Illustrating the Central Limit Theorem
ERIC Educational Resources Information Center
Corcoran, Mimi
2016-01-01
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
Visualizing the Central Limit Theorem through Simulation
ERIC Educational Resources Information Center
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
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.
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.
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.
Optimal Keno Strategies and the Central Limit Theorem
ERIC Educational Resources Information Center
Johnson, Roger W.
2006-01-01
For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…
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.
Exploring central limit theorem on world population density data
NASA Astrophysics Data System (ADS)
Fitrianto, Anwar; Hanafi, Imam
2014-12-01
We do some exploration to Central Limit Theorem on a real dataset. We intend to conduct this study to a real data which has non-normal distribution. Under common sense, it is known that world population density data has right-skewed distribution. A resampling mechanism is done to the original data by varying sample size to study the properties of well-known Central Limit Theorem, such as normality of the sampling distribution and reduction of the standard deviation of sample data due to larger sample size.
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.)
Entropy Inequalities for Stable Densities and Strengthened Central Limit Theorems
NASA Astrophysics Data System (ADS)
Toscani, Giuseppe
2016-09-01
We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy functionals along the sequence we prove convergence with explicit rate in various norms to a Lévy centered density of parameter λ >1 . This introduces a new information-theoretic approach to the central limit theorem for stable laws, in which the main argument is shown to be the relative fractional Fisher information, recently introduced in Toscani (Ricerche Mat 65(1):71-91, 2016). In particular, it is proven that, with respect to the relative fractional Fisher information, the Lévy density satisfies an analogous of the logarithmic Sobolev inequality, which allows to pass from the monotonicity and decay to zero of the relative fractional Fisher information in the standardized sum to the decay to zero in relative entropy with an explicit decay rate.
Entropy Inequalities for Stable Densities and Strengthened Central Limit Theorems
NASA Astrophysics Data System (ADS)
Toscani, Giuseppe
2016-10-01
We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy functionals along the sequence we prove convergence with explicit rate in various norms to a Lévy centered density of parameter λ >1 . This introduces a new information-theoretic approach to the central limit theorem for stable laws, in which the main argument is shown to be the relative fractional Fisher information, recently introduced in Toscani (Ricerche Mat 65(1):71-91, 2016). In particular, it is proven that, with respect to the relative fractional Fisher information, the Lévy density satisfies an analogous of the logarithmic Sobolev inequality, which allows to pass from the monotonicity and decay to zero of the relative fractional Fisher information in the standardized sum to the decay to zero in relative entropy with an explicit decay rate.
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
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).
Planetary Accretion, Oxygen Isotopes and the Central Limit Theorem
NASA Technical Reports Server (NTRS)
Nuth, Joseph A., III; Hill, Hugh G. M.; Vondrak, Richard R. (Technical Monitor)
2001-01-01
The accumulation of presolar dust into increasingly larger aggregates (CAIs and Chondrules, Asteroids, Planets) should result in a very drastic reduction in the numerical spread in oxygen isotopic composition between bodies of similar size, in accord with the Central Limit Theorem. Observed variations in oxygen isotopic composition are many orders of magnitude larger than would be predicted by a simple, random accumulation model that begins in a well-mixed nebula - no matter which size-scale objects are used as the beginning or end points of the calculation. This discrepancy implies either that some as yet unspecified process acted on the solids in the Solar Nebula to increase the spread in oxygen isotopic composition during each and every stage of accumulation or that the nebula was heterogeneous and maintained this heterogeneity throughout most of nebular history. Large-scale nebular heterogeneity would have significant consequences for many areas of cosmochemistry, including the application of some well-known isotopic systems to the dating of nebular events or the prediction of bulk compositions of planetary bodies on the basis of a uniform cosmic abundance.
Central limit theorems and suppression of anomalous diffusion for systems with symmetry
NASA Astrophysics Data System (ADS)
Gottwald, Georg A.; Melbourne, Ian
2016-10-01
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle/functional central limit theorem) to hold for observables of compact group extensions of nonuniformly expanding maps. In particular, our results include situations where the central limit theorem would fail, and anomalous behaviour would prevail, if the compact group were not present. This has important consequences for systems with noncompact Euclidean symmetry and provides the rigorous proof for a conjecture made in our paper: a Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Gottwald and Melbourne (2013 Proc. Natl Acad. Sci. USA 110 8411-6).
A q-analog of the quantum central limit theorem for SUq(2)
NASA Astrophysics Data System (ADS)
Lenczewski, Romuald; Podgórski, Krzysztof
1992-08-01
A q-analog of the central limit theorem for SUq(2), q≳0, is studied. It is shown that the limits of the moments and q-exponential generating functions for coherent states give for q≳1 (0
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…
Taming systematic uncertainties at the LHC with the central limit theorem
NASA Astrophysics Data System (ADS)
Fichet, Sylvain
2016-10-01
We study the simplifications occurring in any likelihood function in the presence of a large number of small systematic uncertainties. We find that the marginalisation of these uncertainties can be done analytically by means of second-order error propagation, error combination, the Lyapunov central limit theorem, and under mild approximations which are typically satisfied for LHC likelihoods. The outcomes of this analysis are i) a very light treatment of systematic uncertainties ii) a convenient way of reporting the main effects of systematic uncertainties, such as the detector effects occurring in LHC measurements.
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.
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.
Central limit theorem for a class of globally correlated random variables.
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.
Quenched Central Limit Theorems for the Ising Model on Random Graphs
NASA Astrophysics Data System (ADS)
Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa
2015-09-01
The main goal of the paper is to prove central limit theorems for the magnetization rescaled by for the Ising model on random graphs with N vertices. Both random quenched and averaged quenched measures are considered. We work in the uniqueness regime or and , where is the inverse temperature, is the critical inverse temperature and B is the external magnetic field. In the random quenched setting our results apply to general tree-like random graphs (as introduced by Dembo, Montanari and further studied by Dommers and the first and third author) and our proof follows that of Ellis in . For the averaged quenched setting, we specialize to two particular random graph models, namely the 2-regular configuration model and the configuration model with degrees 1 and 2. In these cases our proofs are based on explicit computations relying on the solution of the one dimensional Ising models.
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.
