Illustrating the Central Limit Theorem
ERIC Educational Resources Information Center
Corcoran, Mimi
2016-01-01
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
A Randomized Central Limit Theorem
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2010-05-01
The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√{n}), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √{n}. This Letter considers scaling schemes which are stochastic and non-uniform, and presents a "Randomized Central Limit Theorem" (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Lévy laws.
Visualizing the Central Limit Theorem through Simulation
ERIC Educational Resources Information Center
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
Central limit theorems under special relativity
McKeague, Ian W.
2015-01-01
Several relativistic extensions of the Maxwell–Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior. PMID:25798020
Randomized central limit theorems: A unified theory
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
Central limit theorem for reducible and irreducible open quantum walks
NASA Astrophysics Data System (ADS)
Sadowski, Przemysław; Pawela, Łukasz
2016-07-01
In this work we aim at proving central limit theorems for open quantum walks on {mathbb {Z}}^d. We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.
Central limit theorem for reducible and irreducible open quantum walks
NASA Astrophysics Data System (ADS)
Sadowski, Przemysław; Pawela, Łukasz
2016-04-01
In this work we aim at proving central limit theorems for open quantum walks on {{Z}}^d . We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.
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.)
FAST TRACK COMMUNICATION: Central limit theorem and deformed exponentials
NASA Astrophysics Data System (ADS)
Vignat, C.; Plastino, A.
2007-11-01
The central limit theorem (CLT) can be ranked among the most important ones in probability theory and statistics and plays an essential role in several basic and applied disciplines, notably in statistical thermodynamics. We show that there exists a natural extension of the CLT from exponentials to so-called deformed exponentials (also denoted as q-Gaussians). Our proposal applies exactly in the usual conditions in which the classical CLT is used.
On the quenched central limit theorem for random dynamical systems
NASA Astrophysics Data System (ADS)
Abdelkader, Mohamed; Aimino, Romain
2016-06-01
We provide a necessary and sufficient condition under which the quenched central limit theorem without random centering holds for one-dimensional random systems that are uniformly expanding. This condition holds in particular when all the maps preserve a common measure. We also give a counter example which shows that this condition is not necessarily satisfied when the maps do not preserve a common measure.
Central Limit Theorems for the Shrinking Target Problem
NASA Astrophysics Data System (ADS)
Haydn, Nicolai; Nicol, Matthew; Vaienti, Sandro; Zhang, Licheng
2013-12-01
Suppose B i := B( p, r i ) are nested balls of radius r i about a point p in a dynamical system ( T, X, μ). The question of whether T i x∈ B i infinitely often (i.o.) for μ a.e. x is often called the shrinking target problem. In many dynamical settings it has been shown that if diverges then there is a quantitative rate of entry and for μ a.e. x∈ X. This is a self-norming type of strong law of large numbers. We establish self-norming central limit theorems (CLT) of the form (in distribution) for a variety of hyperbolic and non-uniformly hyperbolic dynamical systems, the normalization constants are . Dynamical systems to which our results apply include smooth expanding maps of the interval, Rychlik type maps, Gibbs-Markov maps, rational maps and, in higher dimensions, piecewise expanding maps. For such central limit theorems the main difficulty is to prove that the non-stationary variance has a limit in probability.
Central Limit Theorem: New SOCR Applet and Demonstration Activity
Dinov, Ivo D.; Christou, Nicolas; Sanchez, Juana
2011-01-01
Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multifaceted learning environments, which may facilitate student comprehension and information retention. In this manuscript, we describe one such innovative effort of using technological tools for improving student motivation and learning of the theory, practice and usability of the Central Limit Theorem (CLT) in probability and statistics courses. Our approach is based on harnessing the computational libraries developed by the Statistics Online Computational Resource (SOCR) to design a new interactive Java applet and a corresponding demonstration activity that illustrate the meaning and the power of the CLT. The CLT applet and activity have clear common goals; to provide graphical representation of the CLT, to improve student intuition, and to empirically validate and establish the limits of the CLT. The SOCR CLT activity consists of four experiments that demonstrate the assumptions, meaning and implications of the CLT and ties these to specific hands-on simulations. We include a number of examples illustrating the theory and applications of the CLT. Both the SOCR CLT applet and activity are freely available online to the community to test, validate and extend (Applet: http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and Activity: http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem). PMID:21833159
Central Limit Theorem: New SOCR Applet and Demonstration Activity.
Dinov, Ivo D; Christou, Nicolas; Sanchez, Juana
2008-07-01
Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multifaceted learning environments, which may facilitate student comprehension and information retention. In this manuscript, we describe one such innovative effort of using technological tools for improving student motivation and learning of the theory, practice and usability of the Central Limit Theorem (CLT) in probability and statistics courses. Our approach is based on harnessing the computational libraries developed by the Statistics Online Computational Resource (SOCR) to design a new interactive Java applet and a corresponding demonstration activity that illustrate the meaning and the power of the CLT. The CLT applet and activity have clear common goals; to provide graphical representation of the CLT, to improve student intuition, and to empirically validate and establish the limits of the CLT. The SOCR CLT activity consists of four experiments that demonstrate the assumptions, meaning and implications of the CLT and ties these to specific hands-on simulations. We include a number of examples illustrating the theory and applications of the CLT. Both the SOCR CLT applet and activity are freely available online to the community to test, validate and extend (Applet: http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and Activity: http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem). PMID:21833159
Continuous-variable entanglement distillation and noncommutative central limit theorems
NASA Astrophysics Data System (ADS)
Campbell, Earl T.; Genoni, Marco G.; Eisert, Jens
2013-04-01
Entanglement distillation transforms weakly entangled noisy states into highly entangled states, a primitive to be used in quantum repeater schemes and other protocols designed for quantum communication and key distribution. In this work, we present a comprehensive framework for continuous-variable entanglement distillation schemes that convert noisy non-Gaussian states into Gaussian ones in many iterations of the protocol. Instances of these protocols include (a) the recursive-Gaussifier protocol, (b) the temporally reordered recursive-Gaussifier protocol, and (c) the pumping-Gaussifier protocol. The flexibility of these protocols gives rise to several beneficial trade-offs related to success probabilities or memory requirements, which can be adjusted to reflect experimental demands. Despite these protocols involving measurements, we relate the convergence in this protocol to new instances of noncommutative central limit theorems, in a formalism that we lay out in great detail. Implications of the findings for quantum repeater schemes are discussed.
Planetary Accretion, Oxygen Isotopes and the Central Limit Theorem
NASA Technical Reports Server (NTRS)
Nuth, Joseph A., III; Hill, Hugh G. M.; Vondrak, Richard R. (Technical Monitor)
2001-01-01
The accumulation of presolar dust into increasingly larger aggregates (CAIs and Chondrules, Asteroids, Planets) should result in a very drastic reduction in the numerical spread in oxygen isotopic composition between bodies of similar size, in accord with the Central Limit Theorem. Observed variations in oxygen isotopic composition are many orders of magnitude larger than would be predicted by a simple, random accumulation model that begins in a well-mixed nebula - no matter which size-scale objects are used as the beginning or end points of the calculation. This discrepancy implies either that some as yet unspecified process acted on the solids in the Solar Nebula to increase the spread in oxygen isotopic composition during each and every stage of accumulation or that the nebula was heterogeneous and maintained this heterogeneity throughout most of nebular history. Large-scale nebular heterogeneity would have significant consequences for many areas of cosmochemistry, including the application of some well-known isotopic systems to the dating of nebular events or the prediction of bulk compositions of planetary bodies on the basis of a uniform cosmic abundance.
Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices
NASA Astrophysics Data System (ADS)
Benaych-Georges, Florent; Guionnet, Alice; Male, Camille
2014-07-01
We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.
The Power of Doing: A Learning Exercise That Brings the Central Limit Theorem to Life
ERIC Educational Resources Information Center
Price, Barbara A.; Zhang, Xiaolong
2007-01-01
This article demonstrates an active learning technique for teaching the Central Limit Theorem (CLT) in an introductory undergraduate business statistics class. Groups of students carry out one of two experiments in the lab, tossing a die in sets of 5 rolls or tossing a die in sets of 10 rolls. They are asked to calculate the sample average of each…
Central Limit Theorems and Uniform Laws of Large Numbers for Arrays of Random Fields
Jenish, Nazgul; Prucha, Ingmar R.
2009-01-01
Over the last decades, spatial-interaction models have been increasingly used in economics. However, the development of a sufficiently general asymptotic theory for nonlinear spatial models has been hampered by a lack of relevant central limit theorems (CLTs), uniform laws of large numbers (ULLNs) and pointwise laws of large numbers (LLNs). These limit theorems form the essential building blocks towards developing the asymptotic theory of M-estimators, including maximum likelihood and generalized method of moments estimators. The paper establishes a CLT, ULLN, and LLN for spatial processes or random fields that should be applicable to a broad range of data processes. PMID:20161289
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.
Zipf's law is not a consequence of the central limit theorem
NASA Astrophysics Data System (ADS)
Troll, G.; Beim Graben, P.
1998-02-01
It has been observed that the rank statistics of string frequencies of many symbolic systems (e.g., word frequencies of natural languages) follows Zipf's law in good approximation. We show that, contrary to claims in the literature, Zipf's law cannot be realized by the central limit theorem(s). The observation that a log-normal distribution of string frequencies yields an approximately Zipf-like rank statistics is actually misleading. Indeed, Zipf's law for the rank statistics is strictly equivalent to a power law distribution of frequencies. There are two natural ways to perform the infinite size limit for the vocabulary. The first one is the method of choice in the literature; it makes the upper word length bound tend to infinity and leads in the case of a multistate Bernoulli process via a central limit theorem to a log-normal frequency distribution. An alternative and for text samples actually better realizable way is to make the lower frequency bound tend to zero. This limit procedure leads to a power law distribution and hence to Zipf's law-at least for Bernoulli processes and to a very good approximation for natural languages where it passes the χ2 test. For the Bernoulli case we will give a heuristic proof.
Non-normalizable densities in strong anomalous diffusion: beyond the central limit theorem.
Rebenshtok, Adi; Denisov, Sergey; Hänggi, Peter; Barkai, Eli
2014-03-21
Strong anomalous diffusion, where ⟨|x(t)|(q)⟩ ∼ tqν(q) with a nonlinear spectrum ν(q) ≠ const, is wide spread and has been found in various nonlinear dynamical systems and experiments on active transport in living cells. Using a stochastic approach we show how this phenomenon is related to infinite covariant densities; i.e., the asymptotic states of these systems are described by non-normalizable distribution functions. Our work shows that the concept of infinite covariant densities plays an important role in the statistical description of open systems exhibiting multifractal anomalous diffusion, as it is complementary to the central limit theorem. PMID:24702341
Influence of global correlations on central limit theorems and entropic extensivity
NASA Astrophysics Data System (ADS)
Marsh, John A.; Fuentes, Miguel A.; Moyano, Luis G.; Tsallis, Constantino
2006-12-01
We consider probabilistic models of N identical distinguishable, binary random variables. If these variables are strictly or asymptotically independent, then, for N→∞, (i) the attractor in distribution space is, according to the standard central limit theorem, a Gaussian, and (ii) the Boltzmann-Gibbs-Shannon entropy S≡-∑i=1Wpln pi (where W=2 N) is extensive, meaning that S BGS( N)∼ N. If these variables have any nonvanishing global (i.e., not asymptotically independent) correlations, then the attractor deviates from the Gaussian. The entropy appears to be more robust, in the sense that, in some cases, SBGS remains extensive even in the presence of strong global correlations. In other cases, however, even weak global correlations make the entropy deviate from the normal behavior. More precisely, in such cases the entropic form Sq≡{1}/{q-1} (1-∑i=1Wpiq) (with S 1tbnd6 S BGS) can become extensive for some value of q≠1. This scenario is illustrated with several new as well as previously described models. The discussion illuminates recent progress into q-describable nonextensive probabilistic systems, and the conjectured q-Central Limit Theorem ( q-CLT) which posses a q-Gaussian attractor.
Sanov and central limit theorems for output statistics of quantum Markov chains
Horssen, Merlijn van; Guţă, Mădălin
2015-02-15
In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Such higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.
The Star Forming Main Sequence and its Scatter as Conequences of the Central Limit Theorem
NASA Astrophysics Data System (ADS)
Kelson, Daniel
2015-01-01
Star formation rates of disk galaxies strongly correlate with stellar mass, with a small dispersion in specific star formation rate at fixed mass. With such small scattter this main sequence of star formation has been interpreted as deterministic and fundamental. Here it is demonstrated that it is a simple consequence off he central limit theorem. Treating the star formation histories of galaxies as integrable, non-differentiable functions, where stochastic changes in star formation rate in a galaxy's history are not fully independent of each other, we derive the median specific star formation rate for the flat part of the main sequence from 0
Central limit theorem for a class of globally correlated random variables
NASA Astrophysics Data System (ADS)
Budini, Adrián A.
2016-06-01
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in the presence of strong correlations between the added random contributions. Here, we study this problem for similar interchangeable globally correlated random variables. Under these conditions, a hierarchical set of equations is derived for the conditional transition probabilities. This result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables. Depending on the correlation mechanisms and statistics of the single variables, the corresponding sums are characterized by distinct probability densities. For a class of urn models it is also possible to characterize their domain of attraction, which, as in the standard case, is parametrized by the probability density of each random variable. Symmetric and asymmetric q -Gaussian attractors (q <1 ) arise in a particular two-state case of these urn models.
A central-limit theorem for a single-false match rate
NASA Astrophysics Data System (ADS)
Dietz, Zachariah; Schuckers, Michael E.
2010-04-01
In this paper, we present a central limit theorem (CLT) for the estimation of a false match rate for a single matching system. The false match rate is often a significant factor in an evaluation of such a matching system. To achieve the main result here we utilize the covariance/correlation structure for matching proposed by Schuckers. Along with the main result we present an illustration of the methodology here on biometric authentication data from Ross and Jain. This illustration is from resampling match decisions on three different biometric modalities: hand geometry, fingerprint and facial recognition and shows that as the number of matching pairs grows the sampling distribution for an FMR approaches a Gaussian distribution. These results suggest that statistical inference for a FMR based upon a Gaussian distribution is appropriate.
ERIC Educational Resources Information Center
Yu, Chong Ho; And Others
Central limit theorem (CLT) is considered an important topic in statistics, because it serves as the basis for subsequent learning in other crucial concepts such as hypothesis testing and power analysis. There is an increasing popularity in using dynamic computer software for illustrating CLT. Graphical displays do not necessarily clear up…
Assessment of the statistics of the Strehl ratio: predictions of central limit theorem analysis
NASA Astrophysics Data System (ADS)
Tyler, Glenn A.
2006-11-01
For a beam propagating through turbulence, the statistics of the Strehl ratio are determined by recognizing that the real and imaginary parts of the on-axis far-field pattern can be represented as the sum of many contributions from the aperture. With this in mind, the central limit theorem (CLT) can be used to develop the statistics of the real and imaginary parts of the optical field, which through the appropriate mathematical manipulations as described here can then be used to develop the probability distribution of the far-field irradiance. The results obtained in this way (which we call the CLT theory or analysis) provide an analytic expression that agrees with the results of detailed wave-optics simulations. This provides an approach by which the statistics of the Strehl ratio can be rapidly determined. A key feature of this work is that the analytic results depend on the values of a few relevant turbulence parameters that include r0,fG, and σ2l. Therefore, a measurement of these parameters at various sites of interest allows us to rapidly assess the detailed nature of the statistical fluctuations of the far-field irradiance that will be experienced at these locations.
NASA Astrophysics Data System (ADS)
Salgado-García, R.; Maldonado, Cesar
2013-12-01
We study the diffusion of an ensemble of overdamped particles sliding over a tilted random potential (produced by the interaction of a particle with a random polymer) with long-range correlations. We found that the diffusion properties of such a system are closely related to the correlation function of the corresponding potential. We model the substrate as a symbolic trajectory of a shift space which enables us to obtain a general formula for the diffusion coefficient when normal diffusion occurs. The total time that the particle takes to travel through n monomers can be seen as an ergodic sum to which we can apply the central limit theorem. The latter can be implemented if the correlations decay fast enough in order for the central limit theorem to be valid. On the other hand, we presume that when the central limit theorem breaks down the system give rise to anomalous diffusion. We give two examples exhibiting a transition from normal to anomalous diffusion due to this mechanism. We also give analytical expressions for the diffusion exponents in both cases by assuming convergence to a stable law. Finally we test our predictions by means of numerical simulations.
Salgado-García, R; Maldonado, Cesar
2013-12-01
We study the diffusion of an ensemble of overdamped particles sliding over a tilted random potential (produced by the interaction of a particle with a random polymer) with long-range correlations. We found that the diffusion properties of such a system are closely related to the correlation function of the corresponding potential. We model the substrate as a symbolic trajectory of a shift space which enables us to obtain a general formula for the diffusion coefficient when normal diffusion occurs. The total time that the particle takes to travel through n monomers can be seen as an ergodic sum to which we can apply the central limit theorem. The latter can be implemented if the correlations decay fast enough in order for the central limit theorem to be valid. On the other hand, we presume that when the central limit theorem breaks down the system give rise to anomalous diffusion. We give two examples exhibiting a transition from normal to anomalous diffusion due to this mechanism. We also give analytical expressions for the diffusion exponents in both cases by assuming convergence to a stable law. Finally we test our predictions by means of numerical simulations. PMID:24483421
The Star-Forming Main Sequence as a Natural Consequence of the Central Limit Theorem
NASA Astrophysics Data System (ADS)
Kelson, Daniel David
2015-08-01
Star-formation rates (SFR) of disk galaxies correlate with stellar mass, with a small dispersion in SSFR at fixed mass, sigma~0.3 dex. With such scatter this star-formation main sequence (SFMS) has been interpreted as deterministic and fundamental. Here I demonstrate that such a correlation arises naturally from the central limit theorem. The derivation begins by approximating in situ stellar mass growth as a stochastic process, much like a random walk, where the expectation of SFR at any time is equal to the SFR at the previous time. The SFRs of real galaxies, however, do not experience wholly random stochastic changes over time, but change in a highly correlated fashion due to the long reach of gravity and the correlation of structure in the universe. We therefore generalize the results for star-formation as a stochastic process that has random correlations over random and potentially infinite timescales. For unbiased samples of (disk) galaxies we derive expectation values for SSFR and its scatter, such that
Occupancy of phase space, extensivity of Sq, and q-generalized central limit theorem
NASA Astrophysics Data System (ADS)
Tsallis, Constantino
2006-06-01
Increasing the number N of elements of a system typically makes the entropy to increase. The question arises on what particular entropic form we have in mind and how it increases with N. Thermodynamically speaking it makes sense to choose an entropy which increases linearly with N for large N, i.e., which is extensive. If the N elements are probabilistically independent (no interactions) or quasi-independent (e.g., short-range interacting), it is known that the entropy which is extensive is that of Boltzmann-Gibbs-Shannon, SBG≡-k∑i=1Wpilnpi. If they are, however, globally correlated (e.g., through long-range interactions), the answer depends on the particular nature of the correlations. There is a large class of correlations (in one way or another related to scale-invariance) for which an appropriate entropy is that on which nonextensive statistical mechanics is based, i.e., Sq≡k(1-∑i=1Wpiq)/q-1 ( S1=SBG), where q is determined by the specific correlations. We briefly review and illustrate these ideas through simple examples of occupation of phase space. A very similar scenario emerges with regard to the central limit theorem (CLT). If the variables that are being summed are independent (or quasi-independent, in the sense that they gradually become independent if N→∞), two basic possibilities exist: if the variance of the random variables that are being composed is finite, the N→∞ attractor in the space of distributions is a Gaussian, whereas if it diverges, it is a Lévy distribution. If the variables that are being summed are however globally correlated, there is no reason to expect the usual CLTs to hold. The N→∞ attractor is expected to depend on the nature of the correlations. That class of correlations (or part of it) that makes Sq to be extensive for q≠1 is expected to have a qe-Gaussian as its N→∞ attractor, where qe depends on q [ qe(q) such that qe(1)=1], and where qe-Gaussians are proportional to [1-(1-qe)β x2] ( β>0; qe<3
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…
Limit Theorems for Dispersing Billiards with Cusps
NASA Astrophysics Data System (ADS)
Bálint, P.; Chernov, N.; Dolgopyat, D.
2011-12-01
Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting "intermittent" behavior that alternates between regular and chaotic patterns. Their statistical properties are therefore weak and delicate. They are characterized by a slow (power-law) decay of correlations, and as a result the classical central limit theorem fails. We prove that a non-classical central limit theorem holds, with a scaling factor of {sqrt{nlog n}} replacing the standard {sqrt{n}} . We also derive the respective Weak Invariance Principle, and we identify the class of observables for which the classical CLT still holds.
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…
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.
NASA Astrophysics Data System (ADS)
Pluchino, Alessandro; Rapisarda, Andrea; Tsallis, Constantino
2008-05-01
We give a closer look at the Central Limit Theorem (CLT) behavior in quasi-stationary states of the Hamiltonian Mean Field model, a paradigmatic one for long-range-interacting classical many-body systems. We present new calculations which show that, following their time evolution, we can observe and classify three kinds of long-standing quasi-stationary states (QSS) with different correlations. The frequency of occurrence of each class depends on the size of the system. The different microscopic nature of the QSS leads to different dynamical correlations and therefore to different results for the observed CLT behavior.
Stephan, Carl N
2014-03-01
By pooling independent study means (x¯), the T-Tables use the central limit theorem and law of large numbers to average out study-specific sampling bias and instrument errors and, in turn, triangulate upon human population means (μ). Since their first publication in 2008, new data from >2660 adults have been collected (c.30% of the original sample) making a review of the T-Table's robustness timely. Updated grand means show that the new data have negligible impact on the previously published statistics: maximum change = 1.7 mm at gonion; and ≤1 mm at 93% of all landmarks measured. This confirms the utility of the 2008 T-Table as a proxy to soft tissue depth population means and, together with updated sample sizes (8851 individuals at pogonion), earmarks the 2013 T-Table as the premier mean facial soft tissue depth standard for craniofacial identification casework. The utility of the T-Table, in comparison with shorths and 75-shormaxes, is also discussed. PMID:24313424
A THEOREM ON CENTRAL VELOCITY DISPERSIONS
An, Jin H.; Evans, N. Wyn E-mail: nwe@ast.cam.ac.uk
2009-08-20
It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere (SIS), the logarithmic cusp slope {gamma} of the tracers must be given exactly by {gamma} = 2{beta}, where {beta} is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the SIS, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging velocity dispersion also traces the behavior of the potential. The implication of our theorem on projected quantities is also discussed. We argue that our theorem should be understood as a warning against interpreting results based on simplifying assumptions such as isotropy and spherical symmetry.
Some functional limit theorems for compound Cox processes
NASA Astrophysics Data System (ADS)
Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.
2016-06-01
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
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.
Limit theorems in the imitative monomer-dimer mean-field model via Stein's method
NASA Astrophysics Data System (ADS)
Chen, Wei-Kuo
2016-08-01
We consider the imitative monomer-dimer model on the complete graph introduced in the work of Alberici et al. [J. Math. Phys. 55, 063301-1-063301-27 (2014)]. It was shown that this model is described by the monomer density and has a phase transition along certain coexistence curve, where the monomer and dimer phases coexist. More recently, it was understood [D. Alberici et al., Commun. Math. Phys. (published online, 2016)] that the monomer density exhibits the central limit theorem away from the coexistence curve and enjoys a non-normal limit theorem at criticality with normalized exponent 3/4. By reverting the model to a weighted Curie-Weiss model with hard core interaction, we establish the complete description of the fluctuation properties of the monomer density on the full parameter space via Stein's method of exchangeable pairs. Our approach recovers what were established in the work of Alberici et al. [Commun. Math. Phys. (published online, 2016)] and furthermore allows to obtain the conditional central limit theorems along the coexistence curve. In all these results, the Berry-Esseen inequalities for the Kolmogorov-Smirnov distance are given.
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.
Central limit behavior of deterministic dynamical systems
NASA Astrophysics Data System (ADS)
Tirnakli, Ugur; Beck, Christian; Tsallis, Constantino
2007-04-01
We investigate the probability density of rescaled sums of iterates of deterministic dynamical systems, a problem relevant for many complex physical systems consisting of dependent random variables. A central limit theorem (CLT) is valid only if the dynamical system under consideration is sufficiently mixing. For the fully developed logistic map and a cubic map we analytically calculate the leading-order corrections to the CLT if only a finite number of iterates is added and rescaled, and find excellent agreement with numerical experiments. At the critical point of period doubling accumulation, a CLT is not valid anymore due to strong temporal correlations between the iterates. Nevertheless, we provide numerical evidence that in this case the probability density converges to a q -Gaussian, thus leading to a power-law generalization of the CLT. The above behavior is universal and independent of the order of the maximum of the map considered, i.e., relevant for large classes of critical dynamical systems.
The Free Will Theorem and Limits on Realistic Theories
NASA Astrophysics Data System (ADS)
Godfrey, Christopher
2010-03-01
The rGRWf model (Tumulka 2006) is a proposed solution of the measurement problem of quantum mechanics involving a stochastic nonlinear wave equation embedded in a relativistic framework. Its primary feature is a mechanism that suppresses superpositions of macroscopically different states for macroscopic systems. However, the Free Will Theorem (FWT) proposed by Conway and Kochen (Conway and Kochen 2007, 2009) purports to prove that no theory that is both non-deterministic and relativistic can reproduce all possible measurement results on a system of two entangled spin-one particles. Here we examine both the rGRWf model and the FWT. It is demonstrated that underlying assumptions in the postulates of the FWT rule out certain classes of realistic physical theories. These underlying assumptions and the characteristics of physical theories permitted by the FWT axioms are discussed.
The Implicit Function Theorem and Non-Existence of Limit of Functions of Several Variables
ERIC Educational Resources Information Center
dos Santos, A. L. C.; da Silva, P. N.
2008-01-01
We use the Implicit Function Theorem to establish a result of non-existence of limit to a certain class of functions of several variables. We consider functions given by quotients such that both the numerator and denominator functions are null at the limit point. We show that the non-existence of the limit of such function is related with the…
Pedagogical Simulation of Sampling Distributions and the Central Limit Theorem
ERIC Educational Resources Information Center
Hagtvedt, Reidar; Jones, Gregory Todd; Jones, Kari
2007-01-01
Students often find the fact that a sample statistic is a random variable very hard to grasp. Even more mysterious is why a sample mean should become ever more Normal as the sample size increases. This simulation tool is meant to illustrate the process, thereby giving students some intuitive grasp of the relationship between a parent population…
Central Limit Theorem: New SOCR Applet and Demonstration Activity
ERIC Educational Resources Information Center
Dinov, Ivo D.; Christou, Nicholas; Sanchez, Juana
2008-01-01
Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multi-faceted learning environments, which may facilitate student comprehension and information…
Day, Troy
2012-04-01
The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century, there have been remarkable advances in the development of theory for this diversification, and the theory's success rests, in part, on the scope of its applicability. A great deal of this theory focuses on a relatively small subset of the space of potential genotypes, chosen largely based on historical or contemporary patterns, and then predicts the evolutionary dynamics within this pre-defined set. To what extent can such an approach be pushed to a broader perspective that accounts for the potential open-endedness of evolutionary diversification? There have been a number of significant theoretical developments along these lines but the question of how far such theory can be pushed has not been addressed. Here a theorem is proven demonstrating that, because of the digital nature of inheritance, there are inherent limits on the kinds of questions that can be answered using such an approach. In particular, even in extremely simple evolutionary systems, a complete theory accounting for the potential open-endedness of evolution is unattainable unless evolution is progressive. The theorem is closely related to Gödel's incompleteness theorem, and to the halting problem from computability theory. PMID:21849390
Day, Troy
2012-01-01
The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century, there have been remarkable advances in the development of theory for this diversification, and the theory's success rests, in part, on the scope of its applicability. A great deal of this theory focuses on a relatively small subset of the space of potential genotypes, chosen largely based on historical or contemporary patterns, and then predicts the evolutionary dynamics within this pre-defined set. To what extent can such an approach be pushed to a broader perspective that accounts for the potential open-endedness of evolutionary diversification? There have been a number of significant theoretical developments along these lines but the question of how far such theory can be pushed has not been addressed. Here a theorem is proven demonstrating that, because of the digital nature of inheritance, there are inherent limits on the kinds of questions that can be answered using such an approach. In particular, even in extremely simple evolutionary systems, a complete theory accounting for the potential open-endedness of evolution is unattainable unless evolution is progressive. The theorem is closely related to Gödel's incompleteness theorem, and to the halting problem from computability theory. PMID:21849390
Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs
NASA Astrophysics Data System (ADS)
Roychoudhuri, Chandrasekhar
2007-09-01
We celebrate the two hundred years of successful use of the Fourier theorem in optics. However, there is a great enigma associated with the Fourier transform integral. It is one of the most pervasively productive and useful tool of physics and optics because its foundation is based on the superposition of harmonic functions and yet we have never declared it as a principle of physics for valid reasons. And, yet there are a good number of situations where we pretend it to be equivalent to the superposition principle of physics, creating epistemological problems of enormous magnitude. The purpose of the paper is to elucidate the problems while underscoring the successes and the elegance of the Fourier theorem, which are not explicitly discussed in the literature. We will make our point by taking six major engineering fields of optics and show in each case why it works and under what restricted conditions by bringing in the relevant physics principles. The fields are (i) optical signal processing, (ii) Fourier transform spectrometry, (iii) classical spectrometry of pulsed light, (iv) coherence theory, (v) laser mode locking and (vi) pulse broadening. We underscore that mathematical Fourier frequencies, not being physical frequencies, cannot generate real physical effects on our detectors. Appreciation of this fundamental issue will open up ways to be innovative in many new optical instrument designs. We underscore the importance of always validating our design platforms based on valid physics principles (actual processes undergoing in nature) captured by an appropriate hypothesis based on diverse observations. This paper is a comprehensive view of the power and limitations of Fourier Transform by summarizing a series of SPIE conference papers presented during 2003-2007.
Central limit behavior in the Kuramoto model at the “edge of chaos”
NASA Astrophysics Data System (ADS)
Miritello, Giovanna; Pluchino, Alessandro; Rapisarda, Andrea
2009-12-01
We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong, the Pdfs of the sums tend to a Gaussian, consistently with the standard CLT. On the other hand, when the system is at the “edge of chaos” (i.e. in a regime with vanishing Lyapunov exponents), robust q-Gaussian-like limit distributions naturally emerge, consistently with recently proved generalizations of the CLT.
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.
Nonergodicity and central-limit behavior for long-range Hamiltonians
NASA Astrophysics Data System (ADS)
Pluchino, A.; Rapisarda, A.; Tsallis, C.
2007-10-01
We present a molecular dynamics test of the Central-Limit Theorem (CLT) in a paradigmatic long-range-interacting many-body classical Hamiltonian system, the HMF model. We calculate sums of velocities at equidistant times along deterministic trajectories for different sizes and energy densities. We show that, when the system is in a chaotic regime (specifically, at thermal equilibrium), ergodicity is essentially verified, and the Pdfs of the sums appear to be Gaussians, consistently with the standard CLT. When the system is, instead, only weakly chaotic (specifically, along longstanding metastable Quasi-Stationary States), nonergodicity (i.e., discrepant ensemble and time averages) is observed, and robust q-Gaussian attractors emerge, consistently with recently proved generalizations of the CLT.
Fractional Edgeworth expansion: Corrections to the Gaussian-Lévy central-limit theorem.
