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…
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…
"Dealing" with the Central Limit Theorem
ERIC Educational Resources Information Center
Matz, David C.; Hause, Emily L.
2008-01-01
We describe an easy-to-employ, hands-on demonstration using playing cards to illustrate the central limit theorem. This activity allows students to see how a collection of sample means drawn from a nonnormally distributed population will be normally distributed. Students who took part in the demonstration reported it to be helpful in understanding…
Central limit theorems under special relativity.
McKeague, Ian W
2015-04-01
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
Central limit theorem: the cornerstone of modern statistics
2017-01-01
According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, σ2n. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding. PMID:28367284
Improving Conceptions in Analytical Chemistry: The Central Limit Theorem
ERIC Educational Resources Information Center
Rodriguez-Lopez, Margarita; Carrasquillo, Arnaldo, Jr.
2006-01-01
This article describes the central limit theorem (CLT) and its relation to analytical chemistry. The pedagogic rational, which argues for teaching the CLT in the analytical chemistry classroom, is discussed. Some analytical chemistry concepts that could be improved through an understanding of the CLT are also described. (Contains 2 figures.)
Understanding the Sampling Distribution and the Central Limit Theorem.
ERIC Educational Resources Information Center
Lewis, Charla P.
The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…
Central limit theorems for percolation models
NASA Astrophysics Data System (ADS)
Cox, J. Theodore; Grimmett, Geoffrey
1981-06-01
Let p ≠ 1/2 be the open-bond probability in Broadbent and Hammersley's percolation model on the square lattice. Let W x be the cluster of sites connected to x by open paths, and let γ(n) be any sequence of circuits with interiors|γ limits^ circ (n)| to infty . It is shown that for certain sequences of functions { f n },S_n = sum _{x in γ limits^ circ (n)} f_n (W_x ) converges in distribution to the standard normal law when properly normalized. This result answers a problem posed by Kunz and Souillard, proving that the number S n of sites inside γ(n) which are connected by open paths to γ(n) is approximately normal for large circuits γ(n).
Entropy Inequalities for Stable Densities and Strengthened Central Limit Theorems
NASA Astrophysics Data System (ADS)
Toscani, Giuseppe
2016-10-01
We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy functionals along the sequence we prove convergence with explicit rate in various norms to a Lévy centered density of parameter λ >1 . This introduces a new information-theoretic approach to the central limit theorem for stable laws, in which the main argument is shown to be the relative fractional Fisher information, recently introduced in Toscani (Ricerche Mat 65(1):71-91, 2016). In particular, it is proven that, with respect to the relative fractional Fisher information, the Lévy density satisfies an analogous of the logarithmic Sobolev inequality, which allows to pass from the monotonicity and decay to zero of the relative fractional Fisher information in the standardized sum to the decay to zero in relative entropy with an explicit decay rate.
Using Computers To Teach the Concepts of the Central Limit Theorem.
ERIC Educational Resources Information Center
Mittag, Kathleen Cage
A pivotal theorem which is of critical importance to statistical inference in probability and statistics is the Central Limit Theorem (CLT). The theorem concerns the sampling distribution of random samples taken from a population, including population distributions that do not have to be normal distributions. This paper contains a brief history of…
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.
Central limit theorems and suppression of anomalous diffusion for systems with symmetry
NASA Astrophysics Data System (ADS)
Gottwald, Georg A.; Melbourne, Ian
2016-10-01
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle/functional central limit theorem) to hold for observables of compact group extensions of nonuniformly expanding maps. In particular, our results include situations where the central limit theorem would fail, and anomalous behaviour would prevail, if the compact group were not present. This has important consequences for systems with noncompact Euclidean symmetry and provides the rigorous proof for a conjecture made in our paper: a Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Gottwald and Melbourne (2013 Proc. Natl Acad. Sci. USA 110 8411-6).
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.
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.
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…
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…
ERIC Educational Resources Information Center
Lunsford, M. Leigh; Rowell, Ginger Holmes; Goodson-Espy, Tracy
2006-01-01
We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we…
Kim, Seonjin; Zhao, Zhibiao; Shao, Xiaofeng
2015-01-01
This paper is concerned with the inference of nonparametric mean function in a time series context. The commonly used kernel smoothing estimate is asymptotically normal and the traditional inference procedure then consistently estimates the asymptotic variance function and relies upon normal approximation. Consistent estimation of the asymptotic variance function involves another level of nonparametric smoothing. In practice, the choice of the extra bandwidth parameter can be difficult, the inference results can be sensitive to bandwidth selection and the normal approximation can be quite unsatisfactory in small samples leading to poor coverage. To alleviate the problem, we propose to extend the recently developed self-normalized approach, which is a bandwidth free inference procedure developed for parametric inference, to construct point-wise confidence interval for nonparametric mean function. To justify asymptotic validity of the self-normalized approach, we establish a functional central limit theorem for recursive nonparametric mean regression function estimates under primitive conditions and show that the limiting process is a Gaussian process with non-stationary and dependent increments. The superior finite sample performance of the new approach is demonstrated through simulation studies.
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.
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.
Pérez-Rodríguez, Fernando; Zwietering, Marcel H
2012-02-15
The Central Limit Theorem (CLT) is proposed as a means of understanding microbial risk in foods from a Public Health perspective. One variant of the CLT states that as the number of random variables, each with a finite mean and variance, increases (→∞), the distribution of the sum (or mean) of those variables approximates a normal distribution. On the basis of the CLT, the hypothesis introduced by this paper states that the Coefficient of Variation (CV) of the annual number of food-borne illness cases decreases as a result of a larger number of exposures (or servings) (n). Second-order Monte-Carlo analysis and classical statistics were used to support the hypothesis, based on existing risk models on Listeria monocytogenes in deli meat products focused on elderly people in the United States. Likewise, the hypothesis was tested on epidemiological data of annual incidence of salmonellosis and listeriosis in different countries (i.e. different n). Although different sources of error affected the accuracy of the results, both the Monte-Carlo analysis (in silico) and epidemiological data (in vivo), especially for salmonellosis, demonstrated that the CV of the annual number of cases decreased as n increased as stated by the CLT. Furthermore, results from this work showed that classical statistical methods can be helpful to provide reliable risk estimates based on simple and well-established statistical principles.
Temporal Distributional Limit Theorems for Dynamical Systems
NASA Astrophysics Data System (ADS)
Dolgopyat, Dmitry; Sarig, Omri
2017-02-01
Suppose {T^t} is a Borel flow on a complete separable metric space X, f:X→ R is Borel, and xin X. A temporal distributional limit theorem is a scaling limit for the distributions of the random variables X_T:=int _0^t f(T^s x)ds, where t is chosen randomly uniformly from [0, T], x is fixed, and T→ ∞. We discuss such laws for irrational rotations, Anosov flows, and horocycle flows.
ERIC Educational Resources Information Center
Gkioulekas, Eleftherios
2013-01-01
Many limits, typically taught as examples of applying the "squeeze" theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful…
Mixing rates and limit theorems for random intermittent maps
NASA Astrophysics Data System (ADS)
Bahsoun, Wael; Bose, Christopher
2016-04-01
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps {{T}α} using the full parameter range 0<α <∞ , in general. We derive a number of results around a common theme that illustrates in detail how the constituent map that is fastest mixing (i.e. smallest α) combined with details of the randomizing process, determines the asymptotic properties of the random transformation. Our key result (theorem 1.1) establishes sharp estimates on the position of return time intervals for the quenched dynamics. The main applications of this estimate are to limit laws (in particular, CLT and stable laws, depending on the parameters chosen in the range 0<α <1 ) for the associated skew product; these are detailed in theorem 3.2. Since our estimates in theorem 1.1 also hold for 1≤slant α <∞ we study a second class of random transformations derived from piecewise affine Gaspard-Wang maps, prove existence of an infinite (σ-finite) invariant measure and study the corresponding correlation asymptotics. To the best of our knowledge, this latter kind of result is completely new in the setting of random transformations.
A pointwise limit theorem for filtered backprojection in computed tomography.
Ye, Yangbo; Zhu, Jiehua; Wang, Ge
2003-05-01
Computed tomography (CT) is one of the most important areas in the modern science and technology. The most popular approach for image reconstruction is filtered backprojection. It is essential to understand the limit behavior of the filtered backprojection algorithms. The classic results on the limit of image reconstruction are typically done in the norm sense. In this paper, we use the method of limited bandwidth to handle filtered backprojection-based image reconstruction when the spectrum of an underlying image is not absolutely integrable. Our main contribution is, assuming the method of limited bandwidth, to prove a pointwise limit theorem for a class of functions practically relevant and quite general. Further work is underway to extend the theory and explore its practical applications.
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.
On a new proof of the Lindeberg-Feller classical limit theorem
NASA Astrophysics Data System (ADS)
Formanov, Shakir Kasimovich; Akanbay, Nursadyk; Akhmedov, Askar Bekenovich
2015-09-01
In recent papers researchers describe some of the new types of properties characterization of the normal distribution. This paper gives a new one based on the characterization of these properties, the proof of the classical limit theorem Lindeberg-Feller.
Uniform Limit Theorems for Synchronous Processes with Applications to Queues
1989-10-01
first moment. In the present paper we investi gate conditions under which the Cesaro averaged functionals ;(f) 1- jfoE((6,X))dj converge uniformly...Proposition 3.1 both apply to positive HRMP’s. So, for example, given any initial state Z 0 = :, it follows that the Cesaro averaged measures (A) 1! 7foEIA o...collection of measures (see Theorem 2.1 of [41)). Continuing in the spirit of Cesaro convergence we have Proposition 4.1. If Z is a positive HRMP with
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…
Limit theorems for Lévy walks in d dimensions: rare and bulk fluctuations
NASA Astrophysics Data System (ADS)
Fouxon, Itzhak; Denisov, Sergey; Zaburdaev, Vasily; Barkai, Eli
2017-04-01
We consider super-diffusive Lévy walks in d≥slant 2 dimensions when the duration of a single step, i.e. a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean. We demonstrate that the probability density function (PDF) of the coordinate of the random walker has two different scaling limits at large times. One limit describes the bulk of the PDF. It is the d-dimensional generalization of the one-dimensional Lévy distribution and is the counterpart of the central limit theorem (CLT) for random walks with finite dispersion. In contrast with the one-dimensional Lévy distribution and the CLT this distribution does not have a universal shape. The PDF reflects anisotropy of the single-step statistics however large the time is. The other scaling limit, the so-called ‘infinite density’, describes the tail of the PDF which determines second (dispersion) and higher moments of the PDF. This limit repeats the angular structure of the PDF of velocity in one step. A typical realization of the walk consists of anomalous diffusive motion (described by anisotropic d-dimensional Lévy distribution) interspersed with long ballistic flights (described by infinite density). The long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion. We illustrate the concept by considering two types of Lévy walks, with isotropic and anisotropic distributions of velocities. Furthermore, we show that for isotropic but otherwise arbitrary velocity distributions the d-dimensional process can be reduced to a one-dimensional Lévy walk. We briefly discuss the consequences of non-universality for the d > 1 dimensional fractional diffusion equation, in particular the non-uniqueness of the fractional Laplacian.
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…
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…
Day, Troy
2012-04-07
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.
The Central Role of Bayes' Theorem for Joint Estimation of Causal Effects and Propensity Scores.
Zigler, Corwin Matthew
2016-03-31
Although propensity scores have been central to the estimation of causal effects for over 30 years, only recently has the statistical literature begun to consider in detail methods for Bayesian estimation of propensity scores and causal effects. Underlying this recent body of literature on Bayesian propensity score estimation is an implicit discordance between the goal of the propensity score and the use of Bayes theorem. The propensity score condenses multivariate covariate information into a scalar to allow estimation of causal effects without specifying a model for how each covariate relates to the outcome. Avoiding specification of a detailed model for the outcome response surface is valuable for robust estimation of causal effects, but this strategy is at odds with the use of Bayes theorem, which presupposes a full probability model for the observed data that adheres to the likelihood principle. The goal of this paper is to explicate this fundamental feature of Bayesian estimation of causal effects with propensity scores in order to provide context for the existing literature and for future work on this important topic.
Guseinov, Israfil
2003-06-01
By the use of complete orthonormal sets of psi(alpha)-ETOs (alpha=1, 0, m1, m2,...) introduced by the author, new addition theorems are derived for STOs and arbitrary central and noncentral interaction potentials (CIPs and NCIPs). The expansion coefficients in these addition theorems are expressed through the Gaunt and Gegenbauer coefficients. Using the addition theorems obtained for STOs and potentials, general formulae in terms of three-center overlap integrals are established for the multicenter t-electron integrals of CIPs and NCIPs that arise in the solution of the N-electron atomic and molecular problem (2hthN) when a Hylleraas approximation in Hartree-Fock-Roothaan theory is employed. With the help of expansion formulae for translation of STOs, the three-center overlap integrals are expressed through the two-center overlap integrals. The formulae obtained are valid for arbitrary quantum numbers, screening constants and location of orbitals.
Moons, K G; van Es, G A; Deckers, J W; Habbema, J D; Grobbee, D E
1997-01-01
We evaluated the extent to which the sensitivity, specificity, and likelihood ratio of the exercise test to diagnose coronary artery disease vary across subgroups of a certain patient population. Among 295 patients suspected of coronary artery disease, as independently determined by coronary angiography, we assessed variation in sensitivity and specificity according to patient history, physical examination, exercise test results, and disease severity in 207 patients with and 88 patients without coronary artery disease, respectively. The sensitivity varied substantially according to sex (women 30% and men 64%), systolic blood pressure at baseline (53% to 65%), expected workload (50% to 64%), systolic blood pressure at peak exercise (50% to 67%), relative workload (33% to 68%), and number of diseased vessels (39% to 77%). The specificity varied across subgroups of sex (men 89% and women 97%) and relative workload (85% to 98%). The likelihood ratio varied (3.8 to 17.0) across the same patient subgroups, as did the sensitivity. As each population tends to be heterogeneous with respect to patient characteristics, no single level of these parameters can be given that is adequate for all subgroups. Use of these parameters as a basis for calculating diagnostic probabilities in individual patients using Bayes' theorem has serious limitations.
Levine, James A
2016-08-01
The Wearable Technology market may increase fivefold by the end of the decade. There is almost no academic investigation as to what drives the investment hypothesis in wearable technologies. This paper seeks to examine this issue from an evidence-based perspective. There is a fundamental disconnect in how consumers view wearable sensors and how companies market them; this is called The Baetylus Theorem where people believe (falsely) that by buying a wearable sensor they will receive health benefit; data suggest that this is not the case. This idea is grounded social constructs, psychological theories and marketing approaches. A marketing proposal that fails to recognize The Baetylus Theorem and how it can be integrated into a business offering has not optimized its competitive advantage. More importantly, consumers should not falsely believe that purchasing a wearable technology, improves health.
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 New START Treaty: Central Limits and Key Provisions
2014-04-08
The New START Treaty: Central Limits and Key Provisions Amy F. Woolf Specialist in Nuclear Weapons Policy April 8, 2014 Congressional...Treaty: Central Limits and Key Provisions 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e...Rev. 8-98) Prescribed by ANSI Std Z39-18 The New START Treaty: Central Limits and Key Provisions Congressional Research Service Summary The
The New START Treaty: Central Limits and Key Provisions
2014-08-27
The New START Treaty: Central Limits and Key Provisions Amy F. Woolf Specialist in Nuclear Weapons Policy August 27, 2014 Congressional...START Treaty: Central Limits and Key Provisions 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e...298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 The New START Treaty: Central Limits and Key Provisions Congressional Research Service Summary The
The New START Treaty: Central Limits and Key Provisions
2014-01-08
The New START Treaty: Central Limits and Key Provisions Amy F. Woolf Specialist in Nuclear Weapons Policy January 8, 2014 Congressional...START Treaty: Central Limits and Key Provisions 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e...
Fractional Edgeworth expansion: Corrections to the Gaussian-Lévy central-limit theorem
NASA Astrophysics Data System (ADS)
Hazut, Netanel; Medalion, Shlomi; Kessler, David A.; Barkai, Eli
2015-05-01
In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to PDFs with a diverging variance, which converge to a Lévy α -stable density function. Our correction may be written by means of a series of fractional derivatives of the Lévy and the conjugate Lévy PDFs. This series expansion is general and applies also to the Gaussian regime. To describe the terms in the series expansion, we introduce a new family of special functions and briefly discuss their properties. We implement our generalization to the distribution of the momentum for atoms undergoing Sisyphus cooling, and show the improvement of our leading order approximation compared to previous approximations. In vicinity of the transition between Lévy and Gauss behaviors, convergence to asymptotic results slows down.
A Strong Central Limit Theorem for a Class of Random Surfaces
NASA Astrophysics Data System (ADS)
Conlon, Joseph G.; Spencer, Thomas
2014-01-01
This paper is concerned with d = 2 dimensional lattice field models with action , where is a uniformly convex function. The fluctuations of the variable are studied for large | x| via the generating function given by . In two dimensions is proportional to . The main result of this paper is a bound on which is uniform in for a class of convex V. The proof uses integration by parts following Helffer-Sjöstrand and Witten, and relies on estimates of singular integral operators on weighted Hilbert spaces.
Evaluation of an Interactive Tutorial for Teaching the Central Limit Theorem.
ERIC Educational Resources Information Center
Aberson, Christopher L.; Berger, Dale E.; Healy, Michael R.; Kyle, Diana J.; Romero, Victoria L.
2000-01-01
Evaluates an interactive, Web-based tutorial that helps students learn about sampling distribution. 111 students enrolled in statistics or research methods courses used either the tutorial or attended a lecture/demonstration. Indicates through pre- and post-test quizzes both groups learned comparable amounts and reveals students' ratings of both…
Limit loads for centrally cracked square plates under biaxial tension
NASA Astrophysics Data System (ADS)
Graba, Marcin
2016-12-01
This paper is concerned with the determination of limit loads for centrally cracked square plates subjected to biaxial tension. It briefly discusses the concept of limit loads and some aspects of numerical modelling. It presents results of numerical calculations conducted for two-dimensional (plane strain state and plane stress state) and three-dimensional cases. It also considers the relationship between the limit load and the crack length, the specimen thickness, the yield strength and the biaxial load factor, defined for the purpose of this work. The paper includes approximation formulae to calculate the limit load.
ERIC Educational Resources Information Center
Davis, Philip J.
1993-01-01
Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)
Taylor's power law and fluctuation scaling explained by a central-limit-like convergence
NASA Astrophysics Data System (ADS)
Kendal, Wayne S.; Jørgensen, Bent
2011-06-01
A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.
NASA Astrophysics Data System (ADS)
Evans, Denis J.; Searles, Debra J.
2002-11-01
The question of how reversible microscopic equations of motion can lead to irreversible macroscopic behaviour has been one of the central issues in statistical mechanics for more than a century. The basic issues were known to Gibbs. Boltzmann conducted a very public debate with Loschmidt and others without a satisfactory resolution. In recent decades there has been no real change in the situation. In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in thermostatted dissipative non-equilibrium systems. The relation was derived heuristically and applied to the special case of dissipative non-equilibrium systems subject to constant energy 'thermostatting'. These restrictions meant that the full importance of the Theorem was not immediately apparent. Within a few years, derivations of the Theorem were improved but it has only been in the last few of years that the generality of the Theorem has been appreciated. We now know that the Second Law of Thermodynamics can be derived assuming ergodicity at equilibrium, and causality. We take the assumption of causality to be axiomatic. It is causality which ultimately is responsible for breaking time reversal symmetry and which leads to the possibility of irreversible macroscopic behaviour. The Fluctuation Theorem does much more than merely prove that in large systems observed for long periods of time, the Second Law is overwhelmingly likely to be valid. The Fluctuation Theorem quantifies the probability of observing Second Law violations in small systems observed for a short time. Unlike the Boltzmann equation, the FT is completely consistent with Loschmidt's observation that for time reversible dynamics, every dynamical phase space trajectory and its conjugate time reversed 'anti-trajectory', are both solutions of the underlying equations of motion. Indeed the standard proofs of
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.
The Limits of Subsistence: Agriculture and Industry in Central Appalachia.
ERIC Educational Resources Information Center
Pudup, Mary Beth
Current interpretations of central Appalachia's chronic poverty focus on the region's economic dependence on the bituminous coal industry, controlled by absentee investors and serving an external market. Such theories overlook the ways in which the agricultural sector shaped subsequent industrial development. By analyzing the farm economy of 16…
ERIC Educational Resources Information Center
May, Henry
2014-01-01
Interest in variation in program impacts--How big is it? What might explain it?--has inspired recent work on the analysis of data from multi-site experiments. One critical aspect of this problem involves the use of random or fixed effect estimates to visualize the distribution of impact estimates across a sample of sites. Unfortunately, unless the…
ERIC Educational Resources Information Center
Van Duzer, Eric
2011-01-01
This report introduces a short, hands-on activity that addresses a key challenge in teaching quantitative methods to students who lack confidence or experience with statistical analysis. Used near the beginning of the course, this activity helps students develop an intuitive insight regarding a number of abstract concepts which are key to…
The Sampling Distribution and the Central Limit Theorem: What They Are and Why They're Important.
ERIC Educational Resources Information Center
Kennedy, Charlotte A.
The use of and emphasis on statistical significance testing has pervaded educational and behavioral research for many decades in spite of criticism by prominent researchers in this field. Much of the controversy is caused by lack of understanding or misinterpretations. This paper reviews criticisms of statistical significance testing and discusses…
Bell's theorem and Bayes' theorem
NASA Astrophysics Data System (ADS)
Garrett, A. J. M.
1990-12-01
Bell's theorem is expounded as an analysis in Bayesian probabilistic inference. Assume that the result of a spin measurement on a spin- 1/2 particle is governed by a variable internal to the particle (local, “hidden”), and examine pairs of particles having zero combined angular momentum so that their internal variables are correlated: knowing something about the internal variable of one tells us something about that of the other. By measuring the spin of one particle, we infer something about its internal variable; through the correlation, about the internal variable of the second particle, which may be arbitrarily distant and is by hypothesis unchanged by this measurement (locality); and make (probabilistic) prediction of spin observations on the second particle. Each link in this chain has a counterpart in the Bayesian analysis of the situation. Irrespective of the details of the internal variable description, such prediction is violated by measurements on many particle pairs, so that locality—effectively the only physics invoked—fails. The time ordering of the two measurements is not Lorentz-invariant, implying acausality. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of the statistics of the results imply it has a nonlocal—acausal interpretation; one such, the “transactional” interpretation, is presented to demonstrable advantage, and some misconceptions about quantum theory are pursued. The “unobservability” loophole in photonic Bell experiments is proven to be closed. It is shown that this mechanism cannot be used for signalling; signalling would become possible only if the hidden variables, which we insist must underlie the statistical character of the observations (the alternative is to give up), are uncovered in deviations from quantum predictions. Their reticence is understood as a consequence of their nonlocality: it is not easy to isolate and measure something nonlocal. Once the hidden variables
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.
Vorticity, Stokes' Theorem and the Gauss's Theorem
NASA Astrophysics Data System (ADS)
Narayanan, M.
2004-12-01
Vorticity is a property of the flow of any fluid and moving fluids acquire properties that allow an engineer to describe that particular flow in greater detail. It is important to recognize that mere motion alone does not guarantee that the air or any fluid has vorticity. Vorticity is one of four important quantities that define the kinematic properties of any fluid flow. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. However, the divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into, or away from the region through its boundary. This is also known as Gauss's Theorem. It should also be noted that there are many useful extensions of Gauss's Theorem, including the extension to include surfaces of discontinuity in V. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. Integral (Surface) [(DEL X V)] . dS = Integral (Contour) [V . dx] In this paper, the author outlines and stresses the importance of studying and teaching these mathematical techniques while developing a course in Hydrology and Fluid Mechanics. References Arfken, G. "Gauss's Theorem." 1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. Morse, P. M. and Feshbach, H. "Gauss's Theorem." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 37-38, 1953. Eric W. Weisstein. "Divergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DivergenceTheorem.html
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.
A Central Capacity Limit to the Simultaneous Storage of Visual and Auditory Arrays in Working Memory
ERIC Educational Resources Information Center
Saults, J. Scott; Cowan, Nelson
2007-01-01
If working memory is limited by central capacity (e.g., the focus of attention; N. Cowan, 2001), then storage limits for information in a single modality should apply also to the simultaneous storage of information from different modalities. The authors investigated this by combining a visual-array comparison task with a novel auditory-array…
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…
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…
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
The Floquet Adiabatic Theorem revisited
NASA Astrophysics Data System (ADS)
Weinberg, Phillip; Bukov, Marin; D'Alessio, Luca; Kolodrubetz, Michael; Davidson, Shainen; Polkovnikov, Anatoli
2015-03-01
The existance of the adiabatic theorem for Floquet systems has been the subject of an active debate with different articles reaching opposite conclusions over the years. In this talk we clarify the situation by deriving a systematic expansion in the time-derivatives of a slow parameter for the occupation probabilities of the Floque states. Our analysis shows that the in a certain limit the transition between Floquet eigenstates are suppressed and it is possible to define an adiabatic theorem for Floquet systems. Crucially we observe however that the conditions for adiabaticity in ordinary and Floquet systems are different and that this difference can become important when the amplitude of the periodic driving is large. We illustrate our results with specific examples of a periodically driven harmonic oscillator and cold atoms in optical lattices which are relevant in current experiments.
Energy turnover in European hares is centrally limited during early, but not during peak lactation.
Valencak, Teresa G; Ruf, Thomas
2009-11-01
We investigated metabolizable energy intake (MEI) and milk energy output in European hares throughout gestation and lactation in females raising three young, i.e., close to maximum litter size in this precocial species. We hypothesized that herbivorous hares may face a central limitation of energy turnover during lactation, imposed by maximum capacity of the gastrointestinal tract. Females were provided with low-energy or high-energy diets, either continually, or during lactation only. Unexpectedly, females on either diet reached identical peak MEIs (>6 times BMR) during late lactation, with females on low-energy diet increasing food intake proportionally. Thus, we reject our hypothesis that in lactating hares, peak MEI is centrally limited. During early lactation, MEI and milk transfer was, however, significantly impaired in females on the low-energy diet, indicating a temporal central limitation due to a time-lag caused by the readjustment of energy intake capacity. Importantly, irrespective of the diet, females significantly increased peak MEI late in the breeding season. Consequently, earlier in the season, when energy reserves are still high, energy throughput was not limited by physiological constraints at all. We conclude that extreme MEI may have fitness costs, and that females maximize lifetime reproductive success by actively down-regulating MEI whenever possible.
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages.
Limits to northward drift of the Paleocene Cantwell Formation, central Alaska.
Hillhouse, J.W.; Gromme, C.S.
1982-01-01
Volcanic rocks of the Paleocene Cantwell Formation in central Alaska apparently originated at a paleolatitude of 83oN (alpha 95 = 9.7o), as indicated by paleomagnetic results. When compared with the Paleocene pole for the North American craton, the 95% confidence limits of the results suggest that terranes N of the Denali fault have moved no more than 550km northward relative to the North American craton since Paleocene time.-Authors
Trigonometry, Including Snell's Theorem.
ERIC Educational Resources Information Center
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
ERIC Educational Resources Information Center
Benyi, Arpad; Casu, Ioan
2009-01-01
Pompeiu's theorem states that if ABC is an "equilateral" triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B,…
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
A Central Capacity Limit to the Simultaneous Storage of Visual and Auditory Arrays in Working Memory
Saults, J. Scott; Cowan, Nelson
2008-01-01
If working memory is limited by central capacity (e.g., the focus of attention; Cowan, 2001) then storage limits for information in a single modality should also apply to the simultaneous storage of information from different modalities. We investigated this by combining a visual-array comparison task with a novel auditory-array comparison task in five experiments. Participants were to remember only the visual or only the auditory arrays (unimodal memory conditions) or both arrays (bimodal memory conditions). Experiments 1-2 showed significant dual-task tradeoffs for visual but not auditory capacity. In Experiments 3-5, modality-specific memory was eliminated using post-perceptual masks. Dual-task costs occurred for both modalities and the number of auditory and visual items remembered together was no more than the higher of the unimodal capacities (visual, 3-4 items). The findings suggest a central capacity supplemented by modality- or code-specific storage and point to avenues for further research on the role of processing in central storage. PMID:17999578
STABILITY OF GAS CLOUDS IN GALACTIC NUCLEI: AN EXTENDED VIRIAL THEOREM
Chen, Xian; Cuadra, Jorge; Amaro-Seoane, Pau E-mail: jcuadra@astro.puc.cl
2016-03-10
Cold gas entering the central 1–10{sup 2} pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH) to turn on an active galactic nucleus (AGN). The conventional criteria to assess the stability of these clouds, such as the Jeans criterion and Roche (or tidal) limit, are insufficient here, because they assume the dominance of self-gravity in binding a cloud, and neglect external agents, such as pressure and tidal forces, which are common in galactic nuclei. We 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.
A generalization of Nekhoroshev's theorem
NASA Astrophysics Data System (ADS)
Bates, Larry; Cushman, Richard
2016-11-01
Nekhoroshev discovered a beautiful theorem in Hamiltonian systems that includes as special cases not only the Poincaré theorem on periodic orbits but also the theorem of Liouville-Arnol'd on completely integrable systems [7]. Sadly, his early death precluded him publishing a full account of his proof. The aim of this paper is twofold: first, to provide a complete proof of his original theorem and second a generalization to the noncommuting case. Our generalization of Nekhoroshev's theorem to the nonabelian case subsumes aspects of the theory of noncommutative complete integrability as found in Mishchenko and Fomenko [5] and is similar to what Nekhoroshev's theorem does in the abelian case.
Wheeler, W.
1998-12-01
This report estimates the economic and financial effects and the benefits of compliance with the proposed effluent limitations guidelines and standards for the Centralized Waste Treatment (CWT) industry. The Environmental Protection Agency (EPA) has measured these impacts in terms of changes in the profitability of waste treatment operations at CWT facilities, changes in market prices to CWT services, and changes in the quantities of waste management at CWT facilities in six geographic regions. EPA has also examined the impacts on companies owning CWT facilities (including impacts on small entities), on communities in which CWT facilities are located, and on environmental justice. EPA examined the benefits to society of the CWT effluent limitations guidelines and standards by examining cancer and non-cancer health effects of the regulation, recreational benefits, and cost savings to publicly owned treatment works (POTWs) to which indirect-discharging CWT facilities send their wastewater.
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.
Muscle Strength, Physical Activity, and Functional Limitations in Older Adults with Central Obesity
Germain, Cassandra M.; Batsis, John A.; Vasquez, Elizabeth; McQuoid, Douglas R.
2016-01-01
Background. Obesity and muscle weakness are independently associated with increased risk of physical and functional impairment in older adults. It is unknown whether physical activity (PA) and muscle strength combined provide added protection against functional impairment. This study examines the association between muscle strength, PA, and functional outcomes in older adults with central obesity. Methods. Prevalence and odds of physical (PL), ADL, and IADL limitation were calculated for 6,388 community dwelling adults aged ≥ 60 with central obesity. Individuals were stratified by sex-specific hand grip tertiles and PA. Logistic models were adjusted for age, education, comorbidities, and body-mass index and weighted. Results. Overall prevalence of PL and ADL and IADL limitations were progressively lower by grip category. Within grip categories, prevalence was lower for individuals who were active than those who were inactive. Adjusted models showed significantly lower odds of PL OR 0.42 [0.31, 0.56]; ADL OR 0.60 [0.43, 0.84], and IADL OR 0.46 [0.35, 0.61] for those in the highest grip strength category as compared to those in the lowest grip category. Conclusion. Improving grip strength in obese elders who are not able to engage in traditional exercise is important for reducing odds of physical and functional impairment. PMID:27034833
Virial Theorem and Scale Transformations.
ERIC Educational Resources Information Center
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
Rediscovering Schreinemakers' Theorem.
ERIC Educational Resources Information Center
Bathurst, Bruce
1983-01-01
Schreinemakers' theorem (arrangement of curves around an invariant point), derived from La Chatelier's principle, can be rediscovered by students asked to use the principle when solving a natural problem such as "How does diluting a mineral/fluid alter shape of a pressure/temperature diagram?" Background information and instructional…
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.
