relations in supergravity. We present and apply three theorems useful for blue isocurvature perturbations arising from linear spectator scalar fields. In the process, we give a more precise formula for the blue spectrum associated with the axion model of Kasuya and Kawasaki [Axion Isocurvature Fluctuations with Extremely Blue Spectrum, Phys. Rev. D 80, 023516 (2009).], which can in a parametric corner give a factor of O (10 ) correction. We explain how a conserved current associated with Peccei-Quinn symmetry plays a crucial role and explicitly plot several example spectra including the breaks in the spectra. We also resolve a little puzzle arising from a naive multiplication of isocurvature expression that sheds light on the gravitational imprint of the adiabatic perturbations on the fields responsible for blue isocurvature fluctuations.
Robbing the Bank with a Theorem Prover
NASA Astrophysics Data System (ADS)
Youn, Paul; Adida, Ben; Bond, Mike; Clulow, Jolyon; Herzog, Jonathan; Lin, Amerson; Rivest, Ronald L.; Anderson, Ross
In this work, we present the first automated analysis of security application programming interfaces (security APIs). In particular, we analyze the API of the IBM 4758 CCA, a hardware security module for banking networks. Adapting techniques from formal analyses of security protocols, we model the API purely according its specification and assuming ideal encryption primitives. We then use the automated theorem-prover Otter to analyze this model, combining its standard reasoning strategies with novel techniques of our own (also presented here). In this way, we derive not only all published API-level attacks against the 4758 CCA, but an extension to these attacks as well. Thus, this work represents the first step toward fully-automated, rigorous analyses of security APIs.
Electric-magnetic symmetry and Noether's theorem
NASA Astrophysics Data System (ADS)
Cameron, Robert P.; Barnett, Stephen M.
2012-12-01
In the absence of charges, Maxwell's equations are highly symmetrical. In particular, they place the electric and magnetic fields on equal footing. In light of this electric-magnetic symmetry, we introduce a variational description of the free electromagnetic field that is based upon the acknowledgement of both electric and magnetic potentials. We use our description, together with Noether's theorem, to demonstrate that electric-magnetic symmetry is, in essence, an expression of the conservation of optical helicity. The symmetry associated with the conservation of Lipkin's zilches is also identified. We conclude by considering, with care, the subtle separation of the rotation and boost angular momenta of the field into their ‘spin’ and ‘orbital’ contributions.
Virial Theorem in Nonlocal Newtonian Gravity
NASA Astrophysics Data System (ADS)
Mashhoon, Bahram
2016-05-01
Nonlocal gravity is the recent classical nonlocal generalization of Einstein's theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for "isolated" astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's baryonic diameter---namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time---is predicted to be larger than the effective dark matter fraction times a universal length that is the basic nonlocality length scale of about 3 kpc.
Generalization of Kummer's second theorem with applications
NASA Astrophysics Data System (ADS)
Kim, Yong Sup; Rakha, M. A.; Rathie, A. K.
2010-03-01
The aim of this research paper is to obtain single series expression of e^{ - x/2} _1 F_1 (α ;2α + i;x) for i = 0, ±1, ±2, ±3, ±4, ±5, where 1 F 1(·) is the function of Kummer. For i = 0, we have the well known Kummer second theorem. The results are derived with the help of generalized Gauss second summation theorem obtained earlier by Lavoie et al. In addition to this, explicit expressions of _2 F_1 [ - 2n,α ;2α + i;2]and_2 F_1 [ - 2n - 1,α ;2α + i;2] each for i = 0, ±1, ±2, ±3, ±4, ±5 are also given. For i = 0, we get two interesting and known results recorded in the literature. As an applications of our results, explicit expressions of e^{ - x} _1 F_1 (α ;2α + i;x) × _1 F_1 (α ;2α + j;x) for i, j = 0, ±1, ±2, ±3, ±4, ±5 and (1 - x)^{ - a} _2 F_1 left( {a,b,2b + j; - tfrac{{2x}} {{1 - x}}} right) for j = 0, ±1, ±2, ±3, ±4, ±5 are given. For i = j = 0 and j = 0, we respectively get the well known Preece identity and a well known quadratic transformation formula due to Kummer. The results derived in this paper are simple, interesting, easily established and may be useful in the applicable sciences.
Generalized energy measurements and modified transient quantum fluctuation theorems.
Watanabe, Gentaro; Venkatesh, B Prasanna; Talkner, Peter
2014-05-01
Determining the work which is supplied to a system by an external agent provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a problem for quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modified Crooks relation and Jarzynski equality are found for Gaussian energy measurements. These can be obtained by a sequence of sufficiently many generalized measurements which need not be Gaussian. In accordance with the central limit theorem, this leads to an effective error reduction in the individual measurements and even yields a projective measurement in the limit of infinite repetitions. PMID:25353748
Stability of Gas Clouds in Galactic Nuclei: An Extended Virial Theorem
NASA Astrophysics Data System (ADS)
Chen, Xian; Amaro-Seoane, Pau; Cuadra, Jorge
2016-03-01
Cold gas entering the central 1-102 pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH) to turn on an active galactic nucleus (AGN). The conventional criteria to assess the stability of these clouds, such as the Jeans criterion and Roche (or tidal) limit, are insufficient here, because they assume the dominance of self-gravity in binding a cloud, and neglect external agents, such as pressure and tidal forces, which are common in galactic nuclei. We formulate a new scheme for judging this stability. We first revisit the conventional Virial theorem, taking into account an external pressure, to identify the correct range of masses that lead to stable clouds. We then extend the theorem to further include an external tidal field, which is equally crucial for the stability in the region of our interest—in dense star clusters, around SMBHs. We apply our extended Virial theorem to find new solutions to controversial problems, namely, the stability of the gas clumps in AGN tori, the circum-nuclear disk in the Galactic Center, and the central molecular zone of the Milky Way. The masses we derive for these structures are orders of magnitude smaller than the commonly used Virial masses (equivalent to the Jeans mass). Moreover, we prove that these clumps are stable, contrary to what one would naively deduce from the Roche (tidal) limit.
Gangopadhyay, Aparna; Nath, Partha; Biswas, Jaydip
2015-01-01
Background In our experience, induction docetaxel, platinum, and fluorouracil (TPF) chemotherapy and sequential chemoradiation in locally advanced head and neck cancer lowers compliance owing to their considerable toxicity. Most of our head and neck cancer patients have locally advanced disease at presentation. Physicians frequently prefer paclitaxel–cisplatin induction chemotherapy instead, because of better patient tolerance. Materials and methods A total of 207 locally advanced head and neck cancer patients receiving paclitaxel and cisplatin prior to chemoradiation from November 2010 to October 2013 were studied retrospectively. Parameters like febrile neutropaenia, treatment compliance, and response rates were compared to our institutional retrospective data with TPF chemotherapy. Response was assessed by Response Evaluation Criteria in Solid Tumours (Recist) version 1.1. Toxicity was assessed by Common Terminology Criteria for Adverse Events (CTCAE) version 4.0 during chemotherapy. Radiation Therapy Oncology Group (RTOG) acute toxicity criteria were used for assessment during chemoradiation. Results Febrile neutropaenia with paclitaxel– cisplatin was significantly lower 3.4% (7/207) versus 44.5% (73/164) with TPF chemotherapy (two-tailed P value < 0.0001). A 95.7 % (198/207) paclitaxel–cisplatin patients completed chemoradiation versus 87% with TPF. The difference was significant (two-tailed P value = 0.0070). Response rate at treatment completion with paclitaxel –cisplatin was 89.7% versus 88% with TPF chemotherapy. No significant differences were observed (two-tailed P value = 0.7007). Conclusion Induction paclitaxel and cisplatin with sequential chemoradiation in locally advanced head and neck cancer is more suitable in a limited resource setting. Lower toxicity, better compliance, and comparable response are encouraging in our study cohort. PMID:26082800
Global stabilization using LSS-Theorem: Applications to Robotics and Aerospace Vehicles
NASA Astrophysics Data System (ADS)
Selman, AbdulRazzak
Underactuated mechanical systems are gaining interest as they can sometimes provide the desired motion or functionality at reduced cost due to their using fewer expensive actuators. The term "underactuated" refers to the fact that such mechanical systems have fewer actuators than degrees of freedom, which makes them very difficult to control. Moreover, underactuated robots have nonlinear dynamics which must be tackled with nonlinear control techniques. Furthermore, control theory for underactuated mechanical systems has been an active area of research for the past 15-20 years. Most of the research has focused on local and global asymptotic stabilization by feedback. Underactuated systems can either possess nonminimum phase or minimum phase characteristics. For minimum phase underactuated systems, the stabilization problem is rather simple and many existing control design methodologies have been proved powerful in providing a solution to this problem. For nonminimum phase underactuated systems, asymptotic stabilization problem has been, and still is, an attractive subject to the researchers in the field of nonlinear control system and theory. In particular, global asymptotic stabilization (GAS) at a desired equilibrium point of such systems by means of a single smooth static or dynamic state feedback law is still largely an open problem in the literature. In this thesis, the problem of GAS via a smooth static state feedback law is addressed for a class of an underactuated nonlinear system that is affine (possibly non affine) in the control, partially feedback linearizable, nonminimum phase and (possibly) has a non-integrable acceleration constraint. The core result of the thesis is formulated through a theorem that the author refers to through this thesis as the Legend of Salah Salman (LSS) Theorem. LSS theorem states the existence of a smooth static state feedback law that globally asymptotically stabilizes the origin of the nonlinear underactuated system that is
NASA Astrophysics Data System (ADS)
Ramalho, G.