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
ERIC Educational Resources Information Center
See, Lai-Chu; Huang, Yu-Hsun; Chang, Yi-Hu; Chiu, Yeo-Ju; Chen, Yi-Fen; Napper, Vicki S.
2010-01-01
This study examines the timing using computer-enriched instruction (CEI), before or after a traditional lecture to determine cross-over effect, period effect, and learning effect arising from sequencing of instruction. A 2 x 2 cross-over design was used with CEI to teach central limit theorem (CLT). Two sequences of graduate students in nursing…
ERIC Educational Resources Information Center
Lunsford, M. Leigh; Rowell, Ginger Holmes; Goodson-Espy, Tracy
2006-01-01
We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we…
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.
Central limit theorem for variable size simple random sampling from a finite population
Wright, T.
1986-02-01
This paper introduces a sampling plan for finite populations herein called ''variable size simple random sampling'' and compares properties of estimators based on it with results from the usual fixed size simple random sampling without replacement. Necessary and sufficient conditions (in the spirit of Hajek) for the limiting distribution of the sample total (or sample mean) to be normal are given. 19 refs.
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.
Nixon, Richard M; Wonderling, David; Grieve, Richard D
2010-03-01
Cost-effectiveness analyses (CEA) alongside randomised controlled trials commonly estimate incremental net benefits (INB), with 95% confidence intervals, and compute cost-effectiveness acceptability curves and confidence ellipses. Two alternative non-parametric methods for estimating INB are to apply the central limit theorem (CLT) or to use the non-parametric bootstrap method, although it is unclear which method is preferable. This paper describes the statistical rationale underlying each of these methods and illustrates their application with a trial-based CEA. It compares the sampling uncertainty from using either technique in a Monte Carlo simulation. The experiments are repeated varying the sample size and the skewness of costs in the population. The results showed that, even when data were highly skewed, both methods accurately estimated the true standard errors (SEs) when sample sizes were moderate to large (n>50), and also gave good estimates for small data sets with low skewness. However, when sample sizes were relatively small and the data highly skewed, using the CLT rather than the bootstrap led to slightly more accurate SEs. We conclude that while in general using either method is appropriate, the CLT is easier to implement, and provides SEs that are at least as accurate as the bootstrap.
Pérez-Rodríguez, Fernando; Zwietering, Marcel H
2012-02-15
The Central Limit Theorem (CLT) is proposed as a means of understanding microbial risk in foods from a Public Health perspective. One variant of the CLT states that as the number of random variables, each with a finite mean and variance, increases (→∞), the distribution of the sum (or mean) of those variables approximates a normal distribution. On the basis of the CLT, the hypothesis introduced by this paper states that the Coefficient of Variation (CV) of the annual number of food-borne illness cases decreases as a result of a larger number of exposures (or servings) (n). Second-order Monte-Carlo analysis and classical statistics were used to support the hypothesis, based on existing risk models on Listeria monocytogenes in deli meat products focused on elderly people in the United States. Likewise, the hypothesis was tested on epidemiological data of annual incidence of salmonellosis and listeriosis in different countries (i.e. different n). Although different sources of error affected the accuracy of the results, both the Monte-Carlo analysis (in silico) and epidemiological data (in vivo), especially for salmonellosis, demonstrated that the CV of the annual number of cases decreased as n increased as stated by the CLT. Furthermore, results from this work showed that classical statistical methods can be helpful to provide reliable risk estimates based on simple and well-established statistical principles.
Limit theorems for dilute quantum systems leading to quantum poisson processes
NASA Astrophysics Data System (ADS)
Alicki, Robert; Rudnicki, Sławomir; Sadowski, Sławomir
1993-12-01
The limit theorems for sums of independent or correlated operators representing observables of dilute quantum systems and leading to quantum Poisson processes are proved. Examples of systems of unstable particles and a Fermi lattice gas are discussed. For the latter, relations between low density limit and central limit are given.
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.
Limit Theorems for Monomer-Dimer Mean-Field Models with Attractive Potential
NASA Astrophysics Data System (ADS)
Alberici, Diego; Contucci, Pierluigi; Fedele, Micaela; Mingione, Emanuele
2016-09-01
The number of monomers in a monomer-dimer mean-field model with an attractive potential fluctuates according to the central limit theorem when the parameters are outside the critical curve. At the critical point the model belongs to the same universality class of the mean-field ferromagnet. Along the critical curve the monomer and dimer phases coexist.
Limit theorems in financial market models
NASA Astrophysics Data System (ADS)
Kuroda, Koji; Murai, Joshin
2007-09-01
Invariance principle states that a scaled simple random walk converges to the standard Brownian motion. In this article, we present a discrete time stochastic process, which reflects a microstructure of market dynamics, and prove a convergence to a scaling limit process with a drift term and a jump term. These terms are derived from a macroscopic condition on volumes traded in some time intervals. The mathematical tools for obtaining our results are Dobrushin-Hryniv theory and the method of cluster expansion developed in mathematical studies of statistical mechanics.
The central limit theorem under random truncation
Stute, Winfried; Wang, Jane-Ling
2012-01-01
Under left truncation, data (Xi, Yi) are observed only when Yi ≤ Xi. Usually, the distribution function F of the Xi is the target of interest. In this paper, we study linear functionals ∫ φ dFn of the nonparametric maximum likelihood estimator (MLE) of F, the Lynden-Bell estimator Fn. A useful representation of ∫ φ dFn is derived which yields asymptotic normality under optimal moment conditions on the score function φ. No continuity assumption on F is required. As a by-product, we obtain the distributional convergence of the Lynden-Bell empirical process on the whole real line. PMID:22844204
The infrared limit of the SRG evolution and Levinson's theorem
NASA Astrophysics Data System (ADS)
Arriola, E. Ruiz; Szpigel, S.; Timóteo, V. S.