Non-traditional theorems unfolding
NASA Astrophysics Data System (ADS)
Wares, Arsalan
2015-02-01
The purpose of this paper is to provide examples of 'non-traditional' proof-related activities or theorems that can be explored through paper folding by university and high-school students. These theorems were encountered through playful acts of paper folding by the author. The author used these activities successfully with preservice teachers. The paper contains proof outlines for each theorem.
Generalized no-broadcasting theorem.
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-14
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with "superquantum" correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
Generalized No-Broadcasting Theorem
NASA Astrophysics Data System (ADS)
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-01
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with “superquantum” correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
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.
Upper limits to the magnetic field in central stars of planetary nebulae
Asensio Ramos, A.; Martínez González, M. J.; Manso Sainz, R.; Corradi, R. L. M.; Leone, F.
2014-06-01
More than about 20 central stars of planetary nebulae (CSPNs) have been observed spectropolarimetrically, yet no clear, unambiguous signal of the presence of a magnetic field in these objects has been found. We perform a statistical (Bayesian) analysis of all the available spectropolarimetric observations of CSPN to constrain the magnetic fields in these objects. Assuming that the stellar field is dipolar and that the dipole axis of the objects is oriented randomly (isotropically), we find that the dipole magnetic field strength is smaller than 400 G with 95% probability using all available observations. The analysis introduced allows integration of future observations to further constrain the parameters of the distribution, and it is general, so that it can be easily applied to other classes of magnetic objects. We propose several ways to improve the upper limits found here.
1987-03-20
with standard expressions of spherical trigonometry is sinr)0 = cos0 sini//0 (4.37) which is consistent with the results obtained previously with...theorems for discrete transforms. However, sampling questions inlroduce difficult obstacles in the develop- ment of a discrete theory. First, sampling...additional obstacle to discrete represen- tations of the CT. An example of qualitative predication of the shape of silhouettes with the Silhouette-Slice
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.
Tautenhahn, Susanne; Lichstein, Jeremy W; Jung, Martin; Kattge, Jens; Bohlman, Stephanie A; Heilmeier, Hermann; Prokushkin, Anatoly; Kahl, Anja; Wirth, Christian
2016-06-01
Fire is a primary driver of boreal forest dynamics. Intensifying fire regimes due to climate change may cause a shift in boreal forest composition toward reduced dominance of conifers and greater abundance of deciduous hardwoods, with potential biogeochemical and biophysical feedbacks to regional and global climate. This shift has already been observed in some North American boreal forests and has been attributed to changes in site conditions. However, it is unknown if the mechanisms controlling fire-induced changes in deciduous hardwood cover are similar among different boreal forests, which differ in the ecological traits of the dominant tree species. To better understand the consequences of intensifying fire regimes in boreal forests, we studied postfire regeneration in five burns in the Central Siberian dark taiga, a vast but poorly studied boreal region. We combined field measurements, dendrochronological analysis, and seed-source maps derived from high-resolution satellite images to quantify the importance of site conditions (e.g., organic layer depth) vs. seed availability in shaping postfire regeneration. We show that dispersal limitation of evergreen conifers was the main factor determining postfire regeneration composition and density. Site conditions had significant but weaker effects. We used information on postfire regeneration to develop a classification scheme for successional pathways, representing the dominance of deciduous hardwoods vs. evergreen conifers at different successional stages. We estimated the spatial distribution of different successional pathways under alternative fire regime scenarios. Under intensified fire regimes, dispersal limitation of evergreen conifers is predicted to become more severe, primarily due to reduced abundance of surviving seed sources within burned areas. Increased dispersal limitation of evergreen conifers, in turn, is predicted to increase the prevalence of successional pathways dominated by deciduous hardwoods
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.
Food limitation of sea lion pups and the decline of forage off central and southern California.
McClatchie, Sam; Field, John; Thompson, Andrew R; Gerrodette, Tim; Lowry, Mark; Fiedler, Paul C; Watson, William; Nieto, Karen M; Vetter, Russell D
2016-03-01
California sea lions increased from approximately 50 000 to 340 000 animals in the last 40 years, and their pups are starving and stranding on beaches in southern California, raising questions about the adequacy of their food supply. We investigated whether the declining sea lion pup weight at San Miguel rookery was associated with changes in abundance and quality of sardine, anchovy, rockfish and market squid forage. In the last decade off central California, where breeding female sea lions from San Miguel rookery feed, sardine and anchovy greatly decreased in biomass, whereas market squid and rockfish abundance increased. Pup weights fell as forage food quality declined associated with changes in the relative abundances of forage species. A model explained 67% of the variance in pup weights using forage from central and southern California and 81% of the variance in pup weights using forage from the female sea lion foraging range. A shift from high to poor quality forage for breeding females results in food limitation of the pups, ultimately flooding animal rescue centres with starving sea lion pups. Our study is unusual in using a long-term, fishery-independent dataset to directly address an important consequence of forage decline on the productivity of a large marine predator. Whether forage declines are environmentally driven, are due to a combination of environmental drivers and fishing removals, or are due to density-dependent interactions between forage and sea lions is uncertain. However, declining forage abundance and quality was coherent over a large area (32.5-38° N) for a decade, suggesting that trends in forage are environmentally driven.
Food limitation of sea lion pups and the decline of forage off central and southern California
McClatchie, Sam; Field, John; Thompson, Andrew R.; Gerrodette, Tim; Lowry, Mark; Fiedler, Paul C.; Watson, William; Nieto, Karen M.; Vetter, Russell D.
2016-01-01
California sea lions increased from approximately 50 000 to 340 000 animals in the last 40 years, and their pups are starving and stranding on beaches in southern California, raising questions about the adequacy of their food supply. We investigated whether the declining sea lion pup weight at San Miguel rookery was associated with changes in abundance and quality of sardine, anchovy, rockfish and market squid forage. In the last decade off central California, where breeding female sea lions from San Miguel rookery feed, sardine and anchovy greatly decreased in biomass, whereas market squid and rockfish abundance increased. Pup weights fell as forage food quality declined associated with changes in the relative abundances of forage species. A model explained 67% of the variance in pup weights using forage from central and southern California and 81% of the variance in pup weights using forage from the female sea lion foraging range. A shift from high to poor quality forage for breeding females results in food limitation of the pups, ultimately flooding animal rescue centres with starving sea lion pups. Our study is unusual in using a long-term, fishery-independent dataset to directly address an important consequence of forage decline on the productivity of a large marine predator. Whether forage declines are environmentally driven, are due to a combination of environmental drivers and fishing removals, or are due to density-dependent interactions between forage and sea lions is uncertain. However, declining forage abundance and quality was coherent over a large area (32.5–38° N) for a decade, suggesting that trends in forage are environmentally driven. PMID:27069651
A new VLA/e-MERLIN limit on central images in the gravitational lens system CLASS B1030+074
NASA Astrophysics Data System (ADS)
Quinn, Jonathan; Jackson, Neal; Tagore, Amitpal; Biggs, Andrew; Birkinshaw, Mark; Chapman, Scott; De Zotti, Gianfranco; McKean, John; Pérez-Fournon, Ismael; Scott, Douglas; Serjeant, Stephen
2016-07-01
We present the new Very Large Array 22 GHz and extended Multi-Element Remote-Linked Interferometer Network 5 GHz observations of CLASS B1030+074, a two-image strong gravitational lens system whose background source is a compact flat-spectrum radio quasar. In such systems we expect a third image of the background source to form close to the centre of the lensing galaxy. The existence and brightness of such images is important for investigation of the central mass distributions of lensing galaxies, but only one secure detection has been made so far in a galaxy-scale lens system. The noise levels achieved in our new B1030+074 images reach 3 μJy beam-1 and represent an improvement in central image constraints of nearly an order of magnitude over previous work, with correspondingly better resulting limits on the shape of the central mass profile of the lensing galaxy. Simple models with an isothermal outer power-law slope now require either the influence of a central supermassive black hole (SMBH), or an inner power-law slope very close to isothermal, in order to suppress the central image below our detection limit. Using the central mass profiles inferred from light distributions in Virgo galaxies, moved to z = 0.5, and matching to the observed Einstein radius, we now find that 45 per cent of such mass profiles should give observable central images, 10 per cent should give central images with a flux density still below our limit, and the remaining systems have extreme demagnification produced by the central SMBH. Further observations of similar objects will therefore allow proper statistical constraints to be placed on the central properties of elliptical galaxies at high redshift.
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.
Bayes' theorem in paleopathological diagnosis.
Byers, Steven N; Roberts, Charlotte A
2003-05-01
The utility of Bayes' theorem in paleopathological diagnoses is explored. Since this theorem has been used heavily by modern clinical medicine, its usefulness in that field is described first. Next, the mechanics of the theorem are discussed, along with methods for deriving the prior probabilities needed for its application. Following this, the sources of these prior probabilities and their accompanying problems in paleopathology are considered. Finally, an application using prehistoric rib lesions is presented to demonstrate the utility of this method to paleopathology.
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.
Multidimensional Tauberian theorems for generalized functions
NASA Astrophysics Data System (ADS)
Drozhzhinov, Yu N.
2016-12-01
This is a brief survey of multidimensional Tauberian theorems for generalized functions. Included are theorems of Hardy-Littlewood type, Tauberian and Abelian comparison theorems of Keldysh type, theorems of Wiener type, and Tauberian theorems for generalized functions with values in Banach spaces. Bibliography: 58 titles.
Mlakar, Jernej; Zorman, Jerneja Videčnik; Matičič, Mojca; Vrabec, Matej; Alibegović, Armin; Popović, Mara
2016-02-01
Primary angiitis of the central nervous system is a rare condition, usually with an insidious onset. There is a wide variety of histological types (granulomatous, lymphocytic or necrotizing vasculitis) and types of vessel involved (arteries, veins or both). Most cases are idiopathic. We describe a first case of idiopathic granulomatous central nervous system phlebitis with additional limited involvement of the heart and lung, exclusively affecting small and medium sized veins in a 22-year-old woman, presenting as a sub acute headache. The reasons for this peculiar limitation of inflammation to the veins and the involvement of the heart and lungs are unknown.
Theorems on positive data: on the uniqueness of NMF.
Laurberg, Hans; Christensen, Mads Graesbøll; Plumbley, Mark D; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.
Theorems on Positive Data: On the Uniqueness of NMF
Laurberg, Hans; Christensen, Mads Græsbøll; Plumbley, Mark D.; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors. PMID:18497868
Wigner-Araki-Yanase theorem beyond conservation laws
NASA Astrophysics Data System (ADS)
Tukiainen, Mikko
2017-01-01
The ability to measure every quantum observable is ensured by a fundamental result in quantum measurement theory. Nevertheless, additive conservation laws associated with physical symmetries, such as the angular momentum conservation, may lead to restrictions on the measurability of the observables. Such limitations are imposed by the theorem of Wigner, Araki, and Yanase (WAY). In this paper a formulation of the WAY theorem is presented rephrasing the measurability limitations in terms of quantum incompatibility. This broader mathematical basis enables us to both capture and generalize the WAY theorem by allowing us to drop the assumptions of additivity and even conservation of the involved quantities. Moreover, we extend the WAY theorem to the general level of positive operator-valued measures.
Examples of probabilistic semantics of the basic coding theorem for uncertainty spaces
Diduk, N.N.
1995-03-01
The basic coding theorem for discrete uncertainty spaces is so far the central result of the developing uncertainty theory. The theorem was first published in and its proof in. A refinement of the basic coding theorem with a new proof was subsequently published. The theoretical value of the basic coding theorem is in that it essentially made possible the development of a general theoretical apparatus covering various types of uncertainty. But this theorem should not be regarded as a purely theoretical result, because it also has a clear applied meaning. Indeed, the theorem deals with what can and cannot be accomplished by encoding elements of uncertainty spaces. Such questions are of considerable practical importance, because problems of finding good information encoding techniques are encountered in many spheres of human activity. Moreover, possible applications of the theorem are not restricted to coding problems: we know that prefix coding is analogous to construction of successful search strategies. Search problems therefore constitute another potential application of the proposed theorem. It is thus useful to consider the practical aspects of the basic coding theorem. The basis for the application of the theorem is its semantics, i.e., the system of possible meaningful interpretations. The present paper examines examples of particular cases of the basic coding theorem which admit a probabilistic interpretation. The choice of the topic is motivated by the fact that uncertainty situations that have a probabilistic meaning are undoubtedly of exceptional interest from both theoretical and applied considerations.
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.
ERIC Educational Resources Information Center
Lopez-Real, Francis
2008-01-01
While the author was searching the web, he came across an article by Michael Keyton of IMSA (Illinois Mathematics and Science Academy) called "Theorems of mystery". The phrase is Keyton's own, and he defines such a theorem as "a result that has considerable structure with minimal hypotheses." The simplest of his 10 examples is one that many…
The 1965 Penrose singularity theorem
NASA Astrophysics Data System (ADS)
Senovilla, José M. M.; Garfinkle, David
2015-06-01
We review the first modern singularity theorem, published by Penrose in 1965. This is the first genuine post-Einsteinian result in general relativity, where the fundamental and fruitful concept of the closed trapped surface was introduced. We include historical remarks, an appraisal of the theorem's impact, and relevant current and future work that belongs to its legacy.
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Equivalence theorem in effective theories
NASA Astrophysics Data System (ADS)
Chicherin, D.; Gorbenko, V.; Vereshagin, V.
2011-11-01
The famous equivalence theorem is reexamined in order to make it applicable to the case of effective theories. We slightly modify the formulation of this theorem and prove it based on the notion of the generating functional for Green functions. This allows one to trace (directly in terms of graphs) the mutual cancellation of different groups of contributions.
A Decomposition Theorem for Finite Automata.
ERIC Educational Resources Information Center
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
Generalized Sampling Theorem for Bandpass Signals
NASA Astrophysics Data System (ADS)
Prokes, Ales
2006-12-01
The reconstruction of an unknown continuously defined function[InlineEquation not available: see fulltext.] from the samples of the responses of[InlineEquation not available: see fulltext.] linear time-invariant (LTI) systems sampled by the[InlineEquation not available: see fulltext.]th Nyquist rate is the aim of the generalized sampling. Papoulis (1977) provided an elegant solution for the case where[InlineEquation not available: see fulltext.] is a band-limited function with finite energy and the sampling rate is equal to[InlineEquation not available: see fulltext.] times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST) for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.
Aurora B suppresses microtubule dynamics and limits central spindle size by locally activating KIF4A
Nunes Bastos, Ricardo; Gandhi, Sapan R.; Baron, Ryan D.; Gruneberg, Ulrike; Nigg, Erich A.
2013-01-01
Anaphase central spindle formation is controlled by the microtubule-stabilizing factor PRC1 and the kinesin KIF4A. We show that an MKlp2-dependent pool of Aurora B at the central spindle, rather than global Aurora B activity, regulates KIF4A accumulation at the central spindle. KIF4A phosphorylation by Aurora B stimulates the maximal microtubule-dependent ATPase activity of KIF4A and promotes its interaction with PRC1. In the presence of phosphorylated KIF4A, microtubules grew more slowly and showed long pauses in growth, resulting in the generation of shorter PRC1-stabilized microtubule overlaps in vitro. Cells expressing only mutant forms of KIF4A lacking the Aurora B phosphorylation site overextended the anaphase central spindle, demonstrating that this regulation is crucial for microtubule length control in vivo. Aurora B therefore ensures that suppression of microtubule dynamic instability by KIF4A is restricted to a specific subset of microtubules and thereby contributes to central spindle size control in anaphase. PMID:23940115
Analogues of Chernoff's theorem and the Lie-Trotter theorem
Neklyudov, Alexander Yu
2009-10-31
This paper is concerned with the abstract Cauchy problem .x=Ax, x(0)=x{sub 0} element of D(A), where A is a densely defined linear operator on a Banach space X. It is proved that a solution x( {center_dot} ) of this problem can be represented as the weak limit lim {sub n{yields}}{sub {infinity}}{l_brace}F(t/n){sup n}x{sub 0}{r_brace}, where the function F:[0,{infinity}){yields}L(X) satisfies the equality F'(0)y=Ay, y element of D(A), for a natural class of operators. As distinct from Chernoff's theorem, the existence of a global solution to the Cauchy problem is not assumed. Based on this result, necessary and sufficient conditions are found for the linear operator C to be closable and for its closure to be the generator of a C{sub 0}-semigroup. Also, we obtain new criteria for the sum of two generators of C{sub 0}-semigroups to be the generator of a C{sub 0}-semigroup and for the Lie-Trotter formula to hold. Bibliography: 13 titles.
Wakefield, Ewan D.; Phillips, Richard A.; Matthiopoulos, Jason
2014-01-01
Animal populations are frequently limited by the availability of food or of habitat. In central-place foragers, the cost of accessing these resources is distance-dependent rather than uniform in space. However, in seabirds, a widely studied exemplar of this paradigm, empirical population models have hitherto ignored this cost. In part, this is because non-independence among colonies makes it difficult to define population units. Here, we model the effects of both resource availability and accessibility on populations of a wide-ranging, pelagic seabird, the black-browed albatross Thalassarche melanophris. Adopting a multi-scale approach, we define regional populations objectively as spatial clusters of colonies. We consider two readily quantifiable proxies of resource availability: the extent of neritic waters (the preferred foraging habitat) and net primary production (NPP). We show that the size of regional albatross populations has a strong dependence, after weighting for accessibility, on habitat availability and to a lesser extent, NPP. Our results provide indirect support for the hypothesis that seabird populations are regulated from the bottom-up by food availability during the breeding season, and also suggest that the spatio-temporal predictability of food may be limiting. Moreover, we demonstrate a straightforward, widely applicable method for estimating resource limitation in populations of central-place foragers. PMID:24430849
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.
Berends, Inez E; Reitsma, Pieter
2005-10-01
In two studies it is examined whether lateral presentation of words in remedial practice for reading disabled children has additional effects to central presentation. The effect of limited exposure duration (LED) is also studied as a possible factor in inducing higher level decoding processes or increased processing speed of words. Two groups of Dutch reading disabled children (n1 = 25, mean age = 9;8 years and n2 = 36, mean age = 7;1 years) repeatedly practiced reading words presented in the left, right or the central visual field. The results show that all children improved substantially both in reading speed and accuracy, which demonstrates the importance of repetitive practice in reading to attain fluency in reading disabled children. Further analysis demonstrated that neither site of presentation nor limited exposure duration added significantly to the training results. These findings do not corroborate neuropsychological theories suggesting a special role for lateral presentations.
A low upper mass limit for the central black hole in the late-type galaxy NGC 4414
NASA Astrophysics Data System (ADS)
Thater, S.; Krajnović, D.; Bourne, M. A.; Cappellari, M.; de Zeeuw, T.; Emsellem, E.; Magorrian, J.; McDermid, R. M.; Sarzi, M.; van de Ven, G.
2017-01-01
We present our mass estimate of the central black hole in the isolated spiral galaxy NGC 4414. Using natural guide star adaptive optics assisted observations with the Gemini Near-Infrared Integral Field Spectrometer (NIFS) and the natural seeing Gemini Multi-Object Spectrographs-North (GMOS), we derived two-dimensional stellar kinematic maps of NGC 4414 covering the central 1.5 arcsec and 10 arcsec, respectively, at a NIFS spatial resolution of 0.13 arcsec. The kinematic maps reveal a regular rotation pattern and a central velocity dispersion dip down to around 105 km s-1. We constructed dynamical models using two different methods: Jeans anisotropic dynamical modeling and axisymmetric Schwarzschild modeling. Both modeling methods give consistent results, but we cannot constrain the lower mass limit and only measure an upper limit for the black hole mass of MBH = 1.56 × 106M⊙ (at 3σ level) which is at least 1σ below the recent MBH-σe relations. Further tests with dark matter, mass-to-light ratio variation and different light models confirm that our results are not dominated by uncertainties. The derived upper limit mass is not only below the MBH-σe relation, but is also five times lower than the lower limit black hole mass anticipated from the resolution limit of the sphere of influence. This proves that via high quality integral field data we are now able to push black hole measurements down to at least five times less than the resolution limit. The reduced data cubes (FITS files) are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/597/A18
The Digital Morphological Sampling Theorem
NASA Astrophysics Data System (ADS)
Haralick, Robert M.; Zhuang, Xinhua; Lin, Charlotte; Lee, James
1988-02-01
There are potential industrial applications for any methodology which inherently reduces processing time and cost and yet produces results sufficiently close to the result of full processing. It is for this reason that a morphological sampling theorem is important. The morphological sampling theorem described in this paper states: (1) how a digital image must be morphologically filtered before sampling in order to preserve the relevant information after sampling; (2) to what precision an appropriately morphologically filtered image can be reconstructed after sampling; and (3) the relationship between morphologically operating before sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element. The digital sampling theorem is developed first for the case of binary morphology and then it is extended to gray scale morphology through the use of the umbra homomorphism theorems.
Factor and Remainder Theorems: An Appreciation
ERIC Educational Resources Information Center
Weiss, Michael
2016-01-01
The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
Woolgar, Eric; Wylie, William
2016-02-15
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
Pine (Pinus sylvestris L. ) tree-limit surveillance during recent decades, central Sweden
Kullman, L. )
1993-02-01
The altitudinal tree-limit of Scots pine (Pinus sylvestris L.) has been surveyed at the population level since the early- and mid-1970s in the Swedish Scandes. Elevational tree-limit advance was recorded for the majority of sites, despite statistically stable, although highly fluctuating climate with clusters of exceptionally cold winters and many relatively cool summers. The new tree-limit derived from pines established in the late 1950s. Tree-limit rise was concurrent with net population decline for the period 1972 to 1991, mainly as a result of failing regeneration. The main factor of individual vitality depression and mortality was deduced to be winter desiccation. The progressive tree-limit has a tendency for slow upslope advance during periods of climatic stability, even if punctuated by shorter events of unfavorable climate. Pine tree-limit dynamics is suggested to be a complex of climate/age/disturbance interactions. The tree-limit may decline altitudinally mainly in response to secular climate cooling, which makes it best suited for surveying sustained climatic trends and analogous paleoclimatic reconstruction. 51 refs., 12 figs., 1 tabs.
Merlo, Rion; Witzgall, Bob; Yu, William; Ohlinger, Kurt; Ramberg, Steve; De Las Casas, Carla; Henneman, Seppi; Parker, Denny
2015-12-01
The Sacramento Regional County Sanitation District (District) must be compliant with stringent nitrogen limits by 2021 that the existing treatment facilities cannot meet. An 11-month pilot study was conducted to confirm that these limits could be met with an air activated sludge biological nutrient removal (BNR) process. The pilot BNR treated an average flow of 946 m(3)/d and demonstrated that it could reliably meet the ammonia limit, but that external carbon addition may be necessary to satisfy the nitrate limit. The BNR process performed well throughout the 11 months of operation with good settleability, minimal nocardioform content, and high quality secondary effluent. The BNR process was operated at a minimum pH of 6.4 with no noticeable impact to nitrification rates. Increased secondary sludge production was observed during rainfall events and is attributed to a change in wastewater influent characteristics.
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.
The Limits of Friendship: US Security Cooperation in Central Asia (Walker Paper, Number 9)
2007-10-01
displayed conspicu- ous leadership above and beyond the call of duty involving personal valor and intrepidity at an extreme hazard to life .” Walker is...105 6 CONSTRAINTS AND LIMITATIONS. . . . . . . . . . . 111 Environmental Constraints. . . . . . . . . . . . . . . 112 Bureaucratic and...160 gaining Access and Basing Rights . . . . . . . . . 161 Relative Accomplishments . . . . . . . . . . . . . . . 164 Notes
Limited irrigation of corn-based no-till crop rotations in west central Great Plains.
Technology Transfer Automated Retrieval System (TEKTRAN)
Identifying the most profitable crop rotation for an area is a continuous research challenge. The objective of this study was to evaluate 2, 3, and 4 yr. limited irrigation corn (Zea mays L.) based crop rotations for grain yield, available soil water, crop water productivity, and profitability in co...
Limited irrigation of corn-based no-till crop rotations in West Central Great Plains
Technology Transfer Automated Retrieval System (TEKTRAN)
Due to numerous alternatives in crop sequence and changes in crop yield and price, finding the most profitable crop rotation for an area is a continuous research challenge. The objective of this study was to evaluate 1-, 2-, 3-, and 4-yr limited irrigation corn (Zea mays L.)-based crop rotations for...
Sardiñas, Hillary S; Tom, Kathleen; Ponisio, Lauren Catherine; Rominger, Andrew; Kremen, Claire
2016-03-01
The delivery of ecosystem services by mobile organisms depends on the distribution of those organisms, which is, in turn, affected by resources at local and landscape scales. Pollinator-dependent crops rely on mobile animals like bees for crop production, and the spatial relationship between floral resources and nest location for these central-place foragers influences the delivery of pollination services. Current models that map pollination coverage in agricultural regions utilize landscape-level estimates of floral availability and nesting incidence inferred from expert opinion, rather than direct assessments. Foraging distance is often derived from proxies of bee body size, rather than direct measurements of foraging that account for behavioral responses to floral resource type and distribution. The lack of direct measurements of nesting incidence and foraging distances may lead to inaccurate mapping of pollination services. We examined the role of local-scale floral resource presence from hedgerow plantings on nest incidence of ground-nesting bees in field margins and within monoculture, conventionally managed sunflower fields in California's Central Valley. We tracked bee movement into fields using fluorescent powder. We then used these data to simulate the distribution of pollination services within a crop field. Contrary to expert opinion, we found that ground-nesting native bees nested both in fields and edges, though nesting rates declined with distance into field. Further, we detected no effect of field-margin floral enhancements on nesting. We found evidence of an exponential decay rate of bee movement into fields, indicating that foraging predominantly occurred in less than 1% of medium-sized bees' predicted typical foraging range. Although we found native bees nesting within agricultural fields, their restricted foraging movements likely centralize pollination near nest sites. Our data thus predict a heterogeneous distribution of pollination services
Band limited emission with central frequency around 2 Hz accompanying powerful cyclones
NASA Technical Reports Server (NTRS)
Troitskaia, V. A.; Shepetnov, K. S.; Dvobnia, B. D.
1992-01-01
It has been found that powerful cyclones are proceeded, accompanied and followed by narrow band electromagnetic emission with central frequency around 2 Hz. It is shown that the signal from this emission is unique and clearly distinguishable from known types of magnetic pulsations, spectra of local thunderstorms, and signals from industrial sources. This emission was first observed during an unusually powerful cyclone with tornadoes in the western European part of the Soviet Union, which passed by the observatory of Borok from south to north-east. The emission has been confirmed by analysis of similar events in Antarctica. The phenomenon described presents a new aspect of interactions of processes in the lower atmosphere and the ionosphere.
Time dependent electromagnetic fields and 4-dimensional Stokes' theorem
NASA Astrophysics Data System (ADS)
Andosca, Ryan; Singleton, Douglas
2016-11-01
Stokes' theorem is central to many aspects of physics—electromagnetism, the Aharonov-Bohm effect, and Wilson loops to name a few. However, the pedagogical examples and research work almost exclusively focus on situations where the fields are time-independent so that one need only deal with purely spatial line integrals (e.g., ∮ A . d x ) and purely spatial area integrals (e.g., ∫ ( ∇ × A ) . d a = ∫ B . d a ). Here, we address this gap by giving some explicit examples of how Stokes' theorem plays out with time-dependent fields in a full 4-dimensional spacetime context. We also discuss some unusual features of Stokes' theorem with time-dependent fields related to gauge transformations and non-simply connected topology.
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.
Ferromagnetism beyond Lieb's theorem
NASA Astrophysics Data System (ADS)
Costa, Natanael C.; Mendes-Santos, Tiago; Paiva, Thereza; Santos, Raimundo R. dos; Scalettar, Richard T.
2016-10-01
The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction U is turned on, Lieb proved rigorously that at half-filling (ρ =1 ) the ground state has a nonzero spin. In this paper we consider a "CuO2 lattice" (also known as "Lieb lattice," or as a decorated square lattice), in which "d orbitals" occupy the vertices of the squares, while "p orbitals" lie halfway between two d orbitals; both d and p orbitals can accommodate only up to two electrons. We use exact determinant quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, Ud=Up , originally considered by Lieb, and the inhomogeneous (IH) case, Ud≠Up . For the H case at half-filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all U . For the IH system at half-filling, we argue that the case Up≠Ud falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases Up=0 ,Ud=U and Up=U ,Ud=0 . We found that the different environments of d and p sites lead to a ferromagnetic insulator when Ud=0 ; by contrast, Up=0 leads to to a metal without any magnetic ordering. In addition, we have also established that at density ρ =1 /3 , strong antiferromagnetic correlations set in, caused by the presence of one fermion on each
Nambu-Goldstone theorem and spin-statistics theorem
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
Four theorems on the psychometric function.
May, Keith A; Solomon, Joshua A
2013-01-01
In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus
Restriction limits and main drivers of fruit production in palm in central Amazonia
NASA Astrophysics Data System (ADS)
Freitas, Cintia; Costa, Flávia R. C.; Barbosa, Carlos Eduardo; Cintra, Renato
2016-11-01
Adult plants incapable of producing viable offspring inflate our perception of the size of population distribution. We propose that species occurrence is limited to a subset of the environmental gradient and that it changes as ontogenetic development progresses. Moreover, fruit production is associated with site-specific environmental conditions. We sampled 2988 adult individuals from nine palm species in 30 plots (40 × 250 m) and used a larger data set including 42 other plots distributed along a continuous topo-edaphic gradient in a terra firme forest near Manaus, Brazil. Five out of nine palm species were more restricted to a sub-section of the topo-edaphic gradient in the adult-size phase. More specifically, reproductive individuals of species Attalea attaleoides and A. microcarpa had even more restricted distributions than adult-sized, non-reproductive plants. Successive environmental filtering and competition probably acting through selective mortality led to increasing habitat restriction, with reproductive adults being restricted to a smaller part of the region than juveniles and adults. Water availability and nutrients limited both the ability to produce fruits and the amount of fruit production. Previous studies have reported stronger habitat associations for older plants than for seedlings or juveniles, but we show here that some species are more restricted at their reproductive stage. Plant specializations to local conditions may be more common than currently acknowledged, and a significant portion of individuals in a population might represent sinks. Such strong environmental limitations of reproductive plants should also be considered in management of species with economic value and in conservation planning.
Wu, Gregory F; Shindler, Kenneth S; Allenspach, Eric J; Stephen, Tom L; Thomas, Hannah L; Mikesell, Robert J; Cross, Anne H; Laufer, Terri M
2011-02-01
Experimental autoimmune encephalomyelitis (EAE), a model for the human disease multiple sclerosis (MS), is dependent upon the activation and effector functions of autoreactive CD4 T cells. Multiple interactions between CD4 T cells and major histocompatibility class II (MHCII)+ antigen presenting cells (APCs) must occur in both the periphery and central nervous system (CNS) to elicit autoimmunity. The identity of the MHCII+ APCs involved throughout this process remains in question. We investigated which APC in the periphery and CNS mediates disease using transgenic mice with MHCII expression restricted to dendritic cells (DCs). MHCII expression restricted to DCs results in normal susceptibility to peptide-mediated EAE. Indeed, radiation-sensitive bone marrow-derived DCs were sufficient for all APC functions during peptide-induced disease. However, DCs alone were inefficient at promoting disease after immunization with the myelin protein myelin oligodendrocyte glycoprotein (MOG), even in the presence of MHCII-deficient B cells. Consistent with a defect in disease induction following protein immunization, antigen presentation by DCs alone was incapable of mediating spontaneous optic neuritis. These results indicate that DCs are capable of perpetuating CNS-targeted autoimmunity when antigens are readily available, but other APCs are required to efficiently initiate pathogenic cognate CD4 T cell responses.
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.
Evidence-based evaluation of information: the centrality and limitations of systematic reviews.
Järvholm, Bengt; Bohlin, Ingemar
2014-03-01
This introductory paper considers the value and limitations of the methodology of systematic reviews especially according to the evidence-based movement. It explains some terms and organisations producing systematic reviews. It also discusses controversies. The first concerns the criteria by which the quality of individual studies is assessed, the second the possible effects of the affiliation of some reviewers, and the third the value of formalisation of procedure (i.e. the tensions between formal tools and professional judgments). The article contrasts the evidence-based formalism with other formalisms as those by the Intergovernmental Panel on Climate Change and the International Agency for Research on Cancer. It discusses systematic reviews in social science where interventions are complex, difficult to blind, and depend on context. Systematic reviews in working life research are often focusing on prevention. The formal evidence-based process may devaluate or disregard findings from mechanistic and observational studies. Hence such reviews may falsely conclude that existing knowledge about the risk of the factor is limited or nonexistent.