2016-08-01
Some empirical parametrizations of the γ* N → N (1535) transition amplitudes violate the Siegert's theorem, that relates the longitudinal and the transverse amplitudes in the pseudo-threshold limit (nucleon and resonance at rest). In the case of the electromagnetic transition from the nucleon (mass M) to the resonance N (1525) (mass MR), the Siegert's theorem is sometimes expressed by the relation | q |A1/2 = λS1/2 in the pseudo-threshold limit, when the photon momentum | q | vanishes, and λ =√{ 2} (MR - M). In this article, we argue that the Siegert's theorem should be expressed by the relation A1/2 = λS1/2 / | q |, in the limit | q | → 0. This result is a consequence of the relation S1/2 ∝ | q |, when | q | → 0, as suggested by the analysis of the transition form factors and by the orthogonality between the nucleon and N (1535) states. We propose then new empirical parametrizations for the γ* N → N (1535) helicity amplitudes, that are consistent with the data and the Siegert's theorem. The proposed parametrizations follow closely the MAID2007 parametrization, except for a small deviation in the amplitudes A1/2 and S1/2 when Q2 < 1.5 GeV2.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
NASA Astrophysics Data System (ADS)
Stenlund, Mikko
2016-09-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff's ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
Entropy for quantum pure states and quantum H theorem.
Han, Xizhi; Wu, Biao
2015-06-01
We construct a complete set of Wannier functions that are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability distribution in quantum phase space, we define an entropy for a quantum pure state. We prove an inequality regarding the long-time behavior of our entropy's fluctuation. For a typical initial state, this inequality indicates that our entropy can relax dynamically to a maximized value and stay there most of time with small fluctuations. This result echoes the quantum H theorem proved by von Neumann [Zeitschrift für Physik 57, 30 (1929)]. Our entropy is different from the standard von Neumann entropy, which is always zero for quantum pure states. According to our definition, a system always has bigger entropy than its subsystem even when the system is described by a pure state. As the construction of the Wannier basis can be implemented numerically, the dynamical evolution of our entropy is illustrated with an example. PMID:26172660
Entropy for quantum pure states and quantum H theorem
NASA Astrophysics Data System (ADS)
Han, Xizhi; Wu, Biao
2015-06-01
We construct a complete set of Wannier functions that are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability distribution in quantum phase space, we define an entropy for a quantum pure state. We prove an inequality regarding the long-time behavior of our entropy's fluctuation. For a typical initial state, this inequality indicates that our entropy can relax dynamically to a maximized value and stay there most of time with small fluctuations. This result echoes the quantum H theorem proved by von Neumann [Zeitschrift für Physik 57, 30 (1929), 10.1007/BF01339852]. Our entropy is different from the standard von Neumann entropy, which is always zero for quantum pure states. According to our definition, a system always has bigger entropy than its subsystem even when the system is described by a pure state. As the construction of the Wannier basis can be implemented numerically, the dynamical evolution of our entropy is illustrated with an example.
Isotropy theorem for cosmological Yang-Mills theories
NASA Astrophysics Data System (ADS)
Cembranos, J. A. R.; Maroto, A. L.; Jareño, S. J. Núñez
2013-02-01
We consider homogeneous non-Abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a generalization of the virial theorem that for an arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. We consider also the case in which a gauge-fixing term is introduced in the action and show that the average equation of state does not depend on such a term. Finally, we extend the results to arbitrary background geometries and show that the average energy-momentum tensor of a rapidly evolving Yang-Mills field is always isotropic and has the perfect fluid form for any locally inertial observer.
Fluctuation-dissipation theorem density-functional theory
NASA Astrophysics Data System (ADS)
Furche, Filipp; Van Voorhis, Troy
2005-04-01
Using the fluctuation-dissipation theorem (FDT) in the context of density-functional theory (DFT), one can derive an exact expression for the ground-state correlation energy in terms of the frequency-dependent density response function. When combined with time-dependent density-functional theory, a new class of density functionals results that use approximations to the exchange-correlation kernel fxc as input. This FDT-DFT scheme holds promise to solve two of the most distressing problems of conventional Kohn-Sham DFT: (i) It leads to correlation energy functionals compatible with exact exchange, and (ii) it naturally includes dispersion. The price is a moderately expensive O(N6) scaling of computational cost and a slower basis set convergence. These general features of FDT-DFT have all been recognized previously. In this paper, we present the first benchmark results for a set of molecules using FDT-DFT beyond the random-phase approximation (RPA)—that is, the first such results with fxc≠0. We show that kernels derived from the adiabatic local-density approximation and other semilocal functionals suffer from an "ultraviolet catastrophe," producing a pair density that diverges at small interparticle distance. Nevertheless, dispersion interactions can be treated accurately if hybrid functionals are employed, as is demonstrated for He2 and HeNe. We outline constraints that future approximations to fxc should satisfy and discuss the prospects of FDT-DFT.
Fukumura, K; Yamaoka, K; Higashimori, M; Nakagawa, T
1998-12-01
A pharmacokinetic analysis program based on a tank-in-series model, MULTI(TIS), was developed for the evaluation of dose-dependency in the local disposition of a drug. The program written in FORTRAN was constructed by expanding MULTI(RUNGE). The reliability of MULTI(TIS) was verified by analyzing the experimental data based on linear and nonlinear tank-in-series models. Linear one- and two-compartment tank-in-series models were adopted to analyze outflow time profiles in single-pass hepatic perfusion following a pulse input of 5'-deoxy-5-fluorouridine (DFUR). The estimated parameters agreed well with those by MULTI(FILT) which is widely used for linear kinetic analysis. The nonlinear models adopted were one-compartment model with Michaelis-Menten elimination and two-compartment models with Michaelis-Menten elimination from central and peripheral compartments. Oxacillin was used as a model drug, because time courses of oxacillin show a capacity-limited hepatic disposition following a pulse input in high doses to the liver (300, 1000, 3000 and 5000 microg). The hepatic recovery ratio (F(H)) of oxacillin increased with dose, whereas the mean transit time (tH) was almost constant. The maximum elimination rate constant (Vmax) and Michaelis constant (Km) of oxacillin were estimated to be 1980 microg/ml/min and 54.1 microg/ml, respectively. Thus, the reliability of MULTI(TIS) was demonstrated for the analysis of nonlinear local disposition, especially, capacity-limited elimination in the liver. PMID:9881650
Analysing nature's experiment: Fisher's inductive theorem of natural selection.
Edwards, A W F
2016-06-01
The paper by Ewens and Lessard (2015) adds to the progress that has been made in exploring the discrete-generation analytical version of Fisher's Fundamental Theorem of Natural Selection introduced by Ewens (1989). Fisher's continuous-time theorem differs from the version described by Ewens and Lessard by using a different concept of fitness. Ewens and Lessard use the conventional 'viability' concept whereas for Fisher the fitness of a genotype was its relative rate of increase or decrease in the population. The sole purpose of the present paper is to emphasize the alternative inductive nature of Fisher's theorem, as presented by him in 1930, by placing it in the context of his contemporary development of the analysis of variance in agricultural experiments. It is not a general discussion of the theorem itself. PMID:26581894
Two time physics and Hamiltonian Noether theorem for gauge systems
Nieto, J. A.; Ruiz, L.; Silvas, J.; Villanueva, V. M.
2006-09-25
Motivated by two time physics theory we revisited the Noether theorem for Hamiltonian constrained systems. Our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints.
Oscillation theorems for second order nonlinear forced differential equations.
Salhin, Ambarka A; Din, Ummul Khair Salma; Ahmad, Rokiah Rozita; Noorani, Mohd Salmi Md
2014-01-01
In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature. PMID:25077054
Extension of the Blasius force theorem to subsonic speeds
NASA Astrophysics Data System (ADS)
Barsony-Nagy, A.
1985-11-01
The theorem considered by Blasius (1910) represents a well-known method for calculating the force on a body situated in an incompressible, inviscid two-dimensional flow. The efficiency of the Blasius theorem is due to its quality of expressing the forces with the aid of contour integrals of analytic functions of complex variables. The present note has the objective to deduce an analog of Blasius theorem for the aerodynamic forces in subsonic flow. It is assumed that an approximate velocity potential of the subsonic flow has been calculated by using the Imai-Lamla method. It is pointed out that this method is a variant specially suited for the two-dimensionally flows of the Janzen-Rayleigh expansion method. The derived formula expresses the aerodynamic forces with the aid of contour integrals of analytic complex functions. It can be regarded as the Blasius theorem with first-order compressibility correction for the subsonic speed regime.