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. PMID:26066136
Variances and covariances in the Central Limit Theorem for the output of a transducer
Heuberger, Clemens; Kropf, Sara; Wagner, Stephan
2015-01-01
We study the joint distribution of the input sum and the output sum of a deterministic transducer. Here, the input of this finite-state machine is a uniformly distributed random sequence. We give a simple combinatorial characterization of transducers for which the output sum has bounded variance, and we also provide algebraic and combinatorial characterizations of transducers for which the covariance of input and output sum is bounded, so that the two are asymptotically independent. Our results are illustrated by several examples, such as transducers that count specific blocks in the binary expansion, the transducer that computes the Gray code, or the transducer that computes the Hamming weight of the width-w non-adjacent form digit expansion. The latter two turn out to be examples of asymptotic independence. PMID:27087727
Range-limited centrality measures in complex networks
NASA Astrophysics Data System (ADS)
Ercsey-Ravasz, Mária; Lichtenwalter, Ryan N.; Chawla, Nitesh V.; Toroczkai, Zoltán
2012-06-01
Here we present a range-limited approach to centrality measures in both nonweighted and weighted directed complex networks. We introduce an efficient method that generates for every node and every edge its betweenness centrality based on shortest paths of lengths not longer than ℓ=1,...,L in the case of nonweighted networks, and for weighted networks the corresponding quantities based on minimum weight paths with path weights not larger than wℓ=ℓΔ, ℓ=1,2...,L=R/Δ. These measures provide a systematic description on the positioning importance of a node (edge) with respect to its network neighborhoods one step out, two steps out, etc., up to and including the whole network. They are more informative than traditional centrality measures, as network transport typically happens on all length scales, from transport to nearest neighbors to the farthest reaches of the network. We show that range-limited centralities obey universal scaling laws for large nonweighted networks. As the computation of traditional centrality measures is costly, this scaling behavior can be exploited to efficiently estimate centralities of nodes and edges for all ranges, including the traditional ones. The scaling behavior can also be exploited to show that the ranking top list of nodes (edges) based on their range-limited centralities quickly freezes as a function of the range, and hence the diameter-range top list can be efficiently predicted. We also show how to estimate the typical largest node-to-node distance for a network of N nodes, exploiting the afore-mentioned scaling behavior. These observations were made on model networks and on a large social network inferred from cell-phone trace logs (˜5.5×106 nodes and ˜2.7×107 edges). Finally, we apply these concepts to efficiently detect the vulnerability backbone of a network (defined as the smallest percolating cluster of the highest betweenness nodes and edges) and illustrate the importance of weight-based centrality measures in
Range-limited centrality measures in complex networks.
Ercsey-Ravasz, Mária; Lichtenwalter, Ryan N; Chawla, Nitesh V; Toroczkai, Zoltán
2012-06-01
Here we present a range-limited approach to centrality measures in both nonweighted and weighted directed complex networks. We introduce an efficient method that generates for every node and every edge its betweenness centrality based on shortest paths of lengths not longer than ℓ=1,...,L in the case of nonweighted networks, and for weighted networks the corresponding quantities based on minimum weight paths with path weights not larger than w(ℓ)=ℓΔ, ℓ=1,2...,L=R/Δ. These measures provide a systematic description on the positioning importance of a node (edge) with respect to its network neighborhoods one step out, two steps out, etc., up to and including the whole network. They are more informative than traditional centrality measures, as network transport typically happens on all length scales, from transport to nearest neighbors to the farthest reaches of the network. We show that range-limited centralities obey universal scaling laws for large nonweighted networks. As the computation of traditional centrality measures is costly, this scaling behavior can be exploited to efficiently estimate centralities of nodes and edges for all ranges, including the traditional ones. The scaling behavior can also be exploited to show that the ranking top list of nodes (edges) based on their range-limited centralities quickly freezes as a function of the range, and hence the diameter-range top list can be efficiently predicted. We also show how to estimate the typical largest node-to-node distance for a network of N nodes, exploiting the afore-mentioned scaling behavior. These observations were made on model networks and on a large social network inferred from cell-phone trace logs (∼5.5×10(6) nodes and ∼2.7×10(7) edges). Finally, we apply these concepts to efficiently detect the vulnerability backbone of a network (defined as the smallest percolating cluster of the highest betweenness nodes and edges) and illustrate the importance of weight-based centrality
Kaveh, Kamran; Komarova, Natalia L.; Kohandel, Mohammad
2015-01-01
Evolutionary models on graphs, as an extension of the Moran process, have two major implementations: birth–death (BD) models (or the invasion process) and death–birth (DB) models (or voter models). The isothermal theorem states that the fixation probability of mutants in a large group of graph structures (known as isothermal graphs, which include regular graphs) coincides with that for the mixed population. This result has been proved by Lieberman et al. (2005 Nature 433, 312–316. (doi:10.1038/nature03204)) in the case of BD processes, where mutants differ from the wild-types by their birth rate (and not by their death rate). In this paper, we discuss to what extent the isothermal theorem can be formulated for DB processes, proving that it only holds for mutants that differ from the wild-type by their death rate (and not by their birth rate). For more general BD and DB processes with arbitrary birth and death rates of mutants, we show that the fixation probabilities of mutants are different from those obtained in the mass-action populations. We focus on spatial lattices and show that the difference between BD and DB processes on one- and two-dimensional lattices is non-small even for large population sizes. We support these results with a generating function approach that can be generalized to arbitrary graph structures. Finally, we discuss several biological applications of the results. PMID:26064637
NASA Astrophysics Data System (ADS)
Greaves, Hilary; Thomas, Teruji
2014-02-01
We provide a careful development and rigorous proof of the CPT theorem within the framework of mainstream (Lagrangian) quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches in the mainstream approach. We construct the CPT transformation for a general field directly, without appealing to the enumerative classification of representations, and in a manner that is clearly related to the requirements of our proof. Our approach applies equally in Minkowski spacetimes of any dimension at least three, and is in principle neutral between classical and quantum field theories: the quantum CPT theorem has a natural classical analogue. The key mathematical tool is that of complexification; this tool is central to the existing axiomatic proofs, but plays no overt role in the usual mainstream approaches to CPT.
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 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
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…
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…
Self-organized criticality attributed to a central limit-like convergence effect
NASA Astrophysics Data System (ADS)
Kendal, Wayne S.
2015-03-01
Self-organized criticality is a hypothesis used to explain the origin of 1 / f noise and other scaling behaviors. Despite being proposed nearly 30 years ago, no consensus exists as to its exact definition or mathematical mechanism(s). Recently, a model for 1 / f noise was proposed based on a family of statistical distributions known as the Tweedie exponential dispersion models. These distributions are characterized by an inherent scale invariance that manifests as a variance to mean power law, called fluctuation scaling; they also serve as foci of convergence in a limit theorem on independent and identically distributed distributions. Fluctuation scaling can be modeled by self-similar stochastic processes that relate the variance to mean power law to 1 / f noise through their correlation structure. A hypothesis is proposed whereby the effects of self-organized criticality are mathematically modeled by the Tweedie distributions and their convergence behavior as applied to self-similar stochastic processes. Sandpile model fluctuations are shown to manifest 1 / f noise, fluctuation scaling, and to conform to the Tweedie compound Poisson distribution. The Tweedie models and their convergence theorem allow for a mechanistic explanation of 1 / f noise and fluctuation scaling in phenomena conventionally attributed to self-organized criticality, thus providing a paradigm shift in our understanding of these phenomena.
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.
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.
Douma, Huub; Vasconcelos, Ivan; Snieder, Roel
2011-05-01
By analyzing correlation-type reciprocity theorems for wavefields in perturbed media, it is shown that the correlation-type reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem. This reciprocity theorem, in contrast to the generalized optical theorem, allows for inhomogeneous background properties and does not make use of a far-field condition. This theorem specializes to the generalized optical theorem when considering a finite-size scatterer embedded in a homogeneous background medium and when utilizing the far-field condition. Moreover, it is shown that the reciprocity theorem for the scattered field is responsible for the cancellation of non-physical (spurious) arrivals in seismic interferometry, and as such provides the mathematical description of such arrivals. Even though here only acoustic waves are treated, the presented treatment is not limited to such wavefields and can be generalized to general wavefields. Therefore, this work provides the framework for deriving equivalents of the generalized optical theorem for general wavefields. PMID:21568381
ERIC Educational Resources Information Center
Parameswaran, Revathy
2009-01-01
This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich concept images.…
The Interaction Equivalency Theorem
ERIC Educational Resources Information Center
Miyazoe, Terumi; Anderson, Terry
2010-01-01
This paper examines the key issues regarding The Interaction Equivalency Theorem posited by Anderson (2003a), which consists of the three interaction elements found in formal education courses among teacher, student, and content. It first examines the core concepts of the theorem and argues that two theses of different dimensions can be…
ERIC Educational Resources Information Center
Smith, Michael D.
2016-01-01
The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…
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
A generalization of Bernoulli's theorem
Schaer, C. )
1993-05-15
The conservation of potential vorticity Q can be expressed as [partial derivative]([rho]Q)/[partial derivative]t + [del] [center dot] J = 0, where J denotes the total flux of potential vorticity. It is shown that J is related under statistically steady conditions to the Bernoulli function B by J = [del] [theta] [times] [del] B, where [theta] is the potential temperature. This relation is valid even in the nonhydrostatic limit and in the presence of arbitrary nonconservative forces (such as internal friction) and heating rates. In essence, it can be interpreted as a generalization of Bernoulli's theorem to the frictional and diabatic regime. The classical Bernoulli theorem-valid for inviscid adiabatic and steady flows-states that the intersections of surfaces at constant potential temperature and constant Bernoulli function yield streamlines. In the presence of frictional and diabatic effects, these intersections yield the flux lines along which potential vorticity is transported. 18 refs., 2 figs.
Recursion relations from soft theorems
NASA Astrophysics Data System (ADS)
Luo, Hui; Wen, Congkao
2016-03-01
We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large- z behaviour. This work is a generalization of the recursion relations recently obtained by Cheung et al. for amplitudes in scalar effective field theories with enhanced vanishing soft behaviours, which can be regarded as a special case of those with non-vanishing soft limits. We apply the recursion relations to tree-level amplitudes in various theories, including amplitudes in the Akulov-Volkov theory and amplitudes containing dilatons of spontaneously-broken conformal symmetry.
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,…
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
Ardenghi, Juan S.; Castagnino, M.; Campoamor-Stursberg, R.
2009-10-15
The nonrelativistic limit of the centrally extended Poincare group is considered and their consequences in the modal Hamiltonian interpretation of quantum mechanics are discussed [O. Lombardi and M. Castagnino, Stud. Hist. Philos. Mod. Phys 39, 380 (2008); J. Phys, Conf. Ser. 128, 012014 (2008)]. Through the assumption that in quantum field theory the Casimir operators of the Poincare group actualize, the nonrelativistic limit of the latter group yields to the actualization of the Casimir operators of the Galilei group, which is in agreement with the actualization rule of previous versions of modal Hamiltonian interpretation [Ardenghi et al., Found. Phys. (submitted)].
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
Raychaudhuri equation and singularity theorems in Finsler spacetimes
NASA Astrophysics Data System (ADS)
Minguzzi, E.
2015-09-01
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain. Indeed, so do the theorems by Hawking, Penrose, Hawking and Penrose, Geroch, Gannon, Tipler and Kriele, and also the Topological Censorship theorem and so on. It is argued that the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance and geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure, horizons differentiability and conformal transformations are also included.
Stability of Gas Clouds in Galactic Nuclei: An Extended Virial Theorem
NASA Astrophysics Data System (ADS)
Chen, Xian; Amaro-Seoane, Pau; Cuadra, Jorge
2016-03-01
Cold gas entering the central 1-102 pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH) to turn on an active galactic nucleus (AGN). The conventional criteria to assess the stability of these clouds, such as the Jeans criterion and Roche (or tidal) limit, are insufficient here, because they assume the dominance of self-gravity in binding a cloud, and neglect external agents, such as pressure and tidal forces, which are common in galactic nuclei. We formulate a new scheme for judging this stability. We first revisit the conventional Virial theorem, taking into account an external pressure, to identify the correct range of masses that lead to stable clouds. We then extend the theorem to further include an external tidal field, which is equally crucial for the stability in the region of our interest—in dense star clusters, around SMBHs. We apply our extended Virial theorem to find new solutions to controversial problems, namely, the stability of the gas clumps in AGN tori, the circum-nuclear disk in the Galactic Center, and the central molecular zone of the Milky Way. The masses we derive for these structures are orders of magnitude smaller than the commonly used Virial masses (equivalent to the Jeans mass). Moreover, we prove that these clumps are stable, contrary to what one would naively deduce from the Roche (tidal) limit.
The flat Grothendieck-Riemann-Roch theorem without adiabatic techniques
NASA Astrophysics Data System (ADS)
Ho, Man-Ho
2016-09-01
In this paper we give a simplified proof of the flat Grothendieck-Riemann-Roch theorem. The proof makes use of the local family index theorem and basic computations of the Chern-Simons form. In particular, it does not involve any adiabatic limit computation of the reduced eta-invariant.
NASA Astrophysics Data System (ADS)
Pérez-Espigares, Carlos; Redig, Frank; Giardinà, Cristian
2015-08-01
For non-equilibrium systems of interacting particles and for interacting diffusions in d-dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.
Virial Theorem and Scale Transformations.
ERIC Educational Resources Information Center
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
A Schwinger disentangling theorem
Cross, Daniel J.; Gilmore, Robert
2010-10-15
Baker-Campbell-Hausdorff formulas are exceedingly useful for disentangling operators so that they may be more easily evaluated on particular states. We present such a disentangling theorem for general bilinear and linear combinations of multiple boson creation and annihilation operators. This work generalizes a classical result of Schwinger.
Weinberg, Steven
2008-09-15
It is shown that the generating function for tree graphs in the ''in-in'' formalism may be calculated by solving the classical equations of motion subject to certain constraints. This theorem is illustrated by application to the evolution of a single inflaton field in a Robertson-Walker background.
''CPT Theorem'' for Accelerators
Vladimir Shiltsev
2004-08-05
In this paper we attempt to reveal common features in evolution of various colliders' luminosity over commissioning periods. A simplified formula, ''CPT theorem'' or CP = T, is proposed which relates the time needed for commissioning T, the ''complexity'' of the machine C and performance increase goal P.
ERIC Educational Resources Information Center
Musto, Garrod
2010-01-01
Within his classroom, the author is often confronted by students who fail to see, or accept, the relevance of mathematics both to their lives and the world around them. One topic which is regularly perceived as being disconnected from people's daily lives is that of circle theorems, especially among less motivated students. In this article, the…
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
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.
Soft theorems from effective field theory
NASA Astrophysics Data System (ADS)
Larkoski, Andrew J.; Neill, Duff; Stewart, Iain W.
2015-06-01
The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate this explicitly both at tree-level and at one-loop. The effective theory correctly describes these configurations, and we generalize the Low-Burnett-Kroll theorem into a new one-loop subleading soft theorem for amplitudes. Our analysis is presented in a manner that illustrates the wider utility of using effective theory techniques to understand the perturbative S-matrix.
ERIC Educational Resources Information Center
Abramovitz, Buma; Berezina, Miryam; Berman, Abraham; Shvartsman, Ludmila
2009-01-01
In this article we describe the process of studying the assumptions and the conclusion of a theorem. We tried to provide the students with exercises and problems where we discuss the following questions: What are the assumptions of a theorem and what are the conclusions? What is the geometrical meaning of a theorem? What happens when one or more…
ERIC Educational Resources Information Center
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
Sampling theorems and compressive sensing on the sphere
NASA Astrophysics Data System (ADS)
McEwen, Jason D.; Puy, Gilles; Thiran, Jean-Philippe; Vandergheynst, Pierre; Van De Ville, Dimitri; Wiaux, Yves
2011-09-01
We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a band-limited signal exactly, this new sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere, such as the canonical Driscoll & Healy sampling theorem. A reduction in the number of samples required to represent a band-limited signal on the sphere has important implications for compressive sensing, both in terms of the dimensionality and sparsity of signals. We illustrate the impact of this property with an inpainting problem on the sphere, where we show superior reconstruction performance when adopting the new sampling theorem.
THE PARKER MAGNETOSTATIC THEOREM
Low, B. C.
2010-08-01
We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly conducting fluid bounded by a pair of rigid plates where each field is anchored, taking the plates perpendicular to the uniform field. Those force-free fields obtainable from the uniform field by continuous magnetic footpoint displacements at the plates have field topologies that are shown to be a restricted subset of the field topologies similarly created without imposing the force-free equilibrium condition. The theorem then follows from the deduction that a continuous nonequilibrium field with a topology not in that subset must find a force-free state containing tangential discontinuities.
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.
Marra, Vincenzo; Burden, Jemima J.; Thorpe, Julian R.; Smith, Ikuko T.; Smith, Spencer L.; Häusser, Michael; Branco, Tiago; Staras, Kevin
2012-01-01
Summary At small central synapses, efficient turnover of vesicles is crucial for stimulus-driven transmission, but how the structure of this recycling pool relates to its functional role remains unclear. Here we characterize the organizational principles of functional vesicles at native hippocampal synapses with nanoscale resolution using fluorescent dye labeling and electron microscopy. We show that the recycling pool broadly scales with the magnitude of the total vesicle pool, but its average size is small (∼45 vesicles), highly variable, and regulated by CDK5/calcineurin activity. Spatial analysis demonstrates that recycling vesicles are preferentially arranged near the active zone and this segregation is abolished by actin stabilization, slowing the rate of activity-driven exocytosis. Our approach reveals a similarly biased recycling pool distribution at synapses in visual cortex activated by sensory stimulation in vivo. We suggest that in small native central synapses, efficient release of a limited pool of vesicles relies on their favored spatial positioning within the terminal. PMID:23141069
NASA Astrophysics Data System (ADS)
Sarbicki, Gniewomir; Chruściński, Dariusz; Mozrzymas, Marek
2016-07-01
We analyse linear maps of operator algebras {{ B }}H({ H }) mapping the set of rank-k projectors onto the set of rank-l projectors surjectively. A complete characterisation of such maps for prime n={dim} { H } is provided. A particular case corresponding to k=l=1 is well known as Wigner’s theorem. Hence our result may be considered as a generalisation of this celebrated Wigner’s result.
The Steep Nekhoroshev's Theorem
NASA Astrophysics Data System (ADS)
Guzzo, M.; Chierchia, L.; Benettin, G.
2016-03-01
Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be {1/(2nα_1\\cdotsα_{n-2}}) ({α_i}'s being Nekhoroshev's steepness indices and {n ≥ 3} the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.
HARD X-RAY FLUX UPPER LIMITS OF CENTRAL COMPACT OBJECTS IN SUPERNOVA REMNANTS
Erdeve, I.; Kalemci, E.; Alpar, M. A.
2009-05-10
We searched for hard X-ray (20-300 keV) emission from nine central compact objects (CCOs) 1E 1207.4-5209, 1WGA J1713-3949, J082157.5-430017, J085201.4-461753, J160103.1-513353, J1613483-5055, J181852.0-150213, J185238.6+004020, and J232327.9+584843 with the International Gamma-Ray Astrophysics Laboratory observatory. We applied spectral imaging analysis and did not detect any of the sources with luminosity upper limits in the range of 10{sup 33}-10{sup 34} erg s{sup -1} in the 20-75 keV band. For nearby CCOs (less than 4 kpc), the upper-limit luminosities are an order of magnitude lower than the measured persistent hard X-ray luminosities of anomalous X-ray pulsars. This may indicate that the CCOs are low magnetic field systems with fallback disks around them.
Tau leaping of stiff stochastic chemical systems via local central limit approximation
Yang, Yushu; Rathinam, Muruhan
2013-06-01
Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-stepping method to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods have shortcomings in this regard. The implicit tau method is far more stable than the trapezoidal tau method but underestimates the asymptotic variance. On the other hand, the trapezoidal tau method which estimates the asymptotic variance exactly for linear systems suffers from the fact that the transients of the method do not decay fast enough in the context of very stiff systems. We propose a tau leaping method that possesses the same stability properties as the implicit method while it also captures the asymptotic variance with reasonable accuracy at least for the test system S{sub 1}↔S{sub 2}. The proposed method uses a central limit approximation (CLA) locally over the tau leaping interval and is referred to as the LCLA-τ. The CLA predicts the mean and covariance as solutions of certain differential equations (ODEs) and for efficiency we solve these using a single time step of a suitable low order method. We perform a mean/covariance stability analysis of various possible low order schemes to determine the best scheme. Numerical experiments presented show that LCLA-τ performs favorably for stiff systems and that the LCLA-τ is also able to capture bimodal distributions unlike the CLA itself. The proposed LCLA-τ method uses a split implicit step to compute the mean update. We also prove that any tau leaping method employing a split implicit step converges in the fluid limit to the implicit Euler method as applied to the fluid limit differential equation.
Tau leaping of stiff stochastic chemical systems via local central limit approximation
NASA Astrophysics Data System (ADS)
Yang, Yushu; Rathinam, Muruhan
2013-06-01
Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-stepping method to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods have shortcomings in this regard. The implicit tau method is far more stable than the trapezoidal tau method but underestimates the asymptotic variance. On the other hand, the trapezoidal tau method which estimates the asymptotic variance exactly for linear systems suffers from the fact that the transients of the method do not decay fast enough in the context of very stiff systems. We propose a tau leaping method that possesses the same stability properties as the implicit method while it also captures the asymptotic variance with reasonable accuracy at least for the test system S1↔S2. The proposed method uses a central limit approximation (CLA) locally over the tau leaping interval and is referred to as the LCLA-τ. The CLA predicts the mean and covariance as solutions of certain differential equations (ODEs) and for efficiency we solve these using a single time step of a suitable low order method. We perform a mean/covariance stability analysis of various possible low order schemes to determine the best scheme. Numerical experiments presented show that LCLA-τ performs favorably for stiff systems and that the LCLA-τ is also able to capture bimodal distributions unlike the CLA itself. The proposed LCLA-τ method uses a split implicit step to compute the mean update. We also prove that any tau leaping method employing a split implicit step converges in the fluid limit to the implicit Euler method as applied to the fluid limit differential equation.
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
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2010-07-02
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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
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. 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.
Recurrence theorems: A unified account
Wallace, David
2015-02-15
I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.
A theorem in relativistic electronics
NASA Astrophysics Data System (ADS)
Yongjian, Yu
1990-04-01
This paper presents a theorem that connects the dispersion relation of the Electron Cyclotron Maser' and the oscillation equation of the Gyromonotron. This theorem gives us a simple way of obtaining the osscillating characteristics of the Gyromonotron provided that dispersion relation of the ECRM is given. Though the theorem is proved only with the case of ECRM and Gyromonotron, it holds for other kinds of Electron Masers, FEL4etc. and corresponding osscillators.
A volume-limited sample of X-ray galaxy groups and clusters - III. Central abundance drops
NASA Astrophysics Data System (ADS)
Panagoulia, E. K.; Sanders, J. S.; Fabian, A. C.
2015-02-01
We present the results of a search and study of central abundance drops in a volume-limited sample (z ≤ 0.071) of 101 X-ray galaxy groups and clusters. These are best observed in nearby, and so best resolved, groups and clusters, making our sample ideal for their detection. Out of the 65 groups and clusters in our sample for which we have abundance profiles, 8 of them have certain central abundance drops, with possible central abundance drops in another 6. All sources with central abundance drops have X-ray cavities, and all bar one exception have a central cooling time of ≤1 Gyr. These central abundance drops can be generated if the iron injected by stellar mass-loss processes in the core of these sources is in grains, which then become incorporated in the central dusty filaments. These, in turn, are dragged outwards by the bubbling feedback process in these sources. We find that data quality significantly affects the detection of central abundance drops, inasmuch as a higher number of counts in the central 20 kpc of a source makes it easier to detect a central abundance drop, as long as these counts are more than ˜13 000. On the other hand, the magnitude of the central abundance drop does not depend on the number of these counts, though the statistical significance of the measured drop does. Finally, in line with the scenario briefly outlined above, we find that, for most sources, the location of X-ray cavities acts as an upper limit to the location of the peak in the radial metallicity distribution.
Limits to physiological plasticity of the coral Pocillopora verrucosa from the central Red Sea
NASA Astrophysics Data System (ADS)
Ziegler, Maren; Roder, Cornelia M.; Büchel, Claudia; Voolstra, Christian R.
2014-12-01
Many coral species display changing distribution patterns across coral reef depths. While changes in the underwater light field and the ability to associate with different photosynthetic symbionts of the genus Symbiodinium explain some of the variation, the limits to physiological plasticity are unknown for most corals. In the central Red Sea, colonies of the branching coral Pocillopora verrucosa are most abundant in shallow high light environments and become less abundant in water depths below 10 m. To further understand what determines this narrow distribution, we conducted a cross-depths transplant experiment looking at physiological plasticity and acclimation in regard to depth. Colonies from 5, 10, and 20 m were collected, transplanted to all depths, and re-investigated after 30 and 210 d. All coral colonies transplanted downward from shallow to deep water displayed an increase in photosynthetic light-harvesting pigments, which resulted in higher photosynthetic efficiency. Shallow-water specimens transplanted to deeper water showed a significant decrease in total protein content after 30 and 210 d under low light conditions compared to specimens transplanted to shallow and medium depths. Stable isotope data suggest that heterotrophic input of carbon was not increased under low light, and consequently, decreasing protein levels were symptomatic of decreasing photosynthetic rates that could not be compensated for through higher light-harvesting efficiency. Our results provide insights into the physiological plasticity of P. verrucosa in changing light regimes and explain the observed depth distribution pattern. Despite its high abundance in shallow reef waters, P. verrucosa possesses limited heterotrophic acclimation potential, i.e., the ability to support its mainly photoautotrophic diet through heterotrophic feeding. We conclude that P. verrucosa might be a species vulnerable to sudden changes in underwater light fields resulting from processes such as
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.
Theorems on Positive Data: On the Uniqueness of NMF
Laurberg, Hans; Christensen, Mads Græsbøll; Plumbley, Mark D.; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors. PMID:18497868
Wigner-Araki-Yanase theorem on distinguishability
Miyadera, Takayuki; Imai, Hideki
2006-08-15
The presence of an additive-conserved quantity imposes a limitation on the measurement process. According to the Wigner-Araki-Yanase theorem, perfect repeatability and distinguishability of the apparatus cannot be attained simultaneously. Instead of repeatability, in this paper, the distinguishability in both systems is examined. We derive a trade-off inequality between the distinguishability of the final states on the system and the one on the apparatus. An inequality shows that perfect distinguishability of both systems cannot be attained simultaneously.
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.
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Roo: A parallel theorem prover
Lusk, E.L.; McCune, W.W.; Slaney, J.K.
1991-11-01
We describe a parallel theorem prover based on the Argonne theorem-proving system OTTER. The parallel system, called Roo, runs on shared-memory multiprocessors such as the Sequent Symmetry. We explain the parallel algorithm used and give performance results that demonstrate near-linear speedups on large problems.
A Decomposition Theorem for Finite Automata.
ERIC Educational Resources Information Center
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
Correlation dimension Wonderland theorems
NASA Astrophysics Data System (ADS)
Carvalho, Silas L.; de Oliveira, César R.
2016-06-01
Existence of generic sets of self-adjoint operators, related to correlation dimensions of spectral measures, is investigated in separable Hilbert spaces. Typical results say that, given an orthonormal basis, the set of operators whose corresponding spectral measures are both 0-lower and 1-upper correlation dimensional is generic. The proofs rely on details of the relations among Fourier transform of spectral measures and Hausdorff and packing measures on the real line. Then such results are naturally combined with the Wonderland theorem. Applications are to classes of discrete one-dimensional Schrödinger operators and general (bounded) self-adjoint operators as well. Physical consequences include a proof of exotic dynamical behavior of singular continuous spectrum in some settings.
Soutschek, Alexander; Taylor, Paul C J; Schubert, Torsten
2016-09-01
When humans perform two tasks simultaneously, responses to the second task are increasingly delayed as the interval between the two tasks decreases (psychological refractory period). This delay of the second task is thought to reflect a central processing limitation at the response selection stage. However, the neural mechanisms underlying this central processing limitation remain unclear. Using transcranial magnetic stimulation (TMS), we examined the role of the dorsal medial frontal cortex (dMFC) in a dual-task paradigm in which participants performed an auditory task 1 and a visual task 2. We found that dMFC TMS, relative to control conditions, reduced the psychological refractory period for task 2 processing, whereas we observed no dMFC TMS effects on task 1 processing. This suggests a causal role of the dMFC in coordinating response selection processes at the central bottleneck. PMID:27083589
A generalized antenna theorem for broadband pulses
NASA Astrophysics Data System (ADS)
Johnson, Michael A.
1989-03-01
Using a very general argument, one can place an upper limit on the fluence that can be delivered to a distant point by passing a pulse with finite energy through an aperture of finite area. Based on a time-dependent form of Huygen's principle, shown is the maximum possible fluence produced by an arbitrary scalar field passing through an aperture to an observation point is about equal to the fluence produced by a nearly monochromatic pulse of the same energy. This fictitious pulse uniformly illuminates the aperture and converges to a geometric focal spot at the observation point. The frequency of the monochromatic wave is made equal to the aperture-averaged root-mean-square frequency of the actual diffracting field. Thus, a pulse with arbitrary time dependence satisfies an antenna theorem very similar to the more well-known version of the theorem satisfied by monochromatic waves.
Analogues of Chernoff's theorem and the Lie-Trotter theorem
NASA Astrophysics Data System (ADS)
Neklyudov, Alexander Yu
2009-10-01
This paper is concerned with the abstract Cauchy problem \\dot x=\\mathrm{A}x, x(0)=x_0\\in\\mathscr{D}(\\mathrm{A}), where \\mathrm{A} is a densely defined linear operator on a Banach space \\mathbf X. It is proved that a solution x(\\,\\cdot\\,) of this problem can be represented as the weak limit \\lim_{n\\to\\infty}\\{\\mathrm F(t/n)^nx_0\\}, where the function \\mathrm F\\colon \\lbrack 0,\\infty)\\mapsto\\mathscr L(\\mathrm X) satisfies the equality \\mathrm F'(0)y=\\mathrm{A}y, y\\in\\mathscr{D}(\\mathrm{A}), for a natural class of operators. As distinct from Chernoff's theorem, the existence of a global solution to the Cauchy problem is not assumed. Based on this result, necessary and sufficient conditions are found for the linear operator \\mathrm{C} to be closable and for its closure to be the generator of a C_0-semigroup. Also, we obtain new criteria for the sum of two generators of C_0-semigroups to be the generator of a C_0-semigroup and for the Lie-Trotter formula to hold. Bibliography: 13 titles.
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
Nonrenormalization Theorems without Supersymmetry.
Cheung, Clifford; Shen, Chia-Hsien
2015-08-14
We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and antiholomorphic weights, (w,w[over ¯])=(n-h,n+h), where n and h are the number and sum over helicities of the particles created by that operator. We argue that an operator O_{i} can only be renormalized by an operator O_{j} if w_{i}≥w_{j} and w[over ¯]_{i}≥w[over ¯]_{j}, absent nonholomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally. PMID:26317712
Comparison theorems for causal diamonds
NASA Astrophysics Data System (ADS)
Berthiere, Clément; Gibbons, Gary; Solodukhin, Sergey N.
2015-09-01
We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the redshift factor which, as we show explicitly in the spherically symmetric case, is monotonic in the radial direction, and it takes its maximal value at the center. As a by-product of our discussion we rederive Bishop's inequality without assuming the positivity of the spatial Ricci tensor. We then generalize our considerations to arbitrary, static and not necessarily spherically symmetric, asymptotically flat spacetimes. In the case of spacetimes with a horizon our generalization involves the so-called domain of dependence. The respective volume, expressed in terms of the duration measured by a distant observer compared with the volume of the domain in Minkowski spacetime, exhibits behaviors which differ if d =4 or d >4 . This peculiarity of four dimensions is due to the logarithmic subleading term in the asymptotic expansion of the metric near infinity. In terms of the invariant duration measured by a comoving observer associated with the diamond we establish an inequality which is universal for all d . We suggest some possible applications of our results including comparison theorems for entanglement entropy, causal set theory, and fundamental limits on computation.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
NASA Astrophysics Data System (ADS)
Woolgar, Eric; Wylie, William
2016-02-01
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-Émery" N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (-∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (-∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
Local virial and tensor theorems.
Cohen, Leon
2011-11-17
We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem. PMID:21863837
Coherent cyclotron motion beyond Kohn's theorem
NASA Astrophysics Data System (ADS)
Maag, T.; Bayer, A.; Baierl, S.; Hohenleutner, M.; Korn, T.; Schüller, C.; Schuh, D.; Bougeard, D.; Lange, C.; Huber, R.; Mootz, M.; Sipe, J. E.; Koch, S. W.; Kira, M.