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)
Quantum cryptography without Bell's theorem
NASA Astrophysics Data System (ADS)
Bennett, Charles H.; Brassard, Gilles; Mermin, N. David
1992-02-01
Ekert has described a cryptographic scheme in which Einstein-Podolsky-Rosen (EPR) pairs of particles are used to generate identical random numbers in remote places, while Bell's theorem certifies that the particles have not been measured in transit by an eavesdropper. We describe a related but simpler EPR scheme and, without invoking Bell's theorem, prove it secure against more general attacks, including substitution of a fake EPR source. Finally we show our scheme is equivalent to the original 1984 key distribution scheme of Bennett and Brassard, which uses single particles instead of EPR pairs.
Carbon balance indicates a time limit for cultivation of organic soils in central Switzerland
NASA Astrophysics Data System (ADS)
Paul, Sonja; Ammann, Christof; Alewell, Christine; Leifeld, Jens
2016-04-01
Peatlands serve as important carbon sinks. Globally, more than 30% of the soil organic carbon is stored in organic soils, although they cover only 3% of the land surface. The agricultural use of organic soils usually requires drainage thereby transforming these soils from a net carbon sink into a net source. Currently, about 2 to 3 Gt CO2 are emitted world-wide from degrading organic soils (Joosten 2011; Parish et al. 2008) which is ca. 5% of the total anthropogenic emissions. Besides these CO2 emissions, the resulting subsidence of drained peat soils during agricultural use requires that drainage system are periodically renewed and finally to use pumping systems after progressive subsidence. In Switzerland, the Seeland region is characterised by fens which are intensively used for agriculture since 1900. The organic layer is degrading and subsequently getting shallower and the underlying mineral soil, as lake marl or loam, is approaching the surface. The questions arises for how long and under which land use practises and costs these soils can be cultivated in the near future. The study site was under crop rotation until 2009 when it was converted to extensively used grassland with the water regime still being regulated. The soil is characterised by a degraded organic horizon of 40 to 70 cm. Since December 2014 we are measuring the carbon exchange of this grassland using the Eddy-Covariance method. For 2015, the carbon balance indicates that the degraded fen is a strong carbon source, with approximately 500 g C m-2 a-1. The carbon balance is dominated by CO2 emissions and harvest. Methane emissions are negligible. With the gained emission factors different future scenarios are evaluated for the current cultivation practise of organic soils in central Switzerland. Joosten, H., 2011: Neues Geld aus alten Mooren: Über die Erzeugung von Kohlenstoffzertifikaten aus Moorwiedervernässungen. Telma Beiheft 4, 183-202. Parish, F., A. Sirin, D. Charman, H. Joosten, T
Limitations of selective deltamethrin application for triatomine control in central coastal Ecuador
2011-01-01
Background This year-long study evaluated the effectiveness of a strategy involving selective deltamethrin spraying and community education for control of Chagas disease vectors in domestic units located in rural communities of coastal Ecuador. Results Surveys for triatomines revealed peridomestic infestation with Rhodnius ecuadoriensis and Panstrongylus howardi, with infestation indices remaining high during the study (13%, 17%, and 10%, at initial, 6-month, and 12-month visits, respectively), which indicates a limitation of this strategy for triatomine population control. Infestation was found 6 and 12 months after spraying with deltamethrin. In addition, a large number of previously vector-free domestic units also were found infested at the 6- and 12-month surveys, which indicates new infestations by sylvatic triatomines. The predominance of young nymphs and adults suggests new infestation events, likely from sylvatic foci. In addition, infection with Trypanosoma cruzi was found in 65%, 21% and 29% at initial, 6-month and 12-month visits, respectively. All parasites isolated (n = 20) were identified as TcI. Conclusion New vector control strategies need to be devised and evaluated for reduction of T. cruzi transmission in this region. PMID:21332985
Tschoep, Hendrik; Gibon, Yves; Carillo, Petronia; Armengaud, Patrick; Szecowka, Marek; Nunes-Nesi, Adriano; Fernie, Alisdair R; Koehl, Karin; Stitt, Mark
2009-03-01
We have established a simple soil-based experimental system that allows a small and sustained restriction of growth of Arabidopsis by low nitrogen (N). Plants were grown in a large volume of a peat-vermiculite mix that contained very low levels of inorganic N. As a control, inorganic N was added in solid form to the peat-vermiculite mix, or plants were grown in conventional nutrient-rich solids. The low N growth regime led to a sustained 20% decrease of the relative growth rate over a period of 2 weeks, resulting in a two- to threefold decrease in biomass in 35- to 40-day-old plants. Plants in the low N regime contained lower levels of nitrate, lower nitrate reductase activity, lower levels of malate, fumarate and other organic acids and slightly higher levels of starch, as expected from published studies of N-limited plants. However, their rosette protein content was unaltered, and total and many individual amino acid levels increased compared with N-replete plants. This metabolic phenotype reveals that Arabidopsis responds adaptively to low N by decreasing the rate of growth, while maintaining the overall protein content, and maintaining or even increasing the levels of many amino acids.
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.)
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.
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…
Arriving at the Pythagorean Theorem.
ERIC Educational Resources Information Center
Jaramillo, James; Brown, Jonathan Caius
This lesson plan uses group activity and manipulative materials to teach English-speaking students (ages 15-16) of diverse ethnic backgrounds an operatonal understanding of the Pythagorean Theorem. It is based on theories of constructivism and holism and includes teacher instructions, discussion questions, a retrospective vision, and an ancillary…
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is
Pythagorean Theorem Proofs: Connecting Interactive Websites
ERIC Educational Resources Information Center
Lin, Cheng-Yao
2007-01-01
There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)
A Fundamental Theorem on Particle Acceleration
Xie, Ming
2003-05-01
A fundamental theorem on particle acceleration is derived from the reciprocity principle of electromagnetism and a rigorous proof of the theorem is presented. The theorem establishes a relation between acceleration and radiation, which is particularly useful for insightful understanding of and practical calculation about the first order acceleration in which energy gain of the accelerated particle is linearly proportional to the accelerating field.
A note on generalized Weyl's theorem
NASA Astrophysics Data System (ADS)
Zguitti, H.
2006-04-01
We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.
Generalizations of Ptolemy and Brahmagupta Theorems
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
Khalfin's Theorem and Neutral Mesons Subsystem
NASA Astrophysics Data System (ADS)
Urbanowski, Krzysztof
2009-01-01
The consequences of Khalfin's Theorem are discussed. we find, eg., that diagonal matrix elements of the exact effective Hamiltonian for the neutral meson complex can not be equal if CPT symmetry holds and CP symmetry is violated. Within a given model we examine numerically the Khalfin's Theorem and show in a graphic form how the Khalfin's Theorem works.
Saoithín: A Theorem Prover for UTP
NASA Astrophysics Data System (ADS)
Butterfield, Andrew
Saoithín is a theorem prover developed to support the Unifying Theories of Programming (UTP) framework. Its primary design goal was to support the higher-order logic, alphabets, equational reasoning and "programs as predicates" style that is prevalent in much of the UTP literature, from the seminal work by Hoare & He [HH98] onwards. This paper describes the key features of the theorem prover, with an emphasis on the underlying foundations, and how these affect the design and implementation choices. These key features include: a formalisation of a UTP Theory; support for common proof strategies; sophisticated goal/law matching ; and user-defined language constructs. A simple theory of designs with some proof extracts is used to illustrate the above features. The theorem prover has been used with undergraduate students and we discuss some of those experiences. The paper then concludes with a discussion of current limitations and planned improvements to the tool.
Level reduction and the quantum threshold theorem
NASA Astrophysics Data System (ADS)
Aliferis, Panagiotis (Panos)
Computers have led society to the information age revolutionizing central aspects of our lives from production and communication to education and entertainment. There exist, however, important problems which are intractable with the computers available today and, experience teaches us, will remain so even with the more advanced computers we can envision for tomorrow.Quantum computers promise speedups to some of these important but classically intractable problems. Simulating physical systems, a problem of interest in a diverse range of areas from testing physical theories to understanding chemical reactions, and solving number factoring, a problem at the basis of cryptographic protocols that are used widely today on the internet, are examples of applications for which quantum computers, when built, will offer a great advantage over what is possible with classical computer technology.The construction of a quantum computer of sufficient scale to solve interesting problems is, however, especially challenging. The reason for this is that, by its very nature, operating a quantum computer will require the coherent control of the quantum state of a very large number of particles. Fortunately, the theory of quantum error correction and fault-tolerant quantum computation gives us confidence that such quantum states can be created, can be stored in memory and can also be manipulated provided the quantum computer can be isolated to a sufficient degree from sources of noise.One of the central results in the theory of fault-tolerant quantum computation, the quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum accuracy threshold. This thesis provides a simpler and more transparent non-inductive proof of this theorem based on the concept of level reduction. This concept is also used in proving the
Complex virial theorem and complex scaling
Junker, B.R.
1983-06-01
We present the simple generalization to complex energies of the normal global real scaling used for bound-state calculations to produce a variational energy which satisfies the virial theorem. We show that in two limiting cases, one or the other of which is almost always p satisfied in all calculations, the virially stabilized complex energy is sensitive to only the real part or the imaginary part of the complex virial expression. We then compute the virial expression for a number of wave functions for the 1s2s/sup 2/ /sup 2/S He/sup -/, 1s2s2p /sup 2/P/sup o/ He/sup -/, and 1s/sup 2/2s/sup 2/kp /sup 2/P/sup o/ Be/sup -/ resonances and the corresponding virially stabilized resonance energies. In all calculations one of the limiting cases was applicable.
Generalized Bloch theorem and chiral transport phenomena
NASA Astrophysics Data System (ADS)
Yamamoto, Naoki
2015-10-01
Bloch theorem states the impossibility of persistent electric currents in the ground state of nonrelativistic fermion systems. We extend this theorem to generic systems based on the gauged particle number symmetry and study its consequences on the example of chiral transport phenomena. We show that the chiral magnetic effect can be understood as a generalization of the Bloch theorem to a nonequilibrium steady state, similarly to the integer quantum Hall effect. On the other hand, persistent axial currents are not prohibited by the Bloch theorem and they can be regarded as Pauli paramagnetism of relativistic matter. An application of the generalized Bloch theorem to quantum time crystals is also discussed.
The de Finetti theorem for test spaces
NASA Astrophysics Data System (ADS)
Barrett, Jonathan; Leifer, Matthew
2009-03-01
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
Equivalence theorem of uncertainty relations
NASA Astrophysics Data System (ADS)
Li, Jun-Li; Qiao, Cong-Feng
2017-01-01
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e. the variance-based ones and the entropic forms, showing that the entropy of an operator in a quantum system can be built from the variances of a set of commutative operators. This means that an uncertainty relation in the language of entropy may be mapped onto a variance-based one, and vice versa. Employing the equivalence theorem, alternative formulations of entropic uncertainty relations are obtained for the qubit system that are stronger than the existing ones in the literature, and variance-based uncertainty relations for spin systems are reached from the corresponding entropic uncertainty relations.
Uniqueness Theorem for Black Objects
Rogatko, Marek
2010-06-23
We shall review the current status of uniqueness theorem for black objects in higher dimensional spacetime. At the beginning we consider static charged asymptotically flat spacelike hypersurface with compact interior with both degenerate and non-degenerate components of the event horizon in n-dimensional spacetime. We gave some remarks concerning partial results in proving uniqueness of stationary axisymmetric multidimensional solutions and winding numbers which can uniquely characterize the topology and symmetry structure of black objects.
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.
Victoriano-Romero, Elizabeth; Valencia-Díaz, Susana; Toledo-Hernández, Víctor Hugo; Flores-Palacios, Alejandro
2017-01-01
Seed dispersal permits the colonization of favorable habitats and generation of new populations, facilitating escape from habitats that are in decline. There is little experimental evidence of the factors that limit epiphyte dispersion towards their hosts. In a tropical dry forest in central Mexico, we monitored the phenology of dispersion of epiphyte species of the genus Tillandsia; we tested experimentally whether precipitation could cause failures in seed dispersal and whether seed capture differs among vertical strata and between host species with high (Bursera copallifera) and low (Conzattia multiflora) epiphyte loads. With the exception of one species that presents late dispersion and low abundance, all of the species disperse prior to the onset of the rainy season. However, early rains immobilize the seeds, affecting up to 24% of the fruits in species with late dispersion. We observed that Tillandsia seeds reach both Bursera and Conzattia hosts, but found that adherence to the host is 4-5 times higher in Bursera. Furthermore, seeds liberated from Bursera travel shorter distances and up to half may remain within the same crown, while the highest seed capture takes place in the upper strata of the trees. We conclude that dispersion of Tillandsia seeds is limited by early rains and by the capture of seeds within the trees where populations concentrate. This pattern of capture also helps to explain the high concentrations of epiphytes in certain hosts, while trees with few epiphytes can be simultaneously considered deficient receivers and efficient exporters of seeds.
2017-01-01
Seed dispersal permits the colonization of favorable habitats and generation of new populations, facilitating escape from habitats that are in decline. There is little experimental evidence of the factors that limit epiphyte dispersion towards their hosts. In a tropical dry forest in central Mexico, we monitored the phenology of dispersion of epiphyte species of the genus Tillandsia; we tested experimentally whether precipitation could cause failures in seed dispersal and whether seed capture differs among vertical strata and between host species with high (Bursera copallifera) and low (Conzattia multiflora) epiphyte loads. With the exception of one species that presents late dispersion and low abundance, all of the species disperse prior to the onset of the rainy season. However, early rains immobilize the seeds, affecting up to 24% of the fruits in species with late dispersion. We observed that Tillandsia seeds reach both Bursera and Conzattia hosts, but found that adherence to the host is 4–5 times higher in Bursera. Furthermore, seeds liberated from Bursera travel shorter distances and up to half may remain within the same crown, while the highest seed capture takes place in the upper strata of the trees. We conclude that dispersion of Tillandsia seeds is limited by early rains and by the capture of seeds within the trees where populations concentrate. This pattern of capture also helps to explain the high concentrations of epiphytes in certain hosts, while trees with few epiphytes can be simultaneously considered deficient receivers and efficient exporters of seeds. PMID:28158320
Parrish, Karen E.; Cen, Ling; Murray, James; Calligaris, David; Kizilbash, Sani; Mittapalli, Rajendar K.; Carlson, Brett L.; Schroeder, Mark A.; Sludden, Julieann; Boddy, Alan V.; Agar, Nathalie Y.R.; Curtin, Nicola J.; Elmquist, William F.; Sarkaria, Jann N.
2015-01-01
Poly (ADP-ribose) polymerase (PARP) inhibition can enhance the efficacy of temozolomide (TMZ) and prolong survival in orthotopic glioblastoma (GBM) xenografts. The aim of this study was to evaluate the combination of the PARP inhibitor rucaparib with TMZ and to correlate pharmacokinetic and pharmacodynamic studies with efficacy in patient-derived GBM xenograft models. The combination of rucaparib with TMZ was highly effective in vitro in short-term explant cultures derived from GBM12, and similarly, the combination of rucaparib and TMZ (dosed for 5 days every 28 days × 3 cycles) significantly prolonged the time to tumor regrowth by 40% in heterotopic xenografts. In contrast, the addition of rucaparib had no impact on the efficacy of TMZ in GBM12 or GBM39 orthotopic models. Using Madin-Darby canine kidney (MDCK) II cells stably expressing murine BCRP1 or human MDR1, cell accumulation studies demonstrated that rucaparib is transported by both transporters. Consistent with the influence of these efflux pumps on central nervous system drug distribution, Mdr1a/b−/−Bcrp1−/− knockout mice had a significantly higher brain to plasma ratio for rucaparib (1.61 ± 0.25) than wild-type mice (0.11 ± 0.08). A pharmacokinetic and pharmacodynamic evaluation after a single dose confirmed limited accumulation of rucaparib in the brain associated with substantial residual PARP enzymatic activity. Similarly, matrix-assisted laser desorption/ionization mass spectrometric imaging demonstrated significantly enhanced accumulation of drug in flank tumor compared to normal brain or orthotopic tumors. Collectively, these results suggest that limited drug delivery into brain tumors may significantly limit the efficacy of rucaparib combined with TMZ in GBM. PMID:26438157
Droessler, T.D.
1992-03-01
The proposed research will quantify white spruce growth and document its latitudinal stability at the tree limit in the central Brooks Range over the life span of the living trees. The goal is to link tree growth and tree position to summer temperature and precipitation. Historical records from 1929 to 1938 from work by Robert Marshall have been used to identify tree limit sites and provide information to interpret the present location of the tree limit.
On Liouville's theorem in fluid mechanics
NASA Astrophysics Data System (ADS)
Morrison, P. J.; Bouchet, F.; Thalabard, S.; Zaboronski, O. V.
2011-11-01
Since the early work of Burgers it has been known that discretizations of fluid models possess a version of Liouville's theorem on conservation of phase space volume. In fact, spectral representations of two-dimensional turbulence are known to have a detailed version of this theorem. The existence of such Liouville theorems led many (e.g. Burgers, Lee, Kraichnan and Montgomery) to consider various statistical mechanical approaches to turbulence. We show how this theorem arises naturally from the Hamiltonian structure of inviscid fluid equations.
Cosmological perturbations and the Weinberg theorem
Akhshik, Mohammad; Firouzjahi, Hassan; Jazayeri, Sadra E-mail: firouz@ipm.ir
2015-12-01
The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.
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.
The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces
NASA Astrophysics Data System (ADS)
Huang, Jianhua
2005-12-01
In this paper we present some new matching theorems with open cover and closed cover by using the generalized R-KKM theorems [L. Deng, X. Xia, Generalized R-KKM theorem in topological space and their applications, J. Math. Anal. Appl. 285 (2003) 679-690] in the topological spaces with property (H). As applications, some coincidence theorems are established in topological spaces. Our results extend and generalize some known results.
A mean-field limit for a class of queueing networks
NASA Astrophysics Data System (ADS)
Baccelli, F.; Karpelevich, F. I.; Kelbert, M. Ya.; Puhalskii, A. A.; Rybko, A. N.; Suhov, Yu. M.
1992-02-01
A model of centralized symmetric message-switched networks is considered, where the messages having a common address must be served in the central node in the order which corresponds to their epochs of arrival to the network. The limit N → ∞ is discussed, where N is the branching number of the network graph. This procedure is inspired by an analogy with statistical mechanics (the mean-field approximation). The corresponding limit theorems are established and the limiting probability distribution for the network response time is obtained. Properties of this distribution are discussed in terms of an associated boundary problem.
INTERPOLATION THEOREMS FOR THE SPACES L_{p,q}
NASA Astrophysics Data System (ADS)
Ovchinnikov, V. I.
1989-02-01
A sharp or optimal interpolation theorem is proved for the Lorentz spaces L_{p,q}, generalizing the Marcinkiewicz theorem and refining the Riesz-Thorin theorem and the Stein-Weiss theorem. This theorem extends to the spaces \\overline{X}_{\\theta,p} of the real method constructed from any Banach pair; thus it extends also to Besov spaces.Bibliography: 12 titles.
Uniqueness theorems in bioluminescence tomography.
Wang, Ge; Li, Yi; Jiang, Ming
2004-08-01
Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case the BLT solution is not unique by constructing the set of all the solutions to this inverse problem. Then, we show the uniqueness of the solution in the case of impulse sources. Finally, we present our main theorem that solid/hollow ball sources can be uniquely determined up to nonradiating sources. For better readability, the exact conditions for and rigorous proofs of the theorems are given in the Appendices. Further research directions are also discussed.
NASA Astrophysics Data System (ADS)
Lützgendorf, N.; Kissler-Patig, M.; Gebhardt, K.; Baumgardt, H.; Noyola, E.; Jalali, B.; de Zeeuw, P. T.; Neumayer, N.
2012-06-01
Context. Globular clusters are an excellent laboratory for stellar population and dynamical research. Recent studies have shown that these stellar systems are not as simple as previously assumed. With multiple stellar populations as well as outer rotation and mass segregation they turn out to exhibit high complexity. This includes intermediate-mass black holes (IMBHs) which are proposed to sit at the centers of some massive globular clusters. Today's high angular resolution ground based spectrographs allow velocity-dispersion measurements at a spatial resolution comparable to the radius of influence for plausible IMBH masses, and to detect changes in the inner velocity-dispersion profile. Together with high quality photometric data from HST, it is possible to constrain black-hole masses by their kinematic signatures. Aims: We determine the central velocity-dispersion profile of the globular cluster NGC 2808 using VLT/FLAMES spectroscopy. In combination with HST/ACS data our goal is to probe whether this massive cluster hosts an IMBH at its center and constrain the cluster mass to light ratio as well as its total mass. Methods: We derive a velocity-dispersion profile from integral field spectroscopy in the center and Fabry Perot data for larger radii. High resolution HST data are used to obtain the surface brightness profile. Together, these data sets are compared to dynamical models with varying parameters such as mass to light ratio profiles and black-hole masses. Results: Using analytical Jeans models in combination with variable M/LV profiles from N-body simulations we find that the best fit model is a no black hole solution. After applying various Monte Carlo simulations to estimate the uncertainties, we derive an upper limit of the back hole mass of MBH < 1 × 104 M⊙ (with 95% confidence limits) and a global mass-to-light ratio of M/LV = (2.1 ± 0.2) M⊙/L⊙. Based on observations collected at the European Organization for Astronomical Research in the
Bring the Pythagorean Theorem "Full Circle"
ERIC Educational Resources Information Center
Benson, Christine C.; Malm, Cheryl G.
2011-01-01
Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…
TAUBERIAN THEOREMS FOR MATRIX REGULAR VARIATION
MEERSCHAERT, M. M.; SCHEFFLER, H.-P.
2013-01-01
Karamata’s Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated. PMID:24644367
The Pythagorean Theorem: I. The finite case
Kadison, Richard V.
2002-01-01
The Pythagorean Theorem and variants of it are studied. The variations evolve to a formulation in terms of noncommutative, conditional expectations on von Neumann algebras that displays the theorem as the basic result of noncommutative, metric, Euclidean Geometry. The emphasis in the present article is finite dimensionality, both “discrete” and “continuous.” PMID:11929992
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.)
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…
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)
Using Pictures to Enhance Students' Understanding of Bayes' Theorem
ERIC Educational Resources Information Center
Trafimow, David
2011-01-01
Students often have difficulty understanding algebraic proofs of statistics theorems. However, it sometimes is possible to prove statistical theorems with pictures in which case students can gain understanding more easily. I provide examples for two versions of Bayes' theorem.
2014-01-01
Background Proper malaria diagnosis depends on the detection of asexual forms of Plasmodium spp. in the blood. Thick blood smear microscopy is the accepted gold standard of malaria diagnosis and is widely implemented. Surprisingly, diagnostic performance of this method is not well investigated and many clinicians in African routine settings base treatment decisions independent of microscopy results. This leads to overtreatment and poor management of other febrile diseases. Implementation of quality control programmes is recommended, but requires sustained funding, external logistic support and constant training and supervision of the staff. This study describes an easily applicable method to assess the performance of thick blood smear microscopy by determining the limit of blank and limit of detection. These two values are representative of the diagnostic quality and allow the correct discrimination between positive and negative samples. Methods Standard-conform methodology was applied and adapted to determine the limit of blank and the limit of detection of two thick blood smear microscopy methods (WHO and Lambaréné method) in a research centre in Lambaréné, Gabon. Duplicates of negative and low parasitaemia thick blood smears were read by several microscopists. The mean and standard deviation of the results were used to calculate the limit of blank and subsequently the limit of detection. Results The limit of blank was 0 parasites/μL for both methods. The limit of detection was 62 and 88 parasites/μL for the Lambaréné and WHO method, respectively. Conclusion With a simple, back-of-the-envelope calculation, the performance of two malaria microscopy methods can be measured. These results are specific for each diagnostic unit and cannot be generalized but implementation of a system to control microscopy performance can improve confidence in parasitological results and thereby strengthen malaria control. PMID:24929248
Quantum-mechanical diffraction theory of light from a small hole: Extinction-theorem approach
NASA Astrophysics Data System (ADS)
Jung, Jesper; Keller, Ole
2015-07-01
In a recent paper [Phys. Rev. A 90, 043830 (2014), 10.1103/PhysRevA.90.043830] it was shown that the so-called aperture response tensor is the central concept in the microscopic quantum theory of light diffraction from a small hole in a flat screen. It was further shown that the quantum mechanical theory of diffraction only requires a preknowledge of the incident field plus the electronic properties of identical screens with and without a hole. Starting from the quantum mechanical expression for the linear conductivity tensor, we study the related causal conductivity tensor paying particular attention to diamagnetic electron dynamics. Using a nonlocal-potential separation assumption, we present a calculation of the diamagnetic causal surface conductivity for a jellium quantum-well screen using a two-dimensional Hartree-Fock model. In the diamagnetic case the difference between the light-unperturbed electron densities for screens with (n0) and without (n∞0) holes are the primary quantities for the diffraction theory. In a central part (Sec. IV) of this article we determine n0 via a quantum-mechanical two-dimensional extinction-theorem approach related to elastic electron scattering from a hole with an electronic selvedge. For heuristic purposes we illustrate aspects of the extinction-theorem theory by applying the approach for an infinitely high potential barrier to the vacuum hole. Finally, we calculate and discuss the aperture response tensor in the small hole limit and in the zeroth-order Born approximation. Our final result for the aperture response tensor establishes the bridge to the anisotropic electric dipole polarizability tensor of the hole. It turns out that the effective optical aperture (hole) size relates closely to the extension of the relevant electronic wave functions scattered from the hole.
On the Theorem of Correspondence.
Krøjgaard, Peter
2017-03-01
In a recent paper, Mammen (Integrative Psychological and Behavioral Science, 50, 196-233, 2016a) brought novel arguments into the discussion concerning the importance of being able to single out and track objects through space and time. Mammen offered a formal account of two basic, yet distinct, ways in which we as human beings encounter objects in the real world, that is, sense and choice categories. In this paper I discuss aspects of his theory and in particular the Theorem of Correspondence. I shall attempt to argue that Mammen's formal account is indeed a novel and powerful analytical generic tool allowing us to see the important relevance in different domains of being able to establish choice categories. Meanwhile, I will attempt to show that evidence from the so-called multiple object tracking studies -- even though these use highly artificial stimuli -- provide compelling evidence in support of Mammen's formal account.
Singlet and triplet instability theorems
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Posterior Probability and Fluctuation Theorem in Stochastic Processes
NASA Astrophysics Data System (ADS)
Ohkubo, Jun
2009-12-01
A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via Bayes’ theorem. In conventional fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when suitable assumptions are employed.
Fan beam image reconstruction with generalized Fourier slice theorem.
Zhao, Shuangren; Yang, Kang; Yang, Kevin
2014-01-01
For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N
ERIC Educational Resources Information Center
Andrich, David; Marais, Ida; Humphry, Stephen
2012-01-01
Andersen (1995, 2002) proves a theorem relating variances of parameter estimates from samples and subsamples and shows its use as an adjunct to standard statistical analyses. The authors show an application where the theorem is central to the hypothesis tested, namely, whether random guessing to multiple choice items affects their estimates in the…
[Count on your beliefs. Bayes' theorem in diagnosis].
Taube, A; Malmquist, J
2001-06-13
Bayesian analysis of data finds increasing use in medical statistics, diagnostic evaluation and decision analysis. The central element in bayesian analysis is a set of mathematical rules for integrated evaluation of prior knowledge and new information. In many situations this approach has superior ability to deliver dependable updated knowledge and to provide an optimal probability basis for decisions. This article (the first of two) presents Bayes' theorem and its application in diagnostic work. It is explained how likelihood ratios of diagnostic tests interact with the outcome of such tests in the conversion of initial information (prior odds) to enhanced information (posterior odds).
NASA Astrophysics Data System (ADS)
Young, Eliot F.; Olkin, Catherine B.; Young, Leslie A.; Howell, Robert R.; French, Richard G.
2014-11-01
We report a new analysis of occultation lightcurves observed in 2007 (from Mt John Observatory) and 2011 (from San Pedro Martir Observatory). In both cases, lightcurves were observed simultaneously in two wavelengths, and in the 2007 case, a double-peaked central flash was observed. In contrast to the wavelength-dependent opacities reported by Elliot et al. (Nature 2003; 424:165) in 2002, we see no evidence for an opacity source in Pluto's atmosphere that has greater extinction at shorter wavelengths. From the separation of the peaks in the 2007 central flash lightcurves, we find the oblateness of Pluto's atmosphere (equatorial vs. polar radii of pressure contours near R = 1215 km) of 1.03 ± 0.002. If this oblateness were caused solely by zonal winds, the wind speed at the equator would have to be 206 km/s; an alternative explanation is that the equatorial bulge is caused by warmer temperatures above the equator than the poles. Finally, the amplitudes of the central flash peaks are very sensitive to the surface pressure. If that pressure is driven by the vapor pressure of nitrogen ice, then the ice temperature of 42 ± 2 K reported by Tryka et al. (Icarus 1994; 212:513) is too high and produces central flash amplitudes that are much too bright. We find that the observed central flash peak amplitudes are consistent with nitrogen ice temperatures near 37 K, closer to the alpha-beta transition temperature (35.6 K) of nitrogen ice.
Kato type operators and Weyl's theorem
NASA Astrophysics Data System (ADS)
Duggal, B. P.; Djordjevic, S. V.; Kubrusly, Carlos
2005-09-01
A Banach space operator T satisfies Weyl's theorem if and only if T or T* has SVEP at all complex numbers [lambda] in the complement of the Weyl spectrum of T and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity. If T* (respectively, T) has SVEP and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity (respectively, T is Kato type at all [lambda][set membership, variant]iso[sigma](T)), then T satisfies a-Weyl's theorem (respectively, T* satisfies a-Weyl's theorem).
The Lax-Onsager regression `theorem' revisited
NASA Astrophysics Data System (ADS)
Lax, Melvin
2000-05-01
It is stated by Ford and O'Connell in this festschrift issue and elsewhere that "there is no quantum regression theorem" although Lax "obtained a formula for correlation in a driven quantum system that has come to be called the quantum regression theorem". This produces a puzzle: "How can it be that a non-existent theorem gives correct results?" Clarification will be provided in this paper by a description of the Lax procedure, with a quantitative estimate of the error for a damped harmonic oscillator based on expressions published in the 1960's.
Technology Transfer Automated Retrieval System (TEKTRAN)
The era of expanding irrigated agriculture in the central high plains has come to an end, and we are likely entering a period of contraction. Contraction has begun in Colorado where the state estimates that current consumptive use exceeds sustainable supplies by about 10%. Groundwater pumping has ...
Stojak, Joanna; McDevitt, Allan D.; Herman, Jeremy S.; Kryštufek, Boris; Uhlíková, Jitka; Purger, Jenő J.; Lavrenchenko, Leonid A.; Searle, Jeremy B.; Wójcik, Jan M.
2016-01-01
The common vole (Microtus arvalis) has been a model species of small mammal for studying end-glacial colonization history. In the present study we expanded the sampling from central and eastern Europe, analyzing contemporary genetic structure to identify the role of a potential ‘northern glacial refugium’, i.e. a refugium at a higher latitude than the traditional Mediterranean refugia. Altogether we analyzed 786 cytochrome b (cytb) sequences (representing mitochondrial DNA; mtDNA) from the whole of Europe, adding 177 new sequences from central and eastern Europe, and we conducted analyses on eight microsatellite loci for 499 individuals (representing nuclear DNA) from central and eastern Europe, adding data on 311 new specimens. Our new data fill gaps in the vicinity of the Carpathian Mountains, the potential northern refugium, such that there is now dense sampling from the Balkans to the Baltic Sea. Here we present evidence that the Eastern mtDNA lineage of the common vole was present in the vicinity of this Carpathian refugium during the Last Glacial Maximum and the Younger Dryas. The Eastern lineage expanded from this refugium to the Baltic and shows low cytb nucleotide diversity in those most northerly parts of the distribution. Analyses of microsatellites revealed a similar pattern but also showed little differentiation between all of the populations sampled in central and eastern Europe. PMID:27992546
Stojak, Joanna; McDevitt, Allan D; Herman, Jeremy S; Kryštufek, Boris; Uhlíková, Jitka; Purger, Jenő J; Lavrenchenko, Leonid A; Searle, Jeremy B; Wójcik, Jan M
2016-01-01
The common vole (Microtus arvalis) has been a model species of small mammal for studying end-glacial colonization history. In the present study we expanded the sampling from central and eastern Europe, analyzing contemporary genetic structure to identify the role of a potential 'northern glacial refugium', i.e. a refugium at a higher latitude than the traditional Mediterranean refugia. Altogether we analyzed 786 cytochrome b (cytb) sequences (representing mitochondrial DNA; mtDNA) from the whole of Europe, adding 177 new sequences from central and eastern Europe, and we conducted analyses on eight microsatellite loci for 499 individuals (representing nuclear DNA) from central and eastern Europe, adding data on 311 new specimens. Our new data fill gaps in the vicinity of the Carpathian Mountains, the potential northern refugium, such that there is now dense sampling from the Balkans to the Baltic Sea. Here we present evidence that the Eastern mtDNA lineage of the common vole was present in the vicinity of this Carpathian refugium during the Last Glacial Maximum and the Younger Dryas. The Eastern lineage expanded from this refugium to the Baltic and shows low cytb nucleotide diversity in those most northerly parts of the distribution. Analyses of microsatellites revealed a similar pattern but also showed little differentiation between all of the populations sampled in central and eastern Europe.