Bernoulli theorem generalized to rheologically complex viscous fluid flow
NASA Astrophysics Data System (ADS)
Brutyan, M. A.; Krapivskii, P. L.
1992-08-01
The Bernoulli theorem is generalized to two-dimensional and axisymmetric micropolar incompressible fluid flows. It is shown that the approach developed is also applicable to magnetohydrodynamic flows of a viscous Newtonian fluid.
An Epistemological Criticism to the Bell-Kochen-Specker Theorem
NASA Astrophysics Data System (ADS)
Garola, Claudio
2009-03-01
The Bell-Kochen-Specker theorem is criticized from an epistemological point of view, showing that its proofs rest on an implicit epistemological assumption which does not fit in with the operational and antimetaphysical attitude of orthodox quantum mechanics.
Forest Carbon Uptake and the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Zobitz, John
2013-01-01
Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.
On an order reduction theorem in the Lagrangian formalism
NASA Astrophysics Data System (ADS)
Grigore, D. R.
1996-11-01
We provide a new proof of a important theorem in the Lagrangian formalism about necessary and sufficient conditions for a second-order variational system of equations to follow from a first-order Lagrangian.
Fluctuation theorem in driven nonthermal systems with quenched disorder
Reichhardt, Charles; Reichhardt, C J; Drocco, J A
2009-01-01
We demonstrate that the fluctuation theorem of Evans and Searles can be used to characterize the class of dynamics that arises in nonthermal systems of collectively interacting particles driven over random quenched disorder. By observing the frequency of entropy-destroying trajectories, we show that there are specific dynamical regimes near depinning in which this theorem holds. Hence the fluctuation theorem can be used to characterize a significantly wider class of non-equilibrium systems than previously considered. We discuss how the fluctuation theorem could be tested in specific systems where noisy dynamics appear at the transition from a pinned to a moving phase such as in vortices in type-II superconductors, magnetic domain walls, and dislocation dynamics.
On the generalized virial theorem for systems with variable mass
NASA Astrophysics Data System (ADS)
Ganghoffer, Jean-François; Rahouadj, Rachid
2016-03-01
We presently extend the virial theorem for both discrete and continuous systems of material points with variable mass, relying on developments presented in Ganghoffer (Int J Solids Struct 47:1209-1220, 2010). The developed framework is applicable to describe physical systems at very different scales, from the evolution of a population of biological cells accounting for growth to mass ejection phenomena occurring within a collection of gravitating objects at the very large astrophysical scales. As a starting basis, the field equations in continuum mechanics are written to account for a mass source and a mass flux, leading to a formulation of the virial theorem accounting for non-constant mass within the considered system. The scalar and tensorial forms of the virial theorem are then written successively in both Lagrangian and Eulerian formats, incorporating the mass flux. As an illustration, the averaged stress tensor in accreting gravitating solid bodies is evaluated based on the generalized virial theorem.
Biological fitness and the fundamental theorem of natural selection.
Grafen, Alan
2015-07-01
Fisher's fundamental theorem of natural selection is proved satisfactorily for the first time, resolving confusions in the literature about the nature of reproductive value and fitness. Reproductive value is defined following Fisher, without reference to genetic variation, and fitness is the proportional rate of increase in an individual's contribution to the demographic population size. The mean value of fitness is the same in each age class, and it also equals the population's Malthusian parameter. The statement and derivation are regarded as settled here, and so the general biological significance of the fundamental theorem can be debated. The main purpose of the theorem is to find a quantitative measure of the effect of natural selection in a Mendelian system, thus founding Darwinism on Mendelism and identifying the design criterion for biological adaptation, embodied in Fisher's ingenious definition of fitness. The relevance of the newly understood theorem to five current research areas is discussed. PMID:26098334
Pressman, N.J.; Frost, J.K.; Gupta, P.K.; Showers, R.L.; Gill, G.W.; Cook, D.L.; Frost, J.K. Jr.; Traub, R.K.
1987-08-01
Cellular dynamics often involve extremely low concentrations of biologically active substances, which can be radiolabeled and detected, localized and quantitated by autoradiography. The latter may require exposures from a few days to many months. The objective of this research was to demonstrate the feasibility of reducing this long period of data collection by one to two orders of magnitude, while maintaining or improving the spatial resolution and localization in tissues and the quantitative characteristics inherent in autoradiography. A mathematical model describing the complete system was generated using energy partition calculations to estimate photon production via scintillant per H3 beta particle emission and to estimate the subsequent photon capture based upon imaging system parameters and microscope geometry. Calculations showed that, typically, a single tritium beta particle produces a maximum of 5.8 X 10(3) photons. A photon-limited camera and microscope imaging system were selected and optimized in conjunction with a specially developed physical scintillation model. Results showed that the number of detected photoevents increases monotonically with both signal integration time and, independently, with the concentration of the radionuclide. Consequently, this work demonstrates that video microscopy imaging methods can spatially and temporally quantify very low concentrations of radiolabeled substances and can reduce data acquisition times.
Ziegler, Jörg; Schmidt, Stephan; Chutia, Ranju; Müller, Jens; Böttcher, Christoph; Strehmel, Nadine; Scheel, Dierk; Abel, Steffen
2016-01-01
Plants have evolved two major strategies to cope with phosphate (Pi) limitation. The systemic response, mainly comprising increased Pi uptake and metabolic adjustments for more efficient Pi use, and the local response, enabling plants to explore Pi-rich soil patches by reorganization of the root system architecture. Unlike previous reports, this study focused on root exudation controlled by the local response to Pi deficiency. To approach this, a hydroponic system separating the local and systemic responses was developed. Arabidopsis thaliana genotypes exhibiting distinct sensitivities to Pi deficiency could be clearly distinguished by their root exudate composition as determined by non-targeted reversed-phase ultraperformance liquid chromatography electrospray ionization quadrupole-time-of-flight mass spectrometry metabolite profiling. Compared with wild-type plants or insensitive low phosphate root 1 and 2 (lpr1 lpr2) double mutant plants, the hypersensitive phosphate deficiency response 2 (pdr2) mutant exhibited a reduced number of differential features in root exudates after Pi starvation, suggesting the involvement of PDR2-encoded P5-type ATPase in root exudation. Identification and analysis of coumarins revealed common and antagonistic regulatory pathways between Pi and Fe deficiency-induced coumarin secretion. The accumulation of oligolignols in root exudates after Pi deficiency was inversely correlated with Pi starvation-induced lignification at the root tips. The strongest oligolignol accumulation in root exudates was observed for the insensitive lpr1 lpr2 double mutant, which was accompanied by the absence of Pi deficiency-induced lignin deposition, suggesting a role of LPR ferroxidases in lignin polymerization during Pi starvation. PMID:26685189
Ziegler, Jörg; Schmidt, Stephan; Chutia, Ranju; Müller, Jens; Böttcher, Christoph; Strehmel, Nadine; Scheel, Dierk; Abel, Steffen
2016-03-01
Plants have evolved two major strategies to cope with phosphate (Pi) limitation. The systemic response, mainly comprising increased Pi uptake and metabolic adjustments for more efficient Pi use, and the local response, enabling plants to explore Pi-rich soil patches by reorganization of the root system architecture. Unlike previous reports, this study focused on root exudation controlled by the local response to Pi deficiency. To approach this, a hydroponic system separating the local and systemic responses was developed. Arabidopsis thaliana genotypes exhibiting distinct sensitivities to Pi deficiency could be clearly distinguished by their root exudate composition as determined by non-targeted reversed-phase ultraperformance liquid chromatography electrospray ionization quadrupole-time-of-flight mass spectrometry metabolite profiling. Compared with wild-type plants or insensitive low phosphate root 1 and 2 (lpr1 lpr2) double mutant plants, the hypersensitive phosphate deficiency response 2 (pdr2) mutant exhibited a reduced number of differential features in root exudates after Pi starvation, suggesting the involvement of PDR2-encoded P5-type ATPase in root exudation. Identification and analysis of coumarins revealed common and antagonistic regulatory pathways between Pi and Fe deficiency-induced coumarin secretion. The accumulation of oligolignols in root exudates after Pi deficiency was inversely correlated with Pi starvation-induced lignification at the root tips. The strongest oligolignol accumulation in root exudates was observed for the insensitive lpr1 lpr2 double mutant, which was accompanied by the absence of Pi deficiency-induced lignin deposition, suggesting a role of LPR ferroxidases in lignin polymerization during Pi starvation. PMID:26685189
Strong no-go theorem for Gaussian quantum bit commitment
Magnin, Loieck; Magniez, Frederic; Leverrier, Anthony
2010-01-15
Unconditionally secure bit commitment is forbidden by quantum mechanics. We extend this no-go theorem to continuous-variable protocols where both players are restricted to use Gaussian states and operations, which is a reasonable assumption in current-state optical implementations. Our Gaussian no-go theorem also provides a natural counter-example to a conjecture that quantum mechanics can be rederived from the assumption that key distribution is allowed while bit commitment is forbidden in Nature.