2014-07-01
On a finite momentum grid with N integration points pn and weights wn (n = 1 , … , N) the Similarity Renormalization Group (SRG) with a given generator G unitarily evolves an initial interaction with a cutoff λ on energy differences, steadily driving the starting Hamiltonian in momentum space Hn,m0 = pn2 δn,m +Vn,m to a diagonal form in the infrared limit (λ → 0), Hn,mG, λ → 0 =E π (n)δn,m, where π (n) is a permutation of the eigenvalues En which depends on G. Levinson's theorem establishes a relation between phase-shifts δ (pn) and the number of bound-states, nB, and reads δ (p1) - δ (pN) =nB π. We show that unitarily equivalent Hamiltonians on the grid generate reaction matrices which are compatible with Levinson's theorem but are phase-inequivalent along the SRG trajectory. An isospectral definition of the phase-shift in terms of an energy-shift is possible but requires in addition a proper ordering of states on a momentum grid such as to fulfill Levinson's theorem. We show how the SRG with different generators G induces different isospectral flows in the presence of bound-states, leading to distinct orderings in the infrared limit. While the Wilson generator induces an ascending ordering incompatible with Levinson's theorem, the Wegner generator provides a much better ordering, although not the optimal one. We illustrate the discussion with the nucleon-nucleon (NN) interaction in the S10 and S31 channels.
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.
Entropy production and fluctuation theorem along a stochastic limit cycle.
Xiao, Tie Jun; Hou, Zhonghuai; Xin, Houwen
2008-09-21
Entropy production along a trajectory in the stochastic irreversible Brusselator model of chemical oscillating reactions is discussed. Particular attention is paid to a parameter region near the deterministic supercritical Hopf bifurcation. In the stationary state, detailed fluctuation theorem holds due to the reversibility in the state space, which is verified by direct simulations via Gillespie's algorithm [J. Comput. Phys. 22, 403 (1976); J. Phys. Chem. 81, 2340 (1977)]. In addition, we have considered how the entropy production along a noisy limit cycle depends on the system size. Interestingly, in the large system size limit, the entropy production approaches a constant value when the control parameter stays at the deterministic steady state region, while it increases linearly in the deterministic oscillatory region. Such simulation results can be well understood by a stochastic normal form analysis. PMID:19044968
Entropy production and fluctuation theorem along a stochastic limit cycle
NASA Astrophysics Data System (ADS)
Xiao, Tie Jun; Hou, Zhonghuai; Xin, Houwen
2008-09-01
Entropy production along a trajectory in the stochastic irreversible Brusselator model of chemical oscillating reactions is discussed. Particular attention is paid to a parameter region near the deterministic supercritical Hopf bifurcation. In the stationary state, detailed fluctuation theorem holds due to the reversibility in the state space, which is verified by direct simulations via Gillespie's algorithm [J. Comput. Phys. 22, 403 (1976); J. Phys. Chem. 81, 2340 (1977)]. In addition, we have considered how the entropy production along a noisy limit cycle depends on the system size. Interestingly, in the large system size limit, the entropy production approaches a constant value when the control parameter stays at the deterministic steady state region, while it increases linearly in the deterministic oscillatory region. Such simulation results can be well understood by a stochastic normal form analysis.
Limit theorem for continuous-time quantum walk on the line
NASA Astrophysics Data System (ADS)
Konno, Norio
2005-08-01
Concerning a discrete-time quantum walk Xt(d) with a symmetric distribution on the line, whose evolution is described by the Hadamard transformation, it was proved by the author that the following weak limit theorem holds: Xt(d)/t→dx/π(1-x2)1-2x2 as t→∞ . The present paper shows that a similar type of weak limit theorem is satisfied for a continuous-time quantum walk Xt(c) on the line as follows: Xt(c)/t→dx/π1-x2 as t→∞ . These results for quantum walks form a striking contrast to the central limit theorem for symmetric discrete- and continuous-time classical random walks: Yt/t→e-x2/2dx/2π as t→∞ . The work deals also with the issue of the relationship between discrete and continuous-time quantum walks. This topic, subject of a long debate in the previous literature, is treated within the formalism of matrix representation and the limit distributions are exhaustively compared in the two cases.
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…
A rigorous proof of the Bohr-van Leeuwen theorem in the semiclassical limit
NASA Astrophysics Data System (ADS)
Savoie, Baptiste
2015-10-01
The original formulation of the Bohr-van Leeuwen (BvL) theorem states that, in a uniform magnetic field and in thermal equilibrium, the magnetization of an electron gas in the classical Drude-Lorentz model vanishes identically. This stems from classical statistics which assign the canonical momenta all values ranging from -∞ to ∞ that makes the free energy density magnetic-field-independent. When considering a classical (Maxwell-Boltzmann) interacting electron gas, it is usually admitted that the BvL theorem holds upon condition that the potentials modeling the interactions are particle-velocities-independent and do not cause the system to rotate after turning on the magnetic field. From a rigorous viewpoint, when treating large macroscopic systems, one expects the BvL theorem to hold provided the thermodynamic limit of the free energy density exists (and the equivalence of ensemble holds). This requires suitable assumptions on the many-body interactions potential and on the possible external potentials to prevent the system from collapsing or flying apart. Starting from quantum statistical mechanics, the purpose of this paper is to give, within the linear-response theory, a proof of the BvL theorem in the semiclassical limit when considering a dilute electron gas in the canonical conditions subjected to a class of translational invariant external potentials.
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.
Guseinov, Israfil
2003-06-01
By the use of complete orthonormal sets of psi(alpha)-ETOs (alpha=1, 0, m1, m2,...) introduced by the author, new addition theorems are derived for STOs and arbitrary central and noncentral interaction potentials (CIPs and NCIPs). The expansion coefficients in these addition theorems are expressed through the Gaunt and Gegenbauer coefficients. Using the addition theorems obtained for STOs and potentials, general formulae in terms of three-center overlap integrals are established for the multicenter t-electron integrals of CIPs and NCIPs that arise in the solution of the N-electron atomic and molecular problem (2hthN) when a Hylleraas approximation in Hartree-Fock-Roothaan theory is employed. With the help of expansion formulae for translation of STOs, the three-center overlap integrals are expressed through the two-center overlap integrals. The formulae obtained are valid for arbitrary quantum numbers, screening constants and location of orbitals. PMID:12750966
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.
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.
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
Evaluation of an Interactive Tutorial for Teaching the Central Limit Theorem.
ERIC Educational Resources Information Center
Aberson, Christopher L.; Berger, Dale E.; Healy, Michael R.; Kyle, Diana J.; Romero, Victoria L.