Duality Theorems in Ergodic Transport
NASA Astrophysics Data System (ADS)
Lopes, Artur O.; Mengue, Jairo K.
2012-11-01
We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose σ is the shift acting on Bernoulli space X={1,2,…, d}ℕ, and, consider a fixed continuous cost function c: X× X→ℝ. Denote by Π the set of all Borel probabilities π on X× X, such that, both its x and y marginals are σ-invariant probabilities. We are interested in the optimal plan π which minimizes ∫ c dπ among the probabilities in Π. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on c. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs c the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan π by convex combinations of plans such that the support projects in periodic orbits.
Structure theorem for Vaisman completely solvable solvmanifolds
NASA Astrophysics Data System (ADS)
Sawai, Hiroshi
2017-04-01
Locally conformal Kähler manifold is said to be a Vaisman manifold if the Lee form is parallel with respect to the Riemannian metric. In this paper, we have the structure theorem for Vaisman completely solvable solvmanifolds.
ALGEBRAIC DEPENDENCE THEOREMS ON COMPLEX PSEUDOCONCAVE SPACES
The notion of pseudoconcave space is introduced and classical theorems on algebraic dependence of meromorphic functions are extended for this new class of spaces and for sections in a coherent sheaf. (Author)
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…
The Great Emch Closure Theorem and a combinatorial proof of Poncelet's Theorem
NASA Astrophysics Data System (ADS)
Avksentyev, E. A.
2015-11-01
The relations between the classical closure theorems (Poncelet's, Steiner's, Emch's, and the zigzag theorems) and some of their generalizations are discussed. It is known that Emch's Theorem is the most general of these, while the others follow as special cases. A generalization of Emch's Theorem to pencils of circles is proved, which (by analogy with the Great Poncelet Theorem) can be called the Great Emch Theorem. It is shown that the Great Emch and Great Poncelet Theorems are equivalent and can be derived one from the other using elementary geometry, and also that both hold in the Lobachevsky plane as well. A new closure theorem is also obtained, in which the construction of closure is slightly more involved: closure occurs on a variable circle which is tangent to a fixed pair of circles. In conclusion, a combinatorial proof of Poncelet's Theorem is given, which deduces the closure principle for an arbitrary number of steps from the principle for three steps using combinatorics and number theory. Bibliography: 20 titles.
A Converse of Fermat's Little Theorem
ERIC Educational Resources Information Center
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
A Physical Proof of the Pythagorean Theorem
NASA Astrophysics Data System (ADS)
Treeby, David
2017-02-01
What proof of the Pythagorean theorem might appeal to a physics teacher? A proof that involved the notion of mass would surely be of interest. While various proofs of the Pythagorean theorem employ the circumcenter and incenter of a right-angled triangle, we are not aware of any proof that uses the triangle's center of mass. This note details one such proof. Though far from the most elegant approach, we believe it to be novel.
Littlewood-Paley Theorem for Schrodinger Operators
2006-07-26
26 JUL 2006 2. REPORT TYPE 3. DATES COVERED 00-00-2006 to 00-00-2006 4. TITLE AND SUBTITLE Littlewood -Paley theorem for Schrodinger operators...associated with H are well defined. We further give a Littlewood -Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes...unclassified c THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 LITTLEWOOD -PALEY THEOREM FOR SCHRÖDINGER
Federal Register 2010, 2011, 2012, 2013, 2014
2010-07-02
... requirements of the LLP is intended to provide a limited opportunity for entry level vessel operators to... sufficient, amount of participation in the Pacific cod fishery to indicate some level of dependence on...
The Nekhoroshev Theorem and Long-Term Stabilities in the Solar System
NASA Astrophysics Data System (ADS)
Guzzo, M.
2015-06-01
The Nekhoroshev theorem has been often indicated in the last decades as the reference theorem for explaining the dynamics of several systems which are stable in the long-term. The Solar System dynamics provides a wide range of possible and useful applications. In fact, despite the complicated models which are used to numerically integrate realistic Solar System dynamics as accurately as possible, when the integrated solutions are chaotic the reliability of the numerical integrations is limited, and a theoretical long-term stability analysis is required. After the first formulation of Nekhoroshev's theorem in 1977, many theoretical improvements have been achieved. On the one hand, alternative proofs of the theorem itself led to consistent improvements of the stability estimates; on the other hand, the extensions which were necessary to apply the theorem to the systems of interest for Solar System Dynamics, in particular concerning the removal of degeneracies and the implementation of computer assisted proofs, have been developed. In this review paper we discuss some of the motivations and the results which have made Nekhoroshev's theorem a reference stability result for many applications in the Solar System dynamics.
Conditioned Limit Theorems for Some Null Recurrent Markov Processes
1976-08-01
this conlus ion is the lolloing Suppos I in Pt > t 0 for all (t - nd (iv) hold X10 I J -or each is arN > mtv ,x is an inureas tip function of St hen (v...Diffusion Processes and Their Sample Paths, Springer-Verlag, second printing, (1973). 39. Jacobsen , M., Splitting times for Markov processes and a
NASA Astrophysics Data System (ADS)
Chavanis, Pierre-Henri; Sire, Clément
2006-06-01
We derive the virial theorem appropriate to the generalized Smoluchowski-Poisson (GSP) system describing self-gravitating Brownian particles in an overdamped limit. We extend previous works by considering the case of an unbounded domain and an arbitrary equation of state. We use the virial theorem to study the diffusion (evaporation) of an isothermal Brownian gas above the critical temperature Tc in dimension d=2 and show how the effective diffusion coefficient and the Einstein relation are modified by self-gravity. We also study the collapse at T=Tc and show that the central density increases logarithmically with time instead of exponentially in a bounded domain. Finally, for d>2 , we show that the evaporation of the system is essentially a pure diffusion slightly slowed down by self-gravity. We also study the linear dynamical stability of stationary solutions of the GSP system representing isolated clusters of particles and investigate the influence of the equation of state and of the dimension of space on the dynamical stability of the system.
Szabo, B. J.; Lindsey, D.A.
1986-01-01
Analysis of three travertine samples from the southeast side of The Park (central Montana) yield an average uranium-thorium age of 73 000 yr. Another sample from the west side of The Park is 320 000 yr old. These results indicate that travertine deposits may have formed at several intervals. The surface beneath The Park travertine is older than about 320 000 yr. Number 2 pediment gravels that contain travertine downslope from the oldest dated sample may be younger than about 320 000 yr. -Authors
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.
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.
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.
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
NASA Astrophysics Data System (ADS)
Izmailov, Ramil; Potapov, Alexander A.; Filippov, Alexander I.; Ghosh, Mithun; Nandi, Kamal K.
2015-04-01
We investigate the stability of circular material orbits in the analytic galactic metric recently derived by Harko et al., Mod. Phys. Lett. A29, 1450049 (2014). It turns out that stability depends more strongly on the dark matter central density ρ0 than on other parameters of the solution. This property then yields an upper limit on ρ0 for each individual galaxy, which we call here ρ 0 upper, such that stable circular orbits are possible only when the constraint ρ 0<= ρ 0 upper is satisfied. This is our new result. To approximately quantify the upper limit, we consider as a familiar example our Milky Way galaxy that has a projected dark matter radius RDM 180 kpc and find that ρ 0 upper ˜ 2.37× 1011 Mȯ kpc-3. This limit turns out to be about four orders of magnitude larger than the latest data on central density ρ0 arising from the fit to the Navarro-Frenk-White (NFW) and Burkert density profiles. Such consistency indicates that the Eddington-inspired Born-Infeld (EiBI) solution could qualify as yet another viable alternative model for dark matter.
Perkins, R. J. Bellan, P. M.
2015-02-15
Action integrals are often used to average a system over fast oscillations and obtain reduced dynamics. It is not surprising, then, that action integrals play a central role in the Hellmann-Feynman theorem of classical mechanics, which furnishes the values of certain quantities averaged over one period of rapid oscillation. This paper revisits the classical Hellmann-Feynman theorem, rederiving it in connection to an analogous theorem involving the time-averaged evolution of canonical coordinates. We then apply a modified version of the Hellmann-Feynman theorem to obtain a new result: the magnetic flux enclosed by one period of gyro-motion of a charged particle in a non-uniform magnetic field. These results further demonstrate the utility of the action integral in regards to obtaining orbit-averaged quantities and the usefulness of this formalism in characterizing charged particle motion.
Republication of: A theorem on Petrov types
NASA Astrophysics Data System (ADS)
Goldberg, J. N.; Sachs, R. K.
2009-02-01
This is a republication of the paper “A Theorem on Petrov Types” by Goldberg and Sachs, Acta Phys. Pol. 22 (supplement), 13 (1962), in which they proved the Goldberg-Sachs theorem. The article has been selected for publication in the Golden Oldies series of General Relativity and Gravitation. Typographical errors of the original publication were corrected by the editor. The paper is accompanied by a Golden Oldie Editorial containing an editorial note written by Andrzej Krasiński and Maciej Przanowski and Goldberg’s brief autobiography. The editorial note explains some difficult parts of the proof of the theorem and discusses the influence of results of the paper on later research.
Baur, Hannes
2015-01-01
Two new species, Pteromalusbriani sp. n. and Pteromalusjanstai sp. n., with unusual characters are described from the Central Plateau and the Alps in Switzerland, respectively. Pteromalusbriani sp. n. is remarkable in that it has the metatibia quite abruptly expanded before the middle. This type of modification of the hind tibia is unique within the Pteromalidae and probably also the entire Chalcidoidea. It is also very rare in other parasitic wasps, where it is suspected to be associated with pheromone glands. The species is a gregarious endoparasitoid of pupae of Vanessaatalanta (Linnaeus) and Aglaisurticae (Linnaeus), two common butterflies (Lepidoptera: Nymphalidae) in Europe. It is furthermore a koinobiont parasitoid ovipositing in an early larval stage of the host. The other species, Pteromalusjanstai sp. n., shows a flattened mesosoma. A dorsoventrally depressed body is a unique feature within the genus Pteromalus, but known from a number species in unrelated genera and subfamilies. The two records demonstrate that it is possible to discover entirely new species with extraordinary characters even in one of the taxonomically most thoroughly explored parts of the world.
Craft, Kathleen J; Ashley, Mary V; Koenig, Walter D
2002-11-01
Many oak species are interfertile, and morphological and genetic evidence for hybridization is widespread. Here we use DNA microsatellite markers to characterize hybridization between two closely related oak species in a mixed stand in central coastal California, Quercus lobata (valley oak) and Q. douglasii (blue oak) (Fagaceae). Genotypes from four microsatellite loci indicate that many alleles are shared between the two species. However, each species harbors unique alleles, and allele frequencies differ significantly. A Bayesian analysis of genetic structure in the stand identified two highly differentiated genetic clusters, essentially corresponding to species assignment based on morphology. Data from the four loci were sufficient to assign all 135 trees to one of the two species. In addition, five putative hybrid individuals having intermediate morphologies could be assigned genetically to one or the other species, and all but one had low probability of hybrid ancestry. Overally, only six (4.6%) trees showed >0.05 probability of hybrid ancestry, in all cases their probabilities for nonhybrid ancestry were substantially higher. We conclude that adult hybrids of Q. douglasii × Q. lobata are rare at this site and plasticity in morphological characters may lead to overestimates of hybridization among Quercus species.
Tails of Polynomials of Random Variables and Stable Limits for Nonconventional Sums
NASA Astrophysics Data System (ADS)
Kifer, Yuri; Varadhan, S. R. S.
2017-02-01
First, we obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails. Then we derive stable limit theorems for sums of the form sum _{Nt≥n≥1}Fbig (X_{q_1(n)},ldots ,X_{q_ℓ (n)}big ) where F is a polynomial, q_i(n) is either n-1+i or ni and X_n,n≥0 is a sequence of independent identically distributed random variables with heavy tails. Our results can be viewed as an extension to the heavy tails case of the nonconventional functional central limit theorem from Kifer and Varadhan (Ann Probab 42:649-688, 2014).
An invariance theorem in acoustic scattering theory
NASA Astrophysics Data System (ADS)
Ha-Duong, T.
1996-10-01
Karp's theorem states that if the far-field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle is invariant under the group of orthogonal transformations in 0266-5611/12/5/007/img1 (rotations in 0266-5611/12/5/007/img2), then the scatterer is a sphere (circle). The theorem is generalized to the case where the invariant group of the far field pattern is only a subgroup of the orthogonal group, and for a class of mixed boundary conditions.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.
NASA Astrophysics Data System (ADS)
Thomas, R. Q.; Kellner, J. R.; Peart, D. R.
2005-12-01
Logistical constraints on sample size and spatial scale limit individual-based field research on tropical trees. With remote sensing data, we may escape these limitations if fates of individuals can be tracked rigorously. We assessed the potential of readily available, commercial satellite data (QuickBird, 0.7 m pixels) obtained in 2003, to track the fate of individual crowns (> 40 m height) in tropical rain forest at La Selva, Costa Rica. The positions and shapes of these crowns in 1997 had been established using small-footprint LiDAR data with field verification. We focused first on a subset (n=180) of trees monitored in the field over the period 1997-2003. For the 60% of those trees whose crown positions and shapes could be tracked with confidence in the satellite image, we correctly recorded all 3 actual deaths. But we also incorrectly assigned 4 additional deaths to living individuals, due to the abundance of dark pixels in their crown areas. For the 40% of field-monitored trees for which our tracking in the satellite data was less confident (due to lack of image clarity), we correctly identified the one real death event, but incorrectly assigned 6 additional deaths to living trees. Thus, for the field-monitored trees, we grossly overestimated mortality in the satellite image (by 350%). Although currently available high resolution satellite imagery was not adequate for reliable monitoring of individuals, even for the largest forest trees, time series satellite data, rather than time series LiDAR to satellite data, might provide unbiased estimates of overall tree mortality rates if errors compensate. Satellite data may be also be useful as a labor and time saving complement to fieldwork on individual forest trees.
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.
Fluctuation theorem applied to the Nosé-Hoover thermostated Lorentz gas.
Gilbert, Thomas
2006-03-01
We present numerical evidence supporting the validity of the Gallavotti-Cohen fluctuation theorem applied to the driven Lorentz gas with Nosé-Hoover thermostating. It is moreover argued that the asymptotic form of the fluctuation formula is independent of the amplitude of the driving force in the limit where it is small.
Fluctuation theorem applied to the Nosé-Hoover thermostated Lorentz gas
NASA Astrophysics Data System (ADS)
Gilbert, Thomas
2006-03-01
We present numerical evidence supporting the validity of the Gallavotti-Cohen fluctuation theorem applied to the driven Lorentz gas with Nosé-Hoover thermostating. It is moreover argued that the asymptotic form of the fluctuation formula is independent of the amplitude of the driving force in the limit where it is small.
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…
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.
Type Theory, Computation and Interactive Theorem Proving
2015-09-01
Springer, Heidelberg, 61-76, 2014. [9] Jeremy Avigad and John Harrison , “Formally verified mathematics,” Communications of the ACM, 57(4):66-75, 2014. [10...inequalities," in Gerwin Klein and Ruben Gamboa, eds., Interactive Theorem Proving 2014, Springer, Heidelberg, 61-76, 2014. 9) Jeremy Avigad and John Harrison
Generalized Friedland's theorem for C0-semigroups
NASA Astrophysics Data System (ADS)
Cichon, Dariusz; Jung, Il Bong; Stochel, Jan
2008-07-01
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
On Viviani's Theorem and Its Extensions
ERIC Educational Resources Information Center
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
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.
Codimension- p Paley-Wiener theorems
NASA Astrophysics Data System (ADS)
Yang, Yan; Qian, Tao; Sommen, Frank
2007-04-01
We obtain the generalized codimension- p Cauchy-Kovalevsky extension of the exponential function e^{i
An extension theorem for conformal gauge singularities
NASA Astrophysics Data System (ADS)
Lübbe, Christian; Tod, Paul
2009-11-01
We analyze conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem along a congruence of timelike conformal geodesics.
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.
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…
The soft photon theorem for bremsstrahlung
Heller, L.
1990-01-01
We review this theorem and discuss the possible importance of the second term in the expansion of the cross section in powers of the photon momentum, especially for radiation from particle coming from the decay of resonances. 10 refs., 4 figs.
A non-differentiable Noether's theorem
NASA Astrophysics Data System (ADS)
Cresson, Jacky; Greff, Isabelle
2011-02-01
In the framework of the nondifferentiable embedding of Lagrangian systems, defined by Cresson and Greff [non-dierentiable embedding of lagrangian systems and partial dierential equations. Preprint Max-Plank-Institut für Mathematik in den Naturwissenschaften, Leipzig 16, 26 (2010)], we prove a Noether's theorem based on the lifting of one-parameter groups of diffeomorphisms.
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.
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)
NASA Astrophysics Data System (ADS)
McRae, S. M.; Vrscay, E. R.
1992-09-01
The classical hypervirial and Hellmann-Feynman theorems are used to formulate a "perturbation theory without Fourier series" that can be used to generate canonical series expansions for the energies of perturbed periodic orbits for separable classical Hamiltonians. Here, the method is applied to one-dimensional anharmonic oscillators and radial Kepler problems. In all cases, the classical series for energies and expectation values are seen to correspond to the expansions associated with their quantum mechanical counterparts through an appropriate action preserving classical limit. This "action fixing" is inherent in the classical Hellmann-Feynman theorem applied to periodic orbits.
NASA Astrophysics Data System (ADS)
Commins, Eugene D.; Jackson, J. David; Demille, David P.
2007-06-01
In most experimental searches for the electron electric dipole moment, one searches for a linear Stark effect in a paramagnetic atom or molecule and interprets the result in terms of the electric dipole moment of the unpaired valence electron(s). Schiff's theorem states that in the limit of nonrelativistic quantum mechanics, there can be no linear Stark effect to first order in the electric dipole moment. Sandars has shown that Schiff's theorem is not applicable when special relativity is taken into account. We give a heuristic explanation for this relativistic effect, which corrects a widespread misconception in the literature.
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.
A Simple Geometrical Derivation of the Spatial Averaging Theorem.
ERIC Educational Resources Information Center
Whitaker, Stephen
1985-01-01
The connection between single phase transport phenomena and multiphase transport phenomena is easily accomplished by means of the spatial averaging theorem. Although different routes to the theorem have been used, this paper provides a route to the averaging theorem that can be used in undergraduate classes. (JN)
Extending the Principal Axis Theorem to Fields Other than R.
ERIC Educational Resources Information Center
Friedberg, Stephen H.
1990-01-01
That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)
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…
A generalization of Bertrand's theorem to surfaces of revolution
Zagryadskii, Oleg A; Kudryavtseva, Elena A; Fedoseev, Denis A
2012-08-31
We prove a generalization of Bertrand's theorem to the case of abstract surfaces of revolution that have no 'equators'. We prove a criterion for exactly two central potentials to exist on this type of surface (up to an additive and a multiplicative constant) for which all bounded orbits are closed and there is a bounded nonsingular noncircular orbit. We prove a criterion for the existence of exactly one such potential. We study the geometry and classification of the corresponding surfaces with the aforementioned pair of potentials (gravitational and oscillatory) or unique potential (oscillatory). We show that potentials of the required form do not exist on surfaces that do not belong to any of the classes described. Bibliography: 33 titles.
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.
NASA Astrophysics Data System (ADS)
Gottwald, Georg A.; Wormell, J. P.; Wouters, Jeroen
2016-09-01
Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-fit statistics is developed for a linear statistical model of the observations, based on results for central limit theorems for deterministic dynamical systems, and used to detect linear response breakdown. We apply the method to discrete maps which do not obey linear response and show that the successful detection of breakdown depends on the length of the time series, the magnitude of the perturbation and on the choice of the observable. We find that in order to reliably reject the assumption of linear response for typical observables sufficiently large data sets are needed. Even for simple systems such as the logistic map, one needs of the order of 106 observations to reliably detect the breakdown with a confidence level of 95 %; if less observations are available one may be falsely led to conclude that linear response theory is valid. The amount of data required is larger the smaller the applied perturbation. For judiciously chosen observables the necessary amount of data can be drastically reduced, but requires detailed a priori knowledge about the invariant measure which is typically not available for complex dynamical systems. Furthermore we explore the use of the fluctuation-dissipation theorem (FDT) in cases with limited data length or coarse-graining of observations. The FDT, if applied naively to a system without linear response, is shown to be very sensitive to the details of the sampling method, resulting in erroneous predictions of the response.
Revisiting MHD stability comparison theorems: Some surprising new results
NASA Astrophysics Data System (ADS)
Cerfon, Antoine; Freidberg, Jeffrey
2009-05-01
The classic MHD stability comparison theorems (Kruskal-Oberman, Rosenbluth-Rostoker) show that ideal MHD yields the most stringent stability limits according to the hierarchy δWCGL>δWKIN>δWMHD. This has long justified the use of ideal MHD for conservative predictions of MHD stability boundaries. We reexamine these theorems, with the following conclusions:(1) It is crucial to distinguish between ergodic and closed field line systems.(2) It is essential to account for resonant particles in the kinetic MHD model.(3) For ergodic systems the original kinetic MHD analysis over-estimates stability: δWKIN>δWMHD. Our new result predicts δWKIN=δWMHD.(4) For closed line systems plasma compressibility effects become important, and resonant particle effects vanish. Both the original and new analysis predict δWKIN>δWMHD. However, using a Vlasov-Fluid model with Vlasov ions and fluid electrons we show that both δWKIN and δWMHD, while mathematically correct, yield the wrong physical result. The V-F model shows that at marginal stability the compressibility stabilization term vanishes identically! For ergodic systems, marginal stability is always incompressible, so δWKIN=δWMHD=δWVF. For compressible modes in closed line systems, however, perpendicular resonant particle effects cancel the stabilizing effect of plasma compressibility predicted by ideal and kinetic MHD: δWKIN>δWMHD>δWVF.
Generalized virial theorem in Palatini f(R) gravity
Sefiedgar, A. S.; Atazadeh, K.; Sepangi, H. R.
2009-09-15
We use the collision-free Boltzmann equation in Palatini f(R) gravity to derive the virial theorem within the context of the Palatini approach. It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations which contributes to gravitational energy and that such geometric mass can be attributed to the virial mass discrepancy in a cluster of galaxies. We then derive the velocity dispersion relation for clusters, followed by the metric tensor components inside the cluster as well as the f(R) Lagrangian in terms of the observational parameters. Since these quantities may also be obtained experimentally, the f(R) virial theorem is a convenient tool to test the viability of f(R) theories in different models. Finally, we discuss the limitations of our approach in light of the cosmological averaging used and questions that have been raised in the literature against such averaging procedures in the context of the present work.
Bosonization Theorem and a Model of High-Tc Superconductor.
NASA Astrophysics Data System (ADS)
Ren, Hai-Cang
1996-03-01
For a purely fermionic system on a lattice, there exists a different, but well defined system on the same lattice, consisting both of bona fide fermions and bosons with an interaction depending on a parameter G characterizing on-site repulsion between particles(R. Friedberg, T. D. Lee and H. C. Ren, Phys. Rev. B50, 10190 (1994).). The energy spectrum and the scattering matrix of the former are identical to those in the finite-energy sector of the latter in the hard-core limit, G→∞. This theorem is particularly useful for the description of a fermionic system whose low-lying spectrum consists of bosonic resonances. We argue that the high-Tc superconductors belong to this category and the long-range order in the superphase can be identified with the condensation of resonance bosons. A short coherence length, results from μSR experiments, measurements of the Hall number and the anomalous behavior of H_c2 near T=0 can be understood in terms of this resonance-boson model(R. Friedberg, T. D. Lee and H. C. Ren, Phys. Rev. B42, 4122 (1990).). We have also examined the possibility of a bosonic d-wave resonance(O.Tchernyshyov, A.S.Blaer and H.Ren, in the current Proceedings.). In this case, the bosonization theorem predicts coexistence of an s-wave bosonic condensate and a d-wave gap parameter for fermions.
Brigham-Grette, J.; Gualtieri, L.M.; Glushkova, O.Y.; Hamilton, T.D.; Mostoller, D.; Kotov, A.
2003-01-01
The Pekulney Mountains and adjacent Tanyurer River valley are key regions for examining the nature of glaciation across much of northeast Russia. Twelve new cosmogenic isotope ages and 14 new radiocarbon ages in concert with morphometric analyses and terrace stratigraphy constrain the timing of glaciation in this region of central Chukotka. The Sartan Glaciation (Last Glacial Maximum) was limited in extent in the Pekulney Mountains and dates to ???20,000 yr ago. Cosmogenic isotope ages > 30,000 yr as well as non-finite radiocarbon ages imply an estimated age no younger than the Zyryan Glaciation (early Wisconsinan) for large sets of moraines found in the central Tanyurer Valley. Slope angles on these loess-mantled ridges are less than a few degrees and crest widths are an order of magnitude greater than those found on the younger Sartan moraines. The most extensive moraines in the lower Tanyurer Valley are most subdued implying an even older, probable middle Pleistocene age. This research provides direct field evidence against Grosswald's Beringian ice-sheet hypothesis. ?? 2003 Elsevier Science (USA). All rights reserved.
A torus bifurcation theorem with symmetry
NASA Technical Reports Server (NTRS)
Vangils, S. A.; Golubitsky, M.
1989-01-01
Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-01-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571
Aging and nonergodicity beyond the Khinchin theorem
Burov, S.; Metzler, R.; Barkai, E.
2010-01-01
The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin’s theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics. PMID:20624984
Fluctuation theorem for constrained equilibrium systems.
Gilbert, Thomas; Dorfman, J Robert
2006-02-01
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
Fluctuation theorem for constrained equilibrium systems
NASA Astrophysics Data System (ADS)
Gilbert, Thomas; Dorfman, J. Robert
2006-02-01
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
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.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
About the Stokes decomposition theorem of waves
NASA Astrophysics Data System (ADS)
Lacaze, B.
2011-06-01
The Stokes decomposition theorem deals with the electrical field E→=X,Y of a light beam. The theorem asserts that a beam can be viewed as the sum of two differently polarized parts. This result was recently discussed for light in the frame of the unified theory of coherence. We study the general case of an electromagnetic wave which can be in radio, radar, communications, or light. We assume stationary components with any power spectrum and finite or infinite bandwidth. We show that an accurate definition of polarization and unpolarization is a key parameter which rules the set of solutions of the problem. When dealing with a "strong definition" of unpolarization, the problem is treated in the frame of stationary processes and linear invariant filters. When dealing with a "weak definition", solutions are given by elementary properties of bidimensional random variables.
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
[Objectivity of BSE symptoms using Bayes theorem].
Hässig, M; Urech Hässig, B; Knubben-Schweizer, G
2011-12-01
In clinical epidemiology the Bayes theorem finds ever more use to render clinical acting more objective. It is shown that unusual examinations of BSE (bovine spongiform encephalopathy) as noise producing with ladle covers may quite objectively be evaluated. With the help of the likelihood ratio computed thereby, also a ranking of importance (clinical utility) of symptoms can be provided. The single most important symptom for BSE is photosensibility.
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.
Spontaneously broken spacetime symmetries and Goldstone's theorem.
Low, Ian; Manohar, Aneesh V
2002-03-11
Goldstone's theorem states that there is a massless mode for each broken symmetry generator. It has been known for a long time that the naive generalization of this counting fails to give the correct number of massless modes for spontaneously broken spacetime symmetries. We explain how to get the right count of massless modes in the general case, and discuss examples involving spontaneously broken Poincaré and conformal invariance.
Infinite flag varieties and conjugacy theorems
Peterson, Dale H.; Kac, Victor G.
1983-01-01
We study the orbit of a highest-weight vector in an integrable highest-weight module of the group G associated to a Kac-Moody algebra [unk](A). We obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of [unk](A). In particular, we prove conjugacy theorems for Cartan and Borel subalgebras of [unk](A), so that the Cartan matrix A is an invariant of [unk](A). PMID:16593298
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.
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.
Asynchronous networks: modularization of dynamics theorem
NASA Astrophysics Data System (ADS)
Bick, Christian; Field, Michael
2017-02-01
Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or dynamical modules. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network: the modularization of dynamics theorem. We give examples to illustrate the main results.
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.
Haag's Theorem and Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Edwin
2017-01-01
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
Cueto-Rojas, H F; Maleki Seifar, R; Ten Pierick, A; van Helmond, W; Pieterse M, M; Heijnen, J J; Wahl, S A
2016-09-16
Ammonium is the most common N-source for yeast fermentations. Although, its transport and assimilation mechanisms are well documented, there have been only few attempts to measure the in vivo intracellular concentration of ammonium and assess its impact on gene expression. Using an isotope dilution mass spectrometry (IDMS)-based method we were able to measure the intracellular ammonium concentration in N-limited aerobic chemostat cultivations using three different N-sources (ammonium, urea and glutamate) at the same growth rate (0.05 h(-1)). The experimental results suggest that, at this growth rate, a similar concentration of intracellular ammonium, about 3.6 mmol NH4(+)/LIC, is required to supply the reactions in the central N-metabolism independent of the N-source. Based on the experimental results and different assumptions, the vacuolar and cytosolic ammonium concentrations were estimated. Furthermore, we identified a futile cycle caused by NH3 leakage to the extracellular space, which can cost up to 30% of the ATP production of the cell under N-limited conditions, and a futile redox cycle between reactions Gdh1 and Gdh2. Finally, using shotgun proteomics with labeled reference-relative protein expression, differences between the various environmental conditions were identified and correlated with previously identified N-compound sensing mechanisms.
Yin, Hai-wei; Kong, Fan-hua; Luo, Zhen-dong; Yan, Wei-jiao; Sun, Chang-feng; Xu, Feng
2013-08-01
The suitability assessment of regional construction land is one of the important prerequisites for the spatial arrangement in regional planning, and also, the important foundation for the reasonable utilization of regional land resources. With the support of GIS, and by using the regional comprehensive strength and spatial accessibility analysis and the eco-environmental sensitivity analysis, this paper quantitatively analyzed the development potential and its ecological limitation of the central and southern parts of Hebei Province. Besides, based on the cost-benefit analysis, the potential-limitation model was accordingly developed, and the three land suitability scenarios under different developmental concepts were captured through the interaction matrix. The results indicated that both the comprehensive strength and the development potential of the study area showed a primacy distribution pattern, and presented an obvious pole-axis spatial pattern. The areas with higher eco-environmental sensitivity were mainly distributed in the west regions, while those with lower eco-environmental sensitivity were in the east regions. Regional economic development concept had important effects on the regional ecological security pattern and urban growth. The newly developed principles and methods for the land suitability assessment in this paper could not only scientifically realize the spatial grid of regional development potential and capture the future land development trend and spatial distribution, but also provide scientific basis and effective ways for urban and regional planning to realize region 'smart growth' and 'smart conservation'.