Note on soft graviton theorem by KLT relation
NASA Astrophysics Data System (ADS)
Du, Yi-Jian; Feng, Bo; Fu, Chih-Hao; Wang, Yihong
2014-11-01
Recently, new soft graviton theorem proposed by Cachazo and Strominger has inspired a lot of works. In this note, we use the KLT-formula to investigate the theorem. We have shown how the soft behavior of color ordered Yang-Mills amplitudes can be combined with KLT relation to give the soft behavior of gravity amplitudes. As a byproduct, we find two nontrivial identities of the KLT momentum kernel must hold.
A study on arithmetical functions and the prime number theorem
NASA Astrophysics Data System (ADS)
Imm, Yeoh Saw
2014-06-01
In this paper, Leibniz triangle and suitable binomial coefficients were used to get the bounds of ψ (x) . Using the generalized convolution and the differentiation on generalized convolution of arithmetical functions, we get to prove Tatuzawa-Izeki identity. Selberg's asymptotic formula is included as a special case, which is the beginning of certain elementary proofs of the Prime Number Theorem. Integration is used on some related inequalities to provide a smoother elementary proof of the Prime Number Theorem.
Nyquist-Shannon sampling theorem applied to refinements of the atomic pair distribution function
Farrow, Christopher L.; Shaw, Margaret; Kim, Hyunjeong; Juhás, Pavol; Billinge, Simon J.L.
2011-12-07
We have systematically studied the optimal real-space sampling of atomic pair distribution (PDF) data by comparing refinement results from oversampled and resampled data. Based on nickel and a complex perovskite system, we show that not only is the optimal sampling bounded by the Nyquist interval described by the Nyquist-Shannon (NS) sampling theorem as expected, but near this sampling interval, the data points in the PDF are minimally correlated, which results in more reliable uncertainty estimates in the modeling. Surprisingly, we find that PDF refinements quickly become unstable for data on coarser grids. Although the Nyquist-Shannon sampling theorem is well known, it has not been applied to PDF refinements, despite the growing popularity of the PDF method and its adoption in a growing number of communities. Here, we give explicit expressions for the application of NS sampling theorem to the PDF case, and establish through modeling that it is working in practice, which lays the groundwork for this to become more widely adopted. This has implications for the speed and complexity of possible refinements that can be carried out many times faster than currently with no loss of information, and it establishes a theoretically sound limit on the amount of information contained in the PDF that will prevent over-parametrization during modeling.
Non-linear energy conservation theorem in the framework of special relativity
NASA Astrophysics Data System (ADS)
Pérez Teruel, Ginés R.
2015-07-01
In this work we revisit the study of the gravitational interaction in the context of the special theory of relativity. It is found that, as long as the equivalence principle is respected, a relativistic nonlinear energy conservation theorem arises in a natural way. We interpret that this nonlinear conservation law stresses the nonlinear character of the gravitational interaction. The theorem reproduces the energy conservation theorem of Newtonian mechanics in the corresponding low energy limit, but also allows to derive some standard results of post-Newtonian gravity, such as the formula of the gravitational redshift. Guided by this conservation law, we develop a Lagrangian formalism for a particle in a gravitational field. We realize that the Lagrangian can be written in an explicit covariant fashion, and turns out to be the geodesic Lagrangian of a curved Lorentzian manifold. Therefore, any attempt to describe gravity within the special theory, leads outside their own domains towards a curved space-time. Thus, the pedagogical content of the paper may be useful as a starting point to discuss the problem of gravitation in the context of the special theory, as a preliminary step before introducing general relativity.
On a variational theorem in acousto-elastodynamics
NASA Astrophysics Data System (ADS)
Thompson, B. S.
1982-08-01
A variational theorem is presented which may be used as a basis for developing the equations of motion and the boundary conditions appropriate for studying the vibrational behavior of flexible bodied systems and the surrounding acoustic medium. The theorem is a generalization of two theorems which are both based on the principle of virtual work; the first governs the elastodynamics of the mechanical system and the second governs the behavior of the fluid medium. Lagrange multipliers are used in the development of the two basic theorems and they are also employed to incorporate the constraints at the solid-fluid interface within the functional for the acousto-elastodynamic theorem. When independent arbitrary variations of the system parameters are permitted, this theorem yields as characteristic equations the equations of motion for each member of the mechanical system, the acoustic wave equation, the compatibility conditions at the mechanical joints, the compatibility conditions at the interface and also the mixed boundary conditions for the complete system. As an illustrative example, the derivation of the problem statement for a flexible slider crank mechanism operating in a perfect gas is presented in which it is assumed that the flexural motion of the links is governed by the Timoshenko beam theory.
[Health care systems and impossibility theorems].
Penchas, Shmuel
2004-02-01
results are Kurt Godel's seminal paper in 1931: "Ueber formal unentscheidbare Saetze der Principia Mathematica and verwandter System I" and Arrow's Nobel Prize winning "Impossibility Theorem" (Social Choice and Individual Values, 1951). Godel showed, unequivocally, that there is an enormous gap between what is being perceived as truth and what in fact can be proven as such. Arrow showed that the translation of individual preferences into a social order is impossible--except in a dictatorship. The unsolved controversies concerning the desirable or ideal structure of health care systems are impinged upon by these findings generally, and, in the case of the impossibility theorem, also directly. There is the impossibility of aggregating preferences and, at a deeper level, the impossibility of defining certain fundamental values, coupled with the problematic use of certain words, the absence of the possibility of creating, on a logically defined base, a complex system, complete and comprehensive in its own right. This is added to the fact that according to the elaboration by Stephen Wolfram in "A New Kind of Science", it is not easy to reduce complicated systems to simple components and to predict the continuation of their development even from simple basic laws without complicated calculations. All of these factors impede the construction of satisfying health care systems and leave obvious problems which overshadow the structure and the operation of health care systems. PMID:15143703
NASA Astrophysics Data System (ADS)
Kushwaha, Manvir S.
2016-03-01
We investigate a one-component, quasi-zero-dimensional, quantum plasma exposed to a parabolic potential and an applied magnetic field in the symmetric gauge. If the size of such a system as can be realized in the semiconducting quantum dots is on the order of the de Broglie wavelength, the electronic and optical properties become highly tunable. Then the quantum size effects challenge the observation of many-particle phenomena such as the magneto-optical absorption, Raman intensity, and electron energy loss spectrum. An exact analytical solution of the problem leads us to infer that these many-particle phenomena are, in fact, dictated by the generalized Kohn's theorem in the long-wavelength limit. Maneuvering the confinement and/or the magnetic field furnishes the resonance energy capable of being explored with the FIR, Raman, or electron energy loss spectroscopy. This implies that either of these probes should be competent in observing the localized magnetoplasmons in the system. A deeper insight into the physics of quantum dots is paving the way for their implementation in diverse fields such as quantum computing and medical imaging.
Subexponential estimates in Shirshov's theorem on height
Belov, Aleksei Ya; Kharitonov, Mikhail I
2012-04-30
Suppose that F{sub 2,m} is a free 2-generated associative ring with the identity x{sup m}=0. In 1993 Zelmanov put the following question: is it true that the nilpotency degree of F{sub 2,m} has exponential growth? We give the definitive answer to Zelmanov's question by showing that the nilpotency class of an l-generated associative algebra with the identity x{sup d}=0 is smaller than {Psi}(d,d,l), where {Psi}(n,d,l)=2{sup 18}l(nd){sup 3log}{sub 3}{sup (nd)+13}d{sup 2}. This result is a consequence of the following fact based on combinatorics of words. Let l, n and d{>=}n be positive integers. Then all words over an alphabet of cardinality l whose length is not less than {Psi}(n,d,l) are either n-divisible or contain x{sup d}; a word W is n-divisible if it can be represented in the form W=W{sub 0}W{sub 1} Horizontal-Ellipsis W{sub n} so that W{sub 1},...,W{sub n} are placed in lexicographically decreasing order. Our proof uses Dilworth's theorem (according to V.N. Latyshev's idea). We show that the set of not n-divisible words over an alphabet of cardinality l has height h<{Phi}(n,l) over the set of words of degree {<=}n-1, where {Phi}(n,l)=2{sup 87}l{center_dot}n{sup 12log}{sub 3}{sup n+48}. Bibliography: 40 titles.