2000-01-01
Evaluates an interactive, Web-based tutorial that helps students learn about sampling distribution. 111 students enrolled in statistics or research methods courses used either the tutorial or attended a lecture/demonstration. Indicates through pre- and post-test quizzes both groups learned comparable amounts and reveals students' ratings of both…
Fractional Edgeworth expansion: Corrections to the Gaussian-Lévy central-limit theorem
NASA Astrophysics Data System (ADS)
Hazut, Netanel; Medalion, Shlomi; Kessler, David A.; Barkai, Eli
2015-05-01
In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to PDFs with a diverging variance, which converge to a Lévy α -stable density function. Our correction may be written by means of a series of fractional derivatives of the Lévy and the conjugate Lévy PDFs. This series expansion is general and applies also to the Gaussian regime. To describe the terms in the series expansion, we introduce a new family of special functions and briefly discuss their properties. We implement our generalization to the distribution of the momentum for atoms undergoing Sisyphus cooling, and show the improvement of our leading order approximation compared to previous approximations. In vicinity of the transition between Lévy and Gauss behaviors, convergence to asymptotic results slows down.
ERIC Educational Resources Information Center
Davis, Philip J.
1993-01-01
Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)
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
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
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
Stability Limits in High Performance, Negative Central Shear Discharges
NASA Astrophysics Data System (ADS)
Hanson, J. M.; Bialek, J.; Navratil, G. A.; Olofsson, K. E. J.; Turco, F.; Clement, M.; Ferron, J. R.; Garofalo, A. M.; La Haye, R. J.; Lanctot, M. J.; Strait, E. J.; Holcomb, C. T.
2014-10-01
Exploration of negative central shear equilibria in DIII-D has yielded discharges that transiently achieve βN ~= 4 . The discharges exhibit broad current density profiles, leading to a significant separation in the no- and with-wall ideal kink stability limits predicted by MHD theory. As the no-wall limit is approached and exceeded in experiments, performance is often limited by n = 1 resistive wall mode (RWM) instabilities that lead to abrupt collapses of the plasma stored energy. In addition, instabilities with n = 1 rotating tearing precursors are observed when minimum q value drops below 2. Theoretical calculations predict that magnetic feedback control using the in-vessel coils (internal coils) can provide RWM stabilization to βN values approaching the n = 1 ideal-wall limit. In experiments, applying I-coil control indeed facilitates access to increased βN values above the no-wall limit. Work supported by the US Department of Energy under DE-FG02-04ER54761, DE-FG02-07ER54917, DE-FC02-04ER54698 and DE-AC52-07NA27344.
NASA Astrophysics Data System (ADS)
Greaves, Hilary; Thomas, Teruji
2014-02-01
We provide a careful development and rigorous proof of the CPT theorem within the framework of mainstream (Lagrangian) quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches in the mainstream approach. We construct the CPT transformation for a general field directly, without appealing to the enumerative classification of representations, and in a manner that is clearly related to the requirements of our proof. Our approach applies equally in Minkowski spacetimes of any dimension at least three, and is in principle neutral between classical and quantum field theories: the quantum CPT theorem has a natural classical analogue. The key mathematical tool is that of complexification; this tool is central to the existing axiomatic proofs, but plays no overt role in the usual mainstream approaches to CPT.
NASA 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.
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.
The Limits of Subsistence: Agriculture and Industry in Central Appalachia.
ERIC Educational Resources Information Center
Pudup, Mary Beth
Current interpretations of central Appalachia's chronic poverty focus on the region's economic dependence on the bituminous coal industry, controlled by absentee investors and serving an external market. Such theories overlook the ways in which the agricultural sector shaped subsequent industrial development. By analyzing the farm economy of 16…
ERIC Educational Resources Information Center
May, Henry
2014-01-01
Interest in variation in program impacts--How big is it? What might explain it?--has inspired recent work on the analysis of data from multi-site experiments. One critical aspect of this problem involves the use of random or fixed effect estimates to visualize the distribution of impact estimates across a sample of sites. Unfortunately, unless the…
ERIC Educational Resources Information Center
Van Duzer, Eric
2011-01-01
This report introduces a short, hands-on activity that addresses a key challenge in teaching quantitative methods to students who lack confidence or experience with statistical analysis. Used near the beginning of the course, this activity helps students develop an intuitive insight regarding a number of abstract concepts which are key to…
Double soft theorem for perturbative gravity
NASA Astrophysics Data System (ADS)
Saha, Arnab Priya
2016-09-01
Following up on the recent work of Cachazo, He and Yuan [1], we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
Vorticity, Stokes' Theorem and the Gauss's Theorem
NASA Astrophysics Data System (ADS)
Narayanan, M.
2004-12-01
Vorticity is a property of the flow of any fluid and moving fluids acquire properties that allow an engineer to describe that particular flow in greater detail. It is important to recognize that mere motion alone does not guarantee that the air or any fluid has vorticity. Vorticity is one of four important quantities that define the kinematic properties of any fluid flow. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. However, the divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into, or away from the region through its boundary. This is also known as Gauss's Theorem. It should also be noted that there are many useful extensions of Gauss's Theorem, including the extension to include surfaces of discontinuity in V. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. Integral (Surface) [(DEL X V)] . dS = Integral (Contour) [V . dx] In this paper, the author outlines and stresses the importance of studying and teaching these mathematical techniques while developing a course in Hydrology and Fluid Mechanics. References Arfken, G. "Gauss's Theorem." 1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. Morse, P. M. and Feshbach, H. "Gauss's Theorem." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 37-38, 1953. Eric W. Weisstein. "Divergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DivergenceTheorem.html
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.
A Central Capacity Limit to the Simultaneous Storage of Visual and Auditory Arrays in Working Memory
ERIC Educational Resources Information Center
Saults, J. Scott; Cowan, Nelson
2007-01-01
If working memory is limited by central capacity (e.g., the focus of attention; N. Cowan, 2001), then storage limits for information in a single modality should apply also to the simultaneous storage of information from different modalities. The authors investigated this by combining a visual-array comparison task with a novel auditory-array…
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…
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages.
Trigonometry, Including Snell's Theorem.