Towards a no-lose theorem for naturalness
NASA Astrophysics Data System (ADS)
Curtin, David; Saraswat, Prashant
2016-03-01
We derive a phenomenological no-lose theorem for naturalness up to the TeV scale, which applies when quantum corrections to the Higgs mass from top quarks are canceled by perturbative beyond Standard Model (BSM) particles (top partners) of similar multiplicity due to to some symmetry. Null results from LHC searches already seem to disfavor such partners if they are colored. Any partners with SM charges and ˜TeV masses will be exhaustively probed by the LHC and a future 100 TeV collider. Therefore, we focus on neutral top partners. While these arise in twin Higgs theories, we analyze neutral top partners as model-independently as possible using effective field theory and simplified model methods. We classify all perturbative neutral top partner structures in order to compute their irreducible low-energy signatures at proposed future lepton and hadron colliders, as well as the irreducible tunings suffered in each scenario. Central to our theorem is the assumption that SM-charged BSM states appear in the UV completion of neutral naturalness, which is the case in all known examples. Direct production at the 100 TeV collider then allows this scale to be probed at the ˜10 TeV level. We find that proposed future colliders probe any such scenario of naturalness with tuning of 10% or better. This provides very strong model-independent motivation for both new lepton and hadron colliders, which in tandem act as discovery machines for general naturalness. We put our results in context by discussing other possibilities for naturalness, including "swarms" of top partners, inherently nonperturbative or exotic physics, or theories without SM-charged states in the UV completion. Realizing a concrete scenario which avoids our arguments while still lacking experimental signatures remains an open model-building challenge.
Flores, Noemí; Olvera, Maricela; Sigala, Juan Carlos; Gosset, Guillermo; Morett, Enrique; Bolívar, Francisco
2009-01-01
The phosphoenolpyruvate: carbohydrate transferase system (PTS) transports glucose in Escherichia coli. Previous work demonstrated that strains lacking PTS, such as PB11, grow slow on glucose. PB11 has a reduced expression of glycolytic, and upregulates poxB and acs genes as compared to the parental strain JM101, when growing on glucose. The products of the latter genes are involved in the production of AcetylCoA. Inactivation of rpoS that codes for the RNA polymerase σ38 subunit, reduces further (50%) growth of PB11, indicating that σ38 plays a central role in the expression of central metabolism genes in slowly growing cells. In fact, transcription levels of glycolytic genes is reduced in strain PB11rpoS− as compared to PB11. In this report we studied the role of σ70 and σ38 in the expression of the complete glycolytic pathway and poxB and acs genes in certain PTS− strains and their rpoS− derivatives. We determined the transcription start sites (TSSs) and the corresponding promoters, in strains JM101, PB11, its derivative PB12 that recovered its growth capacity, and in their rpoS− derivatives, by 5′RACE and pyrosequencing. In all these genes the presence of sequences resembling σ38 recognition sites allowed the proposition that they could be transcribed by both sigma factors, from overlapping putative promoters that initiate transcription at the same site. Fourteen new TSSs were identified in seventeen genes. Besides, more than 30 putative promoters were proposed and we confirmed ten previously reported. In vitro transcription experiments support the functionality of putative dual promoters. Alternatives that could also explain lower transcription levels of the rpoS− derivatives are discussed. We propose that the presence if real, of both σ70 and σ38 dependent promoters in all glycolytic genes and operons could allow a differential transcription of these central metabolism genes by both sigma subunits as an adaptation response to carbon
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.
Index theorem for topological excitations on R3 × S1 and Chern-Simons theory
NASA Astrophysics Data System (ADS)
Poppitz, Erich; Ünsal, Mithat
2009-03-01
We derive an index theorem for the Dirac operator in the background of various topological excitations on an R3 × S1 geometry. The index theorem provides more refined data than the APS index for an instanton on R4 and reproduces it in decompactification limit. In the R3 limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the η-invariant associated with the boundary Dirac operator. Neither topological charge nor η-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 S1, confined) phases of gauge theories, center stabilized Yang-Mills theories with vector-like or chiral matter (at S1 of any size), and supersymmetric gauge theories with supersymmetry-preserving boundary conditions (also at any S1). 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 S1 regime.
The van Cittert-Zernike theorem for electromagnetic fields.
Ostrovsky, Andrey S; Martínez-Niconoff, Gabriel; Martínez-Vara, Patricia; Olvera-Santamaría, Miguel A
2009-02-02
The van Cittert-Zernike theorem, well known for the scalar optical fields, is generalized for the case of vector electromagnetic fields. The deduced theorem shows that the degree of coherence of the electromagnetic field produced by the completely incoherent vector source increases on propagation whereas the degree of polarization remains unchanged. The possible application of the deduced theorem is illustrated by an example of optical simulation of partially coherent and partially polarized secondary source with the controlled statistical properties.
Borsuk-Ulam theorem in infinite-dimensional Banach spaces
NASA Astrophysics Data System (ADS)
Gel'man, B. D.
2002-02-01
The well-known classical Borsuk-Ulam theorem has a broad range of applications to various problems. Its generalization to infinite-dimensional spaces runs across substantial difficulties because its statement is essentially finite-dimensional. A result established in the paper is a natural generalization of the Borsuk-Ulam theorem to infinite-dimensional Banach spaces. Applications of this theorem to various problems are discussed.
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)…
A qualitative approach to Bayes' theorem.
Medow, Mitchell A; Lucey, Catherine R
2011-12-01
While decisions made according to Bayes' theorem are the academic normative standard, the theorem is rarely used explicitly in clinical practice. Yet the principles can be followed without intimidating mathematics. To do so, one can first categorise the prior-probability of the disease being tested for as very unlikely (less likely than 10%), unlikely (10-33%), uncertain (34-66%), likely (67-90%) or very likely (more likely than 90%). Usually, for disorders that are very unlikely or very likely, no further testing is needed. If the prior probability is unlikely, uncertain or likely, a test and a Bayesian-inspired update process incorporating the result can help. A positive result of a good test increases the probability of the disorder by one likelihood category (eg, from uncertain to likely) and a negative test decreases the probability by one category. If testing is needed to escape the extremes of likelihood (eg, a very unlikely but particularly dangerous condition or in the circumstance of population screening, or a very likely condition with a particularly noxious treatment), two tests may be needed to achieve. Negative results of tests with sensitivity ≥99% are sufficient to rule-out a diagnosis; positive results of tests with specificity ≥99% are sufficient to rule-in a diagnosis. This method overcomes some common heuristic errors: ignoring the base rate, probability adjustment errors and order effects. The simplicity of the method, while still adhering to the basic principles of Bayes' theorem, has the potential to increase its application in clinical practice.
Stochastic thermodynamics, fluctuation theorems and molecular machines.
Seifert, Udo
2012-12-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Stochastic thermodynamics, fluctuation theorems and molecular machines
NASA Astrophysics Data System (ADS)
Seifert, Udo
2012-12-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
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.
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.
Generalizations of Brandl's theorem on Engel length
NASA Astrophysics Data System (ADS)
Quek, S. G.; Wong, K. B.; Wong, P. C.
2013-04-01
Let n < m be positive integers such that [g,nh] = [g,mh] and assume that n and m are chosen minimal with respect to this property. Let gi = [g,n+ih] where i = 1,2,…,m-n. Then π(g,h) = (g1,…,gm-n) is called the Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.
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.
Fluctuation theorem in dynamical systems with quenched disorder
NASA Astrophysics Data System (ADS)
Drocco, Jeffrey; Olson Reichhardt, Cynthia; Reichhardt, Charles
2010-03-01
We demonstrate that the fluctuation theorem of Gallavotti and Cohen can be used to characterize far from equilibrium dynamical nonthermal systems in the presence of quenched disorder where strong fluctuations or crackling noise occur. By observing the frequency of entropy-destroying trajectories, we show that the theorem holds in specific dynamical regimes near the threshold for motion, indicating that these systems might be ideal candidates for understanding what types of nonthermal fluctuations could be used in constructing generalized fluctuation theorems. We also discuss how the theorem could be tested with global or local probes in systems such as superconducting vortices, magnetic domain walls, stripe phases, Coulomb glasses and earthquake models.
Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics
NASA Astrophysics Data System (ADS)
Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.
2008-11-01
In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.
Equipartition theorem and the dynamics of liquids
Levashov, Valentin A.; Egami, Takeshi; Aga, Rachel S; Morris, James R
2008-01-01
In liquids, phonons have a very short lifetime and the total potential energy does not depend linearly on temperature. Thus it may appear that atomic vibrations in liquids cannot be described by the harmonic-oscillator model and that the equipartition theorem for the potential energy is not upheld. In this paper we show that the description of the local atomic dynamics in terms of the atomic-level stresses provides such a description, satisfying the equipartition theorem. To prove this point we carried out molecular-dynamics simulations with several pairwise potentials, including the Lennard-Jones potential, the modified Johnson potential, and the repulsive part of the Johnson potential, at various particle number densities. In all cases studied the total self-energy of the atomic-level stresses followed the (3/2)kBT law. From these results we suggest that the concept of local atomic stresses can provide description of thermodynamic properties of glasses and liquids on the basis of harmonic atomistic excitations. An example of application of this approach to the description of the glass transition temperature in metallic glasses is discussed.
On the inversion of Fueter's theorem
NASA Astrophysics Data System (ADS)
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2016-10-01
The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space R n + 1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension n. The present work extends the result to all dimensions n by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function f defined in a suitable open set in R n + 1, where n is a positive integer, we can find a slice hyperholomorphic function f → such that f =Δ (n - 1) / 2 f →. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.
Bell's theorem, inference, and quantum transactions
NASA Astrophysics Data System (ADS)
Garrett, A. J. M.
1990-04-01
Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, “local”) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's new transactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the “delayed choice” experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theorem reinforces arguments in favor of hidden variables.
De Finetti Theorem on the CAR Algebra
NASA Astrophysics Data System (ADS)
Crismale, Vitonofrio; Fidaleo, Francesco
2012-10-01
The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend the De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self-containing interest.
Saludes, P; Proença, L; Gruartmoner, G; Enseñat, L; Pérez-Madrigal, A; Espinal, C; Mesquida, J
2016-11-10
Central venous-to-arterial carbon dioxide difference (PcvaCO2) has demonstrated its prognostic value in critically ill patients suffering from shock, and current expert recommendations advocate for further resuscitation interventions when PcvaCO2 is elevated. PcvaCO2 combination with arterial-venous oxygen content difference (PcvaCO2/CavO2) seems to enhance its performance when assessing anaerobic metabolism. However, the fact that PCO2 values might be altered by changes in blood O2 content (the Haldane effect), has been presented as a limitation of PCO2-derived variables. The present study aimed at exploring the impact of hyperoxia on PcvaCO2 and PcvaCO2/CavO2 during the early phase of shock. Prospective interventional study. Ventilated patients suffering from shock within the first 24 h of ICU admission. Patients requiring FiO2 ≥ 0.5 were excluded. At inclusion, simultaneous arterial and central venous blood samples were collected. Patients underwent a hyperoxygenation test (5 min of FiO2 100%), and arterial and central venous blood samples were repeated. Oxygenation and CO2 variables were calculated at both time points. Twenty patients were studied. The main cause of shock was septic shock (70%). The hyperoxygenation trial increased oxygenation parameters in arterial and venous blood, whereas PCO2 only changed at the venous site. Resulting PcvaCO2 and PcvaCO2/CavO2 significantly increased [6.8 (4.9, 8.1) vs. 7.6 (6.7, 8.5) mmHg, p 0.001; and 1.9 (1.4, 2.2) vs. 2.3 (1.8, 3), p < 0.001, respectively]. Baseline PcvaCO2, PcvaCO2/CavO2 and ScvO2 correlated with the magnitude of PO2 augmentation at the venous site within the trial (ρ -0.46, p 0.04; ρ 0.6, p < 0.01; and ρ 0.7, p < 0.001, respectively). Increased PcvaCO2/CavO2 values were associated with higher mortality in our sample [1.46 (1.21, 1.89) survivors vs. 2.23 (1.86, 2.8) non-survivors, p < 0.01]. PcvaCO2 and PcvaCO2/CavO2 are influenced by oxygenation changes not related to flow. Elevated
Caprioli, Riccardo; Cargini, Daniele; Marcacci, Maurilia; Cammà, Cesare; Giansante, Carla; Ferri, Nicola
2013-03-26
Crayfish plague, caused by the oomycete Aphanomyces astaci, is a serious disease of European freshwater crayfish and has eliminated entire populations in several European countries. In September 2011, mortality was observed among the Austropotamobius pallipes population of a river basin in the Abruzzi region (central Italy), and A. astaci DNA was detected by PCR in dead crayfish. A systematic survey was carried out to evaluate the spread and the effects of the plague in the river basin. The source of the outbreak remained unknown since North American crayfish species, which frequently act as subclinical carriers of the infection, were not detected in the area. The A. pallipes population disappeared from a river stretch of ~1 km, where A. astaci infection was detected in dead crayfish. However, apparently unaffected crayfish were still present upstream of that area as well as in a tributary that joined the brook in the apparently depopulated stretch. A. astaci infection was not detected in dead individuals collected in the upstream area and tributary. A follow-up visit conducted in the following season showed the presence of A. pallipes in the river stretch hit by the plague. In this outbreak, the spread of the infection could have been limited by a low density of the crayfish population and by the geographic conformation of the river basin, which includes a dense network of small tributaries, characterized by high flow velocity and low water temperature. In this particular setting, crayfish plague outbreaks can remain undetected. This underlines the importance of active monitoring programs aimed at the prompt recognition of both episodes of mortality and the presence of non-indigenous crayfish species.
NASA Astrophysics Data System (ADS)
Gaines, K.; Meinzer, F. C.; Duffy, C.; Thomas, E.; Eissenstat, D. M.
2014-12-01
Water uptake and retention by trees affects their ability to cope with drought, as well as influences ground water recharge and stream flow. Historically, water has not often been limiting in Eastern U.S. forests. As a result, very little work has been done to understand the basics of timing of water use by vegetation in these systems. As droughts are projected to increase in length and severity in future decades, this focus is increasingly important, particularly for informing hydrologic models. We used deuterium tracer and sap flux techniques to study tree water transport on a forested ridge top with shallow soil in central Pennsylvania. Three trees of each of the species, Acer saccharum, Carya tomentosa, Quercus prinus, and Quercus rubrum were accessed by tree climbing and scaffolding towers. We hypothesized that contrasting vessel size of the tree species would affect the efficiency of water transport (tracer velocity) and contrasting tree size would affect tracer storage as estimated by tracer residence times. Trees were injected with deuterated water in July 2012. Leaves were sampled 15 times over 35 days, initially daily for the first week, then at regular intervals afterwards. The tracer arrived in the canopy of the study trees between 1 and 7 days after injection, traveling at a velocity of 2 to 19 m d-1. The tracer residence time was between 7 and 33 days. Although there was variation in tracer velocity and residence time in individual trees, there were no significant differences among wood types or species (P>0.05). The general patterns in timing of water use were similar to other studies on angiosperm trees in tropical and arid ecosystems. There was no evidence of longer residence times in the larger trees. Sap flux-based estimates of sap velocity were much lower than tracer estimates, which was consistent with other studies. Levels of sap flux and midday water potential measurements suggested that the trees were water-stressed. We observed relatively
Group Theoretical Interpretation of von Neumann's Theorem on Composite Systems.
ERIC Educational Resources Information Center
Bergia, S.; And Others
1979-01-01
Shows that von Neumann's mathematical theorem on composite systems acquires a transparent physical meaning with reference to a suitable physical example; a composite system in a state of definite angular momentum. Gives an outline of the theorem, and the results are restated in Dirac's notation, thus generalizing von Neumann's results which were…
Generalizations of Karp's theorem to elastic scattering theory
NASA Astrophysics Data System (ADS)
Tuong, Ha-Duong
Karp's theorem states that if the far field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle in R2 is invariant under the group of rotations, then the scatterer is a circle. The theorem is generalized to the elastic scattering problems and the axisymmetric scatterers in R3.
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…
Unique Factorization and the Fundamental Theorem of Arithmetic
ERIC Educational Resources Information Center
Sprows, David
2017-01-01
The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a…
On Euler's Theorem for Homogeneous Functions and Proofs Thereof.
ERIC Educational Resources Information Center
Tykodi, R. J.
1982-01-01
Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)
Solving boundary-value electrostatics problems using Green's reciprocity theorem
NASA Astrophysics Data System (ADS)
Hu, Ben Yu-Kuang
2001-12-01
Formal solutions to electrostatics boundary-value problems are derived using Green's reciprocity theorem. This method provides a more transparent interpretation of the solutions than the standard Green's function derivation. An energy-based argument for the reciprocity theorem is also presented.
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2009-02-20
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
Leaning on Socrates to Derive the Pythagorean Theorem
ERIC Educational Resources Information Center
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…
On the Weighted Mean Value Theorem for Integrals
ERIC Educational Resources Information Center
Polezzi, M.
2006-01-01
The Mean Value Theorem for Integrals is a powerful tool, which can be used to prove the Fundamental Theorem of Calculus, and to obtain the average value of a function on an interval. On the other hand, its weighted version is very useful for evaluating inequalities for definite integrals. This article shows the solutions on applying the weighted…
Interactive Theorem Finding through Continuous Variation of Geometric Configurations.
ERIC Educational Resources Information Center
Schumann, Heinz
1991-01-01
Described and evaluated are microcomputers as a tool for construction in geometry education and heuristic theorem finding through interactive continuous variation of geometric configurations. Numerous examples of theorem finding processes are provided using the prototype graphics system CABRI-Geometer. (MDH)
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.
Precise Calibration of the Virial Theorem from Hubble Volume Cluster Catalogs
NASA Astrophysics Data System (ADS)
Evrard, A. E.; Horikawa, T.; Virgo Consortium Collaboration
2000-10-01
The Hubble Volume project of the Virgo Consortium has created 109 particle N-body simulations of large-scale structure formation in ΛCDM and τCDM cosmologies with resolution sufficient to define a virtual Coma cluster with 500 particles. Light-cone survey output from the simulations provide synthetic sky surveys of the dark matter distribution in very large cosmic volumes, ~ 1010 h-3 Mpc3. Cluster catalogs derived from the surveys contain 100,000 to 500,000 clusters with masses exceeding 5 x 1013 h-1 Msun and redshifts extending to z ~ 2. We analyse in detail the virial relation between dark matter mass MΔ c and velocity dispersion σ . We find a unified calibration of the relation in the form H(z) MΔ c = A σ p for which the amplitude A and slope p are independent of cosmology and/or epoch (H(z) is the Hubble parameter at redshift z). This holds for clusters whose properties are defined within a spherical region encompassing a fixed density contrast Δ c (typically 200) with respect to the critical density. Other definitions of clusters require a redshift dependent amplitude A(z). The scatter in σ at fixed H(z) M about the mean relation is small ( ~ 6%) and positively skewed. Subdividing the population into two classes --- `parents' and `children' --- we identify the minority child component as the source of the skewness and infer that the children are merger debris that has not yet been fully incorporated into the parent population. For the parents alone, the probability distribution function of the velocity dispersion residuals is very well modeled by a Gaussian distribution, suggesting a central limit theorem interpretation. The accuracy of the calibration will be addressed by examining Virgo simulations with higher mass resolution and smaller volumes. Connections to obervable measures --- cluster X-ray temperature and galaxy velocity dispersion --- will be briefly discussed.
Merits and qualms of work fluctuations in classical fluctuation theorems
NASA Astrophysics Data System (ADS)
Deng, Jiawen; Tan, Alvis Mazon; Hänggi, Peter; Gong, Jiangbin
2017-01-01
Work is one of the most basic notions in statistical mechanics, with work fluctuation theorems being one central topic in nanoscale thermodynamics. With Hamiltonian chaos commonly thought to provide a foundation for classical statistical mechanics, here we present general salient results regarding how (classical) Hamiltonian chaos generically impacts on nonequilibrium work fluctuations. For isolated chaotic systems prepared with a microcanonical distribution, work fluctuations are minimized and vanish altogether in adiabatic work protocols. For isolated chaotic systems prepared at an initial canonical distribution at inverse temperature β , work fluctuations depicted by the variance of e-β W are also minimized by adiabatic work protocols. This general result indicates that, if the variance of e-β W diverges for an adiabatic work protocol, it diverges for all nonadiabatic work protocols sharing the same initial and final Hamiltonians. Such divergence is hence not an isolated event and thus greatly impacts on the efficiency of using Jarzynski's equality to simulate free-energy differences. Theoretical results are illustrated in a Sinai model. Our general insights shall boost studies in nanoscale thermodynamics and are of fundamental importance in designing useful work protocols.
Merits and qualms of work fluctuations in classical fluctuation theorems.
Deng, Jiawen; Tan, Alvis Mazon; Hänggi, Peter; Gong, Jiangbin
2017-01-01
Work is one of the most basic notions in statistical mechanics, with work fluctuation theorems being one central topic in nanoscale thermodynamics. With Hamiltonian chaos commonly thought to provide a foundation for classical statistical mechanics, here we present general salient results regarding how (classical) Hamiltonian chaos generically impacts on nonequilibrium work fluctuations. For isolated chaotic systems prepared with a microcanonical distribution, work fluctuations are minimized and vanish altogether in adiabatic work protocols. For isolated chaotic systems prepared at an initial canonical distribution at inverse temperature β, work fluctuations depicted by the variance of e^{-βW} are also minimized by adiabatic work protocols. This general result indicates that, if the variance of e^{-βW} diverges for an adiabatic work protocol, it diverges for all nonadiabatic work protocols sharing the same initial and final Hamiltonians. Such divergence is hence not an isolated event and thus greatly impacts on the efficiency of using Jarzynski's equality to simulate free-energy differences. Theoretical results are illustrated in a Sinai model. Our general insights shall boost studies in nanoscale thermodynamics and are of fundamental importance in designing useful work protocols.
Splitting theorem for Z2n -supermanifolds
NASA Astrophysics Data System (ADS)
Covolo, Tiffany; Grabowski, Janusz; Poncin, Norbert
2016-12-01
Smooth Z2n -supermanifolds have been introduced and studied recently. The corresponding sign rule is given by the 'scalar product' of the involved Z2n -degrees. It exhibits interesting changes in comparison with the sign rule using the parity of the total degree. With the new rule, nonzero degree even coordinates are not nilpotent, and even (resp., odd) coordinates do not necessarily commute (resp., anticommute) pairwise. The classical Batchelor-Gawȩdzki theorem says that any smooth supermanifold is diffeomorphic to the 'superization' ΠE of a vector bundle E. It is also known that this result fails in the complex analytic category. Hence, it is natural to ask whether an analogous statement goes through in the category of Z2n -supermanifolds with its local model made of formal power series. We give a positive answer to this question.
Differential diagnosis in immunohistochemistry with Bayes theorem.
Vollmer, Robin T
2009-05-01
When immunohistochemical stains that are specific for specific tumor diagnoses do not yield diagnostic results, we often turn to less specific immunohistochemical stains and consider the resulting lists of possible tumor types. Typically, such lists are ordered according to tumor sensitivities for the stains. In probability terminology, sensitivity is the conditional probability of a positive stain given a specific tumor. Yet, the most useful probability to know is the probability of a specific tumor diagnosis, given a set of staining results. Bayes theorem provides this probability. To illustrate its use for differential diagnosis, I apply it here to the situation of carcinomas of uncertain primary site and use the information provided by stains for cytokeratin 7 and cytokeratin 20.
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.
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.
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
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.
Quantum violation of fluctuation-dissipation theorem
NASA Astrophysics Data System (ADS)
Shimizu, Akira; Fujikura, Kyota
2017-02-01
We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a ‘squeezed equilibrium state’, which is macroscopically identical to the pre-measurement equilibrium state but is squeezed by the measurement. It is a time-evolving state, in which macrovariables fluctuate and relax. We also explain some of subtle but important points, careless treatments of which often lead to unphysical results, of the linear response theory.
NASA Astrophysics Data System (ADS)
Gong, Zongping; Quan, H. T.
2015-07-01
By taking full advantage of the dynamic property imposed by the detailed balance condition, we derive a new refined unified fluctuation theorem (FT) for general stochastic thermodynamic systems. This FT involves the joint probability distribution functions of the final phase-space point and a thermodynamic variable. Jarzynski equality, Crooks fluctuation theorem, and the FTs of heat as well as the trajectory entropy production can be regarded as special cases of this refined unified FT, and all of them are generalized to arbitrary initial distributions. We also find that the refined unified FT can easily reproduce the FTs for processes with the feedback control, due to its unconventional structure that separates the thermodynamic variable from the choices of initial distributions. Our result is heuristic for further understanding of the relations and distinctions between all kinds of FTs and might be valuable for studying thermodynamic processes with information exchange.
From the necessary to the possible: the genesis of the spin-statistics theorem
NASA Astrophysics Data System (ADS)
Blum, Alexander
2014-12-01
The spin-statistics theorem, which relates the intrinsic angular momentum of a single particle to the type of quantum statistics obeyed by a system of many such particles, is one of the central theorems in quantum field theory and the physics of elementary particles. It was first formulated in 1939/40 by Wolfgang Pauli and his assistant Markus Fierz. This paper discusses the developments that led up to this first formulation, starting from early attempts in the late 1920s to explain why charged matter particles obey Fermi-Dirac statistics, while photons obey Bose-Einstein statistics. It is demonstrated how several important developments paved the way from such general philosophical musings to a general (and provable) theorem, most notably the use of quantum field theory, the discovery of new elementary particles, and the generalization of the notion of spin. It is also discussed how the attempts to prove a spin-statistics connection were driven by Pauli from formal to more physical arguments, culminating in Pauli's 1940 proof. This proof was a major success for the beleaguered theory of quantum field theory and the methods Pauli employed proved essential for the renaissance of quantum field theory and the development of renormalization techniques in the late 1940s.
On soft limits of inflationary correlation functions
NASA Astrophysics Data System (ADS)
Assassi, Valentin; Baumann, Daniel; Green, Daniel
2012-11-01
Soft limits of inflationary correlation functions are both observationally relevant and theoretically robust. Various theorems can be proven about them that are insensitive to detailed model-building assumptions. In this paper, we re-derive several of these theorems in a universal way. Our method makes manifest why soft limits are such an interesting probe of the spectrum of additional light fields during inflation. We illustrate these abstract results with a detailed case study of the soft limits of quasi-single-field inflation.
NASA Astrophysics Data System (ADS)
Rayback, S. A.; Shrestha, K. B.; Hofgaard, A.
2015-12-01
Recent evidence indicates changing climatological conditions in the Nepalese Himalayas including decreasing precipitation, a weakening Indian monsoon and rising temperatures. Trees and shrubs found at treeline are considered to be highly sensitive to climate, but the climatic effects on these ecotone species in the Himalayas are not well understood. Dendrochronological techniques applied to co-occurring shrubs and trees up-and down-slope of treeline extend our understanding of vegetation response at range margins and into tree-less environments. We developed tree-ring width and annual height increment chronologies for Abies spectabilis (Himalayan fir) and the first annual growth increment and annual production of leaves chronologies for Cassiope fastigata (Himalayan heather) at a high elevation site in central Nepal. C. fastigata chronologies showed moisture availability in late pre-monsoon and monsoon seasons of the previous year are critical to stem elongation and leaf production (AGI and previous May-August SPEI-12, r = 0.790; LEAF and previous June-September SPEI-12, r = 0.708) A. spectabilis chronologies were significantly and negatively correlated with monsoon season temperature during the current year (tree-ring width and June mean temperature, r = -0.677; height-increment and Sept maximum temperature, r = -0.605). In addition to both long-term and recent declines in moisture in the Himalayas, moisture deficit may be further exacerbated at high elevation sites via run-off and higher levels of evapotranspiration resulting in growth reductions, dieback and even death of these species. These results highlight that not all mid-latitude, high elevation treelines are limited by temperature as previously thought and that severe drought stress may initiate downslope treeline retraction. Understanding the response of co-occurring tree and shrub species to climate, now and in the future, may help to elucidate the physiological mechanisms controlling local and
Generalized Optical Theorem Detection in Random and Complex Media
NASA Astrophysics Data System (ADS)
Tu, Jing
The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar
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.
Fluctuation theorem for Hamiltonian systems: Le Chatelier's principle.
Evans, D J; Searles, D J; Mittag, E
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle
NASA Astrophysics Data System (ADS)
Evans, Denis J.; Searles, Debra J.; Mittag, Emil
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
Spin groups of super metrics and a theorem of Rogers
NASA Astrophysics Data System (ADS)
Fulp, Ronald
2017-01-01
We derive the canonical forms of super Riemannian metrics and the local isometry groups of such metrics. For certain super metrics we also compute the simply connected covering groups of the local isometry groups and interpret these as local spin groups of the super metric. Super metrics define reductions OSg of the relevant frame bundle. When principal bundles S˜g exist with structure group the simply connected covering group G ˜ of the structure group of OSg , representations of G ˜ define vector bundles associated to S˜g whose sections are "spinor fields" associated with the super metric g . Using a generalization of a Theorem of Rogers, which is itself one of the main results of this paper, we show that for super metrics we call body reducible, each such simply connected covering group G ˜ is a super Lie group with a conventional super Lie algebra as its corresponding super Lie algebra. Some of our results were known to DeWitt (1984) using formal Grassmann series and others were known by Rogers using finitely many Grassmann generators and passing to a direct limit. We work exclusively in the category of G∞ supermanifolds with G∞ mappings. Our supernumbers are infinite series of products of Grassmann generators subject to convergence in the ℓ1 norm introduced by Rogers (1980, 2007).
The Pythagorean Theorem and the Solid State
NASA Astrophysics Data System (ADS)
Kelly, Brenda S.; Splittgerber, Allen G.
2005-05-01
Solid-state parameters such as radius ratios, packing efficiencies, and crystal densities may be calculated for various crystal structures from basic Euclidean geometry relating to the Pythagorean theorem of right triangles. Because simpler cases are often discussed in the standard inorganic chemistry texts, this article only presents calculations for closest-packed A-type lattices (one type of particle) and several compound AB lattices (A and B particles) including sodium chloride, cesium chloride, zinc blende (sphalerite), wurtzite, and fluorite. For A-type metallic crystals, the use of recommended values of atomic radii results in calculated densities within 1% of observed values. For AB lattices, assuming ionic crystals, the use of recommended values of ionic radii results in density determinations that are usually but not always close to observed values. When there is covalent character to the bonding, the use of covalent radii results in calculated densities that correlate well with observed values. If interionic or interatomic spacings are used, the calculated densities are always close to the observed values. As indicated by a survey of the standard inorganic texts, these calculations are generally not presented. However, as an illustration of the application of simple mathematical principles to the study of chemistry, discussion of the methods presented in this manuscript may be of value in classroom presentations pertaining to the solid state.
Digital superresolution and the generalized sampling theorem
NASA Astrophysics Data System (ADS)
Prasad, Sudhakar
2007-02-01
The technique of reconstructing a higher-resolution (HR) image of size ML×ML by digitally processing L×L subpixel-shifted lower-resolution (LR) copies of it, each of size M×M, has now become well established. This particular digital superresolution problem is analyzed from the standpoint of the generalized sampling theorem. It is shown both theoretically and by computer simulation that the choice of regularly spaced subpixel shifts for the LR images tends to maximize the robustness and minimize the error of reconstruction of the HR image. In practice, since subpixel-level control of LR image shifts may be nearly impossible to achieve, however, a more likely scenario, which is also discussed, is one involving random subpixel shifts. It is shown that without reasonably tight bounds on the range of random shifts, the reconstruction is likely to fail in the presence of even small amounts of noise unless either reliable prior information or additional data are available.
On the Spin-Statistics Theorem
NASA Astrophysics Data System (ADS)
Peshkin, Murray
2002-05-01
M.V. Berry and J.M. Robbins* (B) have explained the spin-statistics theorem (SST) within nonrelativistic quantum mechanics (QM), without using relativity or field theory. For two identical spinless particles, their starting point is a coordinate space which consists of unordered pairs r,r' where r and r' represent two points in space, not particle labels. The point r,r' is the point r',r\\. That has topological consequences for the 6D configuration space and for the wave functions |r,r'>. More generally, spin variables are appended and there are N vectors. B gave a beautiful mathematical analysis to go from there to the usual SST under stated assumptions of QM. They also explored alternative assumptions that give unusual results but that may not be physical. I seek additional insight by recasting B's analysis into a form that emphasizes the relative orbital angular momenta of pairs of particles. I report here on the spinless case, where boson statistics emerges in a transparent way. This approach appears to exclude unusual possibilities. Work supported by U.S. DOE contract W-31-109-ENG-38. *Proc. R. Soc. Lond. A 453, 1771 (1997).