2016-02-01
In solids, the high density of charged particles makes many-body interactions a pervasive principle governing optics and electronics. However, Walter Kohn found in 1961 that the cyclotron resonance of Landau-quantized electrons is independent of the seemingly inescapable Coulomb interaction between electrons. Although this surprising theorem has been exploited in sophisticated quantum phenomena, such as ultrastrong light-matter coupling, superradiance and coherent control, the complete absence of nonlinearities excludes many intriguing possibilities, such as quantum-logic protocols. Here, we use intense terahertz pulses to drive the cyclotron response of a two-dimensional electron gas beyond the protective limits of Kohn's theorem. Anharmonic Landau ladder climbing and distinct terahertz four- and six-wave mixing signatures occur, which our theory links to dynamic Coulomb effects between electrons and the positively charged ion background. This new context for Kohn's theorem unveils previously inaccessible internal degrees of freedom of Landau electrons, opening up new realms of ultrafast quantum control for electrons.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Lampart, Jonas; Lewin, Mathieu
2015-12-01
We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with {0 ≤slant n ≤slant N} particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.
An evaluation based theorem prover
Degano, P.; Sirovich, F.
1985-01-01
A noninductive method for mechanical theorem proving is presented, which deals with a recursive class of theorems involving iterative functions and predicates. The method is based on the symbolic evaluation of the formula to be proved and requires no inductive step. Induction is avoided since a metatheorem is proved which establishes the conditions on the evaluation of any formula which are sufficient to assure that the formula actually holds. The proof of a supposed theorem consists in evaluating the formula and checking the conditions. The method applies to assertions that involve element-by-element checking of typed homogeneous sequences which are hierarchically constructed out of the primitive type consisting of the truth values. The sequences can be computed by means of iterative and ''accumulator'' functions. The paper includes the definition of a simple typed iterative language in which both predicates and functions are expressed. The language precisely defines the scope of the proof method. The method proves a wide variety of theorems about iterative functions on sequences, including that which states that REVERSE is its own inverse, and that it can be inversely distributed on APPEND, that FLATTEN can be distributed on APPEND and that each element of any sequence is a MEMBER of the sequence itself. Although the method is not complete, it does provide the basis for an extremely efficient tool to be used in a complete mechanical theorem prover.
Nambu-Goldstone theorem and spin-statistics theorem
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra
NASA Astrophysics Data System (ADS)
Hopkins, Mark J.; Molev, Alexander I.
2006-12-01
We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra Uq(gln). We then use it to give an explicit realization of the skew representations of the quantum affine algebra. This allows one to identify them in a simple way by calculating their highest weight, Drinfeld polynomials and the Gelfand-Tsetlin character (or q-character). We also apply the quantum Sylvester theorem to construct a q-analogue of the Olshanski algebra as a projective limit of certain centralizers in Uq(gln) and show that this limit algebra contains the q-Yangian as a subalgebra.
Generalized energy measurements and modified transient quantum fluctuation theorems.
Watanabe, Gentaro; Venkatesh, B Prasanna; Talkner, Peter
2014-05-01
Determining the work which is supplied to a system by an external agent provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a problem for quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modified Crooks relation and Jarzynski equality are found for Gaussian energy measurements. These can be obtained by a sequence of sufficiently many generalized measurements which need not be Gaussian. In accordance with the central limit theorem, this leads to an effective error reduction in the individual measurements and even yields a projective measurement in the limit of infinite repetitions. PMID:25353748
Sustaining Irrigated Agriculture In The Central High Plains With Limited Irrigation Water
Technology Transfer Automated Retrieval System (TEKTRAN)
Increasing demands on limited water supplies will require maximizing crop production per unit water. Field studies are being carried out to develop water production functions for crops grown in the Great Plains. Irrigation water is applied through drip irrigation systems; precipitation and reference...
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.
Siddiqui, Adeel M; Harris, Gregory S; Movahed, Assad; Chiang, Karl S; Chelu, Mihail G; Nekkanti, Rajasekhar
2015-01-01
The end-stage renal disease population poses a challenge for obtaining venous access required for life-saving invasive cardiac procedures. In this case report, we describe an adult patient with end-stage renal disease in whom the hepatic vein was the only available access to implant a single-lead permanent cardiac pacemaker. A 63-year-old male with end-stage renal disease on maintenance hemodialysis and permanent atrial fibrillation/atrial flutter presented with symptomatic bradycardia. Imaging studies revealed all traditional central venous access sites to be occluded/non-accessible. With the assistance of vascular interventional radiology, a trans-hepatic venous catheter was placed. This was then used to place a right ventricular pacing lead with close attention to numerous technical aspects. The procedure was completed successfully with placement of a single-lead permanent cardiac pacemaker. PMID:26380831
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.
Nakagawa, Shunsuke; Shinkoda, Yuichi; Hazeki, Daisuke; Imamura, Mari; Okamoto, Yasuhiro; Kawakami, Kiyoshi; Kawano, Yoshifumi
2016-07-01
Central diabetes insipidus (CDI) and relapse are frequently seen in multifocal Langerhans cell histiocytosis (LCH). We present two females with multifocal LCH who developed CDI 9 and 5 years after the initial diagnosis, respectively, as a relapse limited to the pituitary stalk. Combination chemotherapy with cytarabine reduced the mass in the pituitary stalk. Although CDI did not improve, there has been no anterior pituitary hormone deficiency (APHD), neurodegenerative disease in the central nervous system (ND-CNS) or additional relapse for 2 years after therapy. It was difficult to predict the development of CDI in these cases. CDI might develop very late in patients with multifocal LCH, and therefore strict follow-up is necessary, especially with regard to symptoms of CDI such as polydipsia and polyuria. For new-onset CDI with LCH, chemotherapy with cytarabine might be useful for preventing APHD and ND-CNS. PMID:27089406
The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project
ERIC Educational Resources Information Center
Robiette, Alan G.
1975-01-01
Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)
Khinchin Theorem and Anomalous Diffusion
NASA Astrophysics Data System (ADS)
Lapas, Luciano C.; Morgado, Rafael; Vainstein, Mendeli H.; Rubí, J. Miguel; Oliveira, Fernando A.
2008-12-01
A recent Letter [M. H. Lee, Phys. Rev. Lett. 98, 190601 (2007)PRLTAO0031-900710.1103/PhysRevLett.98.190601] has called attention to the fact that irreversibility is a broader concept than ergodicity, and that therefore the Khinchin theorem [A. I. Khinchin, Mathematical Foundations of Statistical Mechanics (Dover, New York, 1949)] may fail in some systems. In this Letter we show that for all ranges of normal and anomalous diffusion described by a generalized Langevin equation the Khinchin theorem holds.
NASA Astrophysics Data System (ADS)
Fesen, R. A.; Pavlov, G. G.; Sanwal, D.
2006-01-01
We set new near-infrared and optical magnitude limits for the central X-ray point source (XPS) in the Cassiopeia A supernova remnant based on HST images. Near-infrared images of the center of Cas A taken with the NICMOS 2 camera in combination with the F110W and F160W filters (~J and H bands) have magnitude limits >=26.2 and >=24.6, respectively. These images reveal no sources within a 1.2" radius (corresponding to a 99% confidence limit) of the Chandra XPS position. The NICMOS data, taken together with broadband optical magnitude limits (R~28 mag) obtained from a deep STIS CCD exposure taken with a clear filter (50CCD), indicate that the XPS luminosities are very low in the optical/NIR bands (e.g., LH<3×1029 ergs s-1) with no optical, J-, or H-band counterpart to the XPS easily detectable by HST. The closest detected object lies 1.8" from the XPS's nominal coordinates, with magnitudes R=25.7, mF110W=21.9, and mF160W=20.6, and is a foreground, late-type star as suggested by Kaplan, Kulkarni, and Murray. We discuss the nature of the Cas A central compact object on the basis of these near-infrared and optical flux limits. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. These observations are associated with programs GO-8692 and GO-9798.
Maheshwari, Anurag; Janssens, Kris; Bogie, Jeroen; Van Den Haute, Chris; Struys, Tom; Lambrichts, Ivo; Baekelandt, Veerle; Stinissen, Piet; Hendriks, Jerome J A; Slaets, Helena; Hellings, Niels
2013-01-01
Demyelination is one of the pathological hallmarks of multiple sclerosis (MS). To date, no therapy is available which directly potentiates endogenous remyelination. Interleukin-11 (IL-11), a member of the gp130 family of cytokines, is upregulated in MS lesions. Systemic IL-11 treatment was shown to ameliorate clinical symptoms in experimental autoimmune encephalomyelitis (EAE), an animal model of MS. IL-11 modulates immune cells and protects oligodendrocytes in vitro. In this study, the cuprizone-induced demyelination mouse model was used to elucidate effects of IL-11 on de- and remyelination, independent of the immune response. Prophylactic-lentiviral- (LV-) mediated overexpression of IL-11 in mouse brain significantly limited acute demyelination, which was accompanied with the preservation of CC1(+) mature oligodendrocytes (OLs) and a decrease in microglial activation (Mac-2(+)). We further demonstrated that IL-11 directly reduces myelin phagocytosis in vitro. When IL-11 expressing LV was therapeutically applied in animals with extensive demyelination, a significant enhancement of remyelination was observed as demonstrated by Luxol Fast Blue staining and electron microscopy imaging. Our results indicate that IL-11 promotes maturation of NG2(+) OPCs into myelinating CC1(+) OLs and may thus explain the enhanced remyelination. Overall, we demonstrate that IL-11 is of therapeutic interest for MS and other demyelinating diseases by limiting demyelination and promoting remyelination. PMID:23818742
Maheshwari, Anurag; Janssens, Kris; Bogie, Jeroen; Van Den Haute, Chris; Struys, Tom; Lambrichts, Ivo; Baekelandt, Veerle; Stinissen, Piet; Hendriks, Jerome J. A.; Hellings, Niels
2013-01-01
Demyelination is one of the pathological hallmarks of multiple sclerosis (MS). To date, no therapy is available which directly potentiates endogenous remyelination. Interleukin-11 (IL-11), a member of the gp130 family of cytokines, is upregulated in MS lesions. Systemic IL-11 treatment was shown to ameliorate clinical symptoms in experimental autoimmune encephalomyelitis (EAE), an animal model of MS. IL-11 modulates immune cells and protects oligodendrocytes in vitro. In this study, the cuprizone-induced demyelination mouse model was used to elucidate effects of IL-11 on de- and remyelination, independent of the immune response. Prophylactic-lentiviral- (LV-) mediated overexpression of IL-11 in mouse brain significantly limited acute demyelination, which was accompanied with the preservation of CC1+ mature oligodendrocytes (OLs) and a decrease in microglial activation (Mac-2+). We further demonstrated that IL-11 directly reduces myelin phagocytosis in vitro. When IL-11 expressing LV was therapeutically applied in animals with extensive demyelination, a significant enhancement of remyelination was observed as demonstrated by Luxol Fast Blue staining and electron microscopy imaging. Our results indicate that IL-11 promotes maturation of NG2+ OPCs into myelinating CC1+ OLs and may thus explain the enhanced remyelination. Overall, we demonstrate that IL-11 is of therapeutic interest for MS and other demyelinating diseases by limiting demyelination and promoting remyelination. PMID:23818742
Expanding the Interaction Equivalency Theorem
ERIC Educational Resources Information Center
Rodriguez, Brenda Cecilia Padilla; Armellini, Alejandro
2015-01-01
Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner) is present at a high level. This…
Discovering the Inscribed Angle Theorem
ERIC Educational Resources Information Center
Roscoe, Matt B.
2012-01-01
Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…
Generalized Pump-restriction Theorem
Sinitsyn, Nikolai A; Chernyak, Vladimir Y
2008-01-01
We formulate conditions under which periodic modulations of parameters on a finite graph with stochastic transitions among its nodes do not lead to overall pump currents through any given link. Our theorem unifies previously known results with the new ones and provides a universal approach to explore futher restrictions on stochastic pump effect in non-adiabatically driven systems with detailed balance.
Equivalence theorem and infrared divergences
Torma, T.
1996-08-01
We look at the equivalence theorem as a statement about the absence of polynomial infrared divergences when {ital m}{sub {ital W}}{r_arrow}0. We prove their absence in a truncated toy model and conjecture that, if they exist at all, they are due to couplings between light particles. {copyright} {ital 1996 The American Physical Society.}
Angle Defect and Descartes' Theorem
ERIC Educational Resources Information Center
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
Local theorems for nonidentically distributed lattice random variables.
NASA Technical Reports Server (NTRS)
Mason, J. D.
1972-01-01
Derivation of local limit theorems for a sequence X sub n of independent integral-valued lattice random variables involving only a finite number of distinct nondegenerate distributions. Given appropriate sequences A sub n and B sub n of constants such that 1/B sub n (X sub 1 +
An implicit sampling theorem for bounded bandlimited functions
NASA Technical Reports Server (NTRS)
Bar-David, I.
1974-01-01
A rigorous proof of the 'strong bias tone' scheme is embodied in the implicit sampling theorem. The representation of signals that are sample functions of possible nonstationary random processes being of principal interest, the proof could not directly invoke results from classical analysis, which depend on the existence of the Fourier transform of the function under consideration; rather, it is based on Zakai's (1965) theorem on the series expansion of functions, band-limited under a suitably extended definition. A practical circuit that restores an approximate version of the signal from its sine-wave-crossings is presented and possible improvements to it are discussed.
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
Limit Theory for Panel Data Models with Cross Sectional Dependence and Sequential Exogeneity
Kuersteiner, Guido M.; Prucha, Ingmar R.
2013-01-01
The paper derives a general Central Limit Theorem (CLT) and asymptotic distributions for sample moments related to panel data models with large n. The results allow for the data to be cross sectionally dependent, while at the same time allowing the regressors to be only sequentially rather than strictly exogenous. The setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and/or from the presence of common factors. The latter leads to the need for random norming. The limit theorem for sample moments is derived by showing that the moment conditions can be recast such that a martingale difference array central limit theorem can be applied. We prove such a central limit theorem by first extending results for stable convergence in Hall and Hedye (1980) to non-nested martingale arrays relevant for our applications. We illustrate our result by establishing a generalized estimation theory for GMM estimators of a fixed effect panel model without imposing i.i.d. or strict exogeneity conditions. We also discuss a class of Maximum Likelihood (ML) estimators that can be analyzed using our CLT. PMID:23794781
Extension of Euler's theorem to n-dimensional spaces
NASA Technical Reports Server (NTRS)
Bar-Itzhack, Itzhack Y.
1989-01-01
Euler's theorem states that any sequence of finite rotations of a rigid body can be described as a single rotation of the body about a fixed axis in three-dimensional Euclidean space. The usual statement of the theorem in the literature cannot be extended to Euclidean spaces of other dimensions. Equivalent formulations of the theorem are given and proved in a way which does not limit them to the three-dimensional Euclidean space. Thus, the equivalent theorems hold in other dimensions. The proof of one formulation presents an algorithm which shows how to compute an angular-difference matrix that represents a single rotation which is equivalent to the sequence of rotations that have generated the final n-D orientation. This algorithm results also in a constant angular velocity which, when applied to the initial orientation, eventually yields the final orientation regardless of what angular velocity generated the latter. The extension of the theorem is demonstrated in a four-dimensional numerical example.
Extension to Eulers's theorem to n-dimensional spaces
NASA Technical Reports Server (NTRS)
Bar-Itzhack, Itzhack Y.
1989-01-01
Euler's theorem states that any sequence of finite rotations of a rigid body can be described as a single rotation of the body about a fixed axis in three-dimensional Euclidean space. The usual statement of the theorem in the literature cannot be extended to Euclidean spaces of other dimensions. Equivalent formulations of the theorem are given in this paper and proven in a way which does not limit them to the three-dimensional Euclidean space. Thus, the equivalent theorems hold in other dimensions. The proof of one formulation presents an algorithm which shows how to compute an angular-difference matrix that represents a single rotation which is equivalent to the sequence of rotations that have generated the final n-D orientation. This algorithm results also in a constant angular-velocity which, when applied to the initial orientation, yields eventually the final orientation regardless of what angular velocity generated the latter. Finally, the extension of the theorem is demonstrated in a four-dimensional numerical example.
A Fundamental Theorem on Particle Acceleration
Xie, Ming
2003-05-01
A fundamental theorem on particle acceleration is derived from the reciprocity principle of electromagnetism and a rigorous proof of the theorem is presented. The theorem establishes a relation between acceleration and radiation, which is particularly useful for insightful understanding of and practical calculation about the first order acceleration in which energy gain of the accelerated particle is linearly proportional to the accelerating field.
Investigating the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Johnson, Heather L.
2010-01-01
The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were…
Generalizations of Ptolemy and Brahmagupta Theorems
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
Pythagorean Theorem Proofs: Connecting Interactive Websites
ERIC Educational Resources Information Center
Lin, Cheng-Yao
2007-01-01
There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)
Ratz, David; Hofer, Timothy; Flanders, Scott A; Saint, Sanjay; Chopra, Vineet
2016-07-01
BACKGROUND The number of peripherally inserted central catheter (PICC) lumens is associated with thrombotic and infectious complications. Because multilumen PICCs are not necessary in all patients, policies that limit their use may improve safety and cost. OBJECTIVE To design a simulation-based analysis to estimate outcomes and cost associated with a policy that encourages single-lumen PICC use. METHODS Model inputs, including risk of complications and costs associated with single- and multilumen PICCs, were obtained from available literature and a multihospital collaborative quality improvement project. Cost savings and reduction in central line-associated bloodstream infection and deep vein thrombosis events from institution of a single-lumen PICC default policy were reported. RESULTS According to our model, a hospital that places 1,000 PICCs per year (25% of which are single-lumen and 75% multilumen) experiences annual PICC-related maintenance and complication costs of $1,228,598 (95% CI, $1,053,175-$1,430,958). In such facilities, every 5% increase in single-lumen PICC use would prevent 0.5 PICC-related central line-associated bloodstream infections and 0.5 PICC-related deep vein thrombosis events, while saving $23,500. Moving from 25% to 50% single-lumen PICC utilization would result in total savings of $119,283 (95% CI, $74,030-$184,170) per year. Regardless of baseline prevalence, a single-lumen default PICC policy would be associated with approximately 10% cost savings. Findings remained robust in multiway sensitivity analyses. CONCLUSION Hospital policies that limit the number of PICC lumens may enhance patient safety and reduce healthcare costs. Studies measuring intended and unintended consequences of this approach, followed by rapid adoption, appear necessary. Infect Control Hosp Epidemiol 2016;37:811-817. PMID:27033138
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
Aging Wiener-Khinchin Theorem.
Leibovich, N; Barkai, E
2015-08-21
The Wiener-Khinchin theorem shows how the power spectrum of a stationary random signal I(t) is related to its correlation function ⟨I(t)I(t+τ)⟩. We consider nonstationary processes with the widely observed aging correlation function ⟨I(t)I(t+τ)⟩∼t(γ)ϕ(EA)(τ/t) and relate it to the sample spectrum. We formulate two aging Wiener-Khinchin theorems relating the power spectrum to the time- and ensemble-averaged correlation functions, discussing briefly the advantages of each. When the scaling function ϕ(EA)(x) exhibits a nonanalytical behavior in the vicinity of its small argument we obtain the aging 1/f-type of spectrum. We demonstrate our results with three examples: blinking quantum dots, single-file diffusion, and Brownian motion in a logarithmic potential, showing that our approach is valid for a wide range of physical mechanisms. PMID:26340172
Töllner, Thomas; Strobach, Tilo; Schubert, Torsten; Müller, Hermann J.
2012-01-01
In classic Psychological-Refractory-Period (PRP) dual-task paradigms, decreasing stimulus onset asynchronies (SOA) between the two tasks typically lead to increasing reaction times (RT) to the second task and, when task order is non-predictable, to prolonged RTs to the first task. Traditionally, both RT effects have been advocated to originate exclusively from the dynamics of a central bottleneck. By focusing on two specific electroencephalographic brain responses directly linkable to perceptual or motor processing stages, respectively, the present study aimed to provide a more detailed picture as to the origin(s) of these behavioral PRP effects. In particular, we employed 2-alternative forced-choice (2AFC) tasks requiring participants to identify the pitch of a tone (high versus low) in the auditory, and the orientation of a target object (vertical versus horizontal) in the visual, task, with task order being either predictable or non-predictable. Our findings show that task order predictability (TOP) and inter-task SOA interactively determine the speed of (visual) perceptual processes (as indexed by the PCN timing) for both the first and the second task. By contrast, motor response execution times (as indexed by the LRP timing) are influenced independently by TOP for the first, and SOA for the second, task. Overall, this set of findings complements classical as well as advanced versions of the central bottleneck model by providing electrophysiological evidence for modulations of both perceptual and motor processing dynamics that, in summation with central capacity limitations, give rise to the behavioral PRP outcome. PMID:22973208
On Harnack's theorem and extensions
NASA Astrophysics Data System (ADS)
Costa, Antonio F.; Parlier, Hugo
Harnack's theorem states that the fixed points of an orientation reversing involution of a compact orientable surface of genus g are a set of k disjoint simple closed geodesic where 0≤ k≤ g+1 . The first goal of this article is to give a purely geometric, complete and self-contained proof of this fact. In the case where the fixed curves of the involution do not separate the surface, we prove an extension of this theorem, by exhibiting the existence of auxiliary invariant curves with interesting properties. Although this type of extension is well known (see, for instance, Comment. Math. Helv. 57(4): 603-626 (1982) and Transl. Math. Monogr., vol. 225, Amer. Math. Soc., Providence, RI, 2004), our method also extends the theorem in the case where the surface has boundary. As a byproduct, we obtain a geometric method on how to obtain these auxiliary curves. As a consequence of these constructions, we obtain results concerning presentations of Non-Euclidean crystallographic groups and a new proof of a result on the set of points corresponding to real algebraic curves in the compactification of the Moduli space of complex curves of genus g , overline{M_{g}} . More concretely, we establish that given two real curves there is a path in overline{M_{g}} which passes through at most two singular curves, a result of M. Seppaelae (Ann. Sci. Ecole Norm. Sup. (4), 24(5), 519-544 (1991)).
A global conformal extension theorem for perfect fluid Bianchi space-times
Luebbe, Christian Tod, Paul
2008-12-15
A global extension theorem is established for isotropic singularities in polytropic perfect fluid Bianchi space-times. When an extension is possible, the limiting behaviour of the physical space-time near the singularity is analysed.
Isothermal-sweep theorems for ultracold quantum gases in a canonical ensemble
NASA Astrophysics Data System (ADS)
Iskin, M.
2011-03-01
After deriving the isothermal Hellmann-Feynman theorem (IHFT) that is suitable for mixed states in a canonical ensemble, we use this theorem to obtain the isothermal magnetic-field sweep theorems for the free, average, and trapping energies and for the entropy, specific heat, pressure, and atomic compressibility of strongly correlated ultracold quantum gases. In particular, we apply the sweep theorems to two-component Fermi gases in the weakly interacting Bardeen-Cooper-Schrieffer and Bose-Einstein condensate limits, showing that the temperature dependence of the contact parameter can be determined by varying either the entropy or specific heat with respect to the scattering length. We also use the IHFT to obtain the virial theorem in a canonical ensemble and discuss its implications for quantum gases.
Rogers, H.; Birch, P. J.; Harrison, S. M.; Palmer, E.; Manchee, G. R.; Judd, D. B.; Naylor, A.; Scopes, D. I.; Hayes, A. G.
1992-01-01
1. The pharmacological profile of GR94839, a kappa-opioid agonist with limited access to the central nervous system, has been investigated. Its antinociceptive activity has been compared with that of GR103545, a centrally-penetrating kappa-agonist and ICI204448, the previously described peripherally-selective kappa-agonist. 2. GR94839 was a potent agonist in the rabbit vas deferens in vitro assay for kappa-opioid receptors (IC50: 1.4 +/- 0.3 nM; n = 6), but had limited activity at mu- or delta-opioid receptors. 3. In the mouse abdominal constriction test, GR94839 was 238 fold more potent when given i.c.v. (ED50: 0.008 (0.004-0.029) mg kg-1; n = 18) than when s.c. (ED50: 1.9 (0.7-3.1) mg kg-1; n = 30). In comparison, GR103545 was equipotent when given i.c.v. or s.c. 4. After intravenous administration, the maximum plasma to brain concentration-ratio attained by GR94839 was 18 compared with 2 for GR85571, a structurally-related kappa-agonist that is centrally-penetrating. 5. GR94839 inhibited the 2nd phase of the rat formalin response at doses 7 fold lower than those required to inhibit the 1st phase (ED50 vs 1st phase: 10.2 (6.7-17.1) mg kg-1, s.c.; ED50 vs 2nd phase: 1.4 (1.0-1.8) mg kg-1, s.c.; n = 18). GR103545 was equipotent against the two phases. 6. Intraplantar administration of the opioid antagonists, norbinaltorphimine (100 micrograms) or naltrexone (1 microgram), reversed the antinociceptive effect of systemic GR94839 (3 mg kg-1, s.c.) against the 2nd phase of the formalin response and intraplantar injection of GR94839 (30-100 micrograms) selectively inhibited the 2nd phase.(ABSTRACT TRUNCATED AT 250 WORDS) PMID:1327387
NASA Astrophysics Data System (ADS)
Vandebril, Raf; van Barel, Marc
2006-05-01
In this paper we take a closer look at the nullity theorem as formulated by Markham and Fiedler in 1986. The theorem is a valuable tool in the computations with structured rank matrices: it connects ranks of subblocks of an invertible matrix A with ranks of other subblocks in his inverse A-1. A little earlier, Barrett and Feinsilver, 1981, proved a theorem very close to the nullity theorem, but restricted to semiseparable and tridiagonal matrices, which are each others inverses. We will adapt the ideas of Barrett and Feinsilver to come to a new, alternative proof of the nullity theorem, based on determinantal formulas.In the second part of the paper, we extend the nullity theorem to make it suitable for two types of decompositions, namely the LU and the QR-decomposition. These theorems relate the ranks of subblocks of the factors L, U and Q to the ranks of subblocks of the factored matrix. It is shown, that a combination of the nullity theorem and his extended versions is suitable to predict in an easy manner the structure of decompositions and/or of inverses of structured rank matrices, e.g., higher-order band, higher-order semiseparable, Hessenberg, and many other types of matrices.As examples, to show the power of the nullity theorem and the related theorems, we apply them to semiseparable and related matrices.
Scaling Limits of a Tagged Particle in the Exclusion Process with Variable Diffusion Coefficient
NASA Astrophysics Data System (ADS)
Gonçalves, Patrícia; Jara, Milton
2008-09-01
We prove a law of large numbers and a central limit theorem for a tagged particle in a symmetric simple exclusion process in ℤ with variable diffusion coefficient. The scaling limits are obtained from a similar result for the current through -1/2 for a zero-range process with bond disorder. For the CLT, we prove convergence to a fractional Brownian motion of Hurst exponent 1/4.
New Fermionic Soft Theorems for Supergravity Amplitudes.
Chen, Wei-Ming; Huang, Yu-Tin; Wen, Congkao
2015-07-10
Soft limits of a massless S matrix are known to reflect the symmetries of the theory. In particular, for theories with Goldstone bosons, the double-soft limit of scalars reveals the coset structure of the vacuum manifold. In this Letter, we propose that such universal double-soft behavior is not only true for scalars, but also for spin-1/2 particles in four dimensions and fermions in three dimensions. We first consider the Akulov-Volkov theory and demonstrate that the double-soft limit of Goldstinos yields the supersymmetry algebra. More surprisingly, we also find that amplitudes in 4≤N≤8 supergravity theories in four dimensions as well as N=16 supergravity in three dimensions behave universally in the double-soft-fermion limit, analogous to the scalar ones. The validity of the new soft theorems at loop level is also studied. The results for supergravity are beyond what is implied by supersymmetry Ward identities and may impose nontrivial constraints on the possible counterterms for supergravity theories. PMID:26207460
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.
Cosmological perturbations and the Weinberg theorem
NASA Astrophysics Data System (ADS)
Akhshik, Mohammad; Firouzjahi, Hassan; Jazayeri, Sadra
2015-12-01
The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.
Fluctuation theorem for partially masked nonequilibrium dynamics.
Shiraishi, Naoto; Sagawa, Takahiro
2015-01-01
We establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production satisfies the integral fluctuation theorem. Our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines. In particular, our result gives a unified fluctuation theorem for both autonomous and nonautonomous Maxwell's demons, where mutual information plays a crucial role. Furthermore, we derive a fluctuation-dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations. PMID:25679593
Fluctuation theorem for partially masked nonequilibrium dynamics
NASA Astrophysics Data System (ADS)
Shiraishi, Naoto; Sagawa, Takahiro
2015-01-01
We establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production satisfies the integral fluctuation theorem. Our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines. In particular, our result gives a unified fluctuation theorem for both autonomous and nonautonomous Maxwell's demons, where mutual information plays a crucial role. Furthermore, we derive a fluctuation-dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations.
Quantization of Chirikov Map and Quantum KAM Theorem.
NASA Astrophysics Data System (ADS)
Shi, Kang-Jie
KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions
Chand, Priyanka; Amit, Sonal; Gupta, Raghvendra; Agarwal, Asha
2016-01-01
Context: Intraoperative cytology and frozen section play an important role in the diagnosis of neurosurgical specimens. There are limitations in both these procedures but understanding the errors and pitfalls may help in increasing the diagnostic yield. Aims: To find the diagnostic accuracy of intraoperative cytology and frozen section for central and peripheral nervous system (PNS) lesions and analyze the errors, pitfalls, and limitations in these procedures. Settings and Design: Eighty cases were included in this prospective study in a span of 1.5 years. Materials and Methods: The crush preparations and the frozen sections were stained with hematoxylin and eosin method. The diagnosis of crush smears and the frozen sections were compared with the diagnosis in the paraffin section, which was considered as the gold standard. Statistical Analyses Used: Diagnostic accuracy, sensitivity, and specificity. Results: The diagnostic accuracy of crush smears was 91.25% with a sensitivity of 95.5% and specificity of 100%. In the frozen sections, the overall diagnostic accuracy was 95%, sensitivity was 96.8%, and specificity was 100%. The categories of pitfalls noted in this study were categorization of spindle cell lesions, differentiation of oligodendroglioma from astrocytoma in frozen sections, differentiation of coagulative tumor necrosis of glioblastoma multiforme (GBM) from the caseous necrosis of tuberculosis, grading of gliomas in frozen section, and differentiation of the normal granular cells of the cerebellum from the lymphocytes in cytological smears. Conclusions: Crush smear and frozen section are complimentary procedures. When both are used together, the diagnostic yield is substantially increased. PMID:27279685
An elementary derivation of the quantum virial theorem from Hellmann–Feynman theorem
NASA Astrophysics Data System (ADS)
İpekoğlu, Y.; Turgut, S.
2016-07-01
A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann–Feynman theorem produces the final statement of the virial theorem.
NASA Astrophysics Data System (ADS)
Borghi, Riccardo
2014-03-01
In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.
General Theorems about Homogeneous Ellipsoidal Inclusions
ERIC Educational Resources Information Center
Korringa, J.; And Others
1978-01-01
Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)
Bring the Pythagorean Theorem "Full Circle"
ERIC Educational Resources Information Center
Benson, Christine C.; Malm, Cheryl G.
2011-01-01
Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…
The Classical Version of Stokes' Theorem Revisited
ERIC Educational Resources Information Center
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
A Generalization of the Prime Number Theorem
ERIC Educational Resources Information Center
Bruckman, Paul S.
2008-01-01
In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiable…
A Note on Morley's Triangle Theorem
ERIC Educational Resources Information Center
Mueller, Nancy; Tikoo, Mohan; Wang, Haohao
2012-01-01
In this note, we offer a proof of a variant of Morley's triangle theorem, when the exterior angles of a triangle are trisected. We also offer a generalization of Morley's theorem when angles of an "n"-gon are "n"-sected. (Contains 9 figures.)
A Note on Laplace's Expansion Theorem
ERIC Educational Resources Information Center
Janji, Milan
2005-01-01
A short proof of Laplace's expansion theorem is given. The proof is elementary and can be presented at any level of undergraduate studies where determinants are taught. It is derived directly from the definition so that the theorem may be used as a starting point for further investigation of determinants.
Hereditarily polaroid operators, SVEP and Weyl's theorem
NASA Astrophysics Data System (ADS)
Duggal, B. P.