ERIC Educational Resources Information Center
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
Plaisted, David A
2014-03-01
Automated theorem proving is the use of computers to prove or disprove mathematical or logical statements. Such statements can express properties of hardware or software systems, or facts about the world that are relevant for applications such as natural language processing and planning. A brief introduction to propositional and first-order logic is given, along with some of the main methods of automated theorem proving in these logics. These methods of theorem proving include resolution, Davis and Putnam-style approaches, and others. Methods for handling the equality axioms are also presented. Methods of theorem proving in propositional logic are presented first, and then methods for first-order logic. WIREs Cogn Sci 2014, 5:115-128. doi: 10.1002/wcs.1269 CONFLICT OF INTEREST: The authors has declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website. PMID:26304304
ERIC Educational Resources Information Center
Benyi, Arpad; Casu, Ioan
2009-01-01
Pompeiu's theorem states that if ABC is an "equilateral" triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B,…
Navier Stokes Theorem in Hydrology
NASA Astrophysics Data System (ADS)
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
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)].
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)
Technical note: Revisiting the geometric theorems for volume averaging
NASA Astrophysics Data System (ADS)
Wood, Brian D.
2013-12-01
The geometric theorems reported by Quintard and Whitaker [5, Appendix B] are re-examined. We show (1) The geometrical theorems can be interpreted in terms of the raw spatial moments of the pore structure within the averaging volume. (2) For the case where the first spatial moment is aligned with the center of mass of the averaging volume, the geometric theorems can be expressed in terms of the central moments of the porous medium. (3) When the spatial moments of the pore structure are spatially stationary, the geometrical theorems allow substantial simplification of nonlocal terms arising in the averaged equations. (4) In the context of volume averaging, the geometric theorems of Quintard and Whitaker [5, Appendix B] are better interpreted as statements regarding the spatial stationarity of specific volume averaged quantities rather than an explicit statement about the media disorder.
''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.
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.
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…
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.
Rediscovering Schreinemakers' Theorem.
ERIC Educational Resources Information Center
Bathurst, Bruce
1983-01-01
Schreinemakers' theorem (arrangement of curves around an invariant point), derived from La Chatelier's principle, can be rediscovered by students asked to use the principle when solving a natural problem such as "How does diluting a mineral/fluid alter shape of a pressure/temperature diagram?" Background information and instructional strategies…
Lie symmetry theorem of fractional nonholonomic systems
NASA Astrophysics Data System (ADS)
Sun, Yi; Chen, Ben-Yong; Fu, Jing-Li
2014-11-01
The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is established, and the fractional Lagrange equations are obtained by virtue of the d'Alembert—Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal transformations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results.
Generalized no-broadcasting theorem.
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-14
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with "superquantum" correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
Discovering the Theorem of Pythagoras
NASA Technical Reports Server (NTRS)
Lattanzio, Robert (Editor)
1988-01-01
In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.
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.
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.
Wheeler, W.
1998-12-01
This report estimates the economic and financial effects and the benefits of compliance with the proposed effluent limitations guidelines and standards for the Centralized Waste Treatment (CWT) industry. The Environmental Protection Agency (EPA) has measured these impacts in terms of changes in the profitability of waste treatment operations at CWT facilities, changes in market prices to CWT services, and changes in the quantities of waste management at CWT facilities in six geographic regions. EPA has also examined the impacts on companies owning CWT facilities (including impacts on small entities), on communities in which CWT facilities are located, and on environmental justice. EPA examined the benefits to society of the CWT effluent limitations guidelines and standards by examining cancer and non-cancer health effects of the regulation, recreational benefits, and cost savings to publicly owned treatment works (POTWs) to which indirect-discharging CWT facilities send their wastewater.
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
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.
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.
NASA Technical Reports Server (NTRS)
Viera, W. J.
1974-01-01
A method of determining the fuel bias for a bipropellant liquid rocket that minimizes outage associated penalties on payload potential is presented. A fuel bias so derived is normally called the optimum fuel bias. The subjects discussed are: (1) probability density function of outage, (2) computer program listing, and (3) choosing the optimum fuel bias.
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.
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.
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
Tautenhahn, Susanne; Lichstein, Jeremy W; Jung, Martin; Kattge, Jens; Bohlman, Stephanie A; Heilmeier, Hermann; Prokushkin, Anatoly; Kahl, Anja; Wirth, Christian
2016-06-01
Fire is a primary driver of boreal forest dynamics. Intensifying fire regimes due to climate change may cause a shift in boreal forest composition toward reduced dominance of conifers and greater abundance of deciduous hardwoods, with potential biogeochemical and biophysical feedbacks to regional and global climate. This shift has already been observed in some North American boreal forests and has been attributed to changes in site conditions. However, it is unknown if the mechanisms controlling fire-induced changes in deciduous hardwood cover are similar among different boreal forests, which differ in the ecological traits of the dominant tree species. To better understand the consequences of intensifying fire regimes in boreal forests, we studied postfire regeneration in five burns in the Central Siberian dark taiga, a vast but poorly studied boreal region. We combined field measurements, dendrochronological analysis, and seed-source maps derived from high-resolution satellite images to quantify the importance of site conditions (e.g., organic layer depth) vs. seed availability in shaping postfire regeneration. We show that dispersal limitation of evergreen conifers was the main factor determining postfire regeneration composition and density. Site conditions had significant but weaker effects. We used information on postfire regeneration to develop a classification scheme for successional pathways, representing the dominance of deciduous hardwoods vs. evergreen conifers at different successional stages. We estimated the spatial distribution of different successional pathways under alternative fire regime scenarios. Under intensified fire regimes, dispersal limitation of evergreen conifers is predicted to become more severe, primarily due to reduced abundance of surviving seed sources within burned areas. Increased dispersal limitation of evergreen conifers, in turn, is predicted to increase the prevalence of successional pathways dominated by deciduous hardwoods
Tau leaping of stiff stochastic chemical systems via local central limit approximation
NASA Astrophysics Data System (ADS)
Yang, Yushu; Rathinam, Muruhan
2013-06-01
Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-stepping method to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods have shortcomings in this regard. The implicit tau method is far more stable than the trapezoidal tau method but underestimates the asymptotic variance. On the other hand, the trapezoidal tau method which estimates the asymptotic variance exactly for linear systems suffers from the fact that the transients of the method do not decay fast enough in the context of very stiff systems. We propose a tau leaping method that possesses the same stability properties as the implicit method while it also captures the asymptotic variance with reasonable accuracy at least for the test system S1↔S2. The proposed method uses a central limit approximation (CLA) locally over the tau leaping interval and is referred to as the LCLA-τ. The CLA predicts the mean and covariance as solutions of certain differential equations (ODEs) and for efficiency we solve these using a single time step of a suitable low order method. We perform a mean/covariance stability analysis of various possible low order schemes to determine the best scheme. Numerical experiments presented show that LCLA-τ performs favorably for stiff systems and that the LCLA-τ is also able to capture bimodal distributions unlike the CLA itself. The proposed LCLA-τ method uses a split implicit step to compute the mean update. We also prove that any tau leaping method employing a split implicit step converges in the fluid limit to the implicit Euler method as applied to the fluid limit differential equation.