Nonequilibrium fluctuation theorems in the presence of local heating
NASA Astrophysics Data System (ADS)
Pradhan, Punyabrata; Kafri, Yariv; Levine, Dov
2008-04-01
We study two nonequilibrium work fluctuation theorems, the Crooks theorem and the Jarzynski equality, for a test system coupled to a spatially extended heat reservoir whose degrees of freedom are explicitly modeled. The sufficient conditions for the validity of the theorems are discussed in detail and compared to the case of classical Hamiltonian dynamics. When the conditions are met the fluctuation theorems are shown to hold despite the fact that the immediate vicinity of the test system goes out of equilibrium during an irreversible process. We also study the effect of the coupling to the heat reservoir on the convergence of ⟨exp(-βW)⟩ to its theoretical mean value, where W is the work done on the test system and β is the inverse temperature. It is shown that the larger the local heating, the slower the convergence.
Generalized Browder's and Weyl's theorems for Banach space operators
NASA Astrophysics Data System (ADS)
Curto, Raúl E.; Han, Young Min
2007-12-01
We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of [sigma](T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f[set membership, variant]H((T)), the space of functions analytic on an open neighborhood of [sigma](T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f[set membership, variant]H([sigma](T)).
Gibbs Paradox Revisited from the Fluctuation Theorem with Absolute Irreversibility
NASA Astrophysics Data System (ADS)
Murashita, Yûto; Ueda, Masahito
2017-02-01
The inclusion of the factor ln (1 /N !) in the thermodynamic entropy proposed by Gibbs is shown to be equivalent to the validity of the fluctuation theorem with absolute irreversibility for gas mixing.
The Pythagorean Theorem: II. The infinite discrete case
Kadison, Richard V.
2002-01-01
The study of the Pythagorean Theorem and variants of it as the basic result of noncommutative, metric, Euclidean Geometry is continued. The emphasis in the present article is the case of infinite discrete dimensionality. PMID:16578869
Comparison theorems for neutral stochastic functional differential equations
NASA Astrophysics Data System (ADS)
Bai, Xiaoming; Jiang, Jifa
2016-05-01
The comparison theorems under Wu and Freedman's order are proved for neutral stochastic functional differential equations with finite or infinite delay whose drift terms satisfy the quasimonotone condition and diffusion term is the same.
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.
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.
A Computer Science Version of Goedel’s Theorem.
1983-08-01
The author presents a simplified proof of Godel’s theorem by appealing to well-known programming concepts. The significance of Goedel’s result to computer science , mathematics and logic is discussed. (Author)
Two time physics and Hamiltonian Noether theorem for gauge systems
Nieto, J. A.; Ruiz, L.; Silvas, J.; Villanueva, V. M.
2006-09-25
Motivated by two time physics theory we revisited the Noether theorem for Hamiltonian constrained systems. Our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints.
Conformal frames and the validity of Birkhoff's theorem
NASA Astrophysics Data System (ADS)
Capozziello, S.; Sáez-Gómez, D.
2012-07-01
Birkhoff's theorem is one of the most important statements of Einstein's general relativity, which generally can not be extended to modified theories of gravity. Here we study the validity of the theorem in scalar-tensor theories using a perturbative approach, and compare the results in the so-called Einstein and Jordan frames. The implications of the results question the physical equivalence between both frames, at least in perturbations.
No-broadcasting theorem and its classical counterpart.
Kalev, Amir; Hen, Itay
2008-05-30
Although it is widely accepted that "no-broadcasting"-the nonclonability of quantum information-is a fundamental principle of quantum mechanics, an impossibility theorem for the broadcasting of general density matrices has not yet been formulated. In this Letter, we present a general proof for the no-broadcasting theorem, which applies to arbitrary density matrices. The proof relies on entropic considerations, and as such can also be directly linked to its classical counterpart, which applies to probabilistic distributions of statistical ensembles.
Levinson theorem for Aharonov-Bohm scattering in two dimensions
Sheka, Denis D.; Mertens, Franz G.
2006-11-15
We apply the recently generalized Levinson theorem for potentials with inverse-square singularities [Sheka et al., Phys. Rev. A 68, 012707 (2003)] to Aharonov-Bohm systems in two dimensions (2D). By this theorem, the number of bound states in a given mth partial wave is related to the phase shift and the magnetic flux. The results are applied to 2D soliton-magnon scattering.
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.
Nyquist-Shannon sampling theorem applied to refinements of the atomic pair distribution function
NASA Astrophysics Data System (ADS)
Farrow, Christopher L.; Shaw, Margaret; Kim, Hyunjeong; Juhás, Pavol; Billinge, Simon J. L.
2011-10-01
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.
NASA Astrophysics Data System (ADS)
Shargel, Benjamin Hertz; Chou, Tom
2009-10-01
Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics.
The PBR theorem: Whose side is it on?
NASA Astrophysics Data System (ADS)
Ben-Menahem, Yemima
2017-02-01
This paper examines the implications of the PBR theorem for the debate on the reality of the quantum state. The theorem seeks to undermine epistemic interpretations of the quantum state and support realist interpretations thereof, but there remains ambiguity about the precise nature of epistemic interpretations, and thus ambiguity about the implications of the theorem. The aim of this paper is to examine a radical epistemic interpretation that is not undermined by the theorem and is, arguably, strengthened by it. It is this radical interpretation, rather than the one assumed by the PBR theorem, that many epistemic theorists subscribe to. In order to distinguish the radical epistemic interpretation from alternative interpretations of quantum states-in particular, to distinguish it from instrumentalism-a historical comparison of different approaches to the meaning of quantum probabilities is provided. The comparison highlights, in particular, Schrödinger's work on the nature of quantum probabilities as distinct from probabilities in statistical mechanics, and the implications of this distinction for an epistemic interpretation of probability in the two areas. Schrödinger's work also helps to identify the difficulties in the PBR definition of an epistemic interpretation and is shown to anticipate the radical alternative that is not undermined by the theorem.
The HVT technique and the 'uncertainty' relation for central potentials
NASA Astrophysics Data System (ADS)
Grypeos, M. E.; Koutroulos, C. G.; Oyewumi, K. J.; Petridou, Th
2004-08-01
The quantum mechanical hypervirial theorems (HVT) technique is used to treat the so-called 'uncertainty' relation for quite a general class of central potential wells, including the (reduced) Poeschl-Teller and the Gaussian one. It is shown that this technique is quite suitable in deriving an approximate analytic expression in the form of a truncated power series expansion for the dimensionless product Pnl equiv langr2rangnllangp2rangnl/planck2, for every (deeply) bound state of a particle moving non-relativistically in the well, provided that a (dimensionless) parameter s is sufficiently small. Attention is also paid to a number of cases, among the limited existing ones, in which exact analytic or semi-analytic expressions for Pnl can be derived. Finally, numerical results are given and discussed.
Hahn, Noemi; Snedeker, Jesse; Rabagliati, Hugh
2015-12-01
Individuals with autism spectrum disorders (ASD) have often been reported to have difficulty integrating information into its broader context, which has motivated the Weak Central Coherence theory of ASD. In the linguistic domain, evidence for this difficulty comes from reports of impaired use of linguistic context to resolve ambiguous words. However, recent work has suggested that impaired use of linguistic context may not be characteristic of ASD, and is instead better explained by co-occurring language impairments. Here, we provide a strong test of these claims, using the visual world eye tracking paradigm to examine the online mechanisms by which children with autism resolve linguistic ambiguity. To address concerns about both language impairments and compensatory strategies, we used a sample whose verbal skills were strong and whose average age (7; 6) was lower than previous work on lexical ambiguity resolution in ASD. Participants (40 with autism and 40 controls) heard sentences with ambiguous words in contexts that either strongly supported one reading or were consistent with both (John fed/saw the bat). We measured activation of the unintended meaning through implicit semantic priming of an associate (looks to a depicted baseball glove). Contrary to the predictions of weak central coherence, children with ASD, like controls, quickly used context to resolve ambiguity, selecting appropriate meanings within a second. We discuss how these results constrain the generality of weak central coherence.
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.
Dynamical control of quantum systems in the context of mean ergodic theorems
NASA Astrophysics Data System (ADS)
Bernád, J. Z.
2017-02-01
Equidistant and non-equidistant single pulse ‘bang-bang’ dynamical controls are investigated in the context of mean ergodic theorems. We show the requirements in which the limit of infinite pulse control for both the equidistant and the non-equidistant dynamical control converges to the same unitary evolution. It is demonstrated that the generator of this evolution can be obtained by projecting the generator of the free evolution onto the commutant of the unitary operator representing the pulse. Inequalities are derived to prove this statement and in the case of non-equidistant approach these inequalities are optimised as a function of the time intervals.
Asymptotic behavior and Denjoy-Wolff theorems for Hilbert metric nonexpansive maps
NASA Astrophysics Data System (ADS)
Lins, Brian C.
We study the asymptotic behavior of fixed point free Hilbert metric nonexpansive maps on bounded convex domains. For such maps, we prove that the omega limit sets are contained in a convex subset of the boundary when the domain is either polyhedral or two dimensional. Similar results are obtained for several classes of positive operators defined on closed cones, including linear maps, affine linear maps, max-min operators, and reproduction-decimation operators. We discuss the relationship between these results and other Denjoy-Wolff type theorems. In particular, we investigate the interaction of nonexpansive maps with the horofunction boundary in the Hilbert geometry and in finite dimensional normed spaces.
The solution to the phase retrieval problem using the sampling theorem
NASA Astrophysics Data System (ADS)
Arsenault, H. H.; Chalasinska-Macukow, K.
1983-10-01
The 2D phase-retrieval problem is investigated analytically, and the solution is applied to an optics example. In the case considered, only the Fourier-transform modulus and the support of the object function are known. The approach taken is based on the Whittaker-Shannon sampling theorem (Goodman, 1968), using the sin c function as interpolator. The algorithm developed is shown to converge rapidly and give an accurate representation of band-limited objects if the two sampling grids are carefully chosen, as illustrated in a test calculation using a 5 x 5-pixel object.
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.
On local-hidden-variable no-go theorems
NASA Astrophysics Data System (ADS)
Methot, A. A.
2006-06-01
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow.
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.
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.
Remarks on asymptotic symmetries and the subleading soft photon theorem
NASA Astrophysics Data System (ADS)
Conde, Eduardo; Mao, Pujian
2017-01-01
A deep connection has been recently established between soft theorems and symmetries at null infinity in gravity and gauge theories, recasting the former as Ward identities of the latter. In particular, different orders (in the frequency of the soft particle) in the soft theorems are believed to be controlled by different asymptotic symmetries. In this paper we argue that this need not be the case by focusing on the soft photon theorem. We argue that the subleading soft factor follows from the same symmetry responsible for the leading one, namely certain residual (large) gauge transformations of the gauge theory. In particular, expanding the associated charge in inverse powers of the radial coordinate, the (sub)leading charge yields the (sub)leading soft factor.
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
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.
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.
Quantum de Finetti theorem in phase-space representation
NASA Astrophysics Data System (ADS)
Leverrier, Anthony; Cerf, Nicolas J.
2009-07-01
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 σ⊗n . 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).
Strong Kochen-Specker theorem and incomputability of quantum randomness
NASA Astrophysics Data System (ADS)
Abbott, Alastair A.; Calude, Cristian S.; Conder, Jonathan; Svozil, Karl
2012-12-01
The Kochen-Specker theorem shows the impossibility for a hidden variable theory to consistently assign values to certain (finite) sets of observables in a way that is noncontextual and consistent with quantum mechanics. If we require noncontextuality, the consequence is that many observables must not have pre-existing definite values. However, the Kochen-Specker theorem does not allow one to determine which observables must be value indefinite. In this paper we present an improvement on the Kochen-Specker theorem which allows one to actually locate observables which are provably value indefinite. Various technical and subtle aspects relating to this formal proof and its connection to quantum mechanics are discussed. This result is then utilized for the proposal and certification of a dichotomic quantum random number generator operating in a three-dimensional Hilbert space.
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.
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)
Muonium Spectrum Beyond the Nonrelativistic Limit
Weber, Axel
2008-07-02
A generalization of the Gell-Mann-Low theorem is applied to the antimuon-electron system. The bound state spectrum is extracted numerically. As a result, fine and hyperfine structure are reproduced correctly near the nonrelativistic limit (and for arbitrary masses). We compare the spectrum for the relativistic value {alpha} = 0.3 with corresponding calculations in light-front quantization.
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.
Nonlinear Dynamic Maximum Power Theorem, with Numerical Method
1983-09-01
Desoer , "The Maximum Power Transfer Theorem for n-Ports," IEEE Trans. Circuit Theory , vol. CT-20, no. 3, pp. 328-330, May 1973. [2] J.L.Wyatt, Jr. and L.O...327-330, May 1974. [10] H. Flanders, "On the Maximal Power Transfer Theorem for n-Ports," Int. J. Circuit Theory and Applications, vol. 4, pp. 319-344...conditions in section 3.1), then the (noncausal) matched load has the form shown in Fig. 2. 3.3) Circuit Example Suppose the source takes the specific
Quantum Theory of Jaynes' Principle, Bayes' Theorem, and Information
NASA Astrophysics Data System (ADS)
Haken, Hermann
2014-12-01
After a reminder of Jaynes' maximum entropy principle and of my quantum theoretical extension, I consider two coupled quantum systems A,B and formulate a quantum version of Bayes' theorem. The application of Feynman's disentangling theorem allows me to calculate the conditional density matrix ρ (A|B) , if system A is an oscillator (or a set of them), linearly coupled to an arbitrary quantum system B. Expectation values can simply be calculated by means of the normalization factor of ρ (A|B) that is derived.
Fluidized Granular Medium as an Instance of the Fluctuation Theorem
NASA Astrophysics Data System (ADS)
Feitosa, Klebert; Menon, Narayanan
2004-04-01
We study the statistics of the power flux into a collection of inelastic beads maintained in a fluidized steady state by external mechanical driving. The power shows large fluctuations, including frequent large negative fluctuations, about its average value. The relative probabilities of positive and negative fluctuations in the power flux are in close accord with the fluctuation theorem of Gallavotti and Cohen, even at time scales shorter than those required by the theorem. We also compare an effective temperature that emerges from this analysis to the kinetic granular temperature.
Fluidized granular medium as an instance of the fluctuation theorem.
Feitosa, Klebert; Menon, Narayanan
2004-04-23
We study the statistics of the power flux into a collection of inelastic beads maintained in a fluidized steady state by external mechanical driving. The power shows large fluctuations, including frequent large negative fluctuations, about its average value. The relative probabilities of positive and negative fluctuations in the power flux are in close accord with the fluctuation theorem of Gallavotti and Cohen, even at time scales shorter than those required by the theorem. We also compare an effective temperature that emerges from this analysis to the kinetic granular temperature.
Fluctuation theorems for total entropy production in generalized Langevin systems
NASA Astrophysics Data System (ADS)
Ghosh, Bappa; Chaudhury, Srabanti
2017-01-01
The validity of the fluctuation theorems for total entropy production of a colloidal particle embedded in a non-Markovian heat bath driven by a time-dependent force in a harmonic potential is probed here. The dynamics of the system is modeled by the generalized Langevin equation with colored noise. The distribution function of the total entropy production is calculated and the detailed fluctuation theorem contains a renormalized temperature term which arises due to the non-Markovian characteristics of the thermal bath.
Extensions of the Feynman-Hellman theorem and applications
NASA Astrophysics Data System (ADS)
Singh, S. Brajamani; Singh, C. A.
1989-10-01
Epstein's [Am. J. Phys. 22, 613 (1954)] off-diagonal and higher-order extensions of the Feynman-Hellmann theorem, obtained by using the basic technique of parameter differentiation under the integral sign, are further pursued. Epstein's rederivation of the Rayleigh-Schrödinger perturbation expansion is also extended to include the degenerate case. The same approach is also used to obtain the Lennard-Jones-Brillouin-Wigner perturbation theory. The quantum virial theorem and its off-diagonal generalization is deduced and its application is illustrated by taking the example of the linear harmonic oscillator. The semiclassical expression for the kinetic energy is obtained directly from the quantization condition.
Generalization of Carey's equality and a theorem on stationary population.
Srinivasa Rao, Arni S R; Carey, James R
2015-09-01
Carey's Equality pertaining to stationary models is well known. In this paper, we have stated and proved a fundamental theorem related to the formation of this Equality. This theorem will provide an in-depth understanding of the role of each captive subject, and their corresponding follow-up duration in a stationary population. We have demonstrated a numerical example of a captive cohort and the survival pattern of medfly populations. These results can be adopted to understand age-structure and aging process in stationary and non-stationary population models.
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.
Finite de Finetti theorem for infinite-dimensional systems.
D'Cruz, Christian; Osborne, Tobias J; Schack, Rüdiger
2007-04-20
We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state |Psi/Psi| chosen from a family of subsets {Cn} of the full symmetric subspace for n subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give a second equivalent characterization of the family {Cn}.
NASA Astrophysics Data System (ADS)
Belolipetskii, A. A.; Ter-Krikorov, A. M.
2016-11-01
The functional equation f( x,ɛ) = 0 containing a small parameter ɛ and admitting regular and singular degeneracy as ɛ → 0 is considered. By the methods of small parameter, a function x n 0(ɛ) satisfying this equation within a residual error of O(ɛ n+1) is found. A modified Newton's sequence starting from the element x n 0(ɛ) is constructed. The existence of the limit of Newton's sequence is based on the NK theorem proven in this work (a new variant of the proof of the Kantorovich theorem substantiating the convergence of Newton's iterative sequence). The deviation of the limit of Newton's sequence from the initial approximation x n 0(ɛ) has the order of O(ɛ n+1), which proves the asymptotic character of the approximation x n 0(ɛ). The method proposed is implemented in constructing an asymptotic approximation of a system of ordinary differential equations on a finite or infinite time interval with a small parameter multiplying the derivatives, but it can be applied to a wider class of functional equations with a small parameters.
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.
Elliptical billiard systems and the full Poncelet's theorem in n dimensions
NASA Astrophysics Data System (ADS)
Chang, Shau-Jin; Crespi, Bruno; Shi, Kang-Jie
1993-06-01
In this work is presented a generalization of Poncelet's theorem to n dimensions which is refered to as the full Poncelet's theorem. The theorem states that if the reflections of a trajectory by a sequence of confocal quadrics lead to a closed skew polygon, then there exists an (n-1)-parameter family of polygons having the same property. A physical realization and a projective geometrical proof of this theorem are given. If all the reflecting quadrics coincide, the above theorem reduces to the n-dimensional Poncelet's theorem presented by Chang and Friedberg. The geometrical proof is a finite construction based on a preliminary theorem which extends Hart's lemma. The full Poncelet's theorem may thus be extended to projective geometries over most fields, including discrete ones.
Fluctuation Limit for Interacting Diffusions with Partial Annihilations Through Membranes
NASA Astrophysics Data System (ADS)
Chen, Zhen-Qing; Fan, Wai-Tong Louis
2016-08-01
We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in Chen and Fan (Ann Probab, to appear) and establish its functional central limit theorem. This fluctuation limit is a distribution-valued Gaussian Markov process which can be represented as a mild solution of a stochastic partial differential equation. The drift of our fluctuation limit involves a new partial differential equation with nonlinear coupled term on the interface that characterized the hydrodynamic limit of the system. The covariance structure of the Gaussian part consists two parts, one involving the spatial motion of the particles inside the domain and other involving a boundary integral term that captures the boundary interactions between two species. The key is to show that the Boltzmann-Gibbs principle holds for our non-equilibrium system. Our proof relies on generalizing the usual correlation functions to the join correlations at two different times.
Unified limiting form of graviton radiation at extreme energies
NASA Astrophysics Data System (ADS)
Ciafaloni, Marcello; Colferai, Dimitri; Coradeschi, Francesco; Veneziano, Gabriele
2016-02-01
We derive the limiting form of graviton radiation in gravitational scattering at trans-Planckian energies (E ≫MP) and small deflection angles. We show that—owing to the graviton's spin 2—such a limiting form unifies the soft and Regge regimes of emission, by covering a broad angular range, from forward fragmentation to the deeply central region. The single-exchange emission amplitudes have a nice expression in terms of the transformation phases of helicity amplitudes under rotations. As a result, the multiple-exchange emission amplitudes can be resummed via an impact parameter b -space factorization theorem that takes into account all coherence effects. We then see the emergence of an energy spectrum of the emitted radiation which, being tuned on ℏ/R ˜MP2/E ≪MP, is reminiscent of Hawking's radiation. Such a spectrum is much softer than the one naïvely expected for increasing input energies and neatly solves a potential energy crisis. Furthermore, by including rescattering corrections in the (quantum) factorization formula, we are able to recover the classical limit and find the corresponding quantum corrections. Perspectives for the extrapolation of such limiting radiation towards the classical collapse regime (where b is of the order of the gravitational radius R ) are also discussed.
Torres-Peralta, Rafael; Morales-Alamo, David; González-Izal, Miriam; Losa-Reyna, José; Pérez-Suárez, Ismael; Izquierdo, Mikel; Calbet, José A. L.
2016-01-01
To determine whether task failure during incremental exercise to exhaustion (IE) is principally due to reduced neural drive and increased metaboreflex activation eleven men (22 ± 2 years) performed a 10 s control isokinetic sprint (IS; 80 rpm) after a short warm-up. This was immediately followed by an IE in normoxia (Nx, PIO2:143 mmHg) and hypoxia (Hyp, PIO2:73 mmHg) in random order, separated by a 120 min resting period. At exhaustion, the circulation of both legs was occluded instantaneously (300 mmHg) during 10 or 60 s to impede recovery and increase metaboreflex activation. This was immediately followed by an IS with open circulation. Electromyographic recordings were obtained from the vastus medialis and lateralis. Muscle biopsies and blood gases were obtained in separate experiments. During the last 10 s of the IE, pulmonary ventilation, VO2, power output and muscle activation were lower in hypoxia than in normoxia, while pedaling rate was similar. Compared to the control sprint, performance (IS-Wpeak) was reduced to a greater extent after the IE-Nx (11% lower P < 0.05) than IE-Hyp. The root mean square (EMGRMS) was reduced by 38 and 27% during IS performed after IE-Nx and IE-Hyp, respectively (Nx vs. Hyp: P < 0.05). Post-ischemia IS-EMGRMS values were higher than during the last 10 s of IE. Sprint exercise mean (IS-MPF) and median (IS-MdPF) power frequencies, and burst duration, were more reduced after IE-Nx than IE-Hyp (P < 0.05). Despite increased muscle lactate accumulation, acidification, and metaboreflex activation from 10 to 60 s of ischemia, IS-Wmean (+23%) and burst duration (+10%) increased, while IS-EMGRMS decreased (−24%, P < 0.05), with IS-MPF and IS-MdPF remaining unchanged. In conclusion, close to task failure, muscle activation is lower in hypoxia than in normoxia. Task failure is predominantly caused by central mechanisms, which recover to great extent within 1 min even when the legs remain ischemic. There is dissociation between the
No-scalar-hair theorem for spherically symmetric reflecting stars
NASA Astrophysics Data System (ADS)
Hod, Shahar
2016-11-01
It is proved that spherically symmetric compact reflecting objects cannot support static bound-state configurations made of scalar fields whose self-interaction potential V (ψ2) is a monotonically increasing function of its argument. Our theorem rules out, in particular, the existence of massive scalar hair outside the surface of a spherically symmetric compact reflecting star.
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.
Kochen-Specker Theorem as a Precondition for Quantum Computing
NASA Astrophysics Data System (ADS)
Nagata, Koji; Nakamura, Tadao
2016-12-01
We study the relation between the Kochen-Specker theorem (the KS theorem) and quantum computing. The KS theorem rules out a realistic theory of the KS type. We consider the realistic theory of the KS type that the results of measurements are either +1 or -1. We discuss an inconsistency between the realistic theory of the KS type and the controllability of quantum computing. We have to give up the controllability if we accept the realistic theory of the KS type. We discuss an inconsistency between the realistic theory of the KS type and the observability of quantum computing. We discuss the inconsistency by using the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be for an easy detector to a Pauli observable. We cannot accept the realistic theory of the KS type to simulate the double-slit experiment in a significant specific case. The realistic theory of the KS type can not depicture quantum detector. In short, we have to give up both the observability and the controllability if we accept the realistic theory of the KS type. Therefore, the KS theorem is a precondition for quantum computing, i.e., the realistic theory of the KS type should be ruled out.
Fermat's Last Theorem for Factional and Irrational Exponents
ERIC Educational Resources Information Center
Morgan, Frank
2010-01-01
Fermat's Last Theorem says that for integers n greater than 2, there are no solutions to x[superscript n] + y[superscript n] = z[superscript n] among positive integers. What about rational exponents? Irrational n? Negative n? See what an undergraduate senior seminar discovered.
An Experiment on a Physical Pendulum and Steiner's Theorem
ERIC Educational Resources Information Center
Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.
2010-01-01
Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…
A categorical account of the Hofmann-Mislove theorem
NASA Astrophysics Data System (ADS)
Townsend, Christopher F.
2005-11-01
A categorical account is given of the Hofmann-Mislove theorem, describing the Scott open filters on a frame. The account is stable under an order duality and so is shown to also cover Bunge and Funk's constructive description of the points of the lower power locale.
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.…
LETTERS AND COMMENTS: Reply to 'Noether's theorem once again'
NASA Astrophysics Data System (ADS)
Marinho, Rubens M., Jr.
2009-09-01
This reply answers the issues raised in the comment on my paper (Marinho Jr 2007 Eur. J. Phys. 28 37-43), obtains the Laplace-Runge-Lenz vector (Goldstein 2002 Classical Mechanics 3rd edn (Reading, MA: Addison-Wesley)) using Noether's theorem and includes a Maple program used to derive the results.
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…
An Extension of the Mean Value Theorem for Integrals
ERIC Educational Resources Information Center
Khalili, Parviz; Vasiliu, Daniel
2010-01-01
In this note we present an extension of the mean value theorem for integrals. The extension we consider is motivated by an older result (here referred as Corollary 2), which is quite classical for the literature of Mathematical Analysis or Calculus. We also show an interesting application for computing the sum of a harmonic series.
Null conformal Killing-Yano tensors and Birkhoff theorem
NASA Astrophysics Data System (ADS)
Ferrando, Joan Josep; Sáez, Juan Antonio
2016-04-01
We study the space-times admitting a null conformal Killing-Yano tensor whose divergence defines a Killing vector. We analyze the similarities and differences with the recently studied non null case (Ferrando and Sáez in Gen Relativ Gravit 47:1911, 2015). The results by Barnes concerning the Birkhoff theorem for the case of null orbits are analyzed and generalized.
Rotationally invariant proof of Bell's theorem without inequalities
Cabello, Adan
2003-03-01
The singlet state of two spin-(3/2) particles allows a proof of Bell's theorem without inequalities with two distinguishing features: any local observable can be regarded as an Einstein-Podolsky-Rosen element of reality, and the contradiction with local realism occurs not only for some specific local observables but for any rotation whereof.
The Unforgettable Experience of a Workshop on Pythagoras Theorem
ERIC Educational Resources Information Center
Arwani, Salima Shahzad
2011-01-01
The author conducted a workshop with colleagues in which awareness of Pythagoras' theorem was raised. This workshop was an unforgettable event in the author's life because it was the first time that she had interacted with teachers from a different school system, and it allowed her to develop presentation skills and confidence in her own…
Hamiltonian Noether theorem for gauge systems and two time physics
NASA Astrophysics Data System (ADS)
Villanueva, V. M.; Nieto, J. A.; Ruiz, L.; Silvas, J.
2005-08-01
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al model and, with special emphasis, to two time physics.
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…
Weak convergence theorems for a countable family of Lipschitzian mappings
NASA Astrophysics Data System (ADS)
Nilsrakoo, Weerayuth; Saejung, Satit
2009-08-01
This paper is concerned with convergence of an approximating common fixed point sequence of countable Lipschitzian mappings in a uniformly convex Banach space. We also establish weak convergence theorems for finding a common element of the set of fixed points, the set of solutions of an equilibrium problem, and the set of solutions of a variational inequality. With an appropriate setting, we obtain and improve the corresponding results recently proved by Moudafi [A. Moudafi, Weak convergence theorems for nonexpansive mappings and equilibrium problems. J. Nonlinear Convex Anal. 9 (2008) 37-43], Tada-Takahashi [A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem. J. Optim. Theory Appl. 133 (2007) 359-370], and Plubtieng-Kumam [S. Plubtieng and P. Kumam, Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings. J. Comput. Appl. Math. (2008) doi:10.1016/j.cam.2008.05.045]. Some of our results are established with weaker assumptions.
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).
Thermodynamic laws and equipartition theorem in relativistic Brownian motion.
Koide, T; Kodama, T
2011-06-01
We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.
A Computer Algorithm from DeMoivre's Theorem.
ERIC Educational Resources Information Center
Boyd, James N.
1982-01-01
Details are given of a simple computer program written in BASIC which calculates the sine of an angle through an application of DeMoivre's Theorem. The program is included in the material, and the program's success is discussed in terms of why the approximation works. (MP)
On Feynman's Triangle Problem and the Routh Theorem
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2009-01-01
In this article, we give a brief history of the Feynman's Triangle problem and describe a simple method to solve a general version of this problem, which is called the Routh Theorem. This method could be found useful to school teachers, instructors or lecturers who are involved in teaching geometry.
A shape theorem for Riemannian first-passage percolation
NASA Astrophysics Data System (ADS)
LaGatta, T.; Wehr, J.
2010-05-01
Riemannian first-passage percolation is a continuum model, with a distance function arising from a random Riemannian metric in Rd. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability of 1.
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…
Two Theorems on Dissipative Energy Losses in Capacitor Systems
ERIC Educational Resources Information Center
Newburgh, Ronald
2005-01-01
This article examines energy losses in charge motion in two capacitor systems. In the first charge is transferred from a charged capacitor to an uncharged one through a resistor. In the second a battery charges an originally uncharged capacitor through a resistance. Analysis leads to two surprising general theorems. In the first case the fraction…
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.
Fixed point theorems for generalized contractions in ordered metric spaces
NASA Astrophysics Data System (ADS)
O'Regan, Donal; Petrusel, Adrian
2008-05-01
The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, MEC. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petrusel, I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.
ERIC Educational Resources Information Center
Young, Anne Ludington
1996-01-01
Error estimates for tangent line approximations and for numerical integration are found using special cases of the error formulas for Taylor's Theorem and the Trapezoidal Rule, respectively. Proofs of these theorems rely on a modification of Rolle's Theorem. (Author/MKR)
A variational theorem for creep with applications to plates and columns
NASA Technical Reports Server (NTRS)
Sanders, J Lyell, Jr; Mccomb, Harvey G , Jr; Schlechte, Floyd R
1958-01-01
A variational theorem is presented for a body undergoing creep. Solutions to problems of the creep behavior of plates, columns, beams, and shells can be obtained by means of the direct methods of the calculus of variations in conjunction with the stated theorem. The application of the theorem is illustrated for plates and columns by the solution of two sample problems.
Quantization of conductance minimum and index theorem
NASA Astrophysics Data System (ADS)
Ikegaya, Satoshi; Suzuki, Shu-Ichiro; Tanaka, Yukio; Asano, Yasuhiro
2016-08-01
We discuss the minimum value of the zero-bias differential conductance Gmin in a junction consisting of a normal metal and a nodal superconductor preserving time-reversal symmetry. Using the quasiclassical Green function method, we show that Gmin is quantized at (4 e2/h ) NZES in the limit of strong impurity scatterings in the normal metal at the zero temperature. The integer NZES represents the number of perfect transmission channels through the junction. An analysis of the chiral symmetry of the Hamiltonian indicates that NZES corresponds to the Atiyah-Singer index in mathematics.
The physical origins of the uncertainty theorem
NASA Astrophysics Data System (ADS)
Giese, Albrecht
2013-10-01
The uncertainty principle is an important element of quantum mechanics. It deals with certain pairs of physical parameters which cannot be determined to an arbitrary level of precision at the same time. According to the so-called Copenhagen interpretation of quantum mechanics, this uncertainty is an intrinsic property of the physical world. - This paper intends to show that there are good reasons for adopting a different view. According to the author, the uncertainty is not a property of the physical world but rather a limitation of our knowledge about the actual state of a physical process. This view conforms to the quantum theory of Louis de Broglie and to Albert Einstein's interpretation.
Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning
2016-10-01
An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.