2008-04-01
A Banach space operator is hereditarily polaroid, , if every part of T is polaroid. operators have SVEP. It is proved that if has SVEP and is a Riesz operator which commutes with T, then T+R satisfies generalized a-Browder's theorem. If, in particular, R is a quasi-nilpotent operator Q, then both T+Q and T*+Q* satisfy generalized a-Browder's theorem; furthermore, if Q is injective, then also T+Q satisfies Weyl's theorem. If is an algebraic operator which commutes with the polynomially operator T, then T+N is polaroid and has SVEP, f(T+N) satisfies generalized Weyl's theorem for every function f which is analytic on a neighbourhood of [sigma](T+N), and f(T+N)* satisfies generalized a-Weyl's theorem for every function f which is analytic on, and constant on no component of, a neighbourhood of [sigma](T+N).
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.
Singlet and triplet instability theorems
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Singlet and triplet instability theorems
NASA Astrophysics Data System (ADS)
Yamada, Tomonori; Hirata, So
2015-09-01
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Singlet and triplet instability theorems.
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions. PMID:26395692
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…
Quantum macrostates, equivalence of ensembles, and an H-theorem
NASA Astrophysics Data System (ADS)
De Roeck, Wojciech; Maes, Christian; Netočný, Karel
2006-07-01
Before the thermodynamic limit, macroscopic averages need not commute for a quantum system. As a consequence, aspects of macroscopic fluctuations or of constrained equilibrium require a careful analysis, when dealing with several observables. We propose an implementation of ideas that go back to John von Neumann's writing about the macroscopic measurement. We apply our scheme to the relation between macroscopic autonomy and an H-theorem, and to the problem of equivalence of ensembles. In particular, we show how the latter is related to the asymptotic equipartition theorem. The main point of departure is an expression of a law of large numbers for a sequence of states that start to concentrate, as the size of the system gets larger, on the macroscopic values for the different macroscopic observables. Deviations from that law are governed by the entropy.
Testability of the Pusey-Barrett-Rudolph Theorem
NASA Astrophysics Data System (ADS)
Halataei, Seyyed Mohammad Hassan
2014-03-01
Pusey, Barrett, and Rudolph (PBR) proved a mathematically neat theorem which assesses the reality of the quantum state. They proposed a test such that if any pair of quantum states could pass it, then for small deviation in the probabilities of measurement outcomes, ɛ, from the predicted quantum probabilities, one can conclude that the physical state λ ``is normally closely associated with only one of the two quantum states.'' While the mathematics of their theorem is correct, the physical conclusion is incomplete. In this talk, I present an argument which greatly limits the conclusion one can draw from even a successful PBR test. Specifically, I show that the physical state can be associated with several quantum states and, thus, the reality of quantum states cannot be deduced. This work was supported by the MacArthur Professorship endowed by the John D. and Catherine T. MacArthur Foundation at the University of Illinois.
Sampling Theorem in Terms of the Bandwidth and Sampling Interval
NASA Technical Reports Server (NTRS)
Dean, Bruce H.
2011-01-01
An approach has been developed for interpolating non-uniformly sampled data, with applications in signal and image reconstruction. This innovation generalizes the Whittaker-Shannon sampling theorem by emphasizing two assumptions explicitly (definition of a band-limited function and construction by periodic extension). The Whittaker- Shannon sampling theorem is thus expressed in terms of two fundamental length scales that are derived from these assumptions. The result is more general than what is usually reported, and contains the Whittaker- Shannon form as a special case corresponding to Nyquist-sampled data. The approach also shows that the preferred basis set for interpolation is found by varying the frequency component of the basis functions in an optimal way.
Levinson theorem for Dirac particles in n dimensions
Jiang Yu
2005-02-01
We study the Levinson theorem for a Dirac particle in an n-dimensional central field by use of the Green function approach, based on an analysis of the n-dimensional radial Dirac equation obtained through a simple algebraic derivation. We show that the zero-momentum phase shifts are related to the number of bound states with |E|
Kohn's theorem and Newton-Hooke symmetry for Hill's equations
NASA Astrophysics Data System (ADS)
Zhang, P. M.; Gibbons, G. W.; Horvathy, P. A.
2012-02-01
Hill’s equations, which first arose in the study of the Earth-Moon-Sun system, admit the two-parameter centrally extended Newton-Hooke symmetry without rotations. This symmetry allows us to extend Kohn’s theorem about the center-of-mass decomposition. Particular light is shed on the problem using Duval’s “Bargmann” framework. The separation of the center-of-mass motion into that of a guiding center and relative motion is derived by a generalized chiral decomposition.
Geometric optics and the "hairy ball theorem"
NASA Astrophysics Data System (ADS)
Bormashenko, Edward; Kazachkov, Alexander
Applications of the hairy ball theorem to the geometrical optics are discussed. When the ideal mirror, topologically equivalent to a sphere, is illuminated at every point, the "hairy ball theorem" prescribes the existence of at least one point at which the incident light will be normally reflected. For the more general case of the surface, topologically equivalent to a sphere, which is both reflecting and refracting the "hairy ball theorem" predicts the existence of at least one point, at which the incident light will be normally reflected and also normally refracted.
On soft theorems and form factors in N=4 SYM theory
NASA Astrophysics Data System (ADS)
Bork, L. V.; Onishchenko, A. I.
2015-12-01
Soft theorems for the form factors of 1/2-BPS and Konishi operator super-multiplets are derived at tree level in N=4 SYM theory. They have a form identical to the one in the amplitude case. For MHV sectors of stress tensor and Konishi operator supermultiplets loop corrections to soft theorems are considered at one loop level. They also appear to have universal form in the soft limit. Possible generalization of the on-shell diagrams to the form factors based on leading soft behavior is suggested. Finally, we give some comments on inverse soft limit and integrability of form factors in the limit q 2 → 0.
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.
Undecidability Theorem and Quantum Randomness
NASA Astrophysics Data System (ADS)
Berezin, Alexander A.
2005-04-01
As scientific folklore has it, Kurt Godel was once annoyed by question whether he sees any link between his Undecidability Theorem (UT) and Uncertainty Relationship. His reaction, however, may indicate that he probably felt that such a hidden link could indeed exist but he was unable clearly formulate it. Informational version of UT (G.J.Chaitin) states impossibility to rule out algorithmic compressibility of arbitrary digital string. Thus, (mathematical) randomness can only be disproven, not proven. Going from mathematical to physical (mainly quantum) randomness, we encounter seemingly random acts of radioactive decays of isotopes (such as C14), emission of excited atoms, tunneling effects, etc. However, our notion of quantum randomness (QR) may likely hit similarly formidable wall of physical version of UT leading to seemingly bizarre ideas such as Everett many world model (D.Deutsch) or backward causation (J.A.Wheeler). Resolution may potentially lie in admitting some form of Aristotelean final causation (AFC) as an ultimate foundational principle (G.W.Leibniz) connecting purely mathematical (Platonic) grounding aspects with it physically observable consequences, such as plethora of QR effects. Thus, what we interpret as QR may eventually be manifestation of AFC in which UT serves as delivery vehicle. Another example of UT/QR/AFC connection is question of identity (indistinguishability) of elementary particles (are all electrons exactly the same or just approximately so to a very high degree?).
Exchange fluctuation theorem for correlated quantum systems.
Jevtic, Sania; Rudolph, Terry; Jennings, David; Hirono, Yuji; Nakayama, Shojun; Murao, Mio
2015-10-01
We extend the exchange fluctuation theorem for energy exchange between thermal quantum systems beyond the assumption of molecular chaos, and describe the nonequilibrium exchange dynamics of correlated quantum states. The relation quantifies how the tendency for systems to equilibrate is modified in high-correlation environments. In addition, a more abstract approach leads us to a "correlation fluctuation theorem". Our results elucidate the role of measurement disturbance for such scenarios. We show a simple application by finding a semiclassical maximum work theorem in the presence of correlations. We also present a toy example of qubit-qudit heat exchange, and find that non-classical behaviour such as deterministic energy transfer and anomalous heat flow are reflected in our exchange fluctuation theorem. PMID:26565174
Sahoo- and Wayment-Type Integral Mean Value Theorems
ERIC Educational Resources Information Center
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
NASA Astrophysics Data System (ADS)
Fishman, S.; Soffer, A.
2016-07-01
We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.
A Converse of Fermat's Little Theorem
ERIC Educational Resources Information Center
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
No-hair theorem for the Galileon.
Hui, Lam; Nicolis, Alberto
2013-06-14
We consider a Galileon field coupled to gravity. The standard no-hair theorems do not apply because of the Galileon's peculiar derivative interactions. We prove that, nonetheless, static spherically symmetric black holes cannot sustain nontrivial Galileon profiles. Our theorem holds for trivial boundary conditions and for cosmological ones, and regardless of whether there are nonminimal couplings between the Galileon and gravity of the covariant Galileon type. PMID:25165906
Noether's second theorem for BRST symmetries
Bashkirov, D.; Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2005-05-01
We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles Y{yields}X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.
The matrix Euler-Fermat theorem
NASA Astrophysics Data System (ADS)
Arnol'd, Vladimir I.
2004-12-01
We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem.
Optical theorem detectors for active scatterers
NASA Astrophysics Data System (ADS)
Marengo, Edwin A.; Tu, Jing
2015-10-01
We develop a new theory of the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. It applies to arbitrary lossless backgrounds and quite general probing fields. The derived formulation holds for arbitrary passive scatterers, which can be dissipative, as well as for the more general class of active scatterers which are composed of a (passive) scatterer component and an active, radiating (antenna) component. The generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks and invisible scatterers and wireless communications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a novel reactive optical theorem related to the reactive power changes. The developed approach naturally leads to three optical theorem indicators or statistics which can be used to detect changes or targets in unknown complex media. The paper includes numerical simulation results that illustrate the application of the derived optical theorem results to change detection in complex and random media.
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 ...
Stability theorems for multidimensional linear systems with variable parameters
NASA Technical Reports Server (NTRS)
Shrivastava, S. K.
1981-01-01
A Liapunov-type approach is used to derive two equivalent theorems which govern the stability of coupled linear systems with varying multiple parameters. The theorems generalize some of the existing theorems applicable to systems with constant parameters and the Sonin-Polya theorem applicable to a single-degree-of-freedom system with variable coefficients. As an illustration, the proposed theorems are applied to mechanical systems with varying inertia, stiffness, gyroscopic, and damping terms, and velocity and position-dependent forces.
Kharitonov's theorem: Generalizations and algorithms
NASA Technical Reports Server (NTRS)
Rublein, George
1989-01-01
In 1978, the Russian mathematician V. Kharitonov published a remarkably simple necessary and sufficient condition in order that a rectangular parallelpiped of polynomials be a stable set. Here, stable is taken to mean that the polynomials have no roots in the closed right-half of the complex plane. The possibility of generalizing this result was studied by numerous authors. A set, Q, of polynomials is given and a necessary and sufficient condition that the set be stable is sought. Perhaps the most general result is due to Barmish who takes for Q a polytope and proceeds to construct a complicated nonlinear function, H, of the points in Q. With the notion of stability which was adopted, Barmish asks that the boundary of the closed right-half plane be swept, that the set G is considered = to (j(omega)(bar) - infinity is less than omega is less than infinity) and for each j(omega)(sigma)G, require H(delta) is greater than 0. Barmish's scheme has the merit that it describes a true generalization of Kharitonov's theorem. On the other hand, even when Q is a polyhedron, the definition of H requires that one do an optimization over the entire set of vertices, and then a subsequent optimization over an auxiliary parameter. In the present work, only the case where Q is a polyhedron is considered and the standard definition of stability described, is used. There are straightforward generalizations of the method to the case of discrete stability or to cases where certain root positions are deemed desirable. The cases where Q is non-polyhedral are less certain as candidates for the method. Essentially, a method of geometric programming was applied to the problem of finding maximum and minimum angular displacements of points in the Nyquist locus (Q(j x omega)(bar) - infinity is less than omega is less than infinity). There is an obvious connection with the boundary sweeping requirement of Barmish.
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. PMID:16906910
Goldstone's Theorem on a Light-Like Plane
NASA Astrophysics Data System (ADS)
Beane, Silas R.
2015-09-01
I review various aspects of chiral symmetry and its spontaneous breaking on null planes, including the interesting manner in which Goldstone's theorem is realized and the constraints that chiral symmetry imposes on the null-plane Hamiltonians. Specializing to QCD with N massless flavors, I show that there is an interesting limit in which the chiral constraints on the null-plane Hamiltonians can be solved to give the spin-flavor algebra SU(2 N), recovering a result originally found by Weinberg using different methods.
Generalized parametric down conversion, many particle interferometry, and Bell's theorem
NASA Technical Reports Server (NTRS)
Choi, Hyung Sup
1992-01-01
A new field of multi-particle interferometry is introduced using a nonlinear optical spontaneous parametric down conversion (SPDC) of a photon into more than two photons. The study of SPDC using a realistic Hamiltonian in a multi-mode shows that at least a low conversion rate limit is possible. The down converted field exhibits many stronger nonclassical phenomena than the usual two photon parametric down conversion. Application of the multi-particle interferometry to a recently proposed many particle Bell's theorem on the Einstein-Podolsky-Rosen problem is given.
Double soft theorems and shift symmetry in nonlinear sigma models
NASA Astrophysics Data System (ADS)
Low, Ian
2016-02-01
We show that both the leading and subleading double soft theorems of the nonlinear sigma model follow from a shift symmetry enforcing Adler's zero condition in the presence of an unbroken global symmetry. They do not depend on the underlying coset G /H and are universal infrared behaviors of Nambu-Goldstone bosons. Although nonlinear sigma models contain an infinite number of interaction vertices, the double soft limit is determined entirely by a single four-point interaction, together with the existence of Adler's zeros.
A Program Certification Assistant Based on Fully Automated Theorem Provers
NASA Technical Reports Server (NTRS)
Denney, Ewen; Fischer, Bernd
2005-01-01
We describe a certification assistant to support formal safety proofs for programs. It is based on a graphical user interface that hides the low-level details of first-order automated theorem provers while supporting limited interactivity: it allows users to customize and control the proof process on a high level, manages the auxiliary artifacts produced during this process, and provides traceability between the proof obligations and the relevant parts of the program. The certification assistant is part of a larger program synthesis system and is intended to support the deployment of automatically generated code in safety-critical applications.
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
Ergodic theorem, ergodic theory, and statistical mechanics
Moore, Calvin C.
2015-01-01
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697
Ergodic theorem, ergodic theory, and statistical mechanics.
Moore, Calvin C
2015-02-17
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697
Generalized fluctuation theorems for classical systems
NASA Astrophysics Data System (ADS)
Agarwal, G. S.; Dattagupta, Sushanta
2015-11-01
The fluctuation theorem has a very special place in the study of nonequilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen fluctuation theorem which is in terms of the distribution of the work p (W )/p (-W )=exp(α W ) . We derive the general form of the fluctuation theorems for an arbitrary multidimensional Gaussian Markov process. Interestingly, the parameter α is by no means universal, hitherto taken for granted in the case of linear Gaussian processes. As a matter of fact, conditions under which α does become a universal parameter 1 /K T are found to be rather restrictive. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is nontrivial. The generalized theorems are equally valid for nonequilibrium steady states and could be especially important in the presence of anisotropic diffusion.
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.
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.
Causality, Bell's theorem, and Ontic Definiteness
NASA Astrophysics Data System (ADS)
Henson, Joe
2011-03-01
Bell's theorem shows that the reasonable relativistic causal principle known as ``local causality'' is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while dropping any of the better-known assumptions of Bell's theorem. However, another assumption of Bell's theorem is the use of classical logic. One part of this assumption is the principle of ontic definiteness, that is, that it must in principle be possible to assign definite truth values to all propositions treated in the theory. Once the logical setting is clarified somewhat, it can be seen that rejecting this principle does not in any way undermine the type of causal principle used by Bell. Without ontic definiteness, the deterministic causal condition known as Einstein Locality succeeds in banning superluminal influence (including signalling) whilst allowing correlations that violate Bell's inequalities. Objections to altering logic, and the consequences for operational and realistic viewpoints, are also addressed.
Equilibrium fluctuation theorems compatible with anomalous response
NASA Astrophysics Data System (ADS)
Velazquez, L.; Curilef, S.
2010-12-01
Previously, we have derived a generalization of the canonical fluctuation relation between heat capacity and energy fluctuations C = β2langδU2rang, which is able to describe the existence of macrostates with negative heat capacities C < 0. In this work, we extend our previous results for an equilibrium situation with several control parameters to account for the existence of states with anomalous values in other response functions. Our analysis leads to the derivation of three different equilibrium fluctuation theorems: the fundamental and the complementary fluctuation theorems, which represent the generalization of two fluctuation identities already obtained in previous works, and the associated fluctuation theorem, a result that has no counterpart in the framework of Boltzmann-Gibbs distributions. These results are applied to study the anomalous susceptibility of a ferromagnetic system, in particular, the case of the 2D Ising model.
Asymptotic symmetries and subleading soft graviton theorem
NASA Astrophysics Data System (ADS)
Campiglia, Miguel; Laddha, Alok
2014-12-01
Motivated by the equivalence between the soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the Bondi, van der Burg, Metzner and Sachs (BMS) group, we propose a new extension (different from the so-called extended BMS) of the BMS group that is a semidirect product of supertranslations and Diff(S2) . We propose a definition for the canonical generators associated with the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.
Complementary Variational Theorems for inhomogeneous superconductors
NASA Astrophysics Data System (ADS)
Choy, T. C.
1997-03-01
Complementary variational theorems are derived for an inhomogeneous London (local) superconductor in which both the magnetic permeability μ(r) and the London penetration length λ_L(r) vary randomly in space (T.C. Choy, Physical Review B (1997) (to appear)). An essential feature is the close coupling between magnetic and supercurrent polarisation effects, developed self-consistently in this work. Using these theorems and a suitable ansatz for the single particle polarisabilities, we obtained complementary bounds for a composite superconductor near Tc and T=0^circ K. Our results may be important for the empirical study of systems containing magnetic (normal) and superconducting mixtures, including the high Tc oxide superconductors.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime. PMID:17813892
Jarzynski's theorem for lattice gauge theory
NASA Astrophysics Data System (ADS)
Caselle, Michele; Costagliola, Gianluca; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-08-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a nonequilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.
A variational proof of Thomson's theorem
NASA Astrophysics Data System (ADS)
Fiolhais, Miguel C. N.; Essén, Hanno; Gouveia, Tomé M.
2016-08-01
Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.
Statistical properties of the universal limit map of grazing bifurcations
NASA Astrophysics Data System (ADS)
Li, Denghui; Chen, Hebai; Xie, Jianhua
2016-09-01
In this paper, the statistical properties of an interval map, having a square-root singular point which characterizes grazing bifurcations of impact oscillators, are studied. Firstly, we show that in some parameter regions the map admits an induced Markov structure with an exponential decay tail of the return times. Then we prove that the map has a unique mixing absolutely continuous invariant probability measure. Finally, by applying the Markov tower method, we prove that exponential decay of correlations and the central limit theorem hold for Hölder continuous observations.
NASA Astrophysics Data System (ADS)
Izmailov, Ramil; Potapov, Alexander A.; Filippov, Alexander I.; Ghosh, Mithun; Nandi, Kamal K.
2015-03-01
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 M⊙ 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.
Tails of Polynomials of Random Variables and Stable Limits for Nonconventional Sums
NASA Astrophysics Data System (ADS)
Kifer, Yuri; Varadhan, S. R. S.
2016-06-01
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).
Baur, Hannes
2015-01-01
Abstract Two new species, Pteromalus briani sp. n. and Pteromalus janstai sp. n., with unusual characters are described from the Central Plateau and the Alps in Switzerland, respectively. Pteromalus briani 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 Vanessa atalanta (Linnaeus) and Aglais urticae (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, Pteromalus janstai 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. PMID:26261432
Aouad, Maya; Zell, Vivien; Juif, Pierre-Eric; Lacaud, Adrien; Goumon, Yannick; Darbon, Pascal; Lelievre, Vincent; Poisbeau, Pierrick
2014-02-01
Inflammatory and degenerative diseases of the joint are major causes of chronic pain. Long-lasting pain symptoms are thought to result from a central sensitization of nociceptive circuits. These processes include activation of microglia and spinal disinhibition. Using a monoarthritic rat model of pain, we tried to potentiate neural inhibition by using etifoxine (EFX), a nonbenzodiazepine anxiolytic that acts as an allosteric-positive modulator of gamma-aminobutyric acid type A (GABAA) receptor function. Interestingly, EFX also can bind to the mitochondrial translocator protein (TSPO) complex and stimulate the synthesis of 3α-reduced neurosteroids, the most potent positive allosteric modulator of GABAA receptor function. Here we show that a curative and a preventive treatment with 50mg/kg of EFX efficiently reduced neuropathic pain symptoms. In the spinal cord, EFX analgesia was accompanied by a reduction in microglial activation and in the levels of proinflammatory mediators. Using electrophysiological tools, we found that EFX treatment not only amplified spinal GABAergic inhibition, but also prevented prostaglandin E2-induced glycinergic disinhibition and restored a "normal" spinal pain processing. Because EFX is already distributed in several countries under the trade name of Stresam for its anxiolytic actions in humans, new clinical trials are now required to further extend its therapeutic indications as pain killer. PMID:24239672
Ferretti, G; Antonutto, G; Denis, C; Hoppeler, H; Minetti, A E; Narici, M V; Desplanches, D
1997-01-01
1. The effects of bed rest on the cardiovascular and muscular parameters which affect maximal O2 consumption (VO2,max) were studied. The fractional limitation of VO2,max imposed by these parameters after bed rest was analysed. 2. The VO2,max, by standard procedure, and the maximal cardiac output (Qmax), by the pulse contour method, were measured during graded cyclo-ergometric exercise on seven subjects before and after a 42-day head-down tilt bed rest. Blood haemoglobin concentration ([Hb]) and arterialized blood gas analysis were determined at the highest work load. 3. Muscle fibre types, oxidative enzyme activities, and capillary and mitochondrial densities were measured on biopsy samples from the vastus lateralis muscle before and at the end of bed rest. The measure of muscle cross-sectional area (CSA) by NMR imaging at the level of biopsy site allowed computation of muscle oxidative capacity and capillary length. 4. The VO2,max was reduced after bed rest (-16.6%). The concomitant decreases in Qmax (-30.8%), essentially due to a change in stroke volume, and in [Hb] led to a huge decrease in O2 delivery (-39.7%). 5. Fibre type distribution was unaffected by bed rest. The decrease in fibre area corresponded to the significant reduction in muscle CSA (-17%). The volume density of mitochondria was reduced after bed rest (-16.6%), as were the oxidative enzyme activities (-11%). The total mitochondrial volume was reduced by 28.5%. Capillary density was unchanged. Total capillary length was 22.2% lower after bed rest, due to muscle atrophy. 6. The interaction between these muscular and cardiovascular changes led to a smaller reduction in VO2,max than in cardiovascular O2 transport. Yet the latter appears to play the greatest role in limiting VO2,max after bed rest (> 70% of overall limitation), the remaining fraction being shared between peripheral O2 diffusion and utilization. PMID:9218227
Moving mirrors and the fluctuation-dissipation theorem
NASA Astrophysics Data System (ADS)
Stargen, D. Jaffino; Kothawala, Dawood; Sriramkumar, L.
2016-07-01
We investigate the random motion of a mirror in (1 +1 )-dimensions that is immersed in a thermal bath of massless scalar particles which are interacting with the mirror through a boundary condition. Imposing the Dirichlet or the Neumann boundary conditions on the moving mirror, we evaluate the mean radiation reaction force on the mirror and the correlation function describing the fluctuations in the force about the mean value. From the correlation function thus obtained, we explicitly establish the fluctuation-dissipation theorem governing the moving mirror. Using the fluctuation-dissipation theorem, we compute the mean-squared displacement of the mirror at finite and zero temperature. We clarify a few points concerning the various limiting behavior of the mean-squared displacement of the mirror. While we recover the standard result at finite temperature, we find that the mirror diffuses logarithmically at zero temperature, confirming similar conclusions that have been arrived at earlier in this context. We also comment on a subtlety concerning the comparison between zero temperature limit of the finite temperature result and the exact zero temperature result.
Characterizing curves satisfying the Gauss-Christoffel theorem
NASA Astrophysics Data System (ADS)
Berriochoa, E.; Cachafeiro, A.
2009-12-01
In this paper we obtain the reciprocal of the classical Gauss theorem for quadrature formulas. Indeed we characterize the support of the measures having quadrature formulas with the exactness given in the Gauss theorem.
Note on the theorems of Bjerknes and Crocco
NASA Technical Reports Server (NTRS)
Theodorsen, Theodore
1946-01-01
The theorems of Bjerknes and Crocco are of great interest in the theory of flow around airfoils at Mach numbers near and above unity. A brief note shows how both theorems are developed by short vector transformations.
Neuwirth, Ales; Economopoulou, Matina; Chatzigeorgiou, Antonios; Chung, Kyoung-Jin; Bittner, Stefan; Lee, Seung-Hwan; Langer, Harald; Samus, Maryna; Kim, Hyesoon; Cho, Geum-Sil; Ziemssen, Tjalf; Bdeir, Khalil; Chavakis, Emmanouil; Koh, Jae-Young; Boon, Louis; Hosur, Kavita; Bornstein, Stefan R.; Meuth, Sven G.; Hajishengallis, George; Chavakis, Triantafyllos
2014-01-01
Inflammation in the central nervous system (CNS) and disruption of its immune privilege are major contributors to the pathogenesis of multiple sclerosis (MS) and of its rodent counterpart, experimental autoimmune encephalomyelitis (EAE). We have previously identified developmental endothelial locus-1 (Del-1) as an endogenous anti-inflammatory factor, which inhibits integrin-dependent leukocyte adhesion. Here we show that Del-1 contributes to the immune privilege status of the CNS. Intriguingly, Del-1 expression decreased in chronic active MS lesions and in the inflamed CNS in the course of EAE. Del-1-deficiency was associated with increased EAE severity, accompanied by increased demyelination and axonal loss. As compared to control mice, Del-1−/− mice displayed enhanced disruption of the blood brain barrier and increased infiltration of neutrophil granulocytes in the spinal cord in the course of EAE, accompanied by elevated levels of inflammatory cytokines, including IL-17. The augmented levels of IL-17 in Del-1-deficiency derived predominantly from infiltrated CD8+ T cells. Increased EAE severity and neutrophil infiltration due to Del-1-deficiency was reversed in mice lacking both Del-1 and IL-17-receptor, indicating a crucial role for the IL-17/neutrophil inflammatory axis in EAE pathogenesis in Del-1−/− mice. Strikingly, systemic administration of Del-1-Fc ameliorated clinical relapse in relapsing-remitting EAE. Therefore, Del-1 is an endogenous homeostatic factor in the CNS protecting from neuroinflammation and demyelination. Our findings provide mechanistic underpinnings for the previous implication of Del-1 as a candidate MS susceptibility gene and suggest that Del-1-centered therapeutic approaches may be beneficial in neuroinflammatory and demyelinating disorders. PMID:25385367
Choi, E Y; Lim, J-H; Neuwirth, A; Economopoulou, M; Chatzigeorgiou, A; Chung, K-J; Bittner, S; Lee, S-H; Langer, H; Samus, M; Kim, H; Cho, G-S; Ziemssen, T; Bdeir, K; Chavakis, E; Koh, J-Y; Boon, L; Hosur, K; Bornstein, S R; Meuth, S G; Hajishengallis, G; Chavakis, T
2015-07-01
Inflammation in the central nervous system (CNS) and disruption of its immune privilege are major contributors to the pathogenesis of multiple sclerosis (MS) and of its rodent counterpart, experimental autoimmune encephalomyelitis (EAE). We have previously identified developmental endothelial locus-1 (Del-1) as an endogenous anti-inflammatory factor, which inhibits integrin-dependent leukocyte adhesion. Here we show that Del-1 contributes to the immune privilege status of the CNS. Intriguingly, Del-1 expression decreased in chronic-active MS lesions and in the inflamed CNS in the course of EAE. Del-1-deficiency was associated with increased EAE severity, accompanied by increased demyelination and axonal loss. As compared with control mice, Del-1(-/-) mice displayed enhanced disruption of the blood-brain barrier and increased infiltration of neutrophil granulocytes in the spinal cord in the course of EAE, accompanied by elevated levels of inflammatory cytokines, including interleukin-17 (IL-17). The augmented levels of IL-17 in Del-1-deficiency derived predominantly from infiltrated CD8(+) T cells. Increased EAE severity and neutrophil infiltration because of Del-1-deficiency was reversed in mice lacking both Del-1 and IL-17 receptor, indicating a crucial role for the IL-17/neutrophil inflammatory axis in EAE pathogenesis in Del-1(-/-) mice. Strikingly, systemic administration of Del-1-Fc ameliorated clinical relapse in relapsing-remitting EAE. Therefore, Del-1 is an endogenous homeostatic factor in the CNS protecting from neuroinflammation and demyelination. Our findings provide mechanistic underpinnings for the previous implication of Del-1 as a candidate MS susceptibility gene and suggest that Del-1-centered therapeutic approaches may be beneficial in neuroinflammatory and demyelinating disorders. PMID:25385367
Tennis Rackets and the Parallel Axis Theorem
NASA Astrophysics Data System (ADS)
Christie, Derek
2014-04-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
Student Research Project: Goursat's Other Theorem
ERIC Educational Resources Information Center
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
Abel's Theorem Simplifies Reduction of Order
ERIC Educational Resources Information Center
Green, William R.
2011-01-01
We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.
Student Thinking Strategies in Reconstructing Theorems
ERIC Educational Resources Information Center
Siswono, Tatag Yuli Eko
2005-01-01
A mathematics university student as a future mathematician should have the ability to find "new" mathematics structures or construct theorems based on particular axioms. That ability can be created by using problem posing tasks. To do the tasks, students with different abilities will use different thinking strategies. To understand them exactly,…
Tennis Rackets and the Parallel Axis Theorem
ERIC Educational Resources Information Center
Christie, Derek
2014-01-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
On Viviani's Theorem and Its Extensions
ERIC Educational Resources Information Center
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
An Elementary Proof of Pick's Theorem.
ERIC Educational Resources Information Center
Pullman, Howard W.
1979-01-01
Pick's Theorem, a statement of the relationship between the area of a polygonal region on a lattice and its interior and boundary lattice points, is familiar to those whose students have participated in activities and discovery lessons using the geoboard. The proof presented, although rather long, is well within the grasp of the average geometry…
Areas and the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Vajiac, A.; Vajiac, B.
2008-01-01
We present a concise, yet self-contained module for teaching the notion of area and the Fundamental Theorem of Calculus for different groups of students. This module contains two different levels of rigour, depending on the class it used for. It also incorporates a technological component. (Contains 6 figures.)
The Pythagorean Theorem and the Solid State
ERIC Educational Resources Information Center
Kelly, Brenda S.; Splittgerber, Allan G.
2005-01-01
Packing efficiency and crystal density can be calculated from basic geometric principles employing the Pythagorean theorem, if the unit-cell structure is known. The procedures illustrated have applicability in courses such as general chemistry, intermediate and advanced inorganic, materials science, and solid-state physics.
An extension theorem for conformal gauge singularities
Luebbe, Christian; Tod, Paul
2009-11-15
We analyze conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem along a congruence of timelike conformal geodesics.
The Binomial Theorem Tastes the Rainbow.
ERIC Educational Resources Information Center
Cuff, Carolyn K.
1998-01-01
Discusses the commercial for Skittles candies and asks the question "How many flavor combinations can you find?" Focuses on the modeling for a Skittles exercise which includes a brief outline of the mathematical modeling process. Guides students in the use of the binomial theorem and Pascal's triangle in this activity. (ASK)
Special ergodic theorems and dynamical large deviations
NASA Astrophysics Data System (ADS)
Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav
2012-11-01
Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.
Ptolemy's Theorem and Familiar Trigonometric Identities.
ERIC Educational Resources Information Center
Bidwell, James K.