Food limitation of sea lion pups and the decline of forage off central and southern California
McClatchie, Sam; Field, John; Thompson, Andrew R.; Gerrodette, Tim; Lowry, Mark; Fiedler, Paul C.; Watson, William; Nieto, Karen M.; Vetter, Russell D.
2016-01-01
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.
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
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
Theorems on positive data: on the uniqueness of NMF.
Laurberg, Hans; Christensen, Mads Graesbøll; Plumbley, Mark D; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.
A new VLA/e-MERLIN limit on central images in the gravitational lens system CLASS B1030+074
NASA Astrophysics Data System (ADS)
Quinn, Jonathan; Jackson, Neal; Tagore, Amitpal; Biggs, Andrew; Birkinshaw, Mark; Chapman, Scott; De Zotti, Gianfranco; McKean, John; Pérez-Fournon, Ismael; Scott, Douglas; Serjeant, Stephen
2016-07-01
We present the new Very Large Array 22 GHz and extended Multi-Element Remote-Linked Interferometer Network 5 GHz observations of CLASS B1030+074, a two-image strong gravitational lens system whose background source is a compact flat-spectrum radio quasar. In such systems we expect a third image of the background source to form close to the centre of the lensing galaxy. The existence and brightness of such images is important for investigation of the central mass distributions of lensing galaxies, but only one secure detection has been made so far in a galaxy-scale lens system. The noise levels achieved in our new B1030+074 images reach 3 μJy beam-1 and represent an improvement in central image constraints of nearly an order of magnitude over previous work, with correspondingly better resulting limits on the shape of the central mass profile of the lensing galaxy. Simple models with an isothermal outer power-law slope now require either the influence of a central supermassive black hole (SMBH), or an inner power-law slope very close to isothermal, in order to suppress the central image below our detection limit. Using the central mass profiles inferred from light distributions in Virgo galaxies, moved to z = 0.5, and matching to the observed Einstein radius, we now find that 45 per cent of such mass profiles should give observable central images, 10 per cent should give central images with a flux density still below our limit, and the remaining systems have extreme demagnification produced by the central SMBH. Further observations of similar objects will therefore allow proper statistical constraints to be placed on the central properties of elliptical galaxies at high redshift.
NASA Astrophysics Data System (ADS)
Eliazar, Iddo
2011-01-01
In this communication we establish stochastic limit laws leading from Zipf's law to Pareto's and Heaps' laws. We consider finite ensembles governed by Zipf's law and study their asymptotic statistics as the ensemble size tends to infinity. A Lorenz-curve analysis establishes three types of limit laws for the ensembles' statistical structure: 'communist', 'monarchic', and Paretian. Further considering a dynamic setting in which the ensembles grow stochastically in time, a functional central limit theorem analysis establishes a Gaussian approximation for the ensembles' stochastic growth. The Gaussian approximation provides a generalized and corrected formulation of Heaps' law.
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
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.
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.
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.
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.…
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)
Mlakar, Jernej; Zorman, Jerneja Videčnik; Matičič, Mojca; Vrabec, Matej; Alibegović, Armin; Popović, Mara
2016-02-01
Primary angiitis of the central nervous system is a rare condition, usually with an insidious onset. There is a wide variety of histological types (granulomatous, lymphocytic or necrotizing vasculitis) and types of vessel involved (arteries, veins or both). Most cases are idiopathic. We describe a first case of idiopathic granulomatous central nervous system phlebitis with additional limited involvement of the heart and lung, exclusively affecting small and medium sized veins in a 22-year-old woman, presenting as a sub acute headache. The reasons for this peculiar limitation of inflammation to the veins and the involvement of the heart and lungs are unknown.
Federal Register 2010, 2011, 2012, 2013, 2014
2010-07-02
... private contractual arrangements. Second, Amendment 86 would exempt vessels using jig gear from the... Economic Zone Off Alaska; Central Gulf of Alaska License Limitation Program; Amendment 86 AGENCY: National...: Notification of availability of fishery management plan amendment; request for comments. SUMMARY: The...
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
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.
Factor and Remainder Theorems: An Appreciation
ERIC Educational Resources Information Center
Weiss, Michael
2016-01-01
The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
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.
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.