NASA Astrophysics Data System (ADS)
Fernández-Olmo, Ignacio; Andecochea, Carlos; Ruiz, Sara; Fernández-Ferreras, José Antonio; Irabien, Angel
2016-05-01
This study presents the analysis of the concentration levels, inter-site variation and source identification of trace metals at three urban/industrial mixed land-use sites of the Cantabria region (northern Spain), where local air quality plans were recently approved because the number of exceedances of the daily PM10 limit value according to the Directive 2008/50/EC had been relatively high in the last decade (more than 35 instances per year). PM10 samples were collected for over three years at the Torrelavega (TORR) and Los Corrales (CORR) sites and for over two years at the Camargo (GUAR) site and analysed for the presence of arsenic (As), cadmium (Cd), chromium (Cr), copper (Cu), lead (Pb), nickel (Ni), titanium (Ti), vanadium (V), molybdenum (Mo), manganese (Mn), iron (Fe), antimony (Sb) and zinc (Zn). Analysis of enrichment factors revealed an anthropogenic origin of most of the studied elements; Zn, Cd, Mo, Pb and Cu were the most enriched elements at the three sites, with Fe and V as the least enriched elements. Positive Matrix Factorisation (PMF) and pollutant roses (Cu at TORR, Zn at CORR and Mn at GUAR) were used to identify the local sources of the studied metals. Analysis of PMF results revealed the main sources of trace metals at each site as road traffic at the TORR site, iron foundry and casting industry at the CORR site and a ferro-manganese alloy industry at the GUAR site. Other sources were also identified at these sites, but with much lower contributions, such as minor industrial sources, combustion and traffic mixed with the previous sources.
NASA Astrophysics Data System (ADS)
Spruzeniece, L.; Piazolo, S.
2015-07-01
This study focuses on physiochemical processes occurring in a brittle-ductile shear zone at both fluid-present and fluid-limited conditions. In the studied shear zone (Wyangala, SE Australia), a coarse-grained two-feldspar-quartz-biotite granite is transformed into a medium-grained orthogneiss at the shear zone margins and a fine-grained quartz-muscovite phyllonite in the central parts. The orthogneiss displays cataclasis of feldspar and crystal-plastic deformation of quartz. Quartz accommodates most of the deformation and is extensively recrystallized, showing distinct crystallographic preferred orientation (CPO). Feldspar-to-muscovite, biotite-to-muscovite and albitization reactions occur locally at porphyroclasts' fracture surfaces and margins. However, the bulk rock composition shows very little change in respect to the wall rock composition. In contrast, in the shear zone centre quartz occurs as large, weakly deformed porphyroclasts in sizes similar to that in the wall rock, suggesting that it has undergone little deformation. Feldspars and biotite are almost completely reacted to muscovite, which is arranged in a fine-grained interconnected matrix. Muscovite-rich layers contain significant amounts of fine-grained intermixed quartz with random CPO. These domains are interpreted to have accommodated most of the strain. Bulk rock chemistry data show a significant increase in SiO2 and depletion in NaO content compared to the wall rock composition. We suggest that the high- and low-strain microstructures in the shear zone represent markedly different scenarios and cannot be interpreted as a simple sequential development with respect to strain. Instead, we propose that the microstructural and mineralogical changes in the shear zone centre arise from a local metasomatic alteration around a brittle precursor. When the weaker fine-grained microstructure is established, the further flow is controlled by transient porosity created at (i) grain boundaries in fine
Subsubleading soft theorems of gravitons and dilatons in the bosonic string
NASA Astrophysics Data System (ADS)
Di Vecchia, Paolo; Marotta, Raffaele; Mojaza, Matin
2016-06-01
Starting from the amplitude with an arbitrary number of massless closed states of the bosonic string, we compute the soft limit when one of the states becomes soft to subsubleading order in the soft momentum expansion, and we show that when the soft state is a graviton or a dilaton, the full string amplitude can be expressed as a soft theorem through subsubleading order. It turns out that there are string corrections to the field theoretical limit in the case of a soft graviton, while for a soft dilaton the string corrections vanish. We then show that the new soft theorems, including the string corrections, can be simply obtained from the exchange diagrams where the soft state is attached to the other external states through the three-point string vertex of three massless states. In the soft-limit, the propagator of the exchanged state is divergent, and at tree-level these are the only divergent contributions to the full amplitude. However, they do not form a gauge invariant subset and must be supplemented with extra non-singular terms. The requirement of gauge invariance then fixes the complete amplitude through subsubleading order in the soft expansion, reproducing exactly what one gets from the explicit calculation in string theory. From this it is seen that the string corrections at subsubleading order arise as a consequence of the three-point amplitude having string corrections in the bosonic string. When specialized to a soft dilaton, it remarkably turns out that the string corrections vanish and that the non-singular piece of the subsubleading term of the dilaton soft theorem is the generator of space-time special conformal transformation.
Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons.
Giustina, Marissa; Versteegh, Marijn A M; Wengerowsky, Sören; Handsteiner, Johannes; Hochrainer, Armin; Phelan, Kevin; Steinlechner, Fabian; Kofler, Johannes; Larsson, Jan-Åke; Abellán, Carlos; Amaya, Waldimar; Pruneri, Valerio; Mitchell, Morgan W; Beyer, Jörn; Gerrits, Thomas; Lita, Adriana E; Shalm, Lynden K; Nam, Sae Woo; Scheidl, Thomas; Ursin, Rupert; Wittmann, Bernhard; Zeilinger, Anton
2015-12-18
Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in Bell's inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every experiment requires assumptions that provide loopholes for a local realist explanation. Here, we report a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized source of entangled photons, rapid setting generation, and highly efficient superconducting detectors, we observe a violation of a Bell inequality with high statistical significance. The purely statistical probability of our results to occur under local realism does not exceed 3.74×10^{-31}, corresponding to an 11.5 standard deviation effect. PMID:26722905
A Theorem for Two Nucleon Transfer
NASA Astrophysics Data System (ADS)
Zamick, Larry; Mekjian, Aram
2004-05-01
We use the short notation for a unitary 9j symbol U9j(Ja,Jb)=<(jj)Ja(jj)Ja|(jj)Jb(jj)Jb>I=0 The wave fcn of a state of 44Ti with ang momentum I can be written as sum D(Jp,Jn) [(jj)Jp (jj)Jn]I. For the I=0 ground stae Jp=Jn. We found a new relationship SumJp U9j(Jp,Jx) D(Jp,Jp)= 1/2 D(Jx,Jx) for T=0 and =-D(Jx,Jx) for T=2. We could explain this by regarding U9j for even Jp,Jx as a square matrix hamiltonian, which, when diagonalized has eigenvalues of 1/2(triply degenerate) and -1(singly degenerate) corresponding to T=0 and T=2 respectively.*This theorem is useful,in the context of 2 nucleon transfer, for counting the number of pairs of particles in 44Ti with even Jx.The expressions simplifies to 3|D(Jx,Jx|^2,thus eliminating a complex 9jsymbol A deeper understanding of this result arises if we consider the strange interplay of angular momentum and isospin. Consider the interaction 1/4-t(1).t(2),which is unity for T=0 states and zero for T=1. For n nucleons with isospin T the eigenvalues are n^2/8+n/4-T(T+1)/2 But if we evaluate this with the usual Racah algebra then we note that in the single j shell the interaction can also be written as <(jj)Ia V (jj)Ia>= (1-(-1)^Ia)/2 i.e. the interaction acts only in odd J states since they have isospin T=0.In 44Ti the matrix element of the hamiltonian is [2+2U9j(Jp,Jx)].Connecting this with the isospin expression gives us the eigenvalues above for U9j. * L.Zamick, E. Moya de Guerra,P.Sarriguren,A.Raduta and A. Escuderos, preprint.
Use of Lambert's theorem for the n-dimensional Coulomb problem
Kanellopoulos, Vassiliki; Kleber, Manfred; Kramer, Tobias
2009-07-15
We present the analytical solution in closed form for the semiclassical limit of the quantum-mechanical Coulomb Green's function in position space in n dimensions. We utilize a projection method which has its roots in Lambert's theorem and which allows us to treat the system as an essentially one-dimensional problem. The semiclassical result assumes a simple analytical form and is well suited for a numerical evaluation. The method can also be extended to classically forbidden space regions. Already for moderately large principal quantum numbers {nu}{>=}5, the semiclassical Green's function is found to be an excellent approximation to the quantum-mechanical Green's function.
A no-go for no-go theorems prohibiting cosmic acceleration in extra dimensional models
Koster, Rik; Postma, Marieke E-mail: mpostma@nikhef.nl
2011-12-01
A four-dimensional effective theory that arises as the low-energy limit of some extra-dimensional model is constrained by the higher dimensional Einstein equations. Steinhardt and Wesley use this to show that accelerated expansion in our four large dimensions can only be transient in a large class of Kaluza-Klein models that satisfy the (higher dimensional) null energy condition [1]. We point out that these no-go theorems are based on a rather ad-hoc assumption on the metric, without which no strong statements can be made.