1993-01-01
Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)
Fundamental Theorems of Algebra for the Perplexes
ERIC Educational Resources Information Center
Poodiak, Robert; LeClair, Kevin
2009-01-01
The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…
Codimension- p Paley-Wiener theorems
NASA Astrophysics Data System (ADS)
Yang, Yan; Qian, Tao; Sommen, Frank
2007-04-01
We obtain the generalized codimension- p Cauchy-Kovalevsky extension of the exponential function e^{i
An Ordinary but Surprisingly Powerful Theorem
ERIC Educational Resources Information Center
Sultan, Alan
2009-01-01
Being a mathematician, the author started to wonder if there are any theorems in mathematics that seem very ordinary on the outside, but when applied, have surprisingly far reaching consequences. The author thought about this and came up with the following unlikely candidate which follows immediately from the definition of the area of a rectangle…
Reflection theorem for Lorentz-Minkowski spaces
NASA Astrophysics Data System (ADS)
Lee, Nam-Hoon
2016-07-01
We generalize the reflection theorem of the Lorentz-Minkowski plane to that of the Lorentz-Minkowski spaces of higher dimensions. As a result, we show that an isometry of the Lorentz-Minkowski spacetime is a composition of at most 5 reflections.
New Erdős-Kac Type Theorems for Signed Measures on Square-Free Integers
NASA Astrophysics Data System (ADS)
Avdeeva, Maria; Li, Dong; Sinai, Yakov G.
2013-11-01
We consider a family of signed measures supported on the set of square-free numbers. We prove some local limit theorems for the prime divisor counting function ω(n) and establish new Erdős-Kac type results.
Applications of square-related theorems
NASA Astrophysics Data System (ADS)
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
Implications of Tracey's theorem to asynchronous sequential circuit design
NASA Technical Reports Server (NTRS)
Gopalakrishnan, S.; Kim, G.; Maki, G.
1990-01-01
Tracey's Theorem has long been recognized as essential in generating state assignments for asynchronous sequential circuits. This paper shows that Tracey's Theorem also has a significant impact in generating the design equations. Moreover, this theorem is important to the fundamental understanding of asynchronous sequential operation. The results of this work simplify asynchronous logic design. Moreover, detection of safe circuits is made easier.
Using Dynamic Geometry to Explore Non-Traditional Theorems
ERIC Educational Resources Information Center
Wares, Arsalan
2010-01-01
The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…
Local theorems in strengthened form for lattice random variables.
NASA Technical Reports Server (NTRS)
Mason, J. D.
1971-01-01
Investigation of some conditions which are sufficient for a sequence of independent integral-valued lattice random variables to satisfy a local theorem in strengthened form. A number of theorems giving the conditions under which the investigated sequence satisfies a local theorem in strengthened form are proven with the aid of lemmas derived by Kruglov (1968).
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.
Invisibility and cloaking structures as weak or strong solutions of Devaney-Wolf theorem.
Labate, Giuseppe; Matekovits, Ladislau
2016-08-22
Inspired by a general theorem on non-radiating sources demonstrated by Devaney and Wolf, a unified theory for invisible and cloaking structures is here proposed. By solving Devaney-Wolf theorem in the quasi-static limit, a weak solution is obtained, demonstrating the existence of Anapole modes, Mantle Cloaking and Plasmonic Cloaking. Beyond the quasi-static regime, a strong solution of Devaney-Wolf theorem can be formulated, predicting general non-scattering devices based on directional invisibility, Transformation Optics, neutral inclusions and refractive index continuity. Both weak and strong solutions are analytically demonstrated to depend on the concept of contrast, mathematically defined as a normalized difference between constitutive parameters (or wave-impedance property) of a material and its surrounding background. PMID:27557204
Sparse image reconstruction on the sphere: implications of a new sampling theorem.
McEwen, Jason D; Puy, Gilles; Thiran, Jean-Philippe; Vandergheynst, Pierre; Van De Ville, Dimitri; Wiaux, Yves
2013-06-01
We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result, we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations, we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem. PMID:23475360
NASA Astrophysics Data System (ADS)
Eddy, I. M. S.; Gergel, S. E.
2015-12-01
Grazing is the most extensive land use on Earth. Widespread consequences of overgrazing pastures include long-term decreases in plant biomass and limited recovery of vegetation. Remotely-sensed vegetation indices linked to biomass (e.g. NDVI) are routinely used to monitor pasture health over broad areas to track pasture degradation and recovery over time. Unfortunately, overgrazing can impact vegetation in various other ways not easily evaluated using satellite imagery, such as by altering species composition. Furthermore, the response of vegetation to grazing may be influenced by underlying terrain and topographic gradients. We examined multi-decadal trends in pasture condition in Kyrgyzstan, a country where pasture degradation is of serious concern. Using a chronosequence of Moderate-Resolution Imaging Spectroradiometer (MODIS) imagery, we compared fifteen-year trends in NDVI with contemporary field-based measurements of pasture health in thirty 1-km 2 sites. Multivariate regression was used to discern the relationship between long-term NDVI trends and pasture health in pastures of differing terrain (areas of varying topographic wetness index and solar insolation). Preliminary results suggest that pasture degradation can be correlated with either positive or negative changes in NDVI depending upon the topographic position of the pasture. Furthermore, terrain characteristics explained a considerable portion of the observed variance in NDVI trends across the region. Improving our understanding of grazing impacts in montane systems is critical given their vulnerability to impending climate change.
Limits for the central production of Theta+ and Xi(--)pentaquarks in 920-GeV pA collisions.
Abt, I; Adams, M; Agari, M; Albrecht, H; Aleksandrov, A; Amaral, V; Amorim, A; Aplin, S J; Aushev, V; Bagaturia, Y; Balagura, V; Bargiotti, M; Barsukova, O; Bastos, J; Batista, J; Bauer, C; Bauer, Th S; Belkov, A; Belkov, Ar; Belotelov, I; Bertin, A; Bobchenko, B; Böcker, M; Bogatyrev, A; Bohm, G; Bräuer, M; Bruinsma, M; Bruschi, M; Buchholz, P; Buran, T; Carvalho, J; Conde, P; Cruse, C; Dam, M; Danielsen, K M; Danilov, M; Castro, S De; Deppe, H; Dong, X; Dreis, H B; Egorytchev, V; Ehret, K; Eisele, F; Emeliyanov, D; Essenov, S; Fabbri, L; Faccioli, P; Feuerstack-Raible, M; Flammer, J; Fominykh, B; Funcke, M; Garrido, Ll; Giacobbe, B; Gläss, J; Goloubkov, D; Golubkov, Y; Golutvin, A; Golutvin, I; Gorbounov, I; Gorisek, A; Gouchtchine, O; Goulart, D C; Gradl, S; Gradl, W; Grimaldi, F; Groth-Jensen, J; Guilitsky, Yu; Hansen, J D; Hernández, J M; Hofmann, W; Hott, T; Hulsbergen, W; Husemann, U; Igonkina, O; Ispiryan, M; Jagla, T; Jiang, C; Kapitza, H; Karabekyan, S; Karpenko, N; Keller, S; Kessler, J; Khasanov, F; Kiryushin, Yu; Klinkby, E; Knöpfle, K T; Kolanoski, H; Korpar, S; Krauss, C; Kreuzer, P; Krizan, P; Krücker, D; Kupper, S; Kvaratskheliia, T; Lanyov, A; Lau, K; Lewendel, B; Lohse, T; Lomonosov, B; Männer, R; Masciocchi, S; Massa, I; Matchikhilian, I; Medin, G; Medinnis, M; Mevius, M; Michetti, A; Mikhailov, Yu; Mizuk, R; Muresan, R; Zur Nedden, M; Negodaev, M; Nörenberg, M; Nowak, S; Núñez Pardo de Vera, M T; Ouchrif, M; Ould-Saada, F; Padilla, C; Peralta, D; Pernack, R; Pestotnik, R; Piccinini, M; Pleier, M A; Poli, M; Popov, V; Pose, A; Pose, D; Prystupa, S; Pugatch, V; Pylypchenko, Y; Pyrlik, J; Reeves, K; Ressing, D; Rick, H; Riu, I; Robmann, P; Rostovtseva, I; Rybnikov, V; Sánchez, F; Sbrizzi, A; Schmelling, M; Schmidt, B; Schreiner, A; Schröder, H; Schwartz, A J; Schwarz, A S; Schwenninger, B; Schwingenheuer, B; Sciacca, F; Semprini-Cesari, N; Shuvalov, S; Silva, L; Smirnov, K; Sözüer, L; Solunin, S; Somov, A; Somov, S; Spengler, J; Spighi, R; Spiridonov, A; Stanovnik, A; Staric, M; Stegmann, C; Subramania, H S; Symalla, M; Tikhomirov, I; Titov, M; Tsakov, I; Uwer, U; van Eldik, C; Vassiliev, Yu; Villa, M; Vitale, A; Vukotic, I; Wahlberg, H; Walenta, A H; Walter, M; Wang, J J; Wegener, D; Werthenbach, U; Wolters, H; Wurth, R; Wurz, A; Zaitsev, Yu; Zavertyaev, M; Zech, G; Zeuner, T; Zhelezov, A; Zheng, Z; Zimmermann, R; Zivko, T; Zoccoli, A
2004-11-19
We have searched for Theta+(1540) and Xi(--)(1862) pentaquark candidates in proton-induced reactions on C, Ti, and W targets at midrapidity and square root of s = 41.6 GeV. In 2 x 10(8) inelastic events we find no evidence for narrow (sigma approximately 5 MeV) signals in the Theta+ --> pK0(S) and Xi(--) --> Xi- pi- channels; our 95% C.L. upper limits (UL) for the inclusive production cross section times branching fraction B dsigma/dy/(y approximately 0) are (4-16) mub/N for a Theta+ mass between 1521 and 1555 MeV, and 2.5 mub/N for the Xi(--). The UL of the yield ratio of Theta+/Lambda(1520) < (3-12)% is significantly lower than model predictions. Our UL of B Xi(--)/Xi(1530)0 < 4% is at variance with the results that have provided the first evidence for the Xi(--). PMID:15600999
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.
NASA Astrophysics Data System (ADS)
Sæther, O. M.; Reimann, C.; Hilmo, B. O.; Taushani, E.
1995-10-01
Groundwaters from crystalline and metamorphic rocks (hardrocks) and from Quaternary deposits, i.e., alluvial and glacial deposits (softrocks) from the counties of Nord-Trøndelag and Sør-Trøndelag were analyzed for major and minor elements and ions including fluoride. The median concentration of F- in water from the hardrock aquifers is 0.28 mg/l (14.7 μeq/l) in contrast to water from softrock aquifers in which it is found to be 0.05 mg/1 (2.6 μeq/l). More importantly, ca. 15% of the locations where water was abstracted from hardrock wells contain 1.5 mg/l (78.9 μeq/l) F- or more. Thus, 15% of all hardrock wells returned F- results that are at or above the maximum recommended value for drinking water. Of the softrock wells, none are above 1 mg/l. Geologists would normally expect higher F-contents in groundwaters derived from acid rocks, e.g., in granitic or gneissic areas. When comparing the host lithology with the observed F-contents, however, no clear relationship between F- content and lithology is visible. The highest observed F- values actually occur in gneissic host rocks. However, wells drilled in amphibolites/greenstones, mica schists, calcareous rocks, and sedimentary rocks all returned some analytical results above 1.5 mg/l F-. These results suggest that all hardrock wells drilled should be tested for F- and the users informed about the results and advised to take any necessary precautions. When applying the recently proposed Norwegian drinking water limits to our data, 51% of all softrock well waters and 56% of all hardrock well waters are unfit for consumption without prior treatment, although we analyzed only for about half of the proposed elements/parameters. This result seriously questions the concept of fixed action levels—many of them with totally unproven health implications—for so many parameters/elements for hardrock groundwaters.
Sahoo- and Wayment-type integral mean value theorems
NASA Astrophysics Data System (ADS)
Tiryaki, Aydin; Çakmak, Devrim
2010-06-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment [An integral mean value theorem, Math. Gazette 54 (1970), pp. 300-301] and Sahoo [Some results related to the integral mean value theorem, Int. J. Math. Ed. Sci. Tech. 38(6) (2007), pp. 818-822]. The importance of our results are illustrated by interesting examples.
Relativistic Momentum and Manifestly Covariant Equipartition Theorem Revisited
Chacon-Acosta, Guillermo; Dagdug, Leonardo; Morales-Tecotl, Hugo A.
2010-07-12
Recently the discussion about the right relativistic generalization of thermodynamics has been revived. In particular the case of temperature has been investigated by alluding to a form of relativistic equipartition theorem. Now from the kinetic theory point of view a covariant equipartition involves necessarily the relativistic momentum of the system, which is given by an integral of the energy-momentum tensor over a spacelike hypersurface. Some authors have even proposed to trade the spacelike hypersurfaces entering in there by lightlike ones to accommodate Lorentz covariance. In this work we argue that a well defined momentum for a diluted gas can be given by making use of the velocity of the gas as whole and thereby selecting a hypersurface; this being in direct analogy with the case of an extended classical electron model and which turned out to solve the Abraham-Lorentz controversy codified in the wrong non-relativistic limit. We also discuss the effect of such choices on the equipartition theorem calculated through the covariant form of the Juettner distribution function.
Aging and nonergodicity beyond the Khinchin theorem
Burov, S.; Metzler, R.; Barkai, E.
2010-01-01
The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin’s theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics. PMID:20624984
Aging and nonergodicity beyond the Khinchin theorem.
Burov, S; Metzler, R; Barkai, E
2010-07-27
The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin's theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics. PMID:20624984
An analogue of a theorem of Kurzweil
NASA Astrophysics Data System (ADS)
Simmons, David
2015-05-01
A theorem of Kurzweil ('55) on inhomogeneous Diophantine approximation states that if θ is an irrational number, then the following are equivalent: (A) for every decreasing positive function ψ such that \\sumq = 1^∞ \\psi(q) = ∞ , and for almost every s\\in R , there exist infinitely many q\\in N such that ‖qθ - s‖ < ψ(q), and (B) θ is badly approximable. This theorem is not true if one adds to condition (A) the hypothesis that the function q ↦ qψ(q) is decreasing. In this paper we find a condition on the continued fraction expansion of θ which is equivalent to the modified version of condition (A). This expands on a recent paper of Kim (2014 Nonlinearity 27 1985-97).
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-01-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571
A torus bifurcation theorem with symmetry
NASA Technical Reports Server (NTRS)
Vangils, S. A.; Golubitsky, M.
1989-01-01
Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.
A 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.
Construction of momentum theorem using cross moments
NASA Astrophysics Data System (ADS)
Hahm, T. S.; Wang, Lu; Diamond, P. H.
2009-11-01
Charney-Drazin theorem has been extended to Hasegawa Wakatani system for zonal flow problem in magnetic fusion [P.H. Diamond, et al., Plasma Phys. Control. Fusion 50, 124018 (2008)]. For this model, the guiding center density is the potential vorticity and zonal flow is influenced by the particle flux. In this work we construct momentum theorems in terms of a hierarchy of cross moments
Volume integral theorem for exotic matter
Nandi, Kamal Kanti; Zhang Yuanzhong; Kumar, K.B. Vijaya
2004-12-15
We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well-known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.
Tests of the lattice index theorem
Jordan, Gerald; Hoellwieser, Roman; Faber, Manfried; Heller, Urs M.
2008-01-01
We investigate the lattice index theorem and the localization of the zero modes for thick classical center vortices. For nonorientable spherical vortices, the index of the overlap Dirac operator differs from the topological charge although the traces of the plaquettes deviate only by a maximum of 1.5% from trivial plaquettes. This may be related to the fact that even in Landau gauge some links of these configuration are close to the nontrivial center elements.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Joint probability distributions and fluctuation theorems
NASA Astrophysics Data System (ADS)
García-García, Reinaldo; Lecomte, Vivien; Kolton, Alejandro B.; Domínguez, Daniel
2012-02-01
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation-dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators.
Theorem Proving In Higher Order Logics
NASA Technical Reports Server (NTRS)
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
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.
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.
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'. PMID:24380348
Extending Bell's Theorem: Ruling out Paramater Independent Hidden Variable Theories
NASA Astrophysics Data System (ADS)
Leegwater, G. J.
2016-03-01
Bell's Theorem may well be the best known result in the foundations of quantum mechanics. Here, it is presented as stating that for any hidden variable theory the combination of the conditions Parameter Independence, Outcome Independence, Source Independence and Compatibility with Quantum Theory leads to a contradiction. Based on work by Roger Colbeck and Renato Renner, an extension of Bell's Theorem is considered. In this extension the theorem is strengthened by replacing Outcome Independence by a strictly weaker condition.
A unified optical theorem for scalar and vectorial wave fields.
Wapenaar, Kees; Douma, Huub
2012-05-01
The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers. PMID:22559339
Fatou type theorems for series in Mittag-Leffler functions
NASA Astrophysics Data System (ADS)
Paneva-Konovska, Jordanka
2012-11-01
In studying the behaviour of series, defined by means of the Mittag-Leffler functions, on the boundary of its domain of convergence in the complex plane, we give analogues of the classical theorems for the power series like Cauchy-Hadamard, Abel, as well as Fatou theorems. The asymptotic formulae for the Mittag-Leffler functions in the cases of "large" values of indices that are used in the proofs of the convergence theorems for the considered series are also provided.
A Converse of the Mean Value Theorem Made Easy
ERIC Educational Resources Information Center
Mortici, Cristinel
2011-01-01
The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…
Index Theorem for Topological Excitations on R^3 \\times S^1 and Chern-Simons Theory
Poppitz, Erich; Unsal, Mithat
2008-12-12
We derive an index theorem for the Dirac operator in the background of various topological excitations on an R{sup 3} x S{sup 1} geometry. The index theorem provides more refined data than the APS index for an instanton on R{sup 4} and reproduces it in decompactification limit. In the R{sup 3} limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the {eta}-invariant associated with the boundary Dirac operator. Neither topological charge nor {eta}-invariant is typically an integer, however, the non-integer parts cancel to give an integer-valued index. Our derivation is based on axial current non-conservation--an exact operator identity valid on any four-manifold--and on the existence of a center symmetric, or approximately center symmetric, boundary holonomy (Wilson line). We expect the index theorem to usefully apply to many physical systems of interest, such as low temperature (large S{sup 1}, confined) phases of gauge theories, center stabilized Yang-Mills theories with vector-like or chiral matter (at S{sup 1} of any size), and supersymmetric gauge theories with supersymmetry-preserving boundary conditions (also at any S{sup 1}). In QCD-like and chiral gauge theories, the index theorem should shed light into the nature of topological excitations responsible for chiral symmetry breaking and the generation of mass gap in the gauge sector. We also show that imposing chirally-twisted boundary condition in gauge theories with fermions induces a Chern-Simons term in the infrared. This suggests that some QCD-like gauge theories should possess components with a topological Chern-Simons phase in the small S{sup 1} regime.
Generalized acceleration theorem for spatiotemporal Bloch waves
Arlinghaus, Stephan; Holthaus, Martin
2011-08-01
A representation is put forward for wave functions of quantum particles in periodic lattice potentials subjected to homogeneous time-periodic forcing, based on an expansion with respect to Bloch-like states which embody both the spatial and the temporal periodicity. It is shown that there exists a generalization of Bloch's famous acceleration theorem which grows out of this representation and captures the effect of a weak probe force applied in addition to a strong dressing force. Taken together, these elements point at a ''dressing and probing'' strategy for coherent wave-packet manipulation, which could be implemented in present experiments with optical lattices.
Flory Theorem for Structurally Asymmetric Mixtures
NASA Astrophysics Data System (ADS)
Dobrynin, Andrey; Sun, Frank; Shirvanyants, David; Rubinstein, Gregory; Rubinstein, Michael; Sheiko, Sergei; Lee, Hyung-Il; Matyjaszewski, Krzysztof
2008-03-01
The generalization of the Flory theorem for structurally asymmetric mixtures was derived and tested by direct visualization of conformational transformations of brushlike macromolecules embedded in a melt of linear chains. Swelling of a brush molecule was shown to be controlled not only by the degree of polymerization of the surrounding linear chains, NB, but also by the degree of polymerization of the brush's side chains, N, which determines the structural asymmetry of the mixed species. The boundaries of the swelling region were established by scaling analysis as N^2
Flory Theorem for Structurally Asymmetric Mixtures
NASA Astrophysics Data System (ADS)
Sun, Frank C.; Dobrynin, Andrey V.; Shirvanyants, David; Lee, Hyung-Il; Matyjaszewski, Krzysztof; Rubinstein, Gregory J.; Rubinstein, Michael; Sheiko, Sergei S.
2007-09-01
The generalization of the Flory theorem for structurally asymmetric mixtures was derived and tested by direct visualization of conformational transformations of brushlike macromolecules embedded in a melt of linear chains. Swelling of a brush molecule was shown to be controlled not only by the degree of polymerization (DP) of the surrounding linear chains, NB, but also by the DP of the brush’s side chains, N, which determines the structural asymmetry of the mixed species. The boundaries of the swelling region were established by scaling analysis as N2
Generating Test Templates via Automated Theorem Proving
NASA Technical Reports Server (NTRS)
Kancherla, Mani Prasad
1997-01-01
Testing can be used during the software development process to maintain fidelity between evolving specifications, program designs, and code implementations. We use a form of specification-based testing that employs the use of an automated theorem prover to generate test templates. A similar approach was developed using a model checker on state-intensive systems. This method applies to systems with functional rather than state-based behaviors. This approach allows for the use of incomplete specifications to aid in generation of tests for potential failure cases. We illustrate the technique on the cannonical triangle testing problem and discuss its use on analysis of a spacecraft scheduling system.
No-cloning theorem on quantum logics
Miyadera, Takayuki; Imai, Hideki
2009-10-15
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
An investigation of the forward scattering theorem
NASA Technical Reports Server (NTRS)
Karam, M. A.; Fung, A. K.
1987-01-01
The calculation of an EM wave's extinction loss during propagation within an inhomogeneous medium, as in active and passive remote sensing modeling, can be undertaken either through the summation of the scattering and absorption losses or through the use of the forward scattering theorem. Attention is presently given to the similarities and differences of these two approaches as a function of dielectric properties of a spherical scatterer and the incident frequency. Scattering loss is obtainable by integrating the magnitude-squared of the scattered field over a spherical surface surrounding the scatterer; the scattered field and the field within the scatterer are computed according to Mie theory.
Penrose's singularity theorem in a Finsler spacetime
NASA Astrophysics Data System (ADS)
Babak Aazami, Amir; Javaloyes, Miguel Angel
2016-01-01
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting. This activity is supported by the programme 'Young leaders in research' 18942/JLI/13 by Fundación Séneca, Regional Agency for Science and Technology from the Region of Murcia, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
No-cloning theorem on quantum logics
NASA Astrophysics Data System (ADS)
Miyadera, Takayuki; Imai, Hideki
2009-10-01
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
Disentangling theorem and monogamy for entanglement negativity
NASA Astrophysics Data System (ADS)
He, Huan; Vidal, Guifre
2015-01-01
Entanglement negativity is a measure of mixed-state entanglement increasingly used to investigate and characterize emerging quantum many-body phenomena, including quantum criticality and topological order. We present two results for the entanglement negativity: a disentangling theorem, which allows the use of this entanglement measure as a means to detect whether a wave function of three subsystems A ,B , and C factorizes into a product state for parts A B1 and B2C ; and a monogamy relation conjecture based on entanglement negativity, which states that if A is very entangled with B , then A cannot be simultaneously very entangled also with C .
Bayes` theorem and quantitative risk assessment
Kaplan, S.
1994-12-31
This paper argues that for a quantitative risk analysis (QRA) to be useful for public and private decision making, and for rallying the support necessary to implement those decisions, it is necessary that the QRA results be ``trustable.`` Trustable means that the results are based solidly and logically on all the relevant evidence available. This, in turn, means that the quantitative results must be derived from the evidence using Bayes` theorem. Thus, it argues that one should strive to make their QRAs more clearly and explicitly Bayesian, and in this way make them more ``evidence dependent`` than ``personality dependent.``
From Einstein's theorem to Bell's theorem: a history of quantum non-locality
NASA Astrophysics Data System (ADS)
Wiseman, H. M.
2006-04-01
In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.
Fluctuation theorems and work relations for single polymer rheology
NASA Astrophysics Data System (ADS)
Latinwo, Folarin Babajide
Synthetic and biological polymeric materials are ubiquitous in nature and modern technology. The emergent properties afforded by these materials allows for wide a array of applications as found in adhesives, coatings, and synthetic polymers for plastics. Importantly, the molecular properties of polymeric systems ultimately determine their bulk macroscopic response and behavior in equilibrium and highly nonequilibrium conditions. As a result, the field of single polymer rheology can play a key role in establishing a molecular level understanding of polymeric systems by investigating the dynamics of single chains. Single polymer rheology is now a well-established approach to study polymer dynamics from experimental and computational perspectives. In general, this approach allows for the determination of molecular subpopulations, relaxation, and polymer chain dynamics in a wide variety of flows. Despite recent progress, current methods in single polymer rheology do not allow for the determination of equilibrium and nonequilibrium thermodynamic properties of polymeric systems. Moreover, it is challenging to connect backbone dynamics to key macroscopic rheological phenomena. In this context, the impact of single polymer rheology has remained limited for the past two decades. In this thesis, we address these challenges by developing and applying fluctuation theorems and nonequilibrium work relations to the field of single polymer rheology. The discovery of thermodynamic identities known as nonequilibrium work relations (NWRs) and fluctuation theorems (FTs) has catalyzed recent advances in statistical mechanics. In general, work relations provide an unprecedented route to extract fundamental materials properties of equilibrium and nonequilibrium systems. Furthermore, these identities have uncovered a broad range of unexpected and remarkable thermodynamic phenomena, including molecular level violations to the second law of thermodynamics. In the context of rheology and
NASA Astrophysics Data System (ADS)
Miserev, D. S.
2016-06-01
The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincaré index theorem for these closed trajectories. The VPM equation is also reduced to the nonrelativistic and semiclassical limits. The limit of a small momentum p y of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.
Visciano, Pierina; Scortichini, Giampiero; Suzzi, Giovanna; Diletti, Gianfranco; Schirone, Maria; Martino, Giuseppe
2015-09-01
Concentrations of pollutants with regulatory limits were determined in specimens of Chamelea gallina, a species of clam collected along the Abruzzi coastal region of the central Adriatic Sea. Nine sampling sites were selected to evaluate the distribution of contaminants in the environment and the health risk for consumers. The concentrations of all the examined compounds were lower than the maximums set by European legislation. Polycyclic aromatic hydrocarbons and total mercury were below the detection limit (0.18 μg/kg for benzo[a]anthracene, 0.30 μg/kg for chrysene, 0.12 μg/kg for benzo[b]fluoranthene, 0.08 μg/kg for benzo[a]pyrene, and 0.0050 mg/kg for total mercury) in all the analyzed samples. Mean concentrations of lead and cadmium were 0.104 and 0.110 mg/kg, respectively. Of the non-dioxin-like polychlorinated biphenyls, PCB-153, PCB-180, and PCB-138 were the most abundant at all sampling sites (1a to 9a) at 0.25 mi (ca. 0.4 km) and at some sampling sites (1b, 2b, 3b, 5b and 7b) at 0.35 mi (ca. 0.56 km). Principal component analysis revealed that the concentrations of dioxin-like polychlorinated biphenyls were similar at the majority of sampling sites, and O8CDD and 2,3,7,8-T4CDF were the predominant dioxin congeners. PMID:26319726
Bell's theorem, inference, and quantum transactions
NASA Astrophysics Data System (ADS)
Garrett, A. J. M.
1990-04-01
Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, “local”) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's new transactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the “delayed choice” experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theorem reinforces arguments in favor of hidden variables.
Ground-state-energy theorem and the virial theorem of a many-particle system in d dimensions
NASA Technical Reports Server (NTRS)
Iwamoto, N.
1984-01-01
The equivalence of Pauli's ground-state-energy theorem and the virial theorem is demonstrated for a many-particle system interacting with an interparticle potential in d dimensions at zero and finite temperatures. Pauli's theorem has an integral form in which the variable is the coupling constant e-squared, while the virial theorem has a differential form in which the variable has the number density n. The essence of the equivalence proof consists in changing the variable from n to e-squared by noting the dependence of the excess free energy on dimensionless quantities for zero-temperature and classical cases.
The virial theorem for the smoothly and sharply, penetrably and impenetrably confined hydrogen atom.
Katriel, Jacob; Montgomery, H E
2012-09-21
Confinement of atoms by finite or infinite boxes containing sharp (discontinuous) jumps has been studied since the fourth decade of the previous century, modelling the effect of external pressure. Smooth (continuous) counterparts of such confining potentials, that depend on a parameter such that in an appropriate limit they coincide with the sharp confining potentials, are investigated, with an emphasis on deriving the corresponding virial and Hellmann-Feynman theorems. PMID:22998251
Non-equilibrium spin-boson model: counting statistics and the heat exchange fluctuation theorem.
Nicolin, Lena; Segal, Dvira
2011-10-28
We focus on the non-equilibrium two-bath spin-boson model, a toy model for examining quantum thermal transport in many-body open systems. Describing the dynamics within the noninteracting-blip approximation equations, applicable, e.g., in the strong system-bath coupling limit and/or at high temperatures, we derive expressions for the cumulant generating function in both the Markovian and non-Markovian limits by energy-resolving the quantum master equation of the subsystem. For a Markovian bath, we readily demonstrate the validity of a steady-state heat exchange fluctuation theorem. In the non-Markovian limit a "weaker" symmetry relation generally holds, a general outcome of microreversibility. We discuss the reduction of this symmetry relation to the universal steady-state fluctuation theorem. Using the cumulant generating function, an analytic expression for the heat current is obtained. Our results establish the validity of the steady-state heat exchange fluctuation theorem in quantum systems with strong system-bath interactions. From the practical point of view, this study provides tools for exploring transport characteristics of the two-bath spin-boson model, a prototype for a nonlinear thermal conductor. PMID:22047227
Computer Algebra Systems and Theorems on Real Roots of Polynomials
ERIC Educational Resources Information Center
Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.
2010-01-01
A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)
Evaluating a Class of Series Using Taylor's Theorem. Classroom Notes
ERIC Educational Resources Information Center
Glaister, P.
2004-01-01
A class of infinite series is evaluated with the aid of Taylor's theorem and a comparison is made with other methods. In a recent note [1] a class of infinite series was shown to be equivalent to a number of definite integrals, and Taylor's theorem was used to establish convergence and to determine the sums of the series and the integrals to any…
Systematic Approaches to Experimentation: The Case of Pick's Theorem
ERIC Educational Resources Information Center
Papadopoulos, Ioannis; Iatridou, Maria
2010-01-01
In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…
Group Theoretical Interpretation of von Neumann's Theorem on Composite Systems.
ERIC Educational Resources Information Center
Bergia, S.; And Others
1979-01-01
Shows that von Neumann's mathematical theorem on composite systems acquires a transparent physical meaning with reference to a suitable physical example; a composite system in a state of definite angular momentum. Gives an outline of the theorem, and the results are restated in Dirac's notation, thus generalizing von Neumann's results which were…
Stimulating Presentation of Theorems Followed by Responsive Proofs.
ERIC Educational Resources Information Center
Movshovitz-Hadar, Nitsa
1988-01-01
Several ways to present two theorems (concerning a square matrix and a property of prime numbers) are demonstrated. One way for each theorem is more stimulating, better setting the stage for the proofs. Several methods of presenting proofs are illustrated, with the outcomes considered from the learner's viewpoint. (MNS)
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2009-02-20
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2008-03-01
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
Leaning on Socrates to Derive the Pythagorean Theorem
ERIC Educational Resources Information Center
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the formula b2 +…
Discovering Theorems in Abstract Algebra Using the Software "GAP"
ERIC Educational Resources Information Center
Blyth, Russell D.; Rainbolt, Julianne G.
2010-01-01
A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…
When 95% Accurate Isn't: Exploring Bayes's Theorem
ERIC Educational Resources Information Center
CadwalladerOlsker, Todd D.
2011-01-01
Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…
Some Reflections on CAS Assisted Proofs of Theorems
ERIC Educational Resources Information Center
Dana-Picard, Thierry
2005-01-01
A mathematician's work consists of proving theorems, calculating, and making mathematics understandable. An assistant for all three components is a Computer Algebra System. We describe and discuss various CAS-assisted processes for proving theorems, and discuss the constraints which can appear regarding efficiency, confidence in the result and…
Rotation of Axes and the Mean Value Theorem
ERIC Educational Resources Information Center
Price, David
2004-01-01
This article provides a proof of the Mean Value Theorem by rotating a coordinate system through a specified angle. The use of this approach makes it easy to visualize why the Mean Value Theorem is true. An instructor can use the proof as another illustration of the rotation of axis technique in addition to the standard one of simplifying equations…
Three Lectures on Theorem-proving and Program Verification
NASA Technical Reports Server (NTRS)
Moore, J. S.