Multidimensional Yamada-Watanabe theorem and its applications to particle systems
NASA Astrophysics Data System (ADS)
Graczyk, Piotr; Małecki, Jacek
2013-02-01
We prove a multidimensional version of the Yamada-Watanabe theorem, i.e., a theorem giving conditions on coefficients of a stochastic differential equation for existence and pathwise uniqueness of strong solutions. It implies an existence and uniqueness theorem for the eigenvalue and eigenvector processes of matrix-valued stochastic processes, called a "spectral" matrix Yamada-Watanabe theorem. The multidimensional Yamada-Watanabe theorem is also applied to particle systems of squared Bessel processes, corresponding to matrix analogues of squared Bessel processes, Wishart and Jacobi matrix processes. The β-versions of these particle systems are also considered.
Data Outlier Detection using the Chebyshev Theorem
Amidan, Brett G.; Ferryman, Thomas A.; Cooley, Scott K.
2005-05-12
During data collection and analysis, it is often necessary to identify and possibly remove outliers that exist. It is often critical to have an objective method of identifying outliers to be removed. There are many automated outlier detection methods, however, many are limited by assumptions of a distribution or they require upper and lower pre-defined boundaries in which the data should exist. If there is a known distribution for the data, then using that distribution can aid in finding outliers. Often, a distribution is not known, or the experimenter does not want to make an assumption about a certain distribution. Also, enough information may not exist about a set of data to be able to determine reliable upper and lower boundaries. For these cases, an outlier detection method, using the empirical data and based upon Chebyshev's inequality, was formed. This method also allows for detection of multiple outliers, not just one at a time.
Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes
NASA Astrophysics Data System (ADS)
Remmen, Grant N.; Bao, Ning; Pollack, Jason
2016-07-01
We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throat separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. This theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.
Extension of the CPT theorem to non-Hermitian Hamiltonians and unstable states
NASA Astrophysics Data System (ADS)
Mannheim, Philip D.
2016-02-01
We extend the CPT theorem to quantum field theories with non-Hermitian Hamiltonians and unstable states. Our derivation is a quite minimal one as it requires only the time-independent evolution of scalar products, invariance under complex Lorentz transformations, and a non-standard but nonetheless perfectly legitimate interpretation of charge conjugation as an antilinear operator. The first of these requirements does not force the Hamiltonian to be Hermitian. Rather, it forces its eigenvalues to either be real or to appear in complex conjugate pairs, forces the eigenvectors of such conjugate pairs to be conjugates of each other, and forces the Hamiltonian to admit of an antilinear symmetry. The latter two requirements then force this antilinear symmetry to be CPT, while forcing the Hamiltonian to be real rather than Hermitian. Our work justifies the use of the CPT theorem in establishing the equality of the lifetimes of unstable particles that are charge conjugates of each other. We show that the Euclidean time path integrals of a CPT-symmetric theory must always be real. In the quantum-mechanical limit the key results of the PT symmetry program of Bender and collaborators are recovered, with the C-operator of the PT symmetry program being identified with the linear component of the charge conjugation operator.
Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis.
Subaşı, Y; Hu, B L
2012-01-01
In this paper we present a first-principles analysis of the nonequilibrium work distribution and the free energy difference of a quantum system interacting with a general environment (with arbitrary spectral density and for all temperatures) based on a well-understood microphysics (quantum Brownian motion) model under the conditions stipulated by the Jarzynski equality [Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)] and Crooks' fluctuation theorem [Crooks, Phys. Rev. E 60, 2721 (1999)] (in short, fluctuation theorems, FTs). We use the decoherent histories conceptual framework to explain how the notion of trajectories in a quantum system can be made viable and use the environment-induced decoherence scheme to assess the strength of noise that could provide sufficient decoherence to warrant the use of trajectories to define work in open quantum systems. From the solutions to the Langevin equation governing the stochastic dynamics of such systems we were able to produce formal expressions for these quantities entering in the FTs and from them prove explicitly the validity of the FTs at the high temperature limit. At low temperatures our general results would enable one to identify the range of parameters where FTs may not hold or need be expressed differently. We explain the relation between classical and quantum FTs and the advantage of this microphysics open-system approach over the phenomenological modeling and energy-level calculations for substitute closed quantum systems.
Crawford, John R; Garthwaite, Paul H; Betkowska, Karolina
2009-05-01
Most neuropsychologists are aware that, given the specificity and sensitivity of a test and an estimate of the base rate of a disorder, Bayes' theorem can be used to provide a post-test probability for the presence of the disorder given a positive test result (and a post-test probability for the absence of a disorder given a negative result). However, in the standard application of Bayes' theorem the three quantities (sensitivity, specificity, and the base rate) are all treated as fixed, known quantities. This is very unrealistic as there may be considerable uncertainty over these quantities and therefore even greater uncertainty over the post-test probability. Methods of obtaining interval estimates on the specificity and sensitivity of a test are set out. In addition, drawing and extending upon work by Mossman and Berger (2001), a Monte Carlo method is used to obtain interval estimates for post-test probabilities. All the methods have been implemented in a computer program, which is described and made available (www.abdn.ac.uk/~psy086/dept/BayesPTP.htm). When objective data on the base rate are lacking (or have limited relevance to the case at hand) the program elicits opinion for the pre-test probability.
Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes
Remmen, Grant N.; Bao, Ning; Pollack, Jason
2016-07-11
We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throatmore » separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. In conclusion, this theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.« less
Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes
Remmen, Grant N.; Bao, Ning; Pollack, Jason
2016-07-11
We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throat separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. In conclusion, this theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.
Explicit results for the anomalous three point function and non-renormalization theorems
NASA Astrophysics Data System (ADS)
Jegerlehner, F.; Tarasov, O. V.
2006-08-01
Two-loop corrections for the < VVA > correlator of the singlet axial and vector currents in QCD are calculated in the chiral limit for arbitrary momenta. Explicit calculations confirm the non-renormalization theorems derived recently by Vainshtein [A. Vainshtein, Phys. Lett. B 569 (2003) 187] and Knecht et al. [M. Knecht, S. Peris, M. Perrottet, E. de Rafael, JHEP 0403 (2004) 035]. We find that as in the one-loop case also at two loops the < VVA > correlator has only three independent form-factors instead of four. From the explicit results we observe that the two-loop correction to the correlator is equal to the one-loop result times the constant factor C2 (R)αs / π in the MSbar scheme. This holds for the full correlator, for the anomalous longitudinal as well as for the non-anomalous transversal amplitudes. The finite overall αs dependent constant has to be normalized away by renormalizing the axial current according to Witten's algebraic/geometrical constraint on the anomalous Ward identity [ < VV ∂ A > correlator]. Our observations, together with known facts, suggest that in perturbation theory the < VVA > correlator is proportional to the one-loop term to all orders and that the non-renormalization theorem of the Adler-Bell-Jackiw anomaly carries over to the full correlator.
Implications of the Corotation Theorem on the MRI in Axial Symmetry
NASA Astrophysics Data System (ADS)
Montani, G.; Cianfrani, F.; Pugliese, D.
2016-08-01
We analyze the linear stability of an axially symmetric ideal plasma disk, embedded in a magnetic field and endowed with a differential rotation. This study is performed by adopting the magnetic flux function as the fundamental dynamical variable, in order to outline the role played by the corotation theorem on the linear mode structure. Using some specific assumptions (e.g., plasma incompressibility and propagation of the perturbations along the background magnetic field), we select the Alfvénic nature of the magnetorotational instability, and, in the geometric optics limit, we determine the dispersion relation describing the linear spectrum. We show how the implementation of the corotation theorem (valid for the background configuration) on the linear dynamics produces the cancellation of the vertical derivative of the disk angular velocity (we check such a feature also in the standard vector formalism to facilitate comparison with previous literature, in both the axisymmetric and three-dimensional cases). As a result, we clarify that the unstable modes have, for a stratified disk, the same morphology, proper of a thin-disk profile, and the z-dependence has a simple parametric role.
From necklace quivers to the F -theorem, operator counting, and T ( U( N))
NASA Astrophysics Data System (ADS)
Gulotta, Daniel R.; Herzog, Christopher P.; Pufu, Silviu S.
2011-12-01
The matrix model of Kapustin, Willett, and Yaakov is a powerful tool for exploring the properties of strongly interacting superconformal Chern-Simons theories in 2+1 dimensions. In this paper, we use this matrix model to study necklace quiver gauge theories with mathcal{N} = {3} supersymmetry and U( N) d gauge groups in the limit of large N. In its simplest application, the matrix model computes the free energy of the gauge theory on S 3. The conjectured F -theorem states that this quantity should decrease under renormalization group flow. We show that for a simple class of such flows, the F -theorem holds for our necklace theories. We also provide a relationship between matrix model eigenvalue distributions and numbers of chiral operators that we conjecture holds more generally. Through the AdS/CFT correspondence, there is therefore a natural dual geometric interpretation of the matrix model saddle point in terms of volumes of 7-d tri-Sasaki Einstein spaces and some of their 5-d submanifolds. As a final bonus, our analysis gives us the partition function of the T (U( N)) theory on S 3.
Algebraic functions of complexity one, a Weierstrass theorem, and three arithmetic operations
NASA Astrophysics Data System (ADS)
Beloshapka, V. K.
2016-07-01
The Weierstrass theorem concerning functions admitting an algebraic addition theorem enables us to give an explicit description of algebraic functions of two variables of analytical complexity one. Their description is divided into three cases: the general case, which is elliptic, and two special ones, a multiplicative and an additive one. All cases have a unified description; they are the orbits of an action of the gauge pseudogroup. The first case is a 1-parameter family of orbits of "elliptic addition," the second is the orbit of multiplication, and the third of addition. Here the multiplication and addition can be derived from the "elliptic addition" by passages to a limit. On the other hand, the elliptic orbits correspond to complex structures on the torus, the multiplicative orbit corresponds to the complex structure on the cylinder, and the additive one to that on the complex plane. This work was financially supported by the Russian Foundation for Basic Research under grants nos. 14-00709-a and 13-01-12417-ofi-m2.
Reality of the quantum state: Towards a stronger ψ -ontology theorem
NASA Astrophysics Data System (ADS)
Mansfield, Shane
2016-10-01
The Pusey-Barrett-Rudolph (PBR) no-go theorem provides an argument for the reality of the quantum state by ruling out ψ -epistemic ontological theories, in which the quantum state is of a statistical nature. It applies under an assumption of preparation independence, the validity of which has been subject to debate. We propose two plausible and less restrictive alternatives: a weaker notion allowing for classical correlations, and an even weaker, physically motivated notion of independence, which merely prohibits the possibility of superluminal causal influences in the preparation process. The latter is a minimal requirement for enabling a reasonable treatment of subsystems in any theory. It is demonstrated by means of an explicit ψ -epistemic ontological model that the argument of PBR becomes invalid under the alternative notions of independence. As an intermediate step, we recover a result which is valid in the presence of classical correlations. Finally, we obtain a theorem which holds under the minimal requirement, approximating the result of PBR. For this, we consider experiments involving randomly sampled preparations and derive bounds on the degree of ψ epistemicity that is consistent with the quantum-mechanical predictions. The approximation is exact in the limit as the sample space of preparations becomes infinite.
NASA Astrophysics Data System (ADS)
Mahoney, J.; Le Roex, A. P.; Peng, Z.; Fisher, R. L.; Natland, J. H.
1992-12-01
The isotopic characteristics of the Indian Ocean Ridge midocean ridge basalts (MORBs) and of the Atlantic and the Pacific MORBs (north of 25 deg S) were determined in order to estimate the southwestern limits of the Indian Ocean Ridge mantle and the origin of low Pb-206/Pb-204 MORB. In view of the possible importance of a Marion-type mantle along portions of the ridge, lavas from several Marion Island, Prince Edward Island, and Funk Seamount were also analyzed isotopically. The isotopic results include analyses of fields for the Indian Ocean triple junction area, the entire Central Indian and southern Carlsberg ridges, for several oceanic islands, and Pacific and/or North Atlantic MORBs.
The g-theorem and quantum information theory
NASA Astrophysics Data System (ADS)
Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo
2016-10-01
We study boundary renormalization group flows between boundary conformal field theories in 1 + 1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.
Fluctuation theorem for a deterministic one-particle system
NASA Astrophysics Data System (ADS)
Schmick, Malte; Markus, Mario
2004-12-01
A Duffing oscillator is driven by a sum of N chaotic time series. These time series are solutions of the undriven Duffing equation. It is shown that N=1 is sufficient to render the fluctuation theorem [Gallavotti and Cohen, Phys. Rev. Lett. 74, 2694 (1995); Gallavotti, J. Math. Phys. 41, 4061 (2000); Evans and Searles, Adv. Phys. 51, 1529 (2002)] for the power Jτ averaged within intervals of length τ . In particular, the probabilities p(Jτ) follow a nearly Gaussian distribution. Also, ln[p(Jτ)/p(-Jτ)] versus Jτ can be fitted by strikingly linear functions, the slopes being proportional to τ for large τ . These results indicate that validity of the fluctuation theorem requires neither a many-particle system nor a stochastic process, which are requirements used in previous works.
A double commutant theorem for Murray–von Neumann algebras
Liu, Zhe
2012-01-01
Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double commutant theorem characterizes von Neumann algebras as those for which , where , the commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double commutant theorem for Murray–von Neumann algebras. PMID:22543165
Learning-assisted theorem proving with millions of lemmas☆
Kaliszyk, Cezary; Urban, Josef
2015-01-01
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck. PMID:26525678
Learning in neural networks based on a generalized fluctuation theorem
NASA Astrophysics Data System (ADS)
Hayakawa, Takashi; Aoyagi, Toshio
2015-11-01
Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.
Learning in neural networks based on a generalized fluctuation theorem.
Hayakawa, Takashi; Aoyagi, Toshio
2015-01-01
Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.
Virial theorem in quasi-coordinates and Lie algebroid formalism
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Gheorghiu, Irina; Martínez, Eduardo; Santos, Patrícia
2014-04-01
In this paper, the geometric approach to the virial theorem (VT) developed in [J. F. Cariñena, F. Falceto and M. F. Rañada, A geometric approach to a generalized virial theorem, J. Phys. A: Math. Theor. 45 (2012) 395210, 19 pp.] is written in terms of quasi-velocities (see [J. F. Cariñena, J. Nunes da Costa and P. Santos, Quasi-coordinates from the point of view of Lie algebroid structures, J. Phys. A: Math. Theor. 40 (2007) 10031-10048]). A generalization of the VT for mechanical systems on Lie algebroids is also given, using the geometric tools of Lagrangian and Hamiltonian mechanics on the prolongation of the Lie algebroid.
Bell's Theorem and the Issue of Determinism and Indeterminism
NASA Astrophysics Data System (ADS)
Esfeld, Michael
2015-05-01
The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell's theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for the derivation of Bell's theorem. Determinism as such does not undermine that independence (unless there are particular initial conditions of the universe that would amount to conspiracy). Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave-function can go together with effective wave-functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave-functions are sufficient for the mentioned independence premise to hold.
Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper
NASA Technical Reports Server (NTRS)
Schumann, Johann; Koga, Dennis (Technical Monitor)
1999-01-01
In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).
A uniqueness theorem for the anti-de Sitter soliton.
Galloway, G J; Surya, S; Woolgar, E
2002-03-11
The stability of physical systems depends on the existence of a state of least energy. In gravity, this is guaranteed by the positive energy theorem. For topological reasons, this fails for nonsupersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. For related reasons, this also fails for the anti-de Sitter (AdS) soliton, a globally static, asymptotically toroidal Lambda<0 spacetime with negative mass. Nonetheless, arguing from the AdS conformal field theory (AdS/CFT) correspondence, Horowitz and Myers proposed a new positive energy conjecture, which asserts that the AdS soliton is the unique state of least energy in its asymptotic class. We give a new structure theorem for static Lambda<0 spacetimes and use it to prove uniqueness of the AdS soliton. Our results offer significant support for the new positive energy conjecture and add to the body of rigorous results inspired by the AdS/CFT correspondence.
Diffusive Magnetohydrodynamic Instabilities beyond the Chandrasekhar Theorem
NASA Astrophysics Data System (ADS)
Rüdiger, Günther; Schultz, Manfred; Stefani, Frank; Mond, Michael
2015-10-01
We consider the stability of axially unbounded cylindrical flows that contain a toroidal magnetic background field with the same radial profile as their azimuthal velocity. For ideal fluids, Chandrasekhar had shown the stability of this configuration if the Alfvén velocity of the field equals the velocity of the background flow, i.e., if the magnetic Mach number {Mm}=1. We demonstrate that magnetized Taylor-Couette flows with such profiles become unstable against non-axisymmetric perturbations if at least one of the diffusivities is finite. We also find that for small magnetic Prandtl numbers {Pm} the lines of marginal instability scale with the Reynolds number and the Hartmann number. In the limit {Pm}\\to 0 the lines of marginal instability completely lie below the line for {Mm}=1 and for {Pm}\\to ∞ they completely lie above this line. For any finite value of {Pm}, however, the lines of marginal instability cross the line {Mm}=1, which separates slow from fast rotation. The minimum values of the field strength and the rotation rate that are needed for the instability (slightly) grow if the rotation law becomes flat. In this case, the electric current of the background field becomes so strong that the current-driven Tayler instability (which also exists without rotation) appears in the bifurcation map at low Hartmann numbers.
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.
Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces.
Kim, Jong Kyu; Pathak, Ramesh Prasad; Dashputre, Samir; Diwan, Shailesh Dhar; Gupta, Rajlaxmi
2016-01-01
In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditions. Our results are the extension and improvements of the recent well-known results announced in the current literature.
Implementing Metamathematics as an Approach to Automatic Theorem Proving
1989-01-01
set theory the disjoint union is usually defined from the ordinary union by providing a scheme for tagging elements (see [3]). For any type A, another...in preparing this document. 31 References (1] P. Aczel. The type theoretic interpretation of constructive set theory . In Logic Coo- quium ...Amsterdam:North-Holland, 1978. [2] W. Bledsoe and D. Loveland. Automated Theorem Proving: After 25 Years. American Math Soc., 1984. [3] N. Bourbaki . Theory
Bimeasures and Sampling Theorems for Weakly Harmonizable Processes.
1982-09-27
representation theorem and then such a measure has a unique extension of being a Radon measure by the standard theory of Bourbaki (1], one refers to each such...nontrivial, and this approach has other drawbacks. We therefore do not consider this set in the general format of the sampling theory of random processes...for a more general Cramer class. To carry out this analysis, it is neces- sary to use the properties of bimeasures. Some aspects of the bimeasure theory
Applications of Noether conservation theorem to Hamiltonian systems
NASA Astrophysics Data System (ADS)
Mouchet, Amaury
2016-09-01
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether's approach is illustrated on several examples, including classical field theory and quantum dynamics.
Noether's Theorem of Relativistic-Electromagnetic Ideal Hydrodynamics
NASA Astrophysics Data System (ADS)
Gaspar Elsas, J. H.; Koide, T.; Kodama, T.
2015-06-01
We present a variational approach for relativistic ideal hydrodynamics interacting with electromagnetic fields. The momentum of fluid is introduced as the canonical conjugate variable of the position of a fluid element, which coincides with the conserved quantity derived from Noether's theorem. We further show that our formulation can reproduce the usual electromagnetic hydrodynamics which is obtained so as to satisfy the conservation of the inertia of fluid motion.
Noether theorem for Birkhoffian systems on time scales
NASA Astrophysics Data System (ADS)
Song, Chuan-Jing; Zhang, Yi
2015-10-01
Birkhoff equations on time scales and Noether theorem for Birkhoffian system on time scales are studied. First, some necessary knowledge of calculus on time scales are reviewed. Second, Birkhoff equations on time scales are obtained. Third, the conditions for invariance of Pfaff action and conserved quantities are presented under the special infinitesimal transformations and general infinitesimal transformations, respectively. Fourth, some special cases are given. And finally, an example is given to illustrate the method and results.
A notion of graph likelihood and an infinite monkey theorem
NASA Astrophysics Data System (ADS)
Banerji, Christopher R. S.; Mansour, Toufik; Severini, Simone
2014-01-01
We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.
A Quantitative Gibbard-Satterthwaite Theorem Without Neutrality
2014-05-02
circumventing the negative results. One approach, introduced by Bartholdi, Tovey and Trick [3], suggests computational complexity as a barrier against...A quantitative Gibbard-Satterthwaite theorem without neutrality Elchanan Mossel Miklos Racz Electrical Engineering and Computer Sciences University...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) University of California at Berkeley,Electrical Engineering and Computer Sciences,Berkeley,CA,94720 8
Rowlands' Duality Principle: A Generalization of Noether's Theorem?
NASA Astrophysics Data System (ADS)
Karam, Sabah E.
This paper will examine a physical principle that has been used in making valid predictions and generalizes established conservation laws. In a previous paper it was shown how Rowlands' zero-totality condition could be viewed as a generalization of Newton's third law of motion. In this paper it will be argued that Rowlands' Duality Principle is a generalization of Noether's Theorem and that the two principles taken together are truly foundational principles that have tamed Metaphysics.
Normal coderivative for multifunctions and implicit function theorems
NASA Astrophysics Data System (ADS)
Lee, G. M.; Tam, N. N.; Yen, N. D.
2008-02-01
In the framework of the theory of normal coderivative for multifunctions, new implicit function theorems are obtained. The main tools of the proofs are the Ekeland variational principle, a nonsmooth version of Fermat's rule, a sum rule, and the differential estimate for marginal functions established by B.S. Mordukhovich and Y. Shao [B.S. Mordukhovich, Y. Shao, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996) 1235-1280].
Interpretation of the quantum formalism and Bell's theorem
Santos, E. )
1991-02-01
It is argued that quantum mechanics must be interpreted according to the Copenhagen interpretation. Consequently the formalism must be used in a purely operational way. The relation between realism, hidden variables, and the Bell inequalities is discussed. The proof of impossibility of local hidden-variables theories (Bell theorem) is criticized on the basis that the quantum mechanical states violating local realism are not physically realizable states.
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.
Diffusional creep and sintering -- The application of bounding theorems
Cocks, A.C.F.; Aparicio, N.D.
1995-02-01
In this paper upper and lower bound theorems for the creep and sintering response of bodies which deform by grain-boundary diffusion controlled mechanisms are presented. The utility of the bounds is demonstrated by using them to analyze the classical problem of Hull-Rimmer void growth. Further insight into the material response when diffusion mechanisms dominate is provided by analyzing the response of two contacting spheres, which represents a fundamental problem for the analysis of stage 1 sintering.
Black holes, information, and the universal coefficient theorem
NASA Astrophysics Data System (ADS)
Patrascu, Andrei T.
2016-07-01
General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article, I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by the demanding invariance of the laws of physics to the change of coefficient structures in cohomology.
Optical theorem for multipole sources in wave diffraction theory
NASA Astrophysics Data System (ADS)
Eremin, Yu. A.; Sveshnikov, A. G.
2016-05-01
The optical theorem is generalized to the case of local body excitation by multipole sources. It is found that, to calculate the extinction cross section, it is sufficient to calculate the scattered field derivatives at a single point. It is shown that the Purcell factor, which is a rather important parameter, can be represented in analytic form. The result is generalized to the case of a local scatterer incorporated in a homogeneous halfspace.
A rigidity theorem for complete noncompact Bach-flat manifolds
NASA Astrophysics Data System (ADS)
Chu, Yawei
2011-02-01
Let (M4,g) be a four-dimensional complete noncompact Bach-flat Riemannian manifold with positive Yamabe constant. In this paper, we show that (M4,g) has a constant curvature if it has a nonnegative constant scalar curvature and sufficiently small L2-norm of trace-free Riemannian curvature tensor. Moreover, we get a gap theorem for (M4,g) with positive scalar curvature.
Klein's theorem and the proof of E0 = mc2
NASA Astrophysics Data System (ADS)
Ohanian, Hans C.
2012-12-01
Despite repeated attempts, Einstein failed to give us a general and rigorous proof of his E0=mc2 relation. A completely general proof emerged in 1918 from a theorem on the four-vector character of energy-momentum of extended systems by the mathematician Felix Klein, but this proof is not well known, rarely seen in textbooks, and sometimes misunderstood. A simple version of this proof is presented here, with discussion of the crucial role of the energy-momentum tensor.
Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields
Pan, Xiao-Yin; Sahni, Viraht
2015-11-07
The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momenta. The proofs differ from the original HK proof and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function. A Percus-Levy-Lieb constrained-search proof expanding the domain of validity to N-representable functions, and to degenerate states, again for fixed electron number and angular momentum, is also provided.
Projection-slice theorem based 2D-3D registration
NASA Astrophysics Data System (ADS)
van der Bom, M. J.; Pluim, J. P. W.; Homan, R.; Timmer, J.; Bartels, L. W.
2007-03-01
In X-ray guided procedures, the surgeon or interventionalist is dependent on his or her knowledge of the patient's specific anatomy and the projection images acquired during the procedure by a rotational X-ray source. Unfortunately, these X-ray projections fail to give information on the patient's anatomy in the dimension along the projection axis. It would be very profitable to provide the surgeon or interventionalist with a 3D insight of the patient's anatomy that is directly linked to the X-ray images acquired during the procedure. In this paper we present a new robust 2D-3D registration method based on the Projection-Slice Theorem. This theorem gives us a relation between the pre-operative 3D data set and the interventional projection images. Registration is performed by minimizing a translation invariant similarity measure that is applied to the Fourier transforms of the images. The method was tested by performing multiple exhaustive searches on phantom data of the Circle of Willis and on a post-mortem human skull. Validation was performed visually by comparing the test projections to the ones that corresponded to the minimal value of the similarity measure. The Projection-Slice Theorem Based method was shown to be very effective and robust, and provides capture ranges up to 62 degrees. Experiments have shown that the method is capable of retrieving similar results when translations are applied to the projection images.
Generalized F-theorem and the ɛ expansion
NASA Astrophysics Data System (ADS)
Fei, Lin; Giombi, Simone; Klebanov, Igor R.; Tarnopolsky, Grigory
2015-12-01
Some known constraints on Renormalization Group flow take the form of inequalities: in even dimensions they refer to the coefficient a of the Weyl anomaly, while in odd dimensions to the sphere free energy F. In recent work [1] it was suggested that the a- and F-theorems may be viewed as special cases of a Generalized F -Theorem valid in continuous dimension. This conjecture states that, for any RG flow from one conformal fixed point to another, {tilde{F}}_{UV}>{tilde{F}}_{IR} , where tilde{F}= sin (π d/2) log {Z}_{S^d} . Here we provide additional evidence in favor of the Generalized F-Theorem. We show that it holds in conformal perturbation theory, i.e. for RG flows produced by weakly relevant operators. We also study a specific example of the Wilson-Fisher O( N) model and define this CFT on the sphere S 4- ɛ , paying careful attention to the beta functions for the coefficients of curvature terms. This allows us to develop the ɛ expansion of tilde{F} up to order ɛ 5. Padé extrapolation of this series to d = 3 gives results that are around 2-3% below the free field values for small N. We also study RG flows which include an anisotropic perturbation breaking the O( N) symmetry; we again find that the results are consistent with {tilde{F}}_{UV}>{tilde{F}}_{IR}.
An analogue of Wagner's theorem for decompositions of matrix algebras
NASA Astrophysics Data System (ADS)
Ivanov, D. N.
2004-12-01
Wagner's celebrated theorem states that a finite affine plane whose collineation group is transitive on lines is a translation plane. The notion of an orthogonal decomposition (OD) of a classically semisimple associative algebra introduced by the author allows one to draw an analogy between finite affine planes of order n and ODs of the matrix algebra M_n(\\mathbb C) into a sum of subalgebras conjugate to the diagonal subalgebra. These ODs are called WP-decompositions and are equivalent to the well-known ODs of simple Lie algebras of type A_{n-1} into a sum of Cartan subalgebras. In this paper we give a detailed and improved proof of the analogue of Wagner's theorem for WP-decompositions of the matrix algebra of odd non-square order an outline of which was earlier published in a short note in "Russian Math. Surveys" in 1994. In addition, in the framework of the theory of ODs of associative algebras, based on the method of idempotent bases, we obtain an elementary proof of the well-known Kostrikin-Tiep theorem on irreducible ODs of Lie algebras of type A_{n-1} in the case where n is a prime-power.
Quantum regression theorem and non-Markovianity of quantum dynamics
NASA Astrophysics Data System (ADS)
Guarnieri, Giacomo; Smirne, Andrea; Vacchini, Bassano
2014-08-01
We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.
Representations of the language recognition problem for a theorem prover
NASA Technical Reports Server (NTRS)
Minker, J.; Vanderbrug, G. J.
1972-01-01
Two representations of the language recognition problem for a theorem prover in first order logic are presented and contrasted. One of the representations is based on the familiar method of generating sentential forms of the language, and the other is based on the Cocke parsing algorithm. An augmented theorem prover is described which permits recognition of recursive languages. The state-transformation method developed by Cordell Green to construct problem solutions in resolution-based systems can be used to obtain the parse tree. In particular, the end-order traversal of the parse tree is derived in one of the representations. An inference system, termed the cycle inference system, is defined which makes it possible for the theorem prover to model the method on which the representation is based. The general applicability of the cycle inference system to state space problems is discussed. Given an unsatisfiable set S, where each clause has at most one positive literal, it is shown that there exists an input proof. The clauses for the two representations satisfy these conditions, as do many state space problems.
Supersonic limit for the Zakharov-Rubenchik system
NASA Astrophysics Data System (ADS)
Cordero Ceballos, Juan Carlos
2016-11-01
We study the asymptotic behavior of the solutions of Zakharov-Rubenchik system when appropriate parameters go to zero. Namely, we state weak and strong convergence results of these solutions to solutions of Zakharov system. The proof of the weak limit is a classical argument in the theory of compactness, whose main ingredient is the Aubin-Lions Theorem and the Ascoli Theorem. Strong limits are conveniently treated by decomposing the nonlinearities and using the Strichartz estimates associated with the group of the Schrödinger equation and the wave group.
Taylor's power law of fluctuation scaling and the growth-rate theorem.
Cohen, Joel E
2013-09-01
Taylor's law (TL), a widely verified empirical relationship in ecology, states that the variance of population density is approximately a power-law function of mean density. The growth-rate theorem (GR) states that, in a subdivided population, the rate of change of the overall growth rate is proportional to the variance of the subpopulations' growth rates. We show that continuous-time exponential change implies GR at every time and, asymptotically for large time, TL with power-law exponent 2. We also show why diverse population-dynamic models predict TL in the limit of large time by identifying simple features these models share: If the mean population density and the variance of population density are (exactly or asymptotically) non-constant exponential functions of a parameter (e.g., time), then the variance of density is (exactly or asymptotically) a power-law function of mean density.
Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem
NASA Astrophysics Data System (ADS)
Belinschi, Serban; Nowak, Maciej A.; Speicher, Roland; Tarnowski, Wojciech
2017-03-01
We extend the so-called ‘single ring theorem’ (Feinberg and Zee 1997 Nucl. Phys. B 504 579), also known as the Haagerup–Larsen theorem (Haagerup and Larsen 2000 J. Funct. Anal. 176 331). We do this by showing that in the limit when the size of the matrix goes to infinity a particular correlator between left and right eigenvectors of the relevant non-hermitian matrix X, being the spectral density weighted by the squared eigenvalue condition number, is given by a simple formula involving only the radial spectral cumulative distribution function of X. We show that this object allows the calculation of the conditional expectation of the squared eigenvalue condition number. We give examples and provide a cross-check of the analytic prediction by the large scale numerics.
Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem
Chechkin, Aleksei
2015-01-01
In this paper we propose an algorithm to distinguish between light- and heavy-tailed probability laws underlying random datasets. The idea of the algorithm, which is visual and easy to implement, is to check whether the underlying law belongs to the domain of attraction of the Gaussian or non-Gaussian stable distribution by examining its rate of convergence. The method allows to discriminate between stable and various non-stable distributions. The test allows to differentiate between distributions, which appear the same according to standard Kolmogorov–Smirnov test. In particular, it helps to distinguish between stable and Student’s t probability laws as well as between the stable and tempered stable, the cases which are considered in the literature as very cumbersome. Finally, we illustrate the procedure on plasma data to identify cases with so-called L-H transition. PMID:26698863
Gallavotti Cohen Theorem, Chaotic Hypothesis and the Zero-Noise Limit
NASA Astrophysics Data System (ADS)
Kurchan, Jorge
2007-09-01
The Fluctuation Relation for a stationary state, kept at constant energy by a deterministic thermostat—the Gallavotti-Cohen Theorem— relies on the ergodic properties of the system considered. We show that when perturbed by an energy-conserving random noise, the relation follows trivially for any system at finite noise amplitude. The time needed to achieve stationarity may stay finite as the noise tends to zero, or it may diverge. In the former case the Gallavotti-Cohen result is recovered, while in the latter case, the crossover time may be computed from the action of `instanton' orbits that bridge attractors and repellors. We suggest that the `Chaotic Hypothesis' of Gallavotti, Cohen and Ruelle can thus be reformulated as a matter of stochastic stability of the measure in trajectory space. In this form this hypothesis may be directly tested.