NASA Astrophysics Data System (ADS)
Mardirossian, Narbe; Head-Gordon, Martin
2014-05-01
The limit of accuracy for semi-empirical generalized gradient approximation (GGA) density functionals is explored by parameterizing a variety of local, global hybrid, and range-separated hybrid functionals. The training methodology employed differs from conventional approaches in 2 main ways: (1) Instead of uniformly truncating the exchange, same-spin correlation, and opposite-spin correlation functional inhomogeneity correction factors, all possible fits up to fourth order are considered, and (2) Instead of selecting the optimal functionals based solely on their training set performance, the fits are validated on an independent test set and ranked based on their overall performance on the training and test sets. The 3 different methods of accounting for exchange are trained both with and without dispersion corrections (DFT-D2 and VV10), resulting in a total of 491 508 candidate functionals. For each of the 9 functional classes considered, the results illustrate the trade-off between improved training set performance and diminished transferability. Since all 491 508 functionals are uniformly trained and tested, this methodology allows the relative strengths of each type of functional to be consistently compared and contrasted. The range-separated hybrid GGA functional paired with the VV10 nonlocal correlation functional emerges as the most accurate form for the present training and test sets, which span thermochemical energy differences, reaction barriers, and intermolecular interactions involving lighter main group elements.
Mardirossian, Narbe; Head-Gordon, Martin
2014-05-14
The limit of accuracy for semi-empirical generalized gradient approximation (GGA) density functionals is explored by parameterizing a variety of local, global hybrid, and range-separated hybrid functionals. The training methodology employed differs from conventional approaches in 2 main ways: (1) Instead of uniformly truncating the exchange, same-spin correlation, and opposite-spin correlation functional inhomogeneity correction factors, all possible fits up to fourth order are considered, and (2) Instead of selecting the optimal functionals based solely on their training set performance, the fits are validated on an independent test set and ranked based on their overall performance on the training and test sets. The 3 different methods of accounting for exchange are trained both with and without dispersion corrections (DFT-D2 and VV10), resulting in a total of 491 508 candidate functionals. For each of the 9 functional classes considered, the results illustrate the trade-off between improved training set performance and diminished transferability. Since all 491 508 functionals are uniformly trained and tested, this methodology allows the relative strengths of each type of functional to be consistently compared and contrasted. The range-separated hybrid GGA functional paired with the VV10 nonlocal correlation functional emerges as the most accurate form for the present training and test sets, which span thermochemical energy differences, reaction barriers, and intermolecular interactions involving lighter main group elements.
Formalization of the Integral Calculus in the PVS Theorem Prover
NASA Technical Reports Server (NTRS)
Butler, Ricky W.
2004-01-01
The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Dielectric theorem within the Hartree-Fock-Bogoliubov framework
Capelli, Luigi; Colo, Gianluca; Li, Jun
2009-05-15
Excitation spectra usually reveal important features of the many-body systems. The vibrational excitations can be studied through the well-known linear response theory. This theory is realized, in the nuclear case, by means of the random-phase approximation (RPA); the generalization in the case in which one deals with open shells, and the pairing force is active, is the quasiparticle RPA (QRPA). It is useful to have at one's disposal theorems that provide information on, e.g., the sum rules and mean excitation energies associated with given external operators acting on the system. This article focuses on such theorems in the case of self-consistent QRPA based on Hartree-Fock-Bogoliubov (HFB). In particular, the so-called dielectric theorem that provides the value of the inverse-energy-weighted sum rule based on the simple knowledge of the ground state is demonstrated. This theorem is applied to the case of constrained calculations of the average excitation energy of the monopole resonance combined with the Thouless theorem. The pairing correlations are shown to have the effect of increasing the polarizability m{sub -1}. The detailed analysis of the profile of the strength functions by mean of QRPA reveals that the decrease of the average monopole excitation energies in some isotopes is associated with neutron states that emerge at an energy that is lower than the main giant resonance peak.
Attractive Hubbard model with disorder and the generalized Anderson theorem
Kuchinskii, E. Z. Kuleeva, N. A. Sadovskii, M. V.
2015-06-15
Using the generalized DMFT+Σ approach, we study the influence of disorder on single-particle properties of the normal phase and the superconducting transition temperature in the attractive Hubbard model. A wide range of attractive potentials U is studied, from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong-coupling region, where the superconducting transition is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures much higher than the superconducting transition temperature. We study two typical models of the conduction band with semi-elliptic and flat densities of states, respectively appropriate for three-dimensional and two-dimensional systems. For the semi-elliptic density of states, the disorder influence on all single-particle properties (e.g., density of states) is universal for an arbitrary strength of electronic correlations and disorder and is due to only the general disorder widening of the conduction band. In the case of a flat density of states, universality is absent in the general case, but still the disorder influence is mainly due to band widening, and the universal behavior is restored for large enough disorder. Using the combination of DMFT+Σ and Nozieres-Schmitt-Rink approximations, we study the disorder influence on the superconducting transition temperature T{sub c} for a range of characteristic values of U and disorder, including the BCS-BEC crossover region and the limit of strong-coupling. Disorder can either suppress T{sub c} (in the weak-coupling region) or significantly increase T{sub c} (in the strong-coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of the superconducting critical temperature are essentially due to only the general disorder widening of the conduction band.
Model Checking Failed Conjectures in Theorem Proving: A Case Study
NASA Technical Reports Server (NTRS)
Pike, Lee; Miner, Paul; Torres-Pomales, Wilfredo
2004-01-01
Interactive mechanical theorem proving can provide high assurance of correct design, but it can also be a slow iterative process. Much time is spent determining why a proof of a conjecture is not forthcoming. In some cases, the conjecture is false and in others, the attempted proof is insufficient. In this case study, we use the SAL family of model checkers to generate a concrete counterexample to an unproven conjecture specified in the mechanical theorem prover, PVS. The focus of our case study is the ROBUS Interactive Consistency Protocol. We combine the use of a mechanical theorem prover and a model checker to expose a subtle flaw in the protocol that occurs under a particular scenario of faults and processor states. Uncovering the flaw allows us to mend the protocol and complete its general verification in PVS.
Generalized Bezout's Theorem and its applications in coding theory
NASA Technical Reports Server (NTRS)
Berg, Gene A.; Feng, Gui-Liang; Rao, T. R. N.
1996-01-01
This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.
Noether's second theorem and Ward identities for gauge symmetries
NASA Astrophysics Data System (ADS)
Avery, Steven G.; Schwab, Burkhard U. W.
2016-02-01
Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We use Noether's second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether's second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether's second theorem and known results in the recent literature. Our approach suggests a novel point of view with important physical consequences.
Quantum de Finetti theorem in phase-space representation
Leverrier, Anthony; Cerf, Nicolas J.
2009-07-15
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form {sigma}{sup xn}. Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states)
Formulation of Liouville's theorem for grand ensemble molecular simulations
NASA Astrophysics Data System (ADS)
Delle Site, Luigi
2016-02-01
Liouville's theorem in a grand ensemble, that is for situations where a system is in equilibrium with a reservoir of energy and particles, is a subject that, to our knowledge, has not been explicitly treated in literature related to molecular simulation. Instead, Liouville's theorem, a central concept for the correct employment of molecular simulation techniques, is implicitly considered only within the framework of systems where the total number of particles is fixed. However, the pressing demand of applied science in treating open systems leads to the question of the existence and possible exact formulation of Liouville's theorem when the number of particles changes during the dynamical evolution of the system. The intention of this paper is to stimulate a debate about this crucial issue for molecular simulation.
Noncommutative topology and the world’s simplest index theorem
van Erp, Erik
2010-01-01
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool for proving results in classical analysis and geometry. PMID:20418506
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
Canonical Approaches to Applications of the Virial Theorem.
Walton, Jay R; Rivera-Rivera, Luis A; Lucchese, Robert R; Bevan, John W
2016-02-11
Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem. PMID:26788937
Note on identities inspired by new soft theorems
NASA Astrophysics Data System (ADS)
Rao, Junjie; Feng, Bo
2016-04-01
The new soft theorems, for both gravity and gauge amplitudes, have inspired a number of works, including the discovery of new identities related to amplitudes. In this note, we present the proof and discussion for two sets of identities. The first set includes an identity involving the half-soft function which had been used in the soft theorem for one-loop rational gravity amplitudes, and another simpler identity as its byproduct. The second set includes two identities involving the KLT momentum kernel, as the consistency conditions of the KLT relation plus soft theorems for both gravity and gauge amplitudes. We use the CHY formulation to prove the first identity, and transform the second one into a convenient form for future discussion.
The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities
NASA Astrophysics Data System (ADS)
Cain, George L., Jr.; González, Luis
2008-02-01
The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.
Heat Capacity and the Equipartition Theorem
ERIC Educational Resources Information Center
Dence, Joseph B.