Wakefield, Ewan D.; Phillips, Richard A.; Matthiopoulos, Jason
2014-01-01
Animal populations are frequently limited by the availability of food or of habitat. In central-place foragers, the cost of accessing these resources is distance-dependent rather than uniform in space. However, in seabirds, a widely studied exemplar of this paradigm, empirical population models have hitherto ignored this cost. In part, this is because non-independence among colonies makes it difficult to define population units. Here, we model the effects of both resource availability and accessibility on populations of a wide-ranging, pelagic seabird, the black-browed albatross Thalassarche melanophris. Adopting a multi-scale approach, we define regional populations objectively as spatial clusters of colonies. We consider two readily quantifiable proxies of resource availability: the extent of neritic waters (the preferred foraging habitat) and net primary production (NPP). We show that the size of regional albatross populations has a strong dependence, after weighting for accessibility, on habitat availability and to a lesser extent, NPP. Our results provide indirect support for the hypothesis that seabird populations are regulated from the bottom-up by food availability during the breeding season, and also suggest that the spatio-temporal predictability of food may be limiting. Moreover, we demonstrate a straightforward, widely applicable method for estimating resource limitation in populations of central-place foragers. PMID:24430849
Wakefield, Ewan D; Phillips, Richard A; Matthiopoulos, Jason
2014-03-01
Animal populations are frequently limited by the availability of food or of habitat. In central-place foragers, the cost of accessing these resources is distance-dependent rather than uniform in space. However, in seabirds, a widely studied exemplar of this paradigm, empirical population models have hitherto ignored this cost. In part, this is because non-independence among colonies makes it difficult to define population units. Here, we model the effects of both resource availability and accessibility on populations of a wide-ranging, pelagic seabird, the black-browed albatross Thalassarche melanophris. Adopting a multi-scale approach, we define regional populations objectively as spatial clusters of colonies. We consider two readily quantifiable proxies of resource availability: the extent of neritic waters (the preferred foraging habitat) and net primary production (NPP). We show that the size of regional albatross populations has a strong dependence, after weighting for accessibility, on habitat availability and to a lesser extent, NPP. Our results provide indirect support for the hypothesis that seabird populations are regulated from the bottom-up by food availability during the breeding season, and also suggest that the spatio-temporal predictability of food may be limiting. Moreover, we demonstrate a straightforward, widely applicable method for estimating resource limitation in populations of central-place foragers.
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.
Doryńska, Agnieszka; Pająk, Andrzej; Kubinova, Ruzena; Malyutina, Sofia; Tamosiunas, Abdonas; Pikhart, Hynek; Peasey, Anne; Nikitin, Yuri; Marmot, Michael; Bobak, Martin
2012-01-01
Objectives: to investigate functional limitations and their association with socioeconomic factors in four Central and Eastern European populations. Methods: a cross-sectional study of random population samples in Novosibirsk (Russia), Krakow (Poland), Kaunas (Lithuania) and six Czech towns participating in the HAPIEE study. Functional limitations (classified into tertiles of the SF-36 physical functioning subscale), socioeconomic circumstances and health behaviours were available for 34,431 subjects aged 45–69 years. Results: the proportion of subjects in the worst tertile of the functional limitations score (≤80% of the maximum score) ranged from 21% of the men in Kaunas to 48% in Krakow women. In multivariate ordered logistic regression, functional limitations were strongly inversely associated with education and positively with material deprivation and with being economically inactive. Functional limitations were more common in male smokers and less common in alcohol drinkers. Socioeconomic characteristics explained some of the differences in functional limitations between populations. Health behaviours explained some of the differences between social groups in both genders and between populations in women. Conclusion: unexpectedly, functional limitations were not most common in the sample from Russia, the country with the highest mortality rates. All socioeconomic measures were strongly associated with functional limitations and made some contribution towards explaining differences in limitations between populations. PMID:22923605
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.
Ferromagnetism beyond Lieb's theorem
NASA Astrophysics Data System (ADS)
Costa, Natanael C.; Mendes-Santos, Tiago; Paiva, Thereza; Santos, Raimundo R. dos; Scalettar, Richard T.
2016-10-01
The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction U is turned on, Lieb proved rigorously that at half-filling (ρ =1 ) the ground state has a nonzero spin. In this paper we consider a "CuO2 lattice" (also known as "Lieb lattice," or as a decorated square lattice), in which "d orbitals" occupy the vertices of the squares, while "p orbitals" lie halfway between two d orbitals; both d and p orbitals can accommodate only up to two electrons. We use exact determinant quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, Ud=Up , originally considered by Lieb, and the inhomogeneous (IH) case, Ud≠Up . For the H case at half-filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all U . For the IH system at half-filling, we argue that the case Up≠Ud falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases Up=0 ,Ud=U and Up=U ,Ud=0 . We found that the different environments of d and p sites lead to a ferromagnetic insulator when Ud=0 ; by contrast, Up=0 leads to to a metal without any magnetic ordering. In addition, we have also established that at density ρ =1 /3 , strong antiferromagnetic correlations set in, caused by the presence of one fermion on each
Nambu-Goldstone theorem and spin-statistics theorem
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
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.
Merlo, Rion; Witzgall, Bob; Yu, William; Ohlinger, Kurt; Ramberg, Steve; De Las Casas, Carla; Henneman, Seppi; Parker, Denny
2015-12-01
The Sacramento Regional County Sanitation District (District) must be compliant with stringent nitrogen limits by 2021 that the existing treatment facilities cannot meet. An 11-month pilot study was conducted to confirm that these limits could be met with an air activated sludge biological nutrient removal (BNR) process. The pilot BNR treated an average flow of 946 m(3)/d and demonstrated that it could reliably meet the ammonia limit, but that external carbon addition may be necessary to satisfy the nitrate limit. The BNR process performed well throughout the 11 months of operation with good settleability, minimal nocardioform content, and high quality secondary effluent. The BNR process was operated at a minimum pH of 6.4 with no noticeable impact to nitrification rates. Increased secondary sludge production was observed during rainfall events and is attributed to a change in wastewater influent characteristics.
A "fundamental theorem" of biomedical informatics.
Friedman, Charles P
2009-01-01
This paper proposes, in words and pictures, a "fundamental theorem" to help clarify what informatics is and what it is not. In words, the theorem stipulates that a person working in partnership with an information resource is "better" than that same person unassisted. The theorem is applicable to health care, research, education, and administrative activities. Three corollaries to the theorem illustrate that informatics is more about people than technology; that in order for the theorem to hold, resources must be informative in addition to being correct; and that the theorem can fail to hold for reasons explained by understanding the interaction between the person and the resource.
New double soft emission theorems
NASA Astrophysics Data System (ADS)
Cachazo, Freddy; He, Song; Yuan, Ellis Ye
2015-09-01
We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, Dirac-Born-Infeld, Einstein-Maxwell-Scalar, nonlinear sigma model and Yang-Mills-Scalar. We use the recently found Cachazo-He-Yuan representation of these theories in order to give a simple proof of the leading order part of all these theorems.
The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project
ERIC Educational Resources Information Center
Robiette, Alan G.