Limit Theorem and Applications of the Pauli Open Quantum Random Walk on Z
NASA Astrophysics Data System (ADS)
Ampadu, Clement
2013-04-01
Following the recent talk in the ``Workshop of Quantum Dynamics and Quantum Walks'' held at Okazaki Conference Center, Okazaki, Japan. This talk clarifies the relationship between the convergent behavior of the Pauli quantum walk on the line, and the open quantum random walk obtained from the Pauli quantum walk.
Quantum crooks fluctuation theorem and quantum Jarzynski equality in the presence of a reservoir
Quan, H T; Dong, H
2008-01-01
We consider the quantum mechanical generalization of Crooks Fluctuation and Jarzynski Equality Theorem for an open quantum system. The explicit expression for microscopic work for an arbitrary prescribed protocol is obtained, and the relation between quantum Crooks Fluctuation Theorem, quantum Jarzynski Equality and their classical counterparts are clarified. Numerical simulations based on a two-level toy model are used to demonstrate the validity of the quantum version of the two theorems beyond linear response theory regime.
A Polarimetric Extension of the van Cittert-Zernike Theorem for Use with Microwave Interferometers
NASA Technical Reports Server (NTRS)
Piepmeier, J. R.; Simon, N. K.
2004-01-01
The van Cittert-Zernike theorem describes the Fourier-transform relationship between an extended source and its visibility function. Developments in classical optics texts use scalar field formulations for the theorem. Here, we develop a polarimetric extension to the van Cittert-Zernike theorem with applications to passive microwave Earth remote sensing. The development provides insight into the mechanics of two-dimensional interferometric imaging, particularly the effects of polarization basis differences between the scene and the observer.
Altürk, Ahmet
2016-01-01
Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.
An entry in the 1992 Overbeek theorem-proving contest
Lusk, E.L.; McCune, W.W.
1992-11-01
The Conference on Automated Deduction (CADE) has been for nearly twenty years a meeting where both theoreticians and system implementors present their work. Feeling perhaps that the conference was becoming dominated by the theoreticians, Ross Overbeek proposed at CADE-10 in 1990 a contest to stimulate work on the implementation and use of theorem-proving systems. The challenge was to prove a set of theorems, and do so with a uniform approach. That is, it was not allowed to set parameters in the system to specialize it for individual problems. There were actually two separate contests, one represented by a set of seven problems designed to test basic inference components, and the other represented by a set of ten problems designed to test equality-based systems. This paper describes our experiences in preparing to enter the contest with OTTER and Roo, two systems developed at Argonne National Laboratory. Roo is a parallel version of OTTER, but has such different behavior in some cases that we treat them as separate entries. We entered each of them in both contests. Some of the problems are difficult ones; and although many of the problems had been done before with OTTER, in each case we had set OTTER`S many input parameters in a way customized to the problem at hand, and chosen a set of support that appeared to us to be most natural. It was a challenge to come up with a uniform set of parameter settings and a information algorithm for picking the set of support that would allow OTTER to prove each of the theorems.
An entry in the 1992 Overbeek theorem-proving contest
Lusk, E.L.; McCune, W.W.
1992-11-01
The Conference on Automated Deduction (CADE) has been for nearly twenty years a meeting where both theoreticians and system implementors present their work. Feeling perhaps that the conference was becoming dominated by the theoreticians, Ross Overbeek proposed at CADE-10 in 1990 a contest to stimulate work on the implementation and use of theorem-proving systems. The challenge was to prove a set of theorems, and do so with a uniform approach. That is, it was not allowed to set parameters in the system to specialize it for individual problems. There were actually two separate contests, one represented by a set of seven problems designed to test basic inference components, and the other represented by a set of ten problems designed to test equality-based systems. This paper describes our experiences in preparing to enter the contest with OTTER and Roo, two systems developed at Argonne National Laboratory. Roo is a parallel version of OTTER, but has such different behavior in some cases that we treat them as separate entries. We entered each of them in both contests. Some of the problems are difficult ones; and although many of the problems had been done before with OTTER, in each case we had set OTTER'S many input parameters in a way customized to the problem at hand, and chosen a set of support that appeared to us to be most natural. It was a challenge to come up with a uniform set of parameter settings and a information algorithm for picking the set of support that would allow OTTER to prove each of the theorems.
Special relativity theorem and Pythagoras’s magic
NASA Astrophysics Data System (ADS)
Korkmaz, S. D.; Aybek, E. C.; Örücü, M.
2016-03-01
In the modern physics unit included in the course curriculum of grade 10 physics introduced in the 2007-2008 education year, the aim is that students at this grade level are aware of any developments which constitute modern physics and may be considered new, and interpret whether mass, length and time values of the motions at any velocities close to the speed of light vary or not. One of the scientific concepts and subjects among the final ones to be learned in the unit of modern physics with 12 course hours includes the special relativity theorem and its results. The special relativity theorem, the foundation of which was laid by Einstein in 1905, has three significant predictions proven by experiments and observations: time extension, dimensional shortening and mass relativity. At the first stage of this study, a simple and fast solution that uses the Pythagorean relation for problems and must be treated by using the mathematical expressions of the predictions as specified above is given, and this way of solution was taught while the relativity subject was explained to the secondary education students who are fifteen years old from grade 10 in the 2013-2014 education year. At the second stage of the study, a qualitative study is released together with grade 11 students who are sixteen years old in 2014-2015, who learnt to solve any problems in both methods, while the special relativity subject is discussed in the physics course in grade 10. The findings of the study show that the students have a misconception on the relativity theorem and prefer to solve any relativity-related problems by using the Pythagorean method constituting the first stage of this study.
Generalized Levinson theorem: Applications to electron-atom scattering
NASA Astrophysics Data System (ADS)
Rosenberg, Leonard; Spruch, Larry
1996-12-01
A recent formulation provides an absolute definition of the zero-energy phase shift δ for multiparticle single-channel scattering of a particle by a neutral compound target in a given partial wave l. This formulation, along with the minimum principle for the scattering length, leads to a determination of δ that represents a generalization of Levinson's theorem. In its original form that theorem is applicable only to potential scattering of a particle and relates δ/π to the number of bound states of that l. The generalized Levinson theorem relates δ/π for scattering in a state of given angular momentum to the number of composite bound states of that angular momentum plus a calculable number that, for a system described in the Hartree-Fock approximation, is the number of states of that angular momentum excluded by the Pauli principle. Thus, for example, for electron scattering by Na, with its (1s)2(2s)2(2p)63s configuration and with one L=0 singlet composite bound state, δ would be π+2π for s-wave singlet scattering, 0+3π for s-wave triplet scattering, and 0+π for both triplet and singlet p-wave scattering; the Pauli contribution has been listed first. The method is applicable to a number of e+/--atom and nucleon-nucleus scattering processes, but only applications of the former type are described here. We obtain the absolute zero-energy phase shifts for e--H and e--He scattering and, in the Hartree-Fock approximation for the target, for atoms that include the noble gases, the alkali-metal atoms, and, as examples, B, C, N, O, and F, which have one, two, three, four, and five p electrons, respectively, outside of closed shells. In all cases, the applications provide results in agreement with expectations.
On Siegel's linearization theorem for fields of prime characteristic
NASA Astrophysics Data System (ADS)
Lindahl, Karl-Olof
2004-05-01
In 1981, Herman and Yoccoz (1983 Generalizations of some theorems of small divisors to non Archimedean fields Geometric Dynamics (Lecture Notes in Mathematics) ed J Palis Jr, pp 408-47 (Berlin: Springer) Proc. Rio de Janeiro, 1981) proved that Siegel's linearization theorem (Siegel C L 1942 Ann. Math. 43 607-12) is true also for non-Archimedean fields. However, the condition in Siegel's theorem is usually not satisfied over fields of prime characteristic. We consider the following open problem from non-Archimedean dynamics. Given an analytic function f defined over a complete, non-trivial valued field of characteristic p > 0, does there exist a convergent power series solution to the Schröder functional equation (2) that conjugates f to its linear part near an indifferent fixed point? We will give both positive and negative answers to this question, one of the problems being the presence of small divisors. When small divisors are present this brings about a problem of a combinatorial nature, where the convergence of the conjugacy is determined in terms of the characteristic of the state space and the powers of the monomials of f, rather than in terms of the diophantine properties of the multiplier, as in the complex case. In the case that small divisors are present, we show that quadratic polynomials are analytically linearizable if p = 2. We find an explicit formula for the coefficients of the conjugacy, and applying a result of Benedetto (2003 Am. J. Math. 125 581-622), we find the exact size of the corresponding Siegel disc and show that there is an indifferent periodic point on the boundary. In the case p > 2 we give a sufficient condition for divergence of the conjugacy for quadratic maps as well as for a certain class of power series containing a quadratic term (corollary 2.1).
Feynman amplitudes and limits of heights
NASA Astrophysics Data System (ADS)
Amini, O.; Bloch, S. J.; Burgos Gil, J. I.; Fresán, J.
2016-10-01
We investigate from a mathematical perspective how Feynman amplitudes appear in the low-energy limit of string amplitudes. In this paper, we prove the convergence of the integrands. We derive this from results describing the asymptotic behaviour of the height pairing between degree-zero divisors, as a family of curves degenerates. These are obtained by means of the nilpotent orbit theorem in Hodge theory.
A Theorem on Trend-Free Block Designs.
1981-02-01
AD-A09b 575 FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATIST ICS F/A 12/I A THEOREM ON TREND-FREE BLOCK DESIGNS. (U) FEB 81 C YEH R A BRADLEY N0001-80... C -0093 UNCLASSIFIED FSU-STATISTICS-M569 NL.’ II/////I/ *fl4 Low DTIC ELECTE MAR 2 0 1961 E The Florida State University Department of Statistics...1 ) n = hb9 ±, were bisthe b-dimensional colun vector with unit elements and B 9 C is the Kronecker product of B and C . Bradley and Yell (1980
On the Fundamental Theorem of the Theory of Relativity
NASA Astrophysics Data System (ADS)
Mamone-Capria, Marco
2016-12-01
A new formulation of what may be called the "fundamental theorem of the theory of relativity" is presented and proved in (3 + 1)-space-time, based on the full classification of special transformations and the corresponding velocity addition laws. A system of axioms is introduced and discussed leading to the result, and a study is made of several variants of that system. In particular the status of the group axiom is investigated with respect to the condition of the two-way isotropy of light. Several issues which are ignored or misunderstood in the literature are emphasized.
A Victorian Age Proof of the Four Color Theorem
NASA Astrophysics Data System (ADS)
Cahit, I.
2010-11-01
In this paper we have given an algorithmic proof of the four color theorem which is based only on the coloring faces (regions) of a cubic planar maps. Our algorithmic proof has been given in three steps. The first two steps are the maximal mono-chromatic and then maximal dichromatic coloring of the faces in such a way that the resulting uncolored (white) regions of the incomplete two-colored map induce no odd-cycles so that in the (final) third step four coloring of the map has been obtained almost trivially.
Research in advanced formal theorem-proving techniques
NASA Technical Reports Server (NTRS)
Rulifson, J. F.
1971-01-01
The present status is summarized of a continuing research program aimed at the design and implementation of a language for expressing problem-solving procedures in several areas of artificial intelligence, including program synthesis, robot planning, and theorem proving. Notations, concepts, and procedures common to the representation and solution of many of these problems were abstracted and incorporated as features into the language. The areas of research covered are described, and abstracts of six papers that contain extensive description and technical detail of the work are presented.
No-local-broadcasting theorem for multipartite quantum correlations.
Piani, Marco; Horodecki, Paweł; Horodecki, Ryszard
2008-03-07
We prove that the correlations present in a multipartite quantum state have an operational quantum character even if the state is unentangled, as long as it does not simply encode a multipartite classical probability distribution. Said quantumness is revealed by the new task of local broadcasting, i.e., of locally sharing preestablished correlations, which is feasible if and only if correlations are stricly classical. Our operational approach leads to natural definitions of measures for quantumness of correlations. It also reproduces the standard no-broadcasting theorem as a special case.
A no-go theorem for monodromy inflation
Andriot, David
2016-03-01
We study the embedding of the monodromy inflation mechanism by E. Silverstein and A. Westphal (2008) in a concrete compactification setting. To that end, we look for an appropriate vacuum of type IIA supergravity, corresponding to the minimum of the inflaton potential. We prove a no-go theorem on the existence of such a vacuum, using ten-dimensional equations of motion. Anti-de Sitter and Minkowski vacua are ruled out; de Sitter vacua are not excluded, but have a lower bound on their cosmological constant which is too high for phenomenology.
The Reciprocal of the Fundamental Theorem of Riemannian Geometry
NASA Astrophysics Data System (ADS)
Calderon, Hector
2008-05-01
The fundamental theorem of Riemannian geometry is inverted for analytic Christoffel symbols. The inversion formula, henceforth dubbed Ricardo's formula, is obtained without ancillary assumptions and it is well suited to compute the uncertainty in the metric that arises from the uncertainty in the measurement of positions. The solution is given up to a constant conformal factor, in part, because there are no experiments that can fix such factor without probing the whole universe. Ricardo's formula excludes some pathological examples and works for manifolds of any dimension and metrics of any signature.
Examples of the Zeroth Theorem of the History of Science
Jackson, J.D.
2007-08-24
The zeroth theorem of the history of science, enunciated byE. P. Fischer, states that a discovery (rule,regularity, insight) namedafter someone (often) did not originate with that person. I present fiveexamples from physics: the Lorentz condition partial muAmu = 0 definingthe Lorentz gauge of the electromagnetic potentials; the Dirac deltafunction, delta(x); the Schumann resonances of the earth-ionospherecavity; the Weizsacker-Williams method of virtual quanta; the BMTequation of spin dynamics. I give illustrated thumbnail sketches of boththe true and reputed discoverers and quote from their "discovery"publications.
Burg-Metzner-Sachs symmetry, string theory, and soft theorems
NASA Astrophysics Data System (ADS)
Avery, Steven G.; Schwab, Burkhard U. W.
2016-01-01
We study the action of the Burg-Metzner-Sachs (BMS) group in critical, bosonic string theory living on a target space of the form Md×C . Here Md is d -dimensional (asymptotically) flat spacetime and C is an arbitrary compactification. We provide a treatment of generalized Ward-Takahashi identities and derive consistent boundary conditions for any d from string theory considerations. Finally, we derive BMS transformations in higher-dimensional spacetimes and show that the generalized Ward-Takahashi identity of BMS produces Weinberg's soft theorem in string theory.
A Littlewood-Paley type theorem and a corollary
NASA Astrophysics Data System (ADS)
Kudryavtsev, S. N.
2013-12-01
We prove an analogue of the Littlewood-Paley theorem for orthoprojectors onto mutually orthogonal subspaces of piecewise-polynomial functions on the cube I^d. This yields upper bounds for the norms of functions in L_p(I^d) in terms of the corresponding norms of the projections to subspaces of piecewise-polynomial functions of several variables. We use these results to obtain upper bounds for the Kolmogorov widths of Besov classes of (non-periodic) functions satisfying mixed Hölder conditions.
Power and heat fluctuation theorems for electric circuits.
van Zon, R; Ciliberto, S; Cohen, E G D
2004-04-02
Using recent fluctuation theorems from nonequilibrium statistical mechanics, we extend the theory for voltage fluctuations in electric circuits to power and heat fluctuations. They could be of particular relevance for the functioning of small circuits. This is done for a parallel resistor and capacitor with a constant current source for which we use the analogy with a Brownian particle dragged through a fluid by a moving harmonic potential, where circuit-specific analogs are needed on top of the Brownian-Nyquist analogy. The results may also hold for other circuits as another example shows.
NASA Astrophysics Data System (ADS)
Aliouche, A.
2008-05-01
We prove a common fixed point theorem of Gregus type for four mappings satisfying a generalized contractive condition in metric spaces using the concept of weak compatibility which generalizes theorems of [I. Altun, D. Turkoglu, B.E. Rhoades, Fixed points of weakly compatible mappings satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007), article ID 17301; A. Djoudi, L. Nisse, Gregus type fixed points for weakly compatible mappings, Bull. Belg. Math. Soc. 10 (2003) 369-378; A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (1) (2007) 31-45; P. Vijayaraju, B.E. Rhoades, R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 15 (2005) 2359-2364; X. Zhang, Common fixed point theorems for some new generalized contractive type mappings, J. Math. Anal. Appl. 333 (2) (2007) 780-786]. We prove also a common fixed point theorem which generalizes Theorem 3.5 of [H.KE Pathak, M.S. Khan, T. Rakesh, A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl. 53 (2007) 961-971] and common fixed point theorems of Gregus type using a strict generalized contractive condition, a property (E.A) and a common property (E.A).
Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality
NASA Astrophysics Data System (ADS)
Bao, Ning; Pollack, Jason; Remmen, Grant N.
2015-11-01
We analyze the no-cloning theorem in quantum mechanics through the lens of the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between entanglement and wormholes. In particular, we find that the no-cloning theorem is dual on the gravity side to the no-go theorem for topology change, violating the axioms of which allows for wormhole stabilization and causality violation. Such a duality between important no-go theorems elucidates the proposed connection between spacetime geometry and quantum entanglement.
A weak Kantorovich existence theorem for the solution of nonlinear equations
NASA Astrophysics Data System (ADS)
Uko, Livinus U.; Argyros, Ioannis K.
2008-06-01
The Kantorovich theorem is a fundamental tool in nonlinear analysis for proving the existence and uniqueness of solutions of nonlinear equations arising in various fields. This theorem was weakened recently by Argyros who used a combination of Lipschitz and center-Lipschitz conditions in place of the Lipschitz conditions of the Kantorovich theorem. In the present paper we prove a weak Kantorovich-type theorem that gives the same conclusions as the previous two results under weaker conditions. Illustrative examples are provided in the paper.
2014-01-01
Background Knowledge regarding the best approaches to improving the quality of healthcare and their implementation is lacking in many resource-limited settings. The Medical Department of Kamuzu Central Hospital in Malawi set out to improve the quality of care provided to its patients and establish itself as a recognized centre in teaching, operations research and supervision of district hospitals. Efforts in the past to achieve these objectives were short-lived, and largely unsuccessful. Against this background, a situational analysis was performed to aid the Medical Department to define and prioritize its quality improvement activities. Methods A mix of quantitative and qualitative methods was applied using checklists for observed practice, review of registers, key informant interviews and structured patient interviews. The mixed methods comprised triangulation by including the perspectives of the clients, healthcare providers from within and outside the department, and the field researcher’s perspectives by means of document review and participatory observation. Results Human resource shortages, staff attitudes and shortage of equipment were identified as major constraints to patient care, and the running of the Medical Department. Processes, including documentation in registers and files and communication within and across cadres of staff were also found to be insufficient and thus undermining the effort of staff and management in establishing a sustained high quality culture. Depending on their past experience and knowledge, the stakeholder interviewees revealed different perspectives and expectations of quality healthcare and the intended quality improvement process. Conclusions Establishing a quality improvement process in resource-limited settings is an enormous task, considering the host of challenges that these facilities face. The steps towards changing the status quo for improved quality care require critical self-assessment, the willingness to change
No-hair theorem for black holes in astrophysical environments.
Gürlebeck, Norman
2015-04-17
According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.
Fundamental theorem on gauge fixing at the action level
NASA Astrophysics Data System (ADS)
Motohashi, Hayato; Suyama, Teruaki; Takahashi, Kazufumi
2016-12-01
Regardless of the long history of gauge theories, it is not well recognized under which condition gauge fixing at the action level is legitimate. We address this issue from the Lagrangian point of view, and prove the following theorem on the relation between gauge fixing and Euler-Lagrange equations: In any gauge theory, if a gauge fixing is complete, i.e., the gauge functions are determined uniquely by the gauge conditions, the Euler-Lagrange equations derived from the gauge-fixed action are equivalent to those derived from the original action supplemented with the gauge conditions. Otherwise, it is not appropriate to impose the gauge conditions before deriving Euler-Lagrange equations as it may in general lead to inconsistent results. The criterion to check whether a gauge fixing is complete or not is further investigated. We also provide applications of the theorem to scalar-tensor theories and make comments on recent relevant papers on theories of modified gravity, in which there are confusions on gauge fixing and counting physical degrees of freedom.
Fluctuation theorems and entropy production with odd-parity variables
NASA Astrophysics Data System (ADS)
Park, Hyunggyu; Lee, Hyun Keun; Kwon, Chulan
2013-03-01
We show that the total entropy production in stochastic processes with odd-parity variables (under time reversal) is separated into three parts, only two of which satisfy the integral fluctuation theorems in general. One is the usual excess contribution, which can appear only transiently and is called non-adiabatic. Another one is attributed solely to the breakage of detailed balance. The last part not satisfying the fluctuation theorem comes from the steady-state distribution asymmetry for odd-parity variables, which is activated in a non-transient manner. The latter two parts combine together as the house-keeping (adiabatic) contribution, whose positivity is not guaranteed except when the excess contribution completely vanishes. Our finding reveals that the equilibrium requires the steady-state distribution symmetry for odd-parity variables independently, in addition to the usual detailed balance. This work was supported by Mid-career Researcher Program through NRF grant (No. 2010-0026627) funded by the MEST.
Possible violation of the optical theorem in LHC experiments
NASA Astrophysics Data System (ADS)
Kupczynski, M.
2014-12-01
The optical theorem (OT), allowing the determination of the total cross section for a hadron-hadron scattering from the imaginary part of the forward elastic scattering amplitude, is believed to be an unavoidable consequence of the conservation of probability and of the unitary S matrix. This is a fundamental theorem which contains an imaginary part of the forward elastic scattering amplitude that is not directly measurable. The impossibility of scattering phenomena without the elastic channel is considered to be a part of the quantum magic. However, if one takes seriously the idea that the hadrons are extended particles, one may define a unitary S matrix such that one cannot prove the OT. Moreover, data violating the OT do exist, but they are not conclusive due to the uncertainties related to the extrapolation of the differential elastic cross-section to the forward direction. These results were published several years ago, but they were forgotten. In this paper we will recall these results in an understandable way, and we will give the additional arguments why the OT can be violated in high energy strong interaction scattering and why it should be tested and not simply used as a tool in LHC experiments.
Bayes' theorem: a paradigm research tool in biomedical sciences.
Okeh, U M; Ugwu, A C
2009-04-01
One of the most interesting applications of the results of probability theory involves estimating unknown probability and making decisions on the basis of new (sample) information. Biomedical scientists often use the Bayesian decision theory for the purposes of computing diagnostic values such as sensitivity and specificity for a certain diagnostic test and from which positive or negative predictive values are obtained in other to make decisions concerning the well-being of the patient. Often times error rates are encountered and estimated from the results of trials of the screening test with a view to calculating the overall case rate for which an accurate estimate is rarely available. The concept of conditional probability takes into account information about the occurrence of one event to predict the probability of another event. It is on this premise that this article presents Bayes' theorem as a vital tool. A brief intuitive development of this theorem and its application in diagnosis is given with minimum proof and examples.
The generalized second law implies a quantum singularity theorem
NASA Astrophysics Data System (ADS)
Wall, Aron C.
2013-08-01
The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose’s original singularity theorem, it implies that spacetime is null-geodesically incomplete inside black holes, and to the past of spatially infinite Friedmann-Robertson-Walker cosmologies. If space is finite instead, the generalized second law requires that there only be a finite amount of entropy producing processes in the past, unless there is a reversal of the arrow of time. In asymptotically flat spacetime, the generalized second law also rules out traversable wormholes, negative masses, and other forms of faster-than-light travel between asymptotic regions, as well as closed timelike curves. Furthermore it is impossible to form baby universes which eventually become independent of the mother universe, or to restart inflation. Since the semiclassical approximation is used only in regions with low curvature, it is argued that the results may hold in full quantum gravity. The introduction describes the second law and its time-reverse, in ordinary and generalized thermodynamics, using either the fine-grained or the coarse-grained entropy. (The fine-grained version is used in all results except those relating to the arrow of time.)
A double commutant theorem for Murray-von Neumann algebras.
Liu, Zhe
2012-05-15
Murray-von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra A of the Murray-von Neumann algebra A(f)(R) associated with a finite von Neumann algebra R is the Murray-von Neumann algebra A(f)(A(0)), where A(0) is a maximal abelian self-adjoint subalgebra of R and, in addition, A(0) is A Π R. We also prove that the Murray-von Neumann algebra A(f)(C) with C the center of R is the center of the Murray-von Neumann algebra A(f)(R). Von Neumann's celebrated double commutant theorem characterizes von Neumann algebras R as those for which R'' = R, where R', the commutant of R, is the set of bounded operators on the Hilbert space that commute with all operators in R. At the end of this article, we present a double commutant theorem for Murray-von Neumann algebras.
Multivariate numerical integration via fluctuationlessness theorem: Case study
NASA Astrophysics Data System (ADS)
Baykara, N. A.; Gürvit, Ercan
2017-01-01
In this work we come up with the statement of the Fluctuationlessness theorem recently conjectured and proven by M. Demiralp and its application to numerical integration of univariate functions by restructuring the Taylor expansion with explicit remainder term. The Fluctuationlessness theorem is stated. Following this step an orthonormal basis set is formed and the necessary formulae for calculating the coefficients of the three term recursion formula are constructed. Then for multivariate numerical integration, instead of dealing with a single formula for multiple remainder terms, a new approach that is already mentioned for bivariate functions is taken into consideration. At every step of a multivariate integration one variable is considered and the others are held constant. In such a way, this gives us the possibility to get rid of the complexity of calculations. The trivariate case is taken into account and its generalization is step by step explained. At the final stage implementations are done for some trivariate functions and the results are tabulated together with the implementation times.
Harmonic admittance and dispersion equations--the theorem.
Plessky, Viktor P; Biryukov, Sergey V; Koskela, Julius
2002-04-01
The harmonic admittance is known as a powerful tool for analyzing the excitation and propagation of surface acoustic waves (SAWs) in periodic electrode arrays. In particular, the dispersion relationships for open- and short-circuited systems are indicated, respectively, by the zeros and poles of the harmonic admittance. Here, we show that a strict reverse relationship also exists: the harmonic admittance of a periodic system of electrodes may always be expressed as the ratio of two determinants, which have been specifically constructed to describe the eigen-modes of the open- and short-circuited systems. There is no need to solve these equations to find the admittance. The existence of a connection between the excitation and propagation problems was recognized within the coupling-of-modes theory by Chen and Haus and was recently used to model surface transverse waves by Koskela et al., but a rigorous mathematical proof was only found later by Biryukov. Here, we reproduce this theorem in detail, give some examples of calculations based on this theorem, and compare the results with measured admittance curves.
Avoiding Haag's Theorem with Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Ed
2017-03-01
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that Haag's Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues.
RG flows in d dimensions, the dilaton effective action, and the a-theorem
NASA Astrophysics Data System (ADS)
Elvang, Henriette; Olson, Timothy M.
2013-03-01
Motivated by the recent dilaton-based proof of the 4d a-theorem, we study the dilaton effective action for RG flows in d dimensions. When d is even, the action consists of a Wess-Zumino (WZ) term, whose Weyl-variation encodes the trace-anomaly, plus all Weyl-invariants. For d odd, the action consists of Weyl-invariants only. We present explicit results for the flat-space limit of the dilaton effective action in d-dimensions up to and including 8-derivative terms. GJMS-operators from conformal geometry motivate a form of the action that unifies the Weyl-invariants and anomaly-terms into a compact general- d structure. A new feature in 8d is the presence of an 8-derivative Weyl-invariant that pollutes the O( p 8)-contribution from the WZ action to the dilaton scattering amplitudes; this may challenge a dilaton-based proof of an a-theorem in 8d. We use the example of a free massive scalar for two purposes: 1) it allows us to confirm the structure of the d-dimensional dilaton effective action explicitly; we carry out this check for d = 3, 4, 5, . . . , 10; and 2) in 8d we demonstrate how the flow Δ a = a UV - a IR can be extracted systematically from the O( p 8)-amplitudes despite the contamination from the 8-derivative Weyl-invariant. This computation gives a value for the a-anomaly of the 8d free conformal scalar that is shown to match the value obtained from zeta-function regularization of the log-term in the free energy.
ERIC Educational Resources Information Center
Stupel, Moshe; Ben-Chaim, David
2013-01-01
Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this…
State-Independent Proof of Kochen—Specker Theorem with Thirty Rank-Two Projectors
NASA Astrophysics Data System (ADS)
Toh, S. P.
2013-10-01
The Kochen—Specker theorem states that noncontextual hidden variable theories are incompatible with quantum mechanics. We provide a state-independent proof of the Kochen—Specker theorem using the smallest number of projectors, i.e., thirty rank-2 projectors, associated with the Mermin pentagram for a three-qubit system.
Bayes' Theorem: An Old Tool Applicable to Today's Classroom Measurement Needs. ERIC/AE Digest.
ERIC Educational Resources Information Center
Rudner, Lawrence M.
This digest introduces ways of responding to the call for criterion-referenced information using Bayes' Theorem, a method that was coupled with criterion-referenced testing in the early 1970s (see R. Hambleton and M. Novick, 1973). To illustrate Bayes' Theorem, an example is given in which the goal is to classify an examinee as being a master or…
The Poincaré-Bendixson Theorem and the non-linear Cauchy-Riemann equations
NASA Astrophysics Data System (ADS)
van den Berg, J. B.; Munaò, S.; Vandervorst, R. C. A. M.
2016-11-01
Fiedler and Mallet-Paret (1989) prove a version of the classical Poincaré-Bendixson Theorem for scalar parabolic equations. We prove that a similar result holds for bounded solutions of the non-linear Cauchy-Riemann equations. The latter is an application of an abstract theorem for flows with a(n) (unbounded) discrete Lyapunov function.
The Fundamental Theorem of Prevision. Technical Report No. 506. November 1987.
ERIC Educational Resources Information Center
Lad, F. R.; And Others
B. De Finetti's "Fundamental Theorem of Probability" is reformulated as a computable linear programming problem. The theorem is substantially extended, and shown to have fundamental implications for the theory and practice of statistics. It supports an operational meaning for the partial assertion of prevision via asserted bounds. The…
Bell's Theorem and Einstein's "Spooky Actions" from a Simple Thought Experiment
ERIC Educational Resources Information Center
Kuttner, Fred; Rosenblum, Bruce
2010-01-01
In 1964 John Bell proved a theorem allowing the experimental test of whether what Einstein derided as "spooky actions at a distance" actually exist. We will see that they "do". Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at "any" level. And a simple, semi-classical derivation of…
A basic theorem of complementarity for the generalized variational-like inequality problem
Yao, Jen-Chih.
1989-11-01
In this report, a basic theorem of complementarity is established for the generalized variational-like inequality problem introduced by Parida and Sen. Some existence results for both generalized variational inequality and complementarity problems are established by employing this basic theorem of complementarity. In particular, some sets of conditions that are normally satisfied by a nonsolvable generalized complementarity problem are investigated. 16 refs.
Higher order multi-dimensional extensions of Cesàro theorem
NASA Astrophysics Data System (ADS)
Accardi, Luigi; Ji, Un Cig; Saitô, Kimiaki
2015-12-01
The Cesàro theorem is extended to the cases: (1) higher order Cesàro mean for sequence (discrete case); and (2) higher order, multi-dimensional and continuous Cesàro mean for functions. Also, we study the Cesàro theorem for the case of positive-order.
A realization theorem for the Gödel-Löb provability logic
NASA Astrophysics Data System (ADS)
Shamkanov, D. S.
2016-09-01
We present a new justification logic corresponding to the Gödel-Löb provability logic GL and prove the realization theorem connecting these two systems in such a way that all the realizations provided in the theorem are normal. Bibliography: 9 titles.