1983-01-01
Topics concerning theorem proving and program verification are discussed with particlar emphasis on the Boyer/Moore theorem prover, and approaches to program verification such as the functional and interpreter methods and the inductive assertion approach. A history of the discipline and specific program examples are included.
A most compendious and facile quantum de Finetti theorem
Koenig, Robert; Mitchison, Graeme
2009-01-15
In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's 'exponential' approximation by 'almost-product' states, a theorem which deals with certain triples of representations of the unitary group, and the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choice of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states and leads to some new results, including an exponential theorem for infinite-dimensional systems.
The virial theorem for the polarizable continuum model
Cammi, R.
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.
The virial theorem for the Polarizable Continuum Model.
Cammi, R
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential. PMID:24588153
Isotropy theorem for cosmological Yang-Mills theories
NASA Astrophysics Data System (ADS)
Cembranos, J. A. R.; Maroto, A. L.; Jareño, S. J. Núñez
2013-02-01
We consider homogeneous non-Abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a generalization of the virial theorem that for an arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. We consider also the case in which a gauge-fixing term is introduced in the action and show that the average equation of state does not depend on such a term. Finally, we extend the results to arbitrary background geometries and show that the average energy-momentum tensor of a rapidly evolving Yang-Mills field is always isotropic and has the perfect fluid form for any locally inertial observer.
Topological Effective Field Theories for Dirac Fermions from Index Theorem
NASA Astrophysics Data System (ADS)
Palumbo, Giandomenico; Catenacci, Roberto; Marzuoli, Annalisa
2014-01-01
Dirac fermions have a central role in high energy physics but it is well-known that they emerge also as quasiparticles in several condensed matter systems supporting topological order. We present a general method for deriving the topological effective actions of (3+1)-massless Dirac fermions living on general backgrounds and coupled with vector and axial-vector gauge fields. The first step of our strategy is standard (in the Hermitian case) and consists in connecting the determinants of Dirac operators with the corresponding analytical indices through the zeta-function regularization. Then, we introduce a suitable splitting of the heat kernel that naturally selects the purely topological part of the determinant (i.e., the topological effective action). This topological effective action is expressed in terms of gauge fields using the Atiyah-Singer index theorem which computes the analytical index in topological terms. The main new result of this paper is to provide a consistent extension of this method to the non-Hermitian case, where a well-defined determinant does not exist. Quantum systems supporting relativistic fermions can thus be topologically classified on the basis of their response to the presence of (external or emergent) gauge fields through the corresponding topological effective field theories (TEFTs).
A Stochastic Tikhonov Theorem in Infinite Dimensions
Buckdahn, Rainer Guatteri, Giuseppina
2006-03-15
The present paper studies the problem of singular perturbation in the infinite-dimensional framework and gives a Hilbert-space-valued stochastic version of the Tikhonov theorem. We consider a nonlinear system of Hilbert-space-valued equations for a 'slow' and a 'fast' variable; the system is strongly coupled and driven by linear unbounded operators generating a C{sub 0}-semigroup and independent cylindrical Brownian motions. Under well-established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. We avoid differentiability assumptions on the coefficients which would be unnatural in the infinite-dimensional framework.
Extended Ehrenfest theorem with radiative corrections
NASA Astrophysics Data System (ADS)
de la Peña, L.; Cetto, A. M.; Valdés-Hernández, A.
2015-10-01
A set of basic evolution equations for the mean values of dynamical variables is obtained from the Fokker-Planck equation applied to the general problem of a particle subject to a random force. The specific case of stochastic electrodynamics is then considered, in which the random force is due to the zero-point radiation field. Elsewhere it has been shown that when this system reaches a state of energy balance, it becomes controlled by an equation identical to Schrödinger’s, if the radiationless approximation is made. The Fokker-Planck equation was shown to lead to the Ehrenfest theorem under such an approximation. Here we show that when the radiative terms are not neglected, an extended form of the Ehrenfest equation is obtained, from which follow, among others, the correct formulas for the atomic lifetimes and the (nonrelativistic) Lamb shift.
BMS supertranslations and Weinberg's soft graviton theorem
NASA Astrophysics Data System (ADS)
He, Temple; Lysov, Vyacheslav; Mitra, Prahar; Strominger, Andrew
2015-05-01
Recently it was conjectured that a certain infinite-dimensional "diagonal" subgroup of BMS supertranslations acting on past and future null infinity ([InlineMediaObject not available: see fulltext.] and [InlineMediaObject not available: see fulltext.]) is an exact symmetry of the quantum gravity S-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinberg's soft graviton theorem. Along the way we construct the canonical generators of supertranslations at [InlineMediaObject not available: see fulltext.], including the relevant soft graviton contributions. Boundary conditions at the past and future of [InlineMediaObject not available: see fulltext.] and a correspondingly modified Dirac bracket are required. The soft gravitons enter as boundary modes and are manifestly the Goldstone bosons of spontaneously broken supertranslation invariance.
Theorem Proving in Intel Hardware Design
NASA Technical Reports Server (NTRS)
O'Leary, John
2009-01-01
For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.
On the Virial Theorem for Interstellar Medium
Ryutov, D
2007-09-24
An attempt has been made to derive a version of the virial integral that would describe average properties of the interstellar medium (ISM). It is suggested to eliminate the (large) contribution of stellar matter by introducing 'exclusion zones' surrounding stars. Such an approach leads to the appearance of several types of additional surface integrals in the general expression. Their contribution depends on the rate of energy and matter exchange between the stars and ISM. If this exchange is weak, one can obtain a desired virial integral for ISM. However, the presence of intermittent large-scale energetic events significantly constrains the applicability of the virial theorem. If valid, the derived virial integral is dominated by cold molecular/atomic clouds, with only minor contribution of the global magnetic field and low-density warm part.
Walking Through the Impulse-Momentum Theorem
NASA Astrophysics Data System (ADS)
Haugland, Ole Anton
2013-02-01
Modern force platforms are handy tools for investigating forces during human motion. Earlier they were very expensive and were mostly used in research laboratories. But now even platforms that can measure in two directions are quite affordable. In this work we used the PASCO 2-Axis Force Platform. The analysis of the data can serve as a nice illustration of qualitative or quantitative use of the impulse-momentum theorem p - p0 = ∫t0t Fdt = I. The most common use of force platforms is to study the force from the base during the push-off period of a vertical jump. I think this is an activity of great value, and I would recommend it. The use of force platforms in teaching is well documented in research literature.1-4
Elementary theorems regarding blue isocurvature perturbations
NASA Astrophysics Data System (ADS)
Chung, Daniel J. H.; Yoo, Hojin
2015-04-01
Blue CDM-photon isocurvature perturbations are attractive in terms of observability and may be typical from the perspective of generic mass relations in supergravity. We present and apply three theorems useful for blue isocurvature perturbations arising from linear spectator scalar fields. In the process, we give a more precise formula for the blue spectrum associated with the axion model of Kasuya and Kawasaki [Axion Isocurvature Fluctuations with Extremely Blue Spectrum, Phys. Rev. D 80, 023516 (2009).], which can in a parametric corner give a factor of O (10 ) correction. We explain how a conserved current associated with Peccei-Quinn symmetry plays a crucial role and explicitly plot several example spectra including the breaks in the spectra. We also resolve a little puzzle arising from a naive multiplication of isocurvature expression that sheds light on the gravitational imprint of the adiabatic perturbations on the fields responsible for blue isocurvature fluctuations.
Robbing the Bank with a Theorem Prover
NASA Astrophysics Data System (ADS)
Youn, Paul; Adida, Ben; Bond, Mike; Clulow, Jolyon; Herzog, Jonathan; Lin, Amerson; Rivest, Ronald L.; Anderson, Ross
In this work, we present the first automated analysis of security application programming interfaces (security APIs). In particular, we analyze the API of the IBM 4758 CCA, a hardware security module for banking networks. Adapting techniques from formal analyses of security protocols, we model the API purely according its specification and assuming ideal encryption primitives. We then use the automated theorem-prover Otter to analyze this model, combining its standard reasoning strategies with novel techniques of our own (also presented here). In this way, we derive not only all published API-level attacks against the 4758 CCA, but an extension to these attacks as well. Thus, this work represents the first step toward fully-automated, rigorous analyses of security APIs.
Geometry underlying no-hidden-variable theorems
NASA Astrophysics Data System (ADS)
Fivel, Daniel I.
1991-07-01
The set of orientations of a measuring device (e.g., a Stern-Gerlach magnet) produced by the action of a Lie group constitutes a honmogeneous space S (e.g., a sphere). A hidden-variable measure determines a metric D on S, the triangle inequality being Bell's inequality. But identification of S with Hilbert-space projectors induces a locally convex metric d on S. The Einstein-Podolsky-Rosen (EPR) hypotheses imply that D=d2, which is impossible because the square of a locally convex metric cannot be a metric. This proves the Bell-EPR theorem. Classical systems avoid the contradiction by allowing only values d=0,1. The ``watchdog'' effect is shown to result from the form of the quantum-mechanical metric.
Electric-magnetic symmetry and Noether's theorem
NASA Astrophysics Data System (ADS)
Cameron, Robert P.; Barnett, Stephen M.
2012-12-01
In the absence of charges, Maxwell's equations are highly symmetrical. In particular, they place the electric and magnetic fields on equal footing. In light of this electric-magnetic symmetry, we introduce a variational description of the free electromagnetic field that is based upon the acknowledgement of both electric and magnetic potentials. We use our description, together with Noether's theorem, to demonstrate that electric-magnetic symmetry is, in essence, an expression of the conservation of optical helicity. The symmetry associated with the conservation of Lipkin's zilches is also identified. We conclude by considering, with care, the subtle separation of the rotation and boost angular momenta of the field into their ‘spin’ and ‘orbital’ contributions.
Virial Theorem in Nonlocal Newtonian Gravity
NASA Astrophysics Data System (ADS)
Mashhoon, Bahram
2016-05-01
Nonlocal gravity is the recent classical nonlocal generalization of Einstein's theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for "isolated" astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's baryonic diameter---namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time---is predicted to be larger than the effective dark matter fraction times a universal length that is the basic nonlocality length scale of about 3 kpc.
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
Generalization of Kummer's second theorem with applications
NASA Astrophysics Data System (ADS)
Kim, Yong Sup; Rakha, M. A.; Rathie, A. K.
2010-03-01
The aim of this research paper is to obtain single series expression of e^{ - x/2} _1 F_1 (α ;2α + i;x) for i = 0, ±1, ±2, ±3, ±4, ±5, where 1 F 1(·) is the function of Kummer. For i = 0, we have the well known Kummer second theorem. The results are derived with the help of generalized Gauss second summation theorem obtained earlier by Lavoie et al. In addition to this, explicit expressions of _2 F_1 [ - 2n,α ;2α + i;2]and_2 F_1 [ - 2n - 1,α ;2α + i;2] each for i = 0, ±1, ±2, ±3, ±4, ±5 are also given. For i = 0, we get two interesting and known results recorded in the literature. As an applications of our results, explicit expressions of e^{ - x} _1 F_1 (α ;2α + i;x) × _1 F_1 (α ;2α + j;x) for i, j = 0, ±1, ±2, ±3, ±4, ±5 and (1 - x)^{ - a} _2 F_1 left( {a,b,2b + j; - tfrac{{2x}} {{1 - x}}} right) for j = 0, ±1, ±2, ±3, ±4, ±5 are given. For i = j = 0 and j = 0, we respectively get the well known Preece identity and a well known quadratic transformation formula due to Kummer. The results derived in this paper are simple, interesting, easily established and may be useful in the applicable sciences.
From the necessary to the possible: the genesis of the spin-statistics theorem
NASA Astrophysics Data System (ADS)
Blum, Alexander
2014-09-01
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.
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.
NASA Astrophysics Data System (ADS)
Ramalho, G.
2016-08-01
Some empirical parametrizations of the γ* N → N (1535) transition amplitudes violate the Siegert's theorem, that relates the longitudinal and the transverse amplitudes in the pseudo-threshold limit (nucleon and resonance at rest). In the case of the electromagnetic transition from the nucleon (mass M) to the resonance N (1525) (mass MR), the Siegert's theorem is sometimes expressed by the relation | q |A1/2 = λS1/2 in the pseudo-threshold limit, when the photon momentum | q | vanishes, and λ =√{ 2} (MR - M). In this article, we argue that the Siegert's theorem should be expressed by the relation A1/2 = λS1/2 / | q |, in the limit | q | → 0. This result is a consequence of the relation S1/2 ∝ | q |, when | q | → 0, as suggested by the analysis of the transition form factors and by the orthogonality between the nucleon and N (1535) states. We propose then new empirical parametrizations for the γ* N → N (1535) helicity amplitudes, that are consistent with the data and the Siegert's theorem. The proposed parametrizations follow closely the MAID2007 parametrization, except for a small deviation in the amplitudes A1/2 and S1/2 when Q2 < 1.5 GeV2.
The global Utiyama theorem in Einstein-Cartan theory
NASA Astrophysics Data System (ADS)
Bruzzo, Ugo
1987-09-01
A global formulation of Utiyama's theorem for Einstein-Cartan-type gravitational theories regarded as gauge theories of the group of space-time diffeomorphisms is given. The local conditions for the Lagrangian to be gauge invariant coincide with those found by other authors [A. Pérez-Rendón Collantes, ``Utiyama type theorems,'' in Poincaré Gauge Approach to Gravity. I, Proceedings Journées Relativistes 1984; A. Pérez-Rendón and J. J. Seisdedos, ``Utiyama type theorems in Poincaré gauge approach to gravity. II, '' Preprints de Mathematicas, Universidad de Salamanca, 1986] in Kibble's and Hehl's approaches.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
NASA Astrophysics Data System (ADS)
Stenlund, Mikko
2016-09-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff's ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
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
Equipartition theorem in glasses and liquids
NASA Astrophysics Data System (ADS)
Levashov, Valentin A.; Egami, Takeshi; Aga, Rachel S.; Morris, James R.
2008-03-01
In glasses and liquids phonons have very short life-time, whereas the total potential energy is not linear with temperature, but follows the T**(3/5) law. Thus it may appear that atomic vibrations in liquids cannot be described by the harmonic oscillator model that follows the equipartition theorem for the kinetic energy and potential energy. We show that the description of the nearest neighbor oscillation in terms of the atomic level stresses indeed provide such a description. The model was tested for various pair-wise potentials, including the Lennard-Jones potential, the Johnson potentials, and only the repulsive part of the Johnson potential. In all cases each of the local elastic energies of the six independent components of the stress tensor is equal to kT/4, thus the total potential energy is equal to (3/2)kT. Thus this model provides the basis for discussing the thermodynamic properties of glasses and liquids based on atomistic excitations. An example of this model leading to the description of the glass transition temperature in metallic glasses is discussed [1]. [1] T. Egami, et al., Phys. Rev. B 76, 024203 (2007).
No-go theorems for generalized chameleon field theories.
Wang, Junpu; Hui, Lam; Khoury, Justin
2012-12-14
The chameleon, or generalizations thereof, is a light scalar that couples to matter with gravitational strength, but whose manifestation depends on the ambient matter density. A key feature is that the screening mechanism suppressing its effects in high-density environments is determined by the local scalar field value. Under very general conditions, we prove two theorems limiting its cosmological impact: (i) the Compton wavelength of such a scalar can be at most ~/= 1 MPc at the present cosmic density, which restricts its impact to nonlinear scales; and (ii) the conformal factor relating Einstein- and Jordan-frame scale factors is essentially constant over the last Hubble time, which precludes the possibility of self-acceleration. These results imply that chameleonlike scalar fields have a negligible effect on the linear-scale growth history; theories that invoke a chameleonlike scalar to explain cosmic acceleration rely on a form of dark energy rather than a genuine modified gravity effect. Our analysis applies to a broad class of chameleon, symmetron, and dilaton theories. PMID:23368302
Analysing nature's experiment: Fisher's inductive theorem of natural selection.
Edwards, A W F
2016-06-01
The paper by Ewens and Lessard (2015) adds to the progress that has been made in exploring the discrete-generation analytical version of Fisher's Fundamental Theorem of Natural Selection introduced by Ewens (1989). Fisher's continuous-time theorem differs from the version described by Ewens and Lessard by using a different concept of fitness. Ewens and Lessard use the conventional 'viability' concept whereas for Fisher the fitness of a genotype was its relative rate of increase or decrease in the population. The sole purpose of the present paper is to emphasize the alternative inductive nature of Fisher's theorem, as presented by him in 1930, by placing it in the context of his contemporary development of the analysis of variance in agricultural experiments. It is not a general discussion of the theorem itself. PMID:26581894
Two time physics and Hamiltonian Noether theorem for gauge systems
Nieto, J. A.; Ruiz, L.; Silvas, J.; Villanueva, V. M.
2006-09-25
Motivated by two time physics theory we revisited the Noether theorem for Hamiltonian constrained systems. Our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints.
Oscillation theorems for second order nonlinear forced differential equations.
Salhin, Ambarka A; Din, Ummul Khair Salma; Ahmad, Rokiah Rozita; Noorani, Mohd Salmi Md
2014-01-01
In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature. PMID:25077054
Extension of the Blasius force theorem to subsonic speeds
NASA Astrophysics Data System (ADS)
Barsony-Nagy, A.
1985-11-01
The theorem considered by Blasius (1910) represents a well-known method for calculating the force on a body situated in an incompressible, inviscid two-dimensional flow. The efficiency of the Blasius theorem is due to its quality of expressing the forces with the aid of contour integrals of analytic functions of complex variables. The present note has the objective to deduce an analog of Blasius theorem for the aerodynamic forces in subsonic flow. It is assumed that an approximate velocity potential of the subsonic flow has been calculated by using the Imai-Lamla method. It is pointed out that this method is a variant specially suited for the two-dimensionally flows of the Janzen-Rayleigh expansion method. The derived formula expresses the aerodynamic forces with the aid of contour integrals of analytic complex functions. It can be regarded as the Blasius theorem with first-order compressibility correction for the subsonic speed regime.
Bernoulli theorem generalized to rheologically complex viscous fluid flow
NASA Astrophysics Data System (ADS)
Brutyan, M. A.; Krapivskii, P. L.
1992-08-01
The Bernoulli theorem is generalized to two-dimensional and axisymmetric micropolar incompressible fluid flows. It is shown that the approach developed is also applicable to magnetohydrodynamic flows of a viscous Newtonian fluid.
An Epistemological Criticism to the Bell-Kochen-Specker Theorem
NASA Astrophysics Data System (ADS)
Garola, Claudio
2009-03-01
The Bell-Kochen-Specker theorem is criticized from an epistemological point of view, showing that its proofs rest on an implicit epistemological assumption which does not fit in with the operational and antimetaphysical attitude of orthodox quantum mechanics.
Forest Carbon Uptake and the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Zobitz, John
2013-01-01
Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.
On an order reduction theorem in the Lagrangian formalism
NASA Astrophysics Data System (ADS)
Grigore, D. R.
1996-11-01
We provide a new proof of a important theorem in the Lagrangian formalism about necessary and sufficient conditions for a second-order variational system of equations to follow from a first-order Lagrangian.
Fluctuation theorem in driven nonthermal systems with quenched disorder
Reichhardt, Charles; Reichhardt, C J; Drocco, J A
2009-01-01
We demonstrate that the fluctuation theorem of Evans and Searles can be used to characterize the class of dynamics that arises in nonthermal systems of collectively interacting particles driven over random quenched disorder. By observing the frequency of entropy-destroying trajectories, we show that there are specific dynamical regimes near depinning in which this theorem holds. Hence the fluctuation theorem can be used to characterize a significantly wider class of non-equilibrium systems than previously considered. We discuss how the fluctuation theorem could be tested in specific systems where noisy dynamics appear at the transition from a pinned to a moving phase such as in vortices in type-II superconductors, magnetic domain walls, and dislocation dynamics.
On the generalized virial theorem for systems with variable mass
NASA Astrophysics Data System (ADS)
Ganghoffer, Jean-François; Rahouadj, Rachid
2016-03-01
We presently extend the virial theorem for both discrete and continuous systems of material points with variable mass, relying on developments presented in Ganghoffer (Int J Solids Struct 47:1209-1220, 2010). The developed framework is applicable to describe physical systems at very different scales, from the evolution of a population of biological cells accounting for growth to mass ejection phenomena occurring within a collection of gravitating objects at the very large astrophysical scales. As a starting basis, the field equations in continuum mechanics are written to account for a mass source and a mass flux, leading to a formulation of the virial theorem accounting for non-constant mass within the considered system. The scalar and tensorial forms of the virial theorem are then written successively in both Lagrangian and Eulerian formats, incorporating the mass flux. As an illustration, the averaged stress tensor in accreting gravitating solid bodies is evaluated based on the generalized virial theorem.
Biological fitness and the fundamental theorem of natural selection.
Grafen, Alan
2015-07-01
Fisher's fundamental theorem of natural selection is proved satisfactorily for the first time, resolving confusions in the literature about the nature of reproductive value and fitness. Reproductive value is defined following Fisher, without reference to genetic variation, and fitness is the proportional rate of increase in an individual's contribution to the demographic population size. The mean value of fitness is the same in each age class, and it also equals the population's Malthusian parameter. The statement and derivation are regarded as settled here, and so the general biological significance of the fundamental theorem can be debated. The main purpose of the theorem is to find a quantitative measure of the effect of natural selection in a Mendelian system, thus founding Darwinism on Mendelism and identifying the design criterion for biological adaptation, embodied in Fisher's ingenious definition of fitness. The relevance of the newly understood theorem to five current research areas is discussed. PMID:26098334
Strong no-go theorem for Gaussian quantum bit commitment
Magnin, Loieck; Magniez, Frederic; Leverrier, Anthony
2010-01-15
Unconditionally secure bit commitment is forbidden by quantum mechanics. We extend this no-go theorem to continuous-variable protocols where both players are restricted to use Gaussian states and operations, which is a reasonable assumption in current-state optical implementations. Our Gaussian no-go theorem also provides a natural counter-example to a conjecture that quantum mechanics can be rederived from the assumption that key distribution is allowed while bit commitment is forbidden in Nature.
Note on soft graviton theorem by KLT relation
NASA Astrophysics Data System (ADS)
Du, Yi-Jian; Feng, Bo; Fu, Chih-Hao; Wang, Yihong
2014-11-01
Recently, new soft graviton theorem proposed by Cachazo and Strominger has inspired a lot of works. In this note, we use the KLT-formula to investigate the theorem. We have shown how the soft behavior of color ordered Yang-Mills amplitudes can be combined with KLT relation to give the soft behavior of gravity amplitudes. As a byproduct, we find two nontrivial identities of the KLT momentum kernel must hold.
A study on arithmetical functions and the prime number theorem
NASA Astrophysics Data System (ADS)
Imm, Yeoh Saw
2014-06-01
In this paper, Leibniz triangle and suitable binomial coefficients were used to get the bounds of ψ (x) . Using the generalized convolution and the differentiation on generalized convolution of arithmetical functions, we get to prove Tatuzawa-Izeki identity. Selberg's asymptotic formula is included as a special case, which is the beginning of certain elementary proofs of the Prime Number Theorem. Integration is used on some related inequalities to provide a smoother elementary proof of the Prime Number Theorem.
Nyquist-Shannon sampling theorem applied to refinements of the atomic pair distribution function
Farrow, Christopher L.; Shaw, Margaret; Kim, Hyunjeong; Juhás, Pavol; Billinge, Simon J.L.
2011-12-07
We have systematically studied the optimal real-space sampling of atomic pair distribution (PDF) data by comparing refinement results from oversampled and resampled data. Based on nickel and a complex perovskite system, we show that not only is the optimal sampling bounded by the Nyquist interval described by the Nyquist-Shannon (NS) sampling theorem as expected, but near this sampling interval, the data points in the PDF are minimally correlated, which results in more reliable uncertainty estimates in the modeling. Surprisingly, we find that PDF refinements quickly become unstable for data on coarser grids. Although the Nyquist-Shannon sampling theorem is well known, it has not been applied to PDF refinements, despite the growing popularity of the PDF method and its adoption in a growing number of communities. Here, we give explicit expressions for the application of NS sampling theorem to the PDF case, and establish through modeling that it is working in practice, which lays the groundwork for this to become more widely adopted. This has implications for the speed and complexity of possible refinements that can be carried out many times faster than currently with no loss of information, and it establishes a theoretically sound limit on the amount of information contained in the PDF that will prevent over-parametrization during modeling.
Non-linear energy conservation theorem in the framework of special relativity
NASA Astrophysics Data System (ADS)
Pérez Teruel, Ginés R.
2015-07-01
In this work we revisit the study of the gravitational interaction in the context of the special theory of relativity. It is found that, as long as the equivalence principle is respected, a relativistic nonlinear energy conservation theorem arises in a natural way. We interpret that this nonlinear conservation law stresses the nonlinear character of the gravitational interaction. The theorem reproduces the energy conservation theorem of Newtonian mechanics in the corresponding low energy limit, but also allows to derive some standard results of post-Newtonian gravity, such as the formula of the gravitational redshift. Guided by this conservation law, we develop a Lagrangian formalism for a particle in a gravitational field. We realize that the Lagrangian can be written in an explicit covariant fashion, and turns out to be the geodesic Lagrangian of a curved Lorentzian manifold. Therefore, any attempt to describe gravity within the special theory, leads outside their own domains towards a curved space-time. Thus, the pedagogical content of the paper may be useful as a starting point to discuss the problem of gravitation in the context of the special theory, as a preliminary step before introducing general relativity.
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.
On a variational theorem in acousto-elastodynamics
NASA Astrophysics Data System (ADS)
Thompson, B. S.
1982-08-01
A variational theorem is presented which may be used as a basis for developing the equations of motion and the boundary conditions appropriate for studying the vibrational behavior of flexible bodied systems and the surrounding acoustic medium. The theorem is a generalization of two theorems which are both based on the principle of virtual work; the first governs the elastodynamics of the mechanical system and the second governs the behavior of the fluid medium. Lagrange multipliers are used in the development of the two basic theorems and they are also employed to incorporate the constraints at the solid-fluid interface within the functional for the acousto-elastodynamic theorem. When independent arbitrary variations of the system parameters are permitted, this theorem yields as characteristic equations the equations of motion for each member of the mechanical system, the acoustic wave equation, the compatibility conditions at the mechanical joints, the compatibility conditions at the interface and also the mixed boundary conditions for the complete system. As an illustrative example, the derivation of the problem statement for a flexible slider crank mechanism operating in a perfect gas is presented in which it is assumed that the flexural motion of the links is governed by the Timoshenko beam theory.
[Health care systems and impossibility theorems].
Penchas, Shmuel
2004-02-01
results are Kurt Godel's seminal paper in 1931: "Ueber formal unentscheidbare Saetze der Principia Mathematica and verwandter System I" and Arrow's Nobel Prize winning "Impossibility Theorem" (Social Choice and Individual Values, 1951). Godel showed, unequivocally, that there is an enormous gap between what is being perceived as truth and what in fact can be proven as such. Arrow showed that the translation of individual preferences into a social order is impossible--except in a dictatorship. The unsolved controversies concerning the desirable or ideal structure of health care systems are impinged upon by these findings generally, and, in the case of the impossibility theorem, also directly. There is the impossibility of aggregating preferences and, at a deeper level, the impossibility of defining certain fundamental values, coupled with the problematic use of certain words, the absence of the possibility of creating, on a logically defined base, a complex system, complete and comprehensive in its own right. This is added to the fact that according to the elaboration by Stephen Wolfram in "A New Kind of Science", it is not easy to reduce complicated systems to simple components and to predict the continuation of their development even from simple basic laws without complicated calculations. All of these factors impede the construction of satisfying health care systems and leave obvious problems which overshadow the structure and the operation of health care systems. PMID:15143703
Subexponential estimates in Shirshov's theorem on height
Belov, Aleksei Ya; Kharitonov, Mikhail I
2012-04-30
Suppose that F{sub 2,m} is a free 2-generated associative ring with the identity x{sup m}=0. In 1993 Zelmanov put the following question: is it true that the nilpotency degree of F{sub 2,m} has exponential growth? We give the definitive answer to Zelmanov's question by showing that the nilpotency class of an l-generated associative algebra with the identity x{sup d}=0 is smaller than {Psi}(d,d,l), where {Psi}(n,d,l)=2{sup 18}l(nd){sup 3log}{sub 3}{sup (nd)+13}d{sup 2}. This result is a consequence of the following fact based on combinatorics of words. Let l, n and d{>=}n be positive integers. Then all words over an alphabet of cardinality l whose length is not less than {Psi}(n,d,l) are either n-divisible or contain x{sup d}; a word W is n-divisible if it can be represented in the form W=W{sub 0}W{sub 1} Horizontal-Ellipsis W{sub n} so that W{sub 1},...,W{sub n} are placed in lexicographically decreasing order. Our proof uses Dilworth's theorem (according to V.N. Latyshev's idea). We show that the set of not n-divisible words over an alphabet of cardinality l has height h<{Phi}(n,l) over the set of words of degree {<=}n-1, where {Phi}(n,l)=2{sup 87}l{center_dot}n{sup 12log}{sub 3}{sup n+48}. Bibliography: 40 titles.
Quantum duality, unbounded operators, and inductive limits
Dosi, Anar
2010-06-15
In this paper, we investigate the inductive limits of quantum normed (or operator) spaces. This construction allows us to treat the space of all noncommutative continuous functions over a quantum domain as a quantum (or local operator) space of all matrix continuous linear operators equipped with S-quantum topology. In particular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens-Mackey theorem. Further, the inductive limits of operator spaces are used to introduce locally compact and locally trace class unbounded operators on a quantum domain and prove the dual realization theorem for an abstract quantum space.
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. PMID:25820816
Subsubleading soft theorems of gravitons and dilatons in the bosonic string
NASA Astrophysics Data System (ADS)
Di Vecchia, Paolo; Marotta, Raffaele; Mojaza, Matin
2016-06-01
Starting from the amplitude with an arbitrary number of massless closed states of the bosonic string, we compute the soft limit when one of the states becomes soft to subsubleading order in the soft momentum expansion, and we show that when the soft state is a graviton or a dilaton, the full string amplitude can be expressed as a soft theorem through subsubleading order. It turns out that there are string corrections to the field theoretical limit in the case of a soft graviton, while for a soft dilaton the string corrections vanish. We then show that the new soft theorems, including the string corrections, can be simply obtained from the exchange diagrams where the soft state is attached to the other external states through the three-point string vertex of three massless states. In the soft-limit, the propagator of the exchanged state is divergent, and at tree-level these are the only divergent contributions to the full amplitude. However, they do not form a gauge invariant subset and must be supplemented with extra non-singular terms. The requirement of gauge invariance then fixes the complete amplitude through subsubleading order in the soft expansion, reproducing exactly what one gets from the explicit calculation in string theory. From this it is seen that the string corrections at subsubleading order arise as a consequence of the three-point amplitude having string corrections in the bosonic string. When specialized to a soft dilaton, it remarkably turns out that the string corrections vanish and that the non-singular piece of the subsubleading term of the dilaton soft theorem is the generator of space-time special conformal transformation.
A Theorem for Two Nucleon Transfer
NASA Astrophysics Data System (ADS)
Zamick, Larry; Mekjian, Aram
2004-05-01
We use the short notation for a unitary 9j symbol U9j(Ja,Jb)=<(jj)Ja(jj)Ja|(jj)Jb(jj)Jb>I=0 The wave fcn of a state of 44Ti with ang momentum I can be written as sum D(Jp,Jn) [(jj)Jp (jj)Jn]I. For the I=0 ground stae Jp=Jn. We found a new relationship SumJp U9j(Jp,Jx) D(Jp,Jp)= 1/2 D(Jx,Jx) for T=0 and =-D(Jx,Jx) for T=2. We could explain this by regarding U9j for even Jp,Jx as a square matrix hamiltonian, which, when diagonalized has eigenvalues of 1/2(triply degenerate) and -1(singly degenerate) corresponding to T=0 and T=2 respectively.*This theorem is useful,in the context of 2 nucleon transfer, for counting the number of pairs of particles in 44Ti with even Jx.The expressions simplifies to 3|D(Jx,Jx|^2,thus eliminating a complex 9jsymbol A deeper understanding of this result arises if we consider the strange interplay of angular momentum and isospin. Consider the interaction 1/4-t(1).t(2),which is unity for T=0 states and zero for T=1. For n nucleons with isospin T the eigenvalues are n^2/8+n/4-T(T+1)/2 But if we evaluate this with the usual Racah algebra then we note that in the single j shell the interaction can also be written as <(jj)Ia V (jj)Ia>= (1-(-1)^Ia)/2 i.e. the interaction acts only in odd J states since they have isospin T=0.In 44Ti the matrix element of the hamiltonian is [2+2U9j(Jp,Jx)].Connecting this with the isospin expression gives us the eigenvalues above for U9j. * L.Zamick, E. Moya de Guerra,P.Sarriguren,A.Raduta and A. Escuderos, preprint.