1972-01-01
Limitations of classical mechanics in understanding molecular properties are discussed. Modifications introduced by quantum mechanics enable the instructor to include and integrate important concepts from thermodynamics, quantum mechanics, spectroscopy, and statistics. (DF)
NASA Astrophysics Data System (ADS)
Duliere, V.; Zhang, Y.; Salathé, E. P.; Mote, P.
2008-12-01
Recently, there have been increasing efforts over the United States Pacific Northwest in using limited-area climate models for downscaling reanalysis data and global climate model simulations for studies of regional climate and climate change. A minimum condition for the usefulness of such limited-area climate modeling is that these climate models are doing a reasonably good job in simulating the local weather and climate. In this study, we apply the WRF (Weather Research and Forecasting) and HadRM (Hadley Center Regional Model) modeling systems over the Pacific Northwest in downscaling reanalysis data for the period of 2003 through 2007. WRF was developed at NCAR (National Center for Atmospheric Research). HadRM was released as part of the PRECIS (Providing REgional Climates for Impacts Studies) system, which was developed at the Hadley Center of the UK Met Office. The PRECIS system can be easily applied to any area of the globe to generate detailed climate change projections. The WRF domains were set up by using multiple nests at 108 km, 36 km, and 12 km horizontal grid spacing. The domain of HadRM was chosen with the highest available horizontal resolution of 25 km at the equator of the rotated grid. The WRF runs were driven by the NCEP/NCAR (National Centers for Environmental Prediction) reanalysis data (R1) and the HadRM runs were driven by the NCEP-DOE (Department of Energy) reanalysis data (R2). In this study, we validate the model simulations in terms of Tmax, Tmin, precipitation and extreme weather events (extreme precipitation event, drought, and heat wave) at various time scales using the observations from the Historical Climatology Network (HCN). Specific issues we will address in this work include: (a) the skill of WRF and HadRM in simulating the observed Tmin, Tmax and precipitation; (b) the performance of WRF and HadRM in representing the observed extreme weather events; and (c) the effect of differences in driving data and grid spacing on the model
Levinson theorem for the Dirac equation in D+1 dimensions
Gu Xiaoyan; Ma Zhongqi; Dong Shihai
2003-06-01
In terms of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation with a spherically symmetric potential in D+1 dimensions is uniformly established as a relation between the total number of bound states and the sum of the phase shifts of the scattering states at E={+-}M with a given angular momentum. The critical case, where the Dirac equation has a half bound state, is analyzed in detail. A half bound state is a zero-momentum solution if its wave function is finite but does not decay fast enough at infinity to be square integrable.
Reasoning by analogy as an aid to heuristic theorem proving.
NASA Technical Reports Server (NTRS)
Kling, R. E.
1972-01-01
When heuristic problem-solving programs are faced with large data bases that contain numbers of facts far in excess of those needed to solve any particular problem, their performance rapidly deteriorates. In this paper, the correspondence between a new unsolved problem and a previously solved analogous problem is computed and invoked to tailor large data bases to manageable sizes. This paper outlines the design of an algorithm for generating and exploiting analogies between theorems posed to a resolution-logic system. These algorithms are believed to be the first computationally feasible development of reasoning by analogy to be applied to heuristic theorem proving.
Distributed Online Judge System for Interactive Theorem Provers
NASA Astrophysics Data System (ADS)
Mizuno, Takahisa; Nishizaki, Shin-ya
2014-03-01
In this paper, we propose a new software design of an online judge system for interactive theorem proving. The distinctive feature of this architecture is that our online judge system is distributed on the network and especially involves volunteer computing. In volunteers' computers, network bots (software robots) are executed and donate computational resources to the central host of the online judge system. Our proposed design improves fault tolerance and security. We gave an implementation to two different styles of interactive theorem prover, Coq and ACL2, and evaluated our proposed architecture. From the experiment on the implementation, we concluded that our architecture is efficient enough to be used practically.
General self-tuning solutions and no-go theorem
Förste, Stefan; Kim, Jihn E.; Lee, Hyun Min E-mail: jihnekim@gmail.com
2013-03-01
We consider brane world models with one extra dimension. In the bulk there is in addition to gravity a three form gauge potential or equivalently a scalar (by generalisation of electric magnetic duality). We find classical solutions for which the 4d effective cosmological constant is adjusted by choice of integration constants. No go theorems for such self-tuning mechanism are circumvented by unorthodox Lagrangians for the three form respectively the scalar. It is argued that the corresponding effective 4d theory always includes tachyonic Kaluza-Klein excitations or ghosts. Known no go theorems are extended to a general class of models with unorthodox Lagrangians.
Beltran, L; Koenig, M; Egner, W; Howard, M; Butt, A; Austin, M R; Patel, D; Sanderson, R R; Goubet, S; Saleh, F; Lavender, J; Stainer, E; Tarzi, M D
2014-01-01
Numerous studies suggest that high levels of circulating immunoglobulin (Ig)A tissue transglutaminase (TTG2) antibodies predict coeliac disease with high specificity. Accordingly, it has been suggested that duodenal biopsy may not be required routinely for diagnostic confirmation where quantitative serology identifies the presence of high antibody titres. However, defining a cut-off TTG2 threshold is problematic, as the multiple available assay methods are not harmonized and most studies have been focused on the paediatric population. Recent paediatric guidelines proposed a TTG2 antibody diagnostic cut-off at 10 × the upper limit of normal (ULN) for the method; however, concerns remain about errors of generalization, between both methods and laboratories. In this study, we used retrospective laboratory data to investigate the relationship between TTG2 antibody levels and Marsh 3 histology in the seropositive population of adults and children at a single centre. Among 202 seropositive patients with corresponding biopsies, it was possible to define a TTG2 antibody cut-off with 100% specificity for Marsh 3 histology, at just over 10 × ULN for the method. However, UK National External Quality Assurance Scheme returns during the study period showed a wide dispersion of results and poor consensus, both between methods and between laboratories using the same method. Our results support the view that high-titre TTG2 antibody levels have strong predictive value for villous atrophy in adults and children, but suggest that decision cut-offs to guide biopsy requirement will require local validation. TTG2 antibody assay harmonization is a priority, in order to meet the evolving requirements of laboratory users in this field. PMID:24325651
Jeremic, Branislav . E-mail: b.jeremic@iaea.org; Milicic, Biljana
2007-06-01
Purpose: To investigate the influence of interfraction interval (IFI) on local recurrence-free survival (LRFS) in patients with limited-disease small-cell lung cancer (LD SCLC) treated with accelerated hyperfractionated radiotherapy (Acc Hfx RT) and concurrent cisplatin and etoposide (PE). Methods and Materials: A total of 103 patients were treated with either 'early' (Cycle 1) or 'late' (Cycle 4) concurrent Acc Hfx RT/PE. Two daily fractions were nonrandomly given using an IFI of either 4.5-5.0 h ('shorter') (n = 52) or 5.5-6.0 h ('longer') (n = 51). Results: The median LRFS and 5-year LRFS rate for all 103 patients were 52 months and 48%, respectively. Besides gender, Karnofsky performance status, and treatment group, IFI also influenced LRFS, whereas age and weight loss did not. When a multivariate model was used, IFI was marginally insignificant (p = 0.0770) as a predictor of LRFS. In terms of individual treatment groups, IFI was not significant in 'early' Acc Hfx RT/PE but showed a strong trend in a 'late' Acc Hfx RT/PE regimen. Although a shorter IFI led to a higher incidence of high-grade ({>=}3) esophagitis, leukopenia, and infection, a correlation analysis of toxicities with all potential prognostic factors showed that a shorter IFI was not an independent predictor of any acute high-grade toxicity. Conclusion: 'Shorter' IFI had a marginally insignificant influence on LRFS. A strong trend favoring it was observed in patients treated with 'late' concurrent Acc Hfx RT/PE. This may be of interest because it could contribute to further understanding of potential biologic parameters influencing treatment outcome.
NASA Astrophysics Data System (ADS)
Eliazar, Iddo
2011-01-01
In this communication we establish stochastic limit laws leading from Zipf's law to Pareto's and Heaps' laws. We consider finite ensembles governed by Zipf's law and study their asymptotic statistics as the ensemble size tends to infinity. A Lorenz-curve analysis establishes three types of limit laws for the ensembles' statistical structure: 'communist', 'monarchic', and Paretian. Further considering a dynamic setting in which the ensembles grow stochastically in time, a functional central limit theorem analysis establishes a Gaussian approximation for the ensembles' stochastic growth. The Gaussian approximation provides a generalized and corrected formulation of Heaps' law.
Unifying framework for relaxations of the causal assumptions in Bell's theorem.