1975-01-01
Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)
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
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
Nielsen, H B; Angelidaki, I
2008-01-01
The present study focuses on process imbalances in Danish centralized biogas plants treating manure in combination with industrial waste. Collection of process data from various full-scale plants along with a number of interviews showed that imbalances occur frequently. High concentrations of ammonia or long chain fatty acids is in most cases expected to be the cause of microbial inhibitions/imbalances while foaming in the prestorage tanks and digesters is the most important practical process problem at the plants. A correlation between increased residual biogas production (suboptimal process conditions) and high fractions of industrial waste in the feedstock was also observed. The process imbalances and suboptimal conditions are mainly allowed to occur due to 1) inadequate knowledge about the waste composition, 2) inadequate knowledge about the waste degradation characteristics, 3) inadequate process surveillance, especially with regard to volatile fatty acids, and 4) insufficient pre-storage capacity causing inexpedient mixing and hindering exact dosing of the different waste products.
Linear programming analysis of VA/Q distributions: limits on central moments.
Kapitan, K S; Wagner, P D
1986-05-01
Linear programming examines the boundaries of infinite sets. We used this method with the multiple-inert gas-elimination technique to examine the central moments and arterial blood gases of the infinite family of ventilation perfusion (VA/Q) distributions that are compatible with a measured inert gas-retention set. A linear program was applied with Monte-Carlo error simulation to theoretical retention data, and 95% confidence intervals were constructed for the first three moments (mean, dispersion, and skew) and the arterial PO2 and PCO2 of all compatible blood flow distributions. Six typical cases were studied. Results demonstrate narrow confidence intervals for both the lower moments and predicted arterial blood gases of all test cases, which widen as moment number or error increase. We conclude that the blood gas composition and basic structure of all compatible VA/Q distributions are tightly constrained and that even subtle changes in this structure, as may occur experimentally, can be identified.
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.
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.
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.)
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…
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.}
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,…
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.
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 +
Restriction limits and main drivers of fruit production in palm in central Amazonia
NASA Astrophysics Data System (ADS)
Freitas, Cintia; Costa, Flávia R. C.; Barbosa, Carlos Eduardo; Cintra, Renato
2016-11-01
Adult plants incapable of producing viable offspring inflate our perception of the size of population distribution. We propose that species occurrence is limited to a subset of the environmental gradient and that it changes as ontogenetic development progresses. Moreover, fruit production is associated with site-specific environmental conditions. We sampled 2988 adult individuals from nine palm species in 30 plots (40 × 250 m) and used a larger data set including 42 other plots distributed along a continuous topo-edaphic gradient in a terra firme forest near Manaus, Brazil. Five out of nine palm species were more restricted to a sub-section of the topo-edaphic gradient in the adult-size phase. More specifically, reproductive individuals of species Attalea attaleoides and A. microcarpa had even more restricted distributions than adult-sized, non-reproductive plants. Successive environmental filtering and competition probably acting through selective mortality led to increasing habitat restriction, with reproductive adults being restricted to a smaller part of the region than juveniles and adults. Water availability and nutrients limited both the ability to produce fruits and the amount of fruit production. Previous studies have reported stronger habitat associations for older plants than for seedlings or juveniles, but we show here that some species are more restricted at their reproductive stage. Plant specializations to local conditions may be more common than currently acknowledged, and a significant portion of individuals in a population might represent sinks. Such strong environmental limitations of reproductive plants should also be considered in management of species with economic value and in conservation planning.
Fluctuation theorem and mesoscopic chemical clocks.
Andrieux, David; Gaspard, Pierre
2008-04-21
The fluctuation theorems for dissipation and the currents are applied to the stochastic version of the reversible Brusselator model of nonequilibrium oscillating reactions. It is verified that the symmetry of these theorems holds far from equilibrium in the regimes of noisy oscillations. Moreover, the fluctuation theorem for the currents is also verified for a truncated Brusselator model. PMID:18433234
Fluctuation theorem and mesoscopic chemical clocks
NASA Astrophysics Data System (ADS)
Andrieux, David; Gaspard, Pierre
2008-04-01
The fluctuation theorems for dissipation and the currents are applied to the stochastic version of the reversible Brusselator model of nonequilibrium oscillating reactions. It is verified that the symmetry of these theorems holds far from equilibrium in the regimes of noisy oscillations. Moreover, the fluctuation theorem for the currents is also verified for a truncated Brusselator model.
Investigating the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Johnson, Heather L.
2010-01-01
The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were…
A Fundamental Theorem on Particle Acceleration
Xie, Ming
2003-05-01
A fundamental theorem on particle acceleration is derived from the reciprocity principle of electromagnetism and a rigorous proof of the theorem is presented. The theorem establishes a relation between acceleration and radiation, which is particularly useful for insightful understanding of and practical calculation about the first order acceleration in which energy gain of the accelerated particle is linearly proportional to the accelerating field.
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…
Limit Theory for Panel Data Models with Cross Sectional Dependence and Sequential Exogeneity.
Kuersteiner, Guido M; Prucha, Ingmar R
2013-06-01
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.
Level reduction and the quantum threshold theorem
NASA Astrophysics Data System (ADS)
Aliferis, Panagiotis (Panos)
Computers have led society to the information age revolutionizing central aspects of our lives from production and communication to education and entertainment. There exist, however, important problems which are intractable with the computers available today and, experience teaches us, will remain so even with the more advanced computers we can envision for tomorrow.Quantum computers promise speedups to some of these important but classically intractable problems. Simulating physical systems, a problem of interest in a diverse range of areas from testing physical theories to understanding chemical reactions, and solving number factoring, a problem at the basis of cryptographic protocols that are used widely today on the internet, are examples of applications for which quantum computers, when built, will offer a great advantage over what is possible with classical computer technology.The construction of a quantum computer of sufficient scale to solve interesting problems is, however, especially challenging. The reason for this is that, by its very nature, operating a quantum computer will require the coherent control of the quantum state of a very large number of particles. Fortunately, the theory of quantum error correction and fault-tolerant quantum computation gives us confidence that such quantum states can be created, can be stored in memory and can also be manipulated provided the quantum computer can be isolated to a sufficient degree from sources of noise.One of the central results in the theory of fault-tolerant quantum computation, the quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum accuracy threshold. This thesis provides a simpler and more transparent non-inductive proof of this theorem based on the concept of level reduction. This concept is also used in proving the
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
Carbon balance indicates a time limit for cultivation of organic soils in central Switzerland
NASA