Use of Lambert's theorem for the n-dimensional Coulomb problem
Kanellopoulos, Vassiliki; Kleber, Manfred; Kramer, Tobias
2009-07-15
We present the analytical solution in closed form for the semiclassical limit of the quantum-mechanical Coulomb Green's function in position space in n dimensions. We utilize a projection method which has its roots in Lambert's theorem and which allows us to treat the system as an essentially one-dimensional problem. The semiclassical result assumes a simple analytical form and is well suited for a numerical evaluation. The method can also be extended to classically forbidden space regions. Already for moderately large principal quantum numbers {nu}{>=}5, the semiclassical Green's function is found to be an excellent approximation to the quantum-mechanical Green's function.
A no-go for no-go theorems prohibiting cosmic acceleration in extra dimensional models
Koster, Rik; Postma, Marieke E-mail: mpostma@nikhef.nl
2011-12-01
A four-dimensional effective theory that arises as the low-energy limit of some extra-dimensional model is constrained by the higher dimensional Einstein equations. Steinhardt and Wesley use this to show that accelerated expansion in our four large dimensions can only be transient in a large class of Kaluza-Klein models that satisfy the (higher dimensional) null energy condition [1]. We point out that these no-go theorems are based on a rather ad-hoc assumption on the metric, without which no strong statements can be made.
Formalization of the Integral Calculus in the PVS Theorem Prover
NASA Technical Reports Server (NTRS)
Butler, Ricky W.
2004-01-01
The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Dielectric theorem within the Hartree-Fock-Bogoliubov framework
Capelli, Luigi; Colo, Gianluca; Li, Jun
2009-05-15
Excitation spectra usually reveal important features of the many-body systems. The vibrational excitations can be studied through the well-known linear response theory. This theory is realized, in the nuclear case, by means of the random-phase approximation (RPA); the generalization in the case in which one deals with open shells, and the pairing force is active, is the quasiparticle RPA (QRPA). It is useful to have at one's disposal theorems that provide information on, e.g., the sum rules and mean excitation energies associated with given external operators acting on the system. This article focuses on such theorems in the case of self-consistent QRPA based on Hartree-Fock-Bogoliubov (HFB). In particular, the so-called dielectric theorem that provides the value of the inverse-energy-weighted sum rule based on the simple knowledge of the ground state is demonstrated. This theorem is applied to the case of constrained calculations of the average excitation energy of the monopole resonance combined with the Thouless theorem. The pairing correlations are shown to have the effect of increasing the polarizability m{sub -1}. The detailed analysis of the profile of the strength functions by mean of QRPA reveals that the decrease of the average monopole excitation energies in some isotopes is associated with neutron states that emerge at an energy that is lower than the main giant resonance peak.
Attractive Hubbard model with disorder and the generalized Anderson theorem
Kuchinskii, E. Z. Kuleeva, N. A. Sadovskii, M. V.
2015-06-15
Using the generalized DMFT+Σ approach, we study the influence of disorder on single-particle properties of the normal phase and the superconducting transition temperature in the attractive Hubbard model. A wide range of attractive potentials U is studied, from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong-coupling region, where the superconducting transition is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures much higher than the superconducting transition temperature. We study two typical models of the conduction band with semi-elliptic and flat densities of states, respectively appropriate for three-dimensional and two-dimensional systems. For the semi-elliptic density of states, the disorder influence on all single-particle properties (e.g., density of states) is universal for an arbitrary strength of electronic correlations and disorder and is due to only the general disorder widening of the conduction band. In the case of a flat density of states, universality is absent in the general case, but still the disorder influence is mainly due to band widening, and the universal behavior is restored for large enough disorder. Using the combination of DMFT+Σ and Nozieres-Schmitt-Rink approximations, we study the disorder influence on the superconducting transition temperature T{sub c} for a range of characteristic values of U and disorder, including the BCS-BEC crossover region and the limit of strong-coupling. Disorder can either suppress T{sub c} (in the weak-coupling region) or significantly increase T{sub c} (in the strong-coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of the superconducting critical temperature are essentially due to only the general disorder widening of the conduction band.
An application of the tensor virial theorem to hole + vortex + bulge systems
NASA Astrophysics Data System (ADS)
Caimmi, R.
2009-04-01
The tensor virial theorem for subsystems is formulated for three-component systems and further effort is devoted to a special case where the inner subsystems and the central region of the outer one are homogeneous, the last surrounded by an isothermal homeoid. The virial equations are explicitly written under the additional restrictions: (i) similar and similarly placed inner subsystems, and (ii) spherical outer subsystem. An application is made to hole + vortex + bulge systems, in the limit of flattened inner subsystems, which implies three virial equations in three unknowns. Using the Faber-Jackson relation, R∝σ02, the standard M- σ0 form (M∝σ04) is deduced from qualitative considerations. The projected bulge velocity dispersion to projected vortex velocity ratio, η=(σ)33/{[(v)qq]2+[(σ)qq]2}, as a function of the fractional radius, y=R/R, and the fractional masses, m=M/M and m=M/M, is studied in the range of interest, 0⩽m=M/M⩽5 [Escala, A., 2006. ApJ, 648, L13] and 229⩽m⩽795 [Marconi, A., Hunt, L.H., 2003. ApJ 589, L21], consistent with observations. The related curves appear to be similar to Maxwell velocity distributions, which implies a fixed value of η below the maximum corresponds to two different configurations: a compact bulge on the left of the maximum, and an extended bulge on the right. All curves lie very close one to the other on the left of the maximum, and parallel one to the other on the right. On the other hand, fixed m or m, and y, are found to imply more massive bulges passing from bottom to top along a vertical line on the (Oyη) plane, and vice versa. The model is applied to NGC 4374 and NGC 4486, taking the fractional mass, m, and the fractional radius, y, as unknowns, and the bulge mass is inferred from the knowledge of the hole mass, and compared with results from different methods. In presence of a massive vortex (m=5), the hole mass has to be reduced by a factor 2-3 with respect to the case of a massless vortex, to get
Experimentally testing Bell's theorem based on Hardy's nonlocal ladder proofs
NASA Astrophysics Data System (ADS)
Guo, WeiJie; Fan, DaiHe; Wei, LianFu
2015-02-01
Bell's theorem argues the existence of quantum nonlocality which goes basically against the hidden variable theory (HVT). Many experiments have been done via testing the violations of Bell's inequalities to statistically verify the Bell's theorem. Alternatively, by testing the Hardy's ladder proofs we experimentally demonstrate the deterministic violation of HVT and thus confirm the quantum nonlocality. Our tests are implemented with non-maximal entangled photon pairs generated by spontaneous parametric down conversions (SPDCs). We show that the degree freedom of photon entanglement could be significantly enhanced by using interference filters. As a consequence, the Hardy's ladder proofs could be tested and Bell's theorem is verified robustly. The probability of violating the locality reach to 41.9%, which is close to the expectably ideal value 46.4% for the photon pairs with degree of entanglement ɛ = 0.93. The higher violating probability is possible by further optimizing the experimental parameters.
Model Checking Failed Conjectures in Theorem Proving: A Case Study
NASA Technical Reports Server (NTRS)
Pike, Lee; Miner, Paul; Torres-Pomales, Wilfredo
2004-01-01
Interactive mechanical theorem proving can provide high assurance of correct design, but it can also be a slow iterative process. Much time is spent determining why a proof of a conjecture is not forthcoming. In some cases, the conjecture is false and in others, the attempted proof is insufficient. In this case study, we use the SAL family of model checkers to generate a concrete counterexample to an unproven conjecture specified in the mechanical theorem prover, PVS. The focus of our case study is the ROBUS Interactive Consistency Protocol. We combine the use of a mechanical theorem prover and a model checker to expose a subtle flaw in the protocol that occurs under a particular scenario of faults and processor states. Uncovering the flaw allows us to mend the protocol and complete its general verification in PVS.
Generalized Bezout's Theorem and its applications in coding theory
NASA Technical Reports Server (NTRS)
Berg, Gene A.; Feng, Gui-Liang; Rao, T. R. N.
1996-01-01
This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.
Noether's second theorem and Ward identities for gauge symmetries
NASA Astrophysics Data System (ADS)
Avery, Steven G.; Schwab, Burkhard U. W.
2016-02-01
Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We use Noether's second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether's second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether's second theorem and known results in the recent literature. Our approach suggests a novel point of view with important physical consequences.
Quantum de Finetti theorem in phase-space representation
Leverrier, Anthony; Cerf, Nicolas J.
2009-07-15
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form {sigma}{sup xn}. Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states)
Noncommutative topology and the world’s simplest index theorem
van Erp, Erik
2010-01-01
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool for proving results in classical analysis and geometry. PMID:20418506
No-go theorem for ergodicity and an Einstein relation.
Froemberg, D; Barkai, E
2013-08-01
We provide a simple no-go theorem for ergodicity and the generalized Einstein relation for anomalous diffusion processes. The theorem states that either ergodicity in the sense of equal time and ensemble averaged mean squared displacements (MSD) is broken, and/or the generalized Einstein relation for time averaged diffusivity and mobility is invalid, which is in complete contrast to normal diffusion processes. We also give a general relation for the time averages of drift and MSD for ergodic (in the MSD sense) anomalous diffusion processes, showing that the ratio of these quantities depends on the measurement time. The Lévy walk model is used to exemplify the no-go theorem. PMID:24032966
Towards a novel no-hair theorem for black holes
Hertog, Thomas
2006-10-15
We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four-dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.
On the role of sharp chains in the transport theorem
NASA Astrophysics Data System (ADS)
Falach, L.; Segev, R.
2016-03-01
A generalized transport theorem for convecting irregular domains is presented in the setting of Federer's geometric measure theory. A prototypical r-dimensional domain is viewed as a flat r-chain of finite mass in an open set of an n-dimensional Euclidean space. The evolution of such a generalized domain in time is assumed to follow a continuous succession of Lipschitz embedding so that the spatial gradient may be nonexistent in a subset of the domain with zero measure. The induced curve is shown to be continuous with respect to the flat norm and differential with respect to the sharp norm on currents in Rn. A time-dependent property is naturally assigned to the evolving region via the action of an r-cochain on the current associated with the domain. Applying a representation theorem for cochains, the properties are shown to be locally represented by an r-form. Using these notions, a generalized transport theorem is presented.
Canonical Approaches to Applications of the Virial Theorem.
Walton, Jay R; Rivera-Rivera, Luis A; Lucchese, Robert R; Bevan, John W
2016-02-11
Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem. PMID:26788937
Note on identities inspired by new soft theorems
NASA Astrophysics Data System (ADS)
Rao, Junjie; Feng, Bo
2016-04-01
The new soft theorems, for both gravity and gauge amplitudes, have inspired a number of works, including the discovery of new identities related to amplitudes. In this note, we present the proof and discussion for two sets of identities. The first set includes an identity involving the half-soft function which had been used in the soft theorem for one-loop rational gravity amplitudes, and another simpler identity as its byproduct. The second set includes two identities involving the KLT momentum kernel, as the consistency conditions of the KLT relation plus soft theorems for both gravity and gauge amplitudes. We use the CHY formulation to prove the first identity, and transform the second one into a convenient form for future discussion.
NASA Astrophysics Data System (ADS)
Kushner, Paul J.; Shepherd, Theodore G.
1995-05-01
A study of the semi-geostrophic (SG) geophysical fluid dynamics is presented. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. An invariant for the semi-geostrophic equations is derived and use it to obtain: (1) a linear stability theorem analogous to Arnold's first theorem; and (2) a small-amplitude local conservation law for invariant, obeying the group-velocity in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number.
The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities
NASA Astrophysics Data System (ADS)
Cain, George L., Jr.; González, Luis
2008-02-01
The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.
Heat Capacity and the Equipartition Theorem
ERIC Educational Resources Information Center
Dence, Joseph B.
1972-01-01
Limitations of classical mechanics in understanding molecular properties are discussed. Modifications introduced by quantum mechanics enable the instructor to include and integrate important concepts from thermodynamics, quantum mechanics, spectroscopy, and statistics. (DF)
Levinson theorem for the Dirac equation in D+1 dimensions
Gu Xiaoyan; Ma Zhongqi; Dong Shihai
2003-06-01
In terms of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation with a spherically symmetric potential in D+1 dimensions is uniformly established as a relation between the total number of bound states and the sum of the phase shifts of the scattering states at E={+-}M with a given angular momentum. The critical case, where the Dirac equation has a half bound state, is analyzed in detail. A half bound state is a zero-momentum solution if its wave function is finite but does not decay fast enough at infinity to be square integrable.
Reasoning by analogy as an aid to heuristic theorem proving.
NASA Technical Reports Server (NTRS)
Kling, R. E.
1972-01-01
When heuristic problem-solving programs are faced with large data bases that contain numbers of facts far in excess of those needed to solve any particular problem, their performance rapidly deteriorates. In this paper, the correspondence between a new unsolved problem and a previously solved analogous problem is computed and invoked to tailor large data bases to manageable sizes. This paper outlines the design of an algorithm for generating and exploiting analogies between theorems posed to a resolution-logic system. These algorithms are believed to be the first computationally feasible development of reasoning by analogy to be applied to heuristic theorem proving.
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.
Zhao Hongsheng; Famaey, Benoit
2010-04-15
There exists several modified gravity theories designed to reproduce the empirical Milgrom's formula, modified Newtonian dynamics (MOND). Here we derive analytical results in the context of the static weak-field limit of two of them (bimetric MOND, leading for a given set of parameters to the quasilinear MOND, and Bekenstein's Tensor-Vector-Scalar). In this limit, these theories are constructed to give the same force field for spherical symmetry, but their predictions generally differ out of it. However, for certain realizations of these theories (characterized by specific choices for their free functions), the binding potential-energy of a system is increased, compared to its Newtonian counterpart, by a constant amount independent of the shape and size of the system. In that case, the virial theorem is exactly the same in these two theories, for the whole gravity regime and even outside of spherical symmetry, although the exact force fields are different. We explicitly show this for the force field generated by the two theories inside an elliptical shell. For more general free functions, the virial theorems are, however, not identical in these two theories. We finally explore the consequences of these analytical results for the two-body force.
Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
Fujiwara, Takanori; Fukui, Takahiro; Nitta, Muneto; Yasui, Shigehiro
2011-10-01
Color superconductivity in high-density QCD exhibits the color-flavor-locked phase. To explore zero modes in the color-flavor-locked phase in the presence of a non-Abelian vortex with an SU(2) symmetry in the vortex core, we apply the index theorem to the Bogoliubov-de Gennes (BdG) Hamiltonian. From the calculation of the topological index, we find that triplet, doublet and singlet sectors of SU(2) have certain number of chiral Majorana zero modes in the limit of vanishing chemical potential. We also solve the BdG equation by the use of the series expansion to show that the number of zero modes and their chirality match the result of the index theorem. From particle-hole symmetry of the BdG Hamiltonian, we conclude that if and only if the index of a given sector is odd, one zero mode survives generically for a finite chemical potential. We argue that this result should hold nonperturbatively even in the high-density limit.
Schliesser, Joshua A; Gallimore, Gary; Kunjukunju, Nancy; Sabates, Nelson R; Koulen, Peter; Sabates, Felix N
2014-01-01
Purpose While identifying functional and structural parameters of the retina in central serous chorioretinopathy (CSCR) patients, this study investigated how an optical coherence tomography (OCT)-based diagnosis can be significantly supplemented with functional diagnostic tools and to what degree the determination of disease severity and therapy outcome can benefit from diagnostics complementary to OCT. Methods CSCR patients were evaluated prospectively with microperimetry (MP) and spectral domain optical coherence tomography (SD-OCT) to determine retinal sensitivity function and retinal thickness as outcome measures along with measures of visual acuity (VA). Patients received clinical care that involved focal laser photocoagulation or pharmacotherapy targeting inflammation and neovascularization. Results Correlation of clinical parameters with a focus on functional parameters, VA, and mean retinal sensitivity, as well as on the structural parameter mean retinal thickness, showed that functional measures were similar in diagnostic power. A moderate correlation was found between OCT data and the standard functional assessment of VA; however, a strong correlation between OCT and MP data showed that diagnostic measures cannot always be used interchangeably, but that complementary use is of higher clinical value. Conclusion The study indicates that integrating SD-OCT with MP provides a more complete diagnosis with high clinical relevance for complex, difficult to quantify diseases such as CSCR. PMID:25473259
Derivation of a sphere theorem for the Stokes flow following Imai's procedure
NASA Astrophysics Data System (ADS)
Hasimoto, Hidenori
2007-07-01
A sphere theorem for general three-dimensional Stokes flow is shown to be derived by the use of Imai's procedure for solving the Stokes equation for spherical boundary in terms of one vector harmonic function and Kelvin's inversion theorem.
Establishing Appropriate Conditions: Students Learning to Apply a Theorem
ERIC Educational Resources Information Center
Scataglini-Belghitar, Giovanna; Mason, John
2012-01-01
During a sequence of tutorials conducted by the first author, it became evident that students were not seeing how to apply the theorem concerning a continuous function on a closed and bounded interval attaining its extreme values in situations in which it is necessary first to construct the closed and bounded interval by reasoning about properties…
A fixed point theorem for certain operator valued maps
NASA Technical Reports Server (NTRS)
Brown, D. R.; Omalley, M. J.
1978-01-01
In this paper, we develop a family of Neuberger-like results to find points z epsilon H satisfying L(z)z = z and P(z) = z. This family includes Neuberger's theorem and has the additional property that most of the sequences q sub n converge to idempotent elements of B sub 1(H).
Four Proofs of the Converse of the Chinese Remainder Theorem
ERIC Educational Resources Information Center
Dobbs, D. E.
2008-01-01
Four proofs, designed for classroom use in varying levels of courses on abstract algebra, are given for the converse of the classical Chinese Remainder Theorem over the integers. In other words, it is proved that if m and n are integers greater than 1 such that the abelian groups [double-struck z][subscript m] [direct sum] [double-struck…
Externalities and the Coase Theorem: A Diagrammatic Presentation
ERIC Educational Resources Information Center
Halteman, James
2005-01-01
In intermediate microeconomic textbooks the reciprocal nature of externalities is presented using numerical examples of costs and benefits. This treatment of the Coase theorem obscures the fact that externality costs and benefits are best understood as being on a continuum where costs vary with the degree of intensity of the externality. When…
On the Positive Mass Theorem for Manifolds with Corners
NASA Astrophysics Data System (ADS)
McFeron, Donovan; Székelyhidi, Gábor
2012-07-01
We study the positive mass theorem for certain non-smooth metrics following P. Miao's work. Our approach is to smooth the metric using the Ricci flow. As well as improving some previous results on the behaviour of the ADM mass under the Ricci flow, we extend the analysis of the zero mass case to higher dimensions.
Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos
ERIC Educational Resources Information Center
Boozer, A. D.
2011-01-01
We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…
Discovering and Experiencing the Fundamental Theorem of Calculus.
ERIC Educational Resources Information Center
Rosenthal, Bill
1992-01-01
Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…
Start the Year Right-Discover Pick's Theorem.
ERIC Educational Resources Information Center
Wilcock, Douglas
1992-01-01
Describes a problem to challenge students as they come back from summer vacation. Working in small groups, students discover Pick's Theorem, the formula to calculate the area of a polygon constructed on a geoboard. A writing assignment evaluates the students' efforts. (MDH)
Proof by Analogy: The Case of the Pythagorean Theorem.
ERIC Educational Resources Information Center
Levine, Deborah R.
1983-01-01
The proof is given that, if three equilateral triangles are constructed on the sides of a right triangle, then the sum of the areas on the sides equals the area on the hypotenuse. This is based on one of the hundreds of proofs that exist for the Pythogorean theorem. (MP)
A decoupling theorem for the BPHZL-scheme
Aschenbrenner, M.
1996-09-01
Conditions are stated, which are sufficient for the heavy-mass-suppression of BPHZL-subtracted Feynman-integrals containing propagators of {open_quote}{open_quote}heavy fields{close_quote}{close_quote}. This result generalizes the Decoupling Theorems of Ambjo/rn, Manoukian and Landsman to cases, where massless fields (e.g., gauge fields) are present. {copyright} 1996 Academic Press, Inc.
A representation theorem of infimum of bounded quantum observables
Liu Weihua; Wu Junde
2008-07-15
In 2006, Gudder introduced a logic order on the bounded quantum observable set S(H). In 2007, Pulmannova and Vincekova proved that for each subset D of S(H), the infimum of D exists with respect to this logic order. In this paper, we present a representation theorem for the infimum of D.
An Elementary Proof of a Converse Mean-Value Theorem
ERIC Educational Resources Information Center
Almeida, Ricardo
2008-01-01
We present a new converse mean value theorem, with a rather elementary proof. [The work was supported by Centre for Research on Optimization and Control (CEOC) from the "Fundacaopara a Ciencia e a Tecnologia" FCT, co-financed by the European Community Fund FEDER/POCTI.
Geometric Demonstration of the Fundamental Theorems of the Calculus
ERIC Educational Resources Information Center
Sauerheber, Richard D.
2010-01-01
After the monumental discovery of the fundamental theorems of the calculus nearly 350 years ago, it became possible to answer extremely complex questions regarding the natural world. Here, a straightforward yet profound demonstration, employing geometrically symmetric functions, describes the validity of the general power rules for integration and…
Ambarzumyan's theorem for the quasi-periodic boundary conditions
NASA Astrophysics Data System (ADS)
Kıraç, Alp Arslan
2015-10-01
We obtain the classical Ambarzumyan's theorem for the Sturm-Liouville operators Lt(q) with qin L1[0,1] and quasi-periodic boundary conditions, tin [0,2π ) , when there is not any additional condition on the potential q.
A Theorem and its Application to Finite Tampers
DOE R&D Accomplishments Database
Feynman, R. P.
1946-08-15
A theorem is derived which is useful in the analysis of neutron problems in which all neutrons have the same velocity. It is applied to determine extrapolated end-points, the asymptotic amplitude from a point source, and the neutron density at the surface of a medium. Formulas fro the effect of finite tampers are derived by its aid, and their accuracy discussed.
On the Fundamental Theorem of Calculus for Fractal Sets
NASA Astrophysics Data System (ADS)
Bongiorno, Donatella; Corrao, Giuseppa
2015-04-01
The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock-Kurzweil type is introduced.
A strengthening of a theorem of Bourgain and Kontorovich. III
NASA Astrophysics Data System (ADS)
Kan, I. D.
2015-04-01
We prove that the set of positive integers contains a positive proportion of denominators of the finite continued fractions all of whose partial quotients belong to the alphabet \\{1,2,3,4,10\\}. The corresponding theorem was previousy known only for the alphabet \\{1,2,3,4,5\\} and for alphabets of larger cardinality.
The Unforgettable Experience of a Workshop on Pythagoras Theorem
ERIC Educational Resources Information Center
Arwani, Salima Shahzad
2011-01-01
The author conducted a workshop with colleagues in which awareness of Pythagoras' theorem was raised. This workshop was an unforgettable event in the author's life because it was the first time that she had interacted with teachers from a different school system, and it allowed her to develop presentation skills and confidence in her own…
Null conformal Killing-Yano tensors and Birkhoff theorem
NASA Astrophysics Data System (ADS)
Ferrando, Joan Josep; Sáez, Juan Antonio
2016-04-01
We study the space-times admitting a null conformal Killing-Yano tensor whose divergence defines a Killing vector. We analyze the similarities and differences with the recently studied non null case (Ferrando and Sáez in Gen Relativ Gravit 47:1911, 2015). The results by Barnes concerning the Birkhoff theorem for the case of null orbits are analyzed and generalized.
Two Theorems on Dissipative Energy Losses in Capacitor Systems
ERIC Educational Resources Information Center
Newburgh, Ronald
2005-01-01
This article examines energy losses in charge motion in two capacitor systems. In the first charge is transferred from a charged capacitor to an uncharged one through a resistor. In the second a battery charges an originally uncharged capacitor through a resistance. Analysis leads to two surprising general theorems. In the first case the fraction…
Fermat's Last Theorem for Factional and Irrational Exponents
ERIC Educational Resources Information Center
Morgan, Frank
2010-01-01
Fermat's Last Theorem says that for integers n greater than 2, there are no solutions to x[superscript n] + y[superscript n] = z[superscript n] among positive integers. What about rational exponents? Irrational n? Negative n? See what an undergraduate senior seminar discovered.
Solving open questions with an automated theorem-proving program
Wos, L.
1982-01-01
The primary objective of this paper is to demonstrate the feasibility of using an automated theorem-proving program as an automated reasoning assistant. Such usage is not merely a matter of conjecture. As evidence, we cite a number of open questions which were solved with the aid of a theorem-proving program. The open questions are taken from studies of ternary boolean algebra, finite semigroups, equivalential calculus, and the design of digital circuits. Despite the variety of successes, no doubt there still exists many who are very skeptical of the value of automating any form of deep reasoning. It is the nature of this skepticism which brings us to the second objective of the paper. The secondary objective is that of dispelling, at least in part, some of the resistance to such automation. To do this, we discuss two myths which form the basis for the inaccurate evaluation of both the usefulness and the potential of automated theorem proving. Rejection of the two myths removes an important obstacle to assigning to an automated theorem-proving program its proper role - the role of colleague and assistant.
On exponential sums of digital sums related to Gelfond's theorem
NASA Astrophysics Data System (ADS)
Okada, Tatsuya; Kobayashi, Zenji; Sekiguchi, Takeshi; Shiota, Yasunobu
2008-01-01
In this paper, we first give explicit formulas of exponential sums of sum of digits related to Gelfond's theorem. As an application of these formulas, we obtain a simple expression of Newman-Coquet type summation formula related to the number of binary digits in a multiple of a prime number.
An Experiment on a Physical Pendulum and Steiner's Theorem
ERIC Educational Resources Information Center
Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.
2010-01-01
Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…
Optical limiting of short laser pulses
Liu, J.-C.; Wang, C.-K.; Gel'mukhanov, Faris
2007-11-15
The dynamics of pulse propagation accompanied by harmonic generation, stimulated Raman scattering, amplified spontaneous emission, and superfluorescence is studied near the two-photon resonance. We explore the optical limiting of intense and short laser pulses. The numerical solutions of the coupled Bloch and Maxwell's equations for the 4,4{sup '}-bis(dimethylamino) stilbene molecule are compared with the two-photon area theorem. It is shown that the area theorem explains qualitatively the major dynamical properties of pulse propagation even if the propagation is accompanied by the generation of new fields. In agreement with the area theorem, we see that the conventional dependence of the transmittance on the propagation depth is not valid for intense pulses.
NASA Astrophysics Data System (ADS)
Zouaghi, Taher; Bédir, Mourad; Hédi Inoubli, Mohamed
2005-05-01
The Albian-Maastrichtian seismic horizon analysis in central Tunisia (Gafsa-Sidi Bouzid area) using the reflection seismic sections calibrated to the well data, shows buried structures with deposit distributions and sedimentation geometries varying from the depressive to uplifted zones. Pinch outs, unconformities and hiatuses recognized on the folded high structures are caused by reactivation of the bordering faults. The Turonian-Maastrichtian unconformities correspond to the palaeogeographic limits that outline the Kasserine Islets and correspond to the N120, N180 major wrench-salt-intruded corridors and associated N90, N60 strike-slip faults. Formation of the different structures and evolution of the basins and platforms were controlled by conjugate dextral and sinistral strike-slip movements. These structures allow new palaeogeographic limits of the Kasserine Islets to be identified. To cite this article: T. Zouaghi et al., C. R. Geoscience 337 (2005).
Strong converse theorems using Rényi entropies
NASA Astrophysics Data System (ADS)
Leditzky, Felix; Wilde, Mark M.; Datta, Nilanjana
2016-08-01
We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint arXiv:1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.
Neba, Godlove Ambe; Newbery, David McClintock; Chuyong, George Bindeh
2016-01-01
In the ectomycorrhizal caesalpiniaceous groves of southern Korup National Park, the dominant tree species, Microberlinia bisulcata, displays very poor in situ recruitment compared with its codominant, Tetraberlinia bifoliolata. The reported ex situ experiment tested whether availabilities of soil potassium and magnesium play a role. Seedlings of the two species received applications of K and Mg fertilizer in potted native soil in a local shade house, and their responses in terms of growth and nutrient concentrations were recorded over 2 years. Amended soil concentrations were also determined. Microberlinia responded strongly and positively in its growth to Mg, but less to K; Tetraberlinia responded weakly to both. Added Mg led to strongly increased Mg concentration for Microberlinia while added K changed that concentration only slightly; Tetraberlinia strongly increased its concentration of K with added K, but only somewhat its Mg concentration with added Mg. Additions of Mg and K had small but important antagonistic effects. Microberlinia is Mg-demanding and apparently Mg-limited in Korup soil; Tetraberlinia, whilst K-demanding, appeared not to be K-limited (for growth). Added K enhanced plant P concentrations of both species. Extra applied Mg may also be alleviating soil aluminum toxicity, and hence improving growth indirectly and especially to the benefit of Microberlinia. Mg appears to be essential for Microberlinia seedling growth and its low soil availability in grove soils at Korup may be an important contributing factor to its poor recruitment. Microberlinia is highly shade-intolerant and strongly light-responding, whilst Tetraberlinia is more shade-tolerant and moderately light-responding, which affords an interesting contrast with respect to their differing responses to Mg supply. The study revealed novel aspects of functional traits and likely niche-partitioning among ectomycorrhizal caesalps in African rain forests. Identifying the direct and
The Fundamental Theorem of Prevision. Technical Report No. 506. November 1987.
ERIC Educational Resources Information Center
Lad, F. R.; And Others
B. De Finetti's "Fundamental Theorem of Probability" is reformulated as a computable linear programming problem. The theorem is substantially extended, and shown to have fundamental implications for the theory and practice of statistics. It supports an operational meaning for the partial assertion of prevision via asserted bounds. The theorem is…
Use of the sampling theorem to speed up near-field physical optics scattering calculations
NASA Technical Reports Server (NTRS)
Cramer, P. W.; Imbriale, W. A.
1994-01-01
Physical optics scattering calculations performed on the DSN 34-m beam-waveguide antennas at Ka-band (32 GHz) require approximately 12 hr of central processing unit time on a Cray Y-MP2 computer. This is excessive in terms of resource utilization and turnaround time. Typically, the calculations involve five surfaces, and the calculations are done two surfaces at a time. The sampling theorem is used to reduce the number of current values that must be calculated over the second surface by performing a physical optics integration over the first surface. The additional number of current values required on the second surface by subsequent physical optics integrations is obtained by interpolation over the original current values. Time improvements on the order of a factor of 2 to 4 were obtained for typical scattering pairs.
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
Fluctuation Limit for Interacting Diffusions with Partial Annihilations Through Membranes
NASA Astrophysics Data System (ADS)
Chen, Zhen-Qing; Fan, Wai-Tong Louis
2016-06-01
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.
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.
NASA Astrophysics Data System (ADS)
Afeyan, Bedros; Hüller, Stefan; Montgomery, David; Moody, John; Froula, Dustin; Hammer, James; Jones, Oggie; Amendt, Peter
2014-10-01
In mid-Z and high-Z plasmas, it is possible to control crossed bean energy transfer (CBET) and subsequently occurring single or multiple beam instabilities such as Stimulated Raman Scattering (SRS) by novel means. These new techniques are inoperative when the ion acoustic waves are in their strong damping limit, such as occurs in low Z plasmas with comparable electron and ion temperatures. For mid-Z plasmas, such as Z = 10, and near the Mach 1 surface, the strong coupling regime (SCR) can be exploited for LPI mitigation. While at higher Z values, it is thermal filamentation in conjunction with nonlocal heat transport that are useful to exploit. In both these settings, the strategy is to induce laser hot spot intensity dependent, and thus spatially dependent, frequency shifts to the ion acoustic waves in the transient response of wave-wave interactions. The latter is achieved by the on-off nature of spike trains of uneven duration and delay, STUD pulses. The least taxing use of STUD pulses is to modulate the beams at the 10 ps time scale and to choose which crossing beams are overlapping in time and which are not. Work supported by a grant from the DOE NNSA-OFES joint program on HEDP
Sonder, E.; Ahmed, A.B.