Chaves, R; Kueng, R; Brask, J B; Gross, D
2015-04-10
Bell's theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions-e.g., locality or measurement independence-have to be relaxed in order to allow for a classical description of such experiments. Here we develop a conceptual and computational framework for treating this problem. We employ the language of Bayesian networks to systematically construct alternative causal structures and bound the degree of relaxation using quantitative measures that originate from the mathematical theory of causality. The main technical insight is that the resulting problems can often be expressed as computationally tractable linear programs. We demonstrate the versatility of the framework by applying it to a variety of scenarios, ranging from relaxations of the measurement independence, locality, and bilocality assumptions, to a novel causal interpretation of Clauser-Horne-Shimony-Holt inequality violations. PMID:25910096
Unifying Framework for Relaxations of the Causal Assumptions in Bell's Theorem
NASA Astrophysics Data System (ADS)
Chaves, R.; Kueng, R.; Brask, J. B.; Gross, D.
2015-04-01
Bell's theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions—e.g., locality or measurement independence—have to be relaxed in order to allow for a classical description of such experiments. Here we develop a conceptual and computational framework for treating this problem. We employ the language of Bayesian networks to systematically construct alternative causal structures and bound the degree of relaxation using quantitative measures that originate from the mathematical theory of causality. The main technical insight is that the resulting problems can often be expressed as computationally tractable linear programs. We demonstrate the versatility of the framework by applying it to a variety of scenarios, ranging from relaxations of the measurement independence, locality, and bilocality assumptions, to a novel causal interpretation of Clauser-Horne-Shimony-Holt inequality violations.
Zhao Hongsheng; Famaey, Benoit
2010-04-15
There exists several modified gravity theories designed to reproduce the empirical Milgrom's formula, modified Newtonian dynamics (MOND). Here we derive analytical results in the context of the static weak-field limit of two of them (bimetric MOND, leading for a given set of parameters to the quasilinear MOND, and Bekenstein's Tensor-Vector-Scalar). In this limit, these theories are constructed to give the same force field for spherical symmetry, but their predictions generally differ out of it. However, for certain realizations of these theories (characterized by specific choices for their free functions), the binding potential-energy of a system is increased, compared to its Newtonian counterpart, by a constant amount independent of the shape and size of the system. In that case, the virial theorem is exactly the same in these two theories, for the whole gravity regime and even outside of spherical symmetry, although the exact force fields are different. We explicitly show this for the force field generated by the two theories inside an elliptical shell. For more general free functions, the virial theorems are, however, not identical in these two theories. We finally explore the consequences of these analytical results for the two-body force.
Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
Fujiwara, Takanori; Fukui, Takahiro; Nitta, Muneto; Yasui, Shigehiro
2011-10-01
Color superconductivity in high-density QCD exhibits the color-flavor-locked phase. To explore zero modes in the color-flavor-locked phase in the presence of a non-Abelian vortex with an SU(2) symmetry in the vortex core, we apply the index theorem to the Bogoliubov-de Gennes (BdG) Hamiltonian. From the calculation of the topological index, we find that triplet, doublet and singlet sectors of SU(2) have certain number of chiral Majorana zero modes in the limit of vanishing chemical potential. We also solve the BdG equation by the use of the series expansion to show that the number of zero modes and their chirality match the result of the index theorem. From particle-hole symmetry of the BdG Hamiltonian, we conclude that if and only if the index of a given sector is odd, one zero mode survives generically for a finite chemical potential. We argue that this result should hold nonperturbatively even in the high-density limit.
Derivation of a sphere theorem for the Stokes flow following Imai's procedure
NASA Astrophysics Data System (ADS)
Hasimoto, Hidenori
2007-07-01
A sphere theorem for general three-dimensional Stokes flow is shown to be derived by the use of Imai's procedure for solving the Stokes equation for spherical boundary in terms of one vector harmonic function and Kelvin's inversion theorem.
Establishing Appropriate Conditions: Students Learning to Apply a Theorem
ERIC Educational Resources Information Center
Scataglini-Belghitar, Giovanna; Mason, John
2012-01-01
During a sequence of tutorials conducted by the first author, it became evident that students were not seeing how to apply the theorem concerning a continuous function on a closed and bounded interval attaining its extreme values in situations in which it is necessary first to construct the closed and bounded interval by reasoning about properties…
A fixed point theorem for certain operator valued maps
NASA Technical Reports Server (NTRS)
Brown, D. R.; Omalley, M. J.
1978-01-01
In this paper, we develop a family of Neuberger-like results to find points z epsilon H satisfying L(z)z = z and P(z) = z. This family includes Neuberger's theorem and has the additional property that most of the sequences q sub n converge to idempotent elements of B sub 1(H).
Four Proofs of the Converse of the Chinese Remainder Theorem
ERIC Educational Resources Information Center
Dobbs, D. E.
2008-01-01
Four proofs, designed for classroom use in varying levels of courses on abstract algebra, are given for the converse of the classical Chinese Remainder Theorem over the integers. In other words, it is proved that if m and n are integers greater than 1 such that the abelian groups [double-struck z][subscript m] [direct sum] [double-struck…
Externalities and the Coase Theorem: A Diagrammatic Presentation
ERIC Educational Resources Information Center
Halteman, James
2005-01-01
In intermediate microeconomic textbooks the reciprocal nature of externalities is presented using numerical examples of costs and benefits. This treatment of the Coase theorem obscures the fact that externality costs and benefits are best understood as being on a continuum where costs vary with the degree of intensity of the externality. When…
On the Positive Mass Theorem for Manifolds with Corners
NASA Astrophysics Data System (ADS)
McFeron, Donovan; Székelyhidi, Gábor
2012-07-01
We study the positive mass theorem for certain non-smooth metrics following P. Miao's work. Our approach is to smooth the metric using the Ricci flow. As well as improving some previous results on the behaviour of the ADM mass under the Ricci flow, we extend the analysis of the zero mass case to higher dimensions.
Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos
ERIC Educational Resources Information Center
Boozer, A. D.
2011-01-01
We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…
Discovering and Experiencing the Fundamental Theorem of Calculus.
ERIC Educational Resources Information Center
Rosenthal, Bill
1992-01-01
Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…
Start the Year Right-Discover Pick's Theorem.
ERIC Educational Resources Information Center
Wilcock, Douglas
1992-01-01
Describes a problem to challenge students as they come back from summer vacation. Working in small groups, students discover Pick's Theorem, the formula to calculate the area of a polygon constructed on a geoboard. A writing assignment evaluates the students' efforts. (MDH)
Proof by Analogy: The Case of the Pythagorean Theorem.
ERIC Educational Resources Information Center
Levine, Deborah R.
1983-01-01
The proof is given that, if three equilateral triangles are constructed on the sides of a right triangle, then the sum of the areas on the sides equals the area on the hypotenuse. This is based on one of the hundreds of proofs that exist for the Pythogorean theorem. (MP)
A decoupling theorem for the BPHZL-scheme
Aschenbrenner, M.
1996-09-01
Conditions are stated, which are sufficient for the heavy-mass-suppression of BPHZL-subtracted Feynman-integrals containing propagators of {open_quote}{open_quote}heavy fields{close_quote}{close_quote}. This result generalizes the Decoupling Theorems of Ambjo/rn, Manoukian and Landsman to cases, where massless fields (e.g., gauge fields) are present. {copyright} 1996 Academic Press, Inc.
A representation theorem of infimum of bounded quantum observables
Liu Weihua; Wu Junde
2008-07-15
In 2006, Gudder introduced a logic order on the bounded quantum observable set S(H). In 2007, Pulmannova and Vincekova proved that for each subset D of S(H), the infimum of D exists with respect to this logic order. In this paper, we present a representation theorem for the infimum of D.
An Elementary Proof of a Converse Mean-Value Theorem
ERIC Educational Resources Information Center
Almeida, Ricardo
2008-01-01
We present a new converse mean value theorem, with a rather elementary proof. [The work was supported by Centre for Research on Optimization and Control (CEOC) from the "Fundacaopara a Ciencia e a Tecnologia" FCT, co-financed by the European Community Fund FEDER/POCTI.
Geometric Demonstration of the Fundamental Theorems of the Calculus
ERIC Educational Resources Information Center
Sauerheber, Richard D.
2010-01-01
After the monumental discovery of the fundamental theorems of the calculus nearly 350 years ago, it became possible to answer extremely complex questions regarding the natural world. Here, a straightforward yet profound demonstration, employing geometrically symmetric functions, describes the validity of the general power rules for integration and…
Ambarzumyan's theorem for the quasi-periodic boundary conditions
NASA Astrophysics Data System (ADS)
Kıraç, Alp Arslan
2015-10-01
We obtain the classical Ambarzumyan's theorem for the Sturm-Liouville operators Lt(q) with qin L1[0,1] and quasi-periodic boundary conditions, tin [0,2π ) , when there is not any additional condition on the potential q.
A Theorem and its Application to Finite Tampers
DOE R&D Accomplishments Database
Feynman, R. P.
1946-08-15
A theorem is derived which is useful in the analysis of neutron problems in which all neutrons have the same velocity. It is applied to determine extrapolated end-points, the asymptotic amplitude from a point source, and the neutron density at the surface of a medium. Formulas fro the effect of finite tampers are derived by its aid, and their accuracy discussed.