1991-12-01
A value for ``average background radiation`` of 0.75 mR/week has been determined from a total of 1680 thermoluminescent dosimeters (TLD`s) exposed in 70 houses for periods up to one year. The distribution of results indicates a rather large variation among houses, with a few locations exhibiting backgrounds double the general average. Some discrepancies in the short-term background accumulation of TLD`s have been explained as being due to light leakage through the dosimeter cases. In addition the lower limit of detection (L{sub D}) for deep and shallow dose equivalents has been determined for these dosimeters. The L{sub D} for occupational exposure depends strongly on the time a dosimeter is exposed to background radiation in the field. The L{sub D} can vary from a low of 2.4 mrem for high energy gamma rays when the background accumulation period is less than a few weeks to values as high as 66 mrem for uranium beta particles when background has been allowed to accumulate for more than 21 weeks.
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.
George Sudarshan, No-Go theorems and the exclusion principle
NASA Astrophysics Data System (ADS)
Han, M. Y.
2009-11-01
We review two areas of my work that were directly and indirectly initiated and inspired by George. One is the proofs of no-go theorems in combining the spacetime and internal symmetries in non-trivial ways and the other is how Georges firm conviction on the fundamentality of the spin-statistics theorem helped to expand the domain of applicability of the spin-statistics theorem into the arena of quarks and gluons, going far beyond the original application of the exclusion principle in atomic physics. In order to provide deeper understanding of mass differences of particles belonging to spin-degenerate multiplets, attempts have been made to see if some non-trivial way of embedding the Lorentz group and internal symmetry groups such as SU(2) and SU(3) into a larger group. When a hint of no-go theorem (that such non-trivial embedding cannot be achieved) first appeared, George went to work and led many of us, including myself, into this area of research. A series of proofs of no-go theorems by George, myself and others eventually led to the definitive proof by Lochlainn O'Raifeartaigh that came to be known as the ORaifeartaigh theorem. Lochlainn also joined George at Syracuse at the same time I went there. The second area in which George had significant influence on my work is his fervent belief in the fundamental importance of the spin-statistics relationship. First postulated by Worlfgang Pauli to explain the periodic table of elements, the relationship the exclusion principle has exceeded far beyond its original domain of validity. The relationship has been upheld across the scale molecular, atomic, and nuclear structures. What is less known is the fact the relationship continues to remain valid in scales smaller than nucleons. The spin-statistics relationship was one of the compelling reasons for Nambu and I to introduce a new set of then undiscovered degrees freedom for quarks inside nucleons. This new degrees of freedom came to be called the color charges of
Coherent state transforms and the Mackey-Stone-Von Neumann theorem
NASA Astrophysics Data System (ADS)
Kirwin, William D.; Mourão, José M.; Nunes, João P.
2014-10-01
Mackey showed that for a compact Lie group K, the pair (K, C 0(K)) has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an infinite-dimensional family of K × K invariant polarizations on T*K. The Kähler polarizations in the family are generated by (complex) time-τ Hamiltonian flows applied to the (Schrödinger) vertical real polarization. The unitary equivalence of the corresponding quantizations of T*K is then studied by considering covariant pairs of representations of K defined by geometric prequantization and of representations of C 0(K) defined via Heisenberg time-(-τ) evolution followed by time-(+τ) geometric-quantization-induced evolution. We show that in the semiclassical and large imaginary time limits, the unitary transform whose existence is guaranteed by Mackey's theorem can be approximated by composition of the time-(+τ) geometric-quantization-induced evolution with the time-(-τ) evolution associated with the momentum space [W. D. Kirwin and S. Wu, "Momentum space for compact Lie groups and the Peter-Weyl theorem" (unpublished)] quantization of the Hamiltonian function generating the flow. In the case of quadratic Hamiltonians, this asymptotic result is exact and unitary equivalence between quantizations is achieved by identifying the Heisenberg imaginary time evolution with heat operator evolution, in accordance with the coherent state transform of Hall.
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.
The fluctuation-dissipation theorem for stochastic kinetics—Implications on genetic regulations
Yan, Ching-Cher Sanders; Hsu, Chao-Ping
2013-12-14
The Fluctuation-Dissipation theorem (FDT) connects the “memory” in the fluctuation in equilibrium to the response of a system after a perturbation, which has been a fundamental ground in many branches of physics. When viewing a cell as a stochastic biochemical system, the cell's response under a perturbation is related to its intrinsic steady-state correlation functions via the FDT, a theorem we derived and present in this work. FDT allows us to use the noise to derive dynamic response and infer dynamic properties in the system. We tested FDT's validity with gene regulation models and found that it is limited to the linear response. For an indirect regulation pathway where unknown components may exist, FDT still works within the linear response region. Thus, FDT may be used for systems with partial knowledge, and it is potentially possible to identify the existence of unobserved components. With FDT, the dynamic response can be composed of steady-state measurements without the complete detailed knowledge for the regulation or kinetics. The response function derived can give important insights into the dynamics and time scales of the system.
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.
NASA Astrophysics Data System (ADS)
Qiu, Zhiping; Wang, Xiaojun
2005-04-01
Generalized eigenvalue problems from the modal analysis are often converted to the standard eigenvalue problems. In this paper, it evaluates the upper and lower bounds on the eigenvalues of the standard eigenvalue problem of structures subject to severely deficient information about the structural parameters. Here, we focus on non-probabilistic interval analysis models of uncertainty, which are adapted to the case of severe lack of information on uncertainty. Non-probabilistic, interval analysis method in which uncertainties are defined by interval numbers appears as an alternative to the classical probabilistic models. For the standard eigenvalue problem of structures with uncertain-but-bounded parameters, the vertex solution theorem, the positive semi-definite solution theorem and the parameter decomposition solution theorem for the standard eigenvalue problem are presented, and compared with Deif's solution theorem in numerical examples. It is shown that, for the upper and lower bounds on the eigenvalues of the standard eigenvalue problem with uncertain-but-bounded parameters, the presented vertex solution theorem is unconditional, and the positive semi-definite solution theorem and the parameter decomposition solution theorem have less limitary conditions compared with Deif's solution theorem. The effectiveness of the vertex solution theorem, the positive semi-definite solution theorem and the parameter decomposition solution theorem are illustrated by numerical examples
Learning in neural networks based on a generalized fluctuation theorem
NASA Astrophysics Data System (ADS)
Hayakawa, Takashi; Aoyagi, Toshio
2015-11-01
Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.
Boltzmann's H theorem for systems with frictional dissipation.
Bizarro, João P S
2011-03-01
By use of Boltzmann's equation to describe an ensemble of particles under the influence of a friction force, Boltzmann's H theorem is refined to explicitly include frictional dissipation, the accompanying fluctuations being modeled via an added diffusive, Fokker-Planck term. If the friction force per particle mass is proportional to velocity, as is the case with viscous drag with a friction coefficient γ, Boltzmann's H theorem for the time rate of change of the quantity H reads dH/dt ≤ γ. The classical formulation stating that H can never increase is thus replaced by the statement that H cannot increase at a rate higher than γ, a general result but of particular relevance when fluctuations are negligible and the system is far from equilibrium. When the particles are not far from thermal equilibrium, an alternative, more suitable expression emerges which can be written in the form of a Clausius inequality. PMID:21517545
A General No-Cloning Theorem for an infinite Multiverse
NASA Astrophysics Data System (ADS)
Gauthier, Yvon
2013-10-01
In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.
Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper
NASA Technical Reports Server (NTRS)
Schumann, Johann; Koga, Dennis (Technical Monitor)
1999-01-01
In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).
Levinson theorem for the Dirac equation in one dimension
Ma Zhongqi; Dong Shihai; Wang Luya
2006-07-15
The Levinson theorem for the (1+1)-dimensional Dirac equation with a symmetric potential is proved with the Sturm-Liouville theorem. The half-bound states at the energies E={+-}M, whose wave function is finite but does not decay at infinity fast enough to be square integrable, are discussed. The number n{sub {+-}} of bound states is equal to the sum of the phase shifts at the energies E={+-}M:{delta}{sub {+-}}(M)+{delta}{sub {+-}}(-M)=(n{sub {+-}}+a){pi}, where the subscript {+-} denotes the parity and the constant a is equal to -1/2 when no half-bound state occurs, to 0 when one half-bound state occurs at E=M or at E=-M, and to 1/2 when two half-bound states occur at both E={+-}M.
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.
Random numbers certified by Bell's theorem.
Pironio, S; Acín, A; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C
2010-04-15
Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based and device-independent quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory. PMID:20393558
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.
Opposites attract: a theorem about the Casimir Force.
Kenneth, Oded; Klich, Israel
2006-10-20
We consider the Casimir interaction between (nonmagnetic) dielectric bodies or conductors. Our main result is a proof that the Casimir force between two bodies related by reflection is always attractive, independent of the exact form of the bodies or dielectric properties. Apart from being a fundamental property of fields, the theorem and its corollaries also rule out a class of suggestions to obtain repulsive forces, such as the two hemisphere repulsion suggestion and its relatives. PMID:17155375
Watson's theorem and the N Δ (1232 ) axial transition
NASA Astrophysics Data System (ADS)
Alvarez-Ruso, L.; Hernández, E.; Nieves, J.; Vacas, M. J. Vicente
2016-01-01
We present a new determination of the N Δ axial form factors from neutrino induced pion production data. For this purpose, the model of Hernandez et al. [Phys. Rev. D 76, 033005 (2007)] is improved by partially restoring unitarity. This is accomplished by imposing Watson's theorem on the dominant vector and axial multipoles. As a consequence, a larger C5A(0 ), in good agreement with the prediction from the off-diagonal Goldberger-Treiman relation, is now obtained.
Applications of Noether conservation theorem to Hamiltonian systems
NASA Astrophysics Data System (ADS)
Mouchet, Amaury
2016-09-01
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether's approach is illustrated on several examples, including classical field theory and quantum dynamics.
A notion of graph likelihood and an infinite monkey theorem
NASA Astrophysics Data System (ADS)
Banerji, Christopher R. S.; Mansour, Toufik; Severini, Simone
2014-01-01
We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.
A proof of van Aubel's theorem using orthogonal vectors
NASA Astrophysics Data System (ADS)
Glaister, P.
2016-04-01
We show how two linearly independent vectors can be used to construct two orthogonal vectors of equal magnitude in a simple way. The proof that the constructed vectors are orthogonal and of equal magnitude is a good exercise for students studying properties of scalar and vector triple products. We then show how this result can be used to prove van Aubel's theorem that relates the two line segments joining the centres of squares on opposite sides of a plane quadrilateral.
Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces.
Kim, Jong Kyu; Pathak, Ramesh Prasad; Dashputre, Samir; Diwan, Shailesh Dhar; Gupta, Rajlaxmi
2016-01-01
In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditions. Our results are the extension and improvements of the recent well-known results announced in the current literature. PMID:27386356
Analytical proof of Gisin's theorem for three qubits
Choudhary, Sujit K.; Ghosh, Sibasish; Kar, Guruprasad; Rahaman, Ramij
2010-04-15
Gisin's theorem assures that for any pure bipartite entangled state, there is violation of the inequality of Bell and of Clauser, Horne, Shimony, and Holt, revealing its contradiction with local realistic model. Whether a similar result holds for three-qubit pure entangled states remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy's nonlocality argument.
Klein's theorem and the proof of E0 = mc2
NASA Astrophysics Data System (ADS)
Ohanian, Hans C.
2012-12-01
Despite repeated attempts, Einstein failed to give us a general and rigorous proof of his E0=mc2 relation. A completely general proof emerged in 1918 from a theorem on the four-vector character of energy-momentum of extended systems by the mathematician Felix Klein, but this proof is not well known, rarely seen in textbooks, and sometimes misunderstood. A simple version of this proof is presented here, with discussion of the crucial role of the energy-momentum tensor.
Black holes, information, and the universal coefficient theorem
NASA Astrophysics Data System (ADS)
Patrascu, Andrei T.
2016-07-01
General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article, I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by the demanding invariance of the laws of physics to the change of coefficient structures in cohomology.
Extremely localized nonorthogonal orbitals by the pairing theorem.
Zoboki, T; Mayer, I
2011-03-01
Using the concepts of Löwdin pairing theorem, a method is developed to calculate extremely localized, but nonorthogonal, sets of molecular orbitals and their strictly localized counterparts. The method is very suitable to study to what extent a given model of bonding in a given molecule can be considered adequate from the point of view of the actual LCAO-MO (Hartree Fock or DFT) wave function and is expected to be useful for doing local approximations of electron correlation. PMID:20941738
Derivation of the Direct-Interaction Approximation Using Novikov's Theorem
NASA Astrophysics Data System (ADS)
Krommes, J. A.
2015-11-01
The direct-interaction approximation (DIA) is a crucially important statistical closure for both neutral fluids and plasmas. Kraichnan's original derivation proceeded in k space and assumed a large number N of interacting Fourier modes. That is problematic; the DIA can be formulated even for N = 3 . In the present work an alternate x-space procedure based on Novikov's theorem is described. That theorem is a statement about the correlations of certain Gaussian functionals. Turbulence cannot be Gaussian due to nonlinearity, but Novikov's theorem can be used to formulate self-consistent equations for a Gaussian component of the turbulence. The DIA emerges under the assumption that certain higher-order correlations are small. In essence, this procedure is merely a restatement of Kraichnan's arguments, but it adds additional perspective because the assumption of large N is not required. Details can be found in a lengthy set of tutorial Lecture Notes. Work supported by U.S.D.o.E. Contract DE-AC02-09CH11466.
Representations of the language recognition problem for a theorem prover
NASA Technical Reports Server (NTRS)
Minker, J.; Vanderbrug, G. J.
1972-01-01
Two representations of the language recognition problem for a theorem prover in first order logic are presented and contrasted. One of the representations is based on the familiar method of generating sentential forms of the language, and the other is based on the Cocke parsing algorithm. An augmented theorem prover is described which permits recognition of recursive languages. The state-transformation method developed by Cordell Green to construct problem solutions in resolution-based systems can be used to obtain the parse tree. In particular, the end-order traversal of the parse tree is derived in one of the representations. An inference system, termed the cycle inference system, is defined which makes it possible for the theorem prover to model the method on which the representation is based. The general applicability of the cycle inference system to state space problems is discussed. Given an unsatisfiable set S, where each clause has at most one positive literal, it is shown that there exists an input proof. The clauses for the two representations satisfy these conditions, as do many state space problems.
Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields
Pan, Xiao-Yin; Sahni, Viraht
2015-11-07
The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momenta. The proofs differ from the original HK proof and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function. A Percus-Levy-Lieb constrained-search proof expanding the domain of validity to N-representable functions, and to degenerate states, again for fixed electron number and angular momentum, is also provided.
Manifestly covariant Jüttner distribution and equipartition theorem
NASA Astrophysics Data System (ADS)
Chacón-Acosta, Guillermo; Dagdug, Leonardo; Morales-Técotl, Hugo A.
2010-02-01
The relativistic equilibrium velocity distribution plays a key role in describing several high-energy and astrophysical effects. Recently, computer simulations favored Jüttner’s as the relativistic generalization of Maxwell’s distribution for d=1,2,3 spatial dimensions and pointed to an invariant temperature. In this work, we argue an invariant temperature naturally follows from manifest covariance. We present a derivation of the manifestly covariant Jüttner’s distribution and equipartition theorem. The standard procedure to get the equilibrium distribution as a solution of the relativistic Boltzmann’s equation, which holds for dilute gases, is here adopted. However, contrary to previous analysis, we use Cartesian coordinates in d+1 momentum space, with d spatial components. The use of the multiplication theorem of Bessel functions turns crucial to regain the known invariant form of Jüttner’s distribution. Since equilibrium kinetic-theory results should agree with thermodynamics in the comoving frame to the gas the covariant pseudonorm of a vector entering the distribution can be identified with the reciprocal of temperature in such comoving frame. Then by combining the covariant statistical moments of Jüttner’s distribution a form of the equipartition theorem is advanced which also accommodates the invariant comoving temperature and it contains, as a particular case, a previous not manifestly covariant form.
NASA Astrophysics Data System (ADS)
Lipiński, Józef
2002-09-01
The general relation between one-electron electric properties ɛ (dipole moment, polarizability, hyperpolarizability, etc.) of molecules calculated as energy derivatives (E) and as dipole expansion (D) is derived: ɛE= ɛD+ ɛNHF, where ɛNHF represents the non-Hellmann-Feynman correction, which vanishes for wave functions satisfying the Hellmann-Feynman theorem. It is shown that in cases when the wave function does not satisfy the Hellmann-Feynman theorem (e.g., limited CI) not only the NHF correction may be very large, but what is more important, the elements of static polarizability tensors ( α, β, γ, etc.) obtained via the dipole expansion are non-physical because they do not satisfy the Kleinman symmetry, and for example αijD≠ αjiD, βijjD≠ βjjiD or γiijjD= γijjiD≠ γjjiiD (for i≠j, i=x,y,z ). Finally, it is concluded that in the case of wave functions which do not satisfy the Hellmann-Feynman theorem only energy derivative methods are the correct way for calculations of one-electron electric properties of molecules.
Schwarz, Doreen; Orf, Isabel; Kopka, Joachim; Hagemann, Martin
2014-01-01
Cyanobacteria are the only prokaryotes performing oxygenic photosynthesis. Non-diazotrophic strains such as the model Synechocystis sp. PCC 6803 depend on a balanced uptake and assimilation of inorganic carbon and nitrogen sources. The internal C/N ratio is sensed via the PII protein (GlnB). We analyzed metabolic changes of the ΔglnB mutant of Synechocystis sp. PCC 6803 under different CO2 availability. The identified metabolites provided a snapshot of the central C/N metabolism. Cells of the ΔglnB mutant shifted to carbon-limiting conditions, i.e. a decreased C/N ratio, showed changes in intermediates of the sugar storage and particularly of the tricarboxylic acid cycle, arginine, and glutamate metabolism. The changes of the metabolome support the notion that the PII protein is primarily regulating the N-metabolism whereas the changes in C-metabolism are probably secondary effects of the PII deletion. PMID:24957024
Migdal's theorem and electron-phonon vertex corrections in Dirac materials
NASA Astrophysics Data System (ADS)
Roy, Bitan; Sau, Jay D.; Das Sarma, S.
2014-04-01
Migdal's theorem plays a central role in the physics of electron-phonon interactions in metals and semiconductors, and has been extensively studied theoretically for parabolic band electronic systems in three-, two-, and one-dimensional systems over the last fifty years. In the current work, we theoretically study the relevance of Migdal's theorem in graphene and Weyl semimetals which are examples of 2D and 3D Dirac materials, respectively, with linear and chiral band dispersion. Our work also applies to 2D and 3D topological insulator systems. In Fermi liquids, the renormalization of the electron-phonon vertex scales as the ratio of sound (vs) to Fermi (vF) velocity, which is typically a small quantity. In two- and three-dimensional quasirelativistic systems, such as undoped graphene and Weyl semimetals, the one loop electron-phonon vertex renormalization, which also scales as η =vs/vF as η →0, is, however, enhanced by an ultraviolet logarithmic divergent correction, arising from the linear, chiral Dirac band dispersion. Such enhancement of the electron-phonon vertex can be significantly softened due to the logarithmic increment of the Fermi velocity, arising from the long range Coulomb interaction, and therefore, the electron-phonon vertex correction does not have a logarithmic divergence at low energy. Otherwise, the Coulomb interaction does not lead to any additional renormalization of the electron-phonon vertex. Therefore, electron-phonon vertex corrections in two- and three-dimensional Dirac fermionic systems scale as vs/vF0, where vF0 is the bare Fermi velocity, and small when vs≪vF0. These results, although explicitly derived for the intrinsic undoped systems, should hold even when the chemical potential is tuned away from the Dirac points.
A fluctuation theorem for non-equilibrium relaxational systems driven by external forces
NASA Astrophysics Data System (ADS)
Zamponi, Francesco; Bonetto, Federico; Cugliandolo, Leticia F.; Kurchan, Jorge
2005-09-01
We discuss an extension of the fluctuation theorem to stochastic models that, in the limit of zero external drive, are not able to equilibrate with their environment, extending earlier results of Sellitto. We show that if the entropy production rate is suitably defined, its probability distribution function verifies the fluctuation relation with the ambient temperature replaced by a (frequency dependent) effective temperature. We derive modified Green-Kubo relations. We illustrate these results with the simple example of an oscillator coupled to a non-equilibrium bath driven by an external force. We discuss the relevance of our results for driven glasses and the diffusion of Brownian particles in out-of-equilibrium media and propose a concrete experimental strategy for measuring the low frequency value of the effective temperature using the fluctuations of the work done by an ac conservative field. We compare our results to related ones that appeared in the literature recently.
Theoretical Foundation for the Index Theorem on the Lattice with Staggered Fermions
Adams, David H.
2010-04-09
A way to identify the would-be zero modes of staggered lattice fermions away from the continuum limit is presented. Our approach also identifies the chiralities of these modes, and their index is seen to be determined by gauge field topology in accordance with the index theorem. The key idea is to consider the spectral flow of a certain Hermitian version of the staggered Dirac operator. The staggered fermion index thus obtained can be used as a new way to assign the topological charge of lattice gauge fields. In a numerical study in U(1) backgrounds in two dimensions it is found to perform as well as the Wilson index while being computationally more efficient. It can also be expressed as the index of an overlap Dirac operator with a new staggered fermion kernel.
NASA Astrophysics Data System (ADS)
Colalongo, Luigi; Ghittorelli, Matteo; Torricelli, Fabrizio; Kovács-Vajna, Zsolt Miklos
2015-12-01
Surface-potential-based mathematical models are among the most accurate and physically based compact models of Thin-Film Transistors (TFTs) and, in turn, of Organic Thin-Film Transistors (OTFTs), available today. However, the need for iterative computations of the surface potential limits their computational efficiency and diffusion in CAD applications. The existing closed-form approximations of the surface potential are based on regional approximations and empirical smoothing functions that could result not enough accurate to model OTFTs and, in particular, transconductances and transcapacitances. In this paper we present an accurate and computationally efficient closed-form approximation of the surface potential, based on the Lagrange Reversion Theorem, that can be exploited in advanced surface-potential-based OTFTs and TFTs device models.
NASA Astrophysics Data System (ADS)
Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A.
2015-08-01
This letter shows an incorrect application of the chain rule for fractional order derivatives reported in paper (Chen et al., 2014). Due to this misleading application, the proof of Theorem 2 and Theorem 5 in Chen et al., (2014) are incorrect. However, the mentioned Theorem 2 is a straightforward conclusion from results already available in literature (Jarad et al., 2013; Matignon 1996), and consequently there is no need to prove it, as it is stated in this letter. In the same way, although the proof of Theorem 5 in Chen et al. (2014) is not valid, Theorem 5 is indeed true, and a recommendation as to how to prove it is made to the authors. Besides, this letter shows that the proposed Theorem 1 in Chen et al., (2014) is also a straightforward conclusion from well known results available in literature (Jarad et al., 2013; Slotine and Li, 1999), so no demonstration is needed for this result neither.
Generalized virial theorem for massless electrons in graphene and other Dirac materials
NASA Astrophysics Data System (ADS)
Sokolik, A. A.; Zabolotskiy, A. D.; Lozovik, Yu. E.
2016-05-01
The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in the particular case of interacting massless electrons in graphene and other Dirac materials, the conventional virial theorem is violated. Starting from the tight-binding model, we derive the generalized virial theorem for Dirac electron systems, which contains an additional term associated with a momentum cutoff at the bottom of the energy band. Additionally, we derive the generalized virial theorem within the Dirac model using the minimization of the variational energy. The obtained theorem is illustrated by many-body calculations of the ground-state energy of an electron gas in graphene carried out in Hartree-Fock and self-consistent random-phase approximations. Experimental verification of the theorem in the case of graphene is discussed.
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.
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.
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
Golin, M.J.
1996-12-31
Let MWT(n) be the weight of a minimum-weight triangulation of n points chosen independently from the uniform distribution over [0, 1]{sup 2}. Previous work has shown that E(MWT(n)) = {Theta} ({radical}n). In this paper we develop techniques for proving that MWT(n)/{radical}n actually converges to a constant in both expectation and in probability. An immediate consequence is the development of an O(n{sup 2}) time algorithm that finds a triangulation whose competive ratio with the MWT is, in a probabilistic sense, exactly one. The techniques developed to prove the above results are quite general and can also prove the convergence of certain types of probabilistic recurrence equations and other Euclidean Functionals. This is illustrated by using them to prove the convergence of the weight of MWTs of random points in higher dimensions and a sketch of how to use them to prove the convergence of the degree probabilities for Delaunay triangulations in {Re}{sup 2}.
Some Extensions of Discrete Fixed Point Theorems and Their Applications to the Game Theory
NASA Astrophysics Data System (ADS)
Kawasaki, Hidefumi
2009-09-01
As is well-known in the game theory, fixed point theorems are useful to show the existence of Nash equilibrium. Since they are mathematical tools in continuous variables, it is expected that discrete fixed point theorems also useful to guarantee the existence of pure-strategy Nash equilibrium. In this talk, we review three types of discrete fixed point theorems, give some extensions, and apply them to non-cooperative games.
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.
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.
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.
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 generalization of Nash's theorem with higher-order functionals
Hedges, Julian
2013-01-01
The recent theory of sequential games and selection functions by Escardó & Oliva is extended to games in which players move simultaneously. The Nash existence theorem for mixed-strategy equilibria of finite games is generalized to games defined by selection functions. A normal form construction is given, which generalizes the game-theoretic normal form, and its soundness is proved. Minimax strategies also generalize to the new class of games, and are computed by the Berardi–Bezem–Coquand functional, studied in proof theory as an interpretation of the axiom of countable choice. PMID:23750111
Multiplicative-theorem-based fast Williamson-Hadamard transforms
NASA Astrophysics Data System (ADS)
Agaian, Sos S.; Sarukhanian, Hakob; Astola, Jaakko T.
2002-05-01
Hadamard matrices have received much attention in recent years, owing to their numerous known and promising applications. The difficulties of construction of N equalsV 0(mod 4)-point Hadamard transforms are related to the existence of Hadamard matrices problem. In this paper algorithms for fast computation of N-point Williamson-Hadamard transform based on multiplicative theorems are presented. Comparative estimates revealing the efficiency of the proposed algorithms with respect to the known ones are given. The results of numerical examples are presented.
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.
One-loop soft theorems via dual superconformal symmetry
NASA Astrophysics Data System (ADS)
Brandhuber, Andreas; Hughes, Edward; Spence, Bill; Travaglini, Gabriele
2016-03-01
We study soft theorems at one loop in planar {N}=4 super Yang-Mills theory through finite order in the infrared regulator and to subleading order in the soft parameter δ. In particular, we derive a universal constraint from dual superconformal symmetry, which we use to bootstrap subleading log δ behaviour. Moreover, we determine the complete infrared-finite subleading soft contribution of n-point MHV amplitudes using momentum twistors. Finally, we compute the subleading log δ behaviour of one-loop NMHV ratio functions at six and seven points, finding that universality holds within but not between helicity sectors.
Evidence for a fluctuation theorem in an atmospheric circulation model.
Schalge, B; Blender, R; Wouters, J; Fraedrich, K; Lunkeit, F
2013-05-01
An investigation of the distribution of finite time trajectory divergence is performed on an atmospheric global circulation model. The distribution of the largest local Lyapunov exponent shows a significant probability for negative values over time spans up to 10 days. This effect is present for resolutions up to wave numbers ℓ=42 (≈250 km). The probability for a negative local largest Lyapunov exponent decreases over time, similarly to the predictions of the fluctuation theorem for entropy production. The model used is hydrostatic with variable numbers of vertical levels and different horizontal resolutions. PMID:23767493
Evidence for a fluctuation theorem in an atmospheric circulation model
NASA Astrophysics Data System (ADS)
Schalge, B.; Blender, R.; Wouters, J.; Fraedrich, K.; Lunkeit, F.
2013-05-01
An investigation of the distribution of finite time trajectory divergence is performed on an atmospheric global circulation model. The distribution of the largest local Lyapunov exponent shows a significant probability for negative values over time spans up to 10 days. This effect is present for resolutions up to wave numbers ℓ=42 (≈250 km). The probability for a negative local largest Lyapunov exponent decreases over time, similarly to the predictions of the fluctuation theorem for entropy production. The model used is hydrostatic with variable numbers of vertical levels and different horizontal resolutions.
Quantum anonymous ranking based on the Chinese remainder theorem
NASA Astrophysics Data System (ADS)
Lin, Song; Guo, Gong-De; Huang, Feng; Liu, Xiao-Fen
2016-01-01
In this paper, an efficient quantum anonymous ranking protocol with single particles is proposed. A semitrusted server is introduced to help multiple users achieve this secure task. At the end of the protocol, each user can obtain the rankings of his private data, and keep these data secret. The Chinese remainder theorem is utilized to reduce the level of signal particles and to improve the efficiency of the presented protocol. Meanwhile, a secret transmission order of the signal particles is used to keep the traveling particles secure. Finally, we discuss the security of this protocol and prove it to be secure against certain common attacks under ideal conditions.
The Cauchy-Kovalevskaya Extension Theorem in Discrete Clifford Analysis
NASA Astrophysics Data System (ADS)
De Ridder, H.; De Schepper, H.; Sommen, F.
2010-09-01
Discrete Clifford analysis is a higher dimensional discrete function theory based on skew Weyl relations. It is centered around the study of Clifford algebra valued null solutions, called discrete monogenic functions, of a discrete Dirac operator, i.e. a first order, Clifford vector valued difference operator. In this contribution, we establish a Cauchy-Kovalevskaya extension theorem for discrete monogenic functions defined on the grid Zhm of m-tuples of integer multiples of a variable mesh width h. Convergence to the continuous case is investigated. As illustrative examples we explicitly construct the Cauchy-Kovalevskaya extensions of the discrete delta function and of a discretized exponential.
Extended Hellmann-Feynman theorem for degenerate eigenstates
NASA Astrophysics Data System (ADS)
Zhang, G. P.; George, Thomas F.
2004-04-01
In a previous paper, we reported a failure of the traditional Hellmann-Feynman theorem (HFT) for degenerate eigenstates. This has generated enormous interest among different groups. In four independent papers by Fernandez, by Balawender, Hola, and March, by Vatsya, and by Alon and Cederbaum, an elegant method to solve the problem was devised. The main idea is that one has to construct and diagonalize the force matrix for the degenerate case, and only the eigenforces are well defined. We believe this is an important extension to HFT. Using our previous example for an energy level of fivefold degeneracy, we find that those eigenforces correctly reflect the symmetry of the molecule.
H-theorem for a relativistic plasma around black holes
Nicolini, P.; Tessarotto, M.
2006-05-15
A statistical description of matter, formed by a relativistic plasma infalling into a black hole, is formulated, adopting a covariant kinetic approach in terms of classical point particles. By assuming that the charged particles are described by the collisionless Vlasov equation and the event horizon can be treated as a classical porous wall, the theory permits us to evaluate the entropy production rate of classical matter in the presence of an event horizon. As a result, an H-theorem is established for the classical (Shannon) kinetic entropy of the infalling matter, which holds for arbitrary models of black holes and is valid also in the presence of contracting (or expanding) event horizons.
Area Theorem and Smoothness of Compact Cauchy Horizons
NASA Astrophysics Data System (ADS)
Minguzzi, E.
2015-10-01
We obtain an improved version of the area theorem for not necessarily differentiable horizons which, in conjunction with a recent result on the completeness of generators, allows us to prove that under the null energy condition every compactly generated Cauchy horizon is smooth and compact. We explore the consequences of this result for time machines, topology change, black holes and cosmic censorship. For instance, it is shown that compact Cauchy horizons cannot form in a non-empty spacetime which satisfies the stable dominant energy condition wherever there is some source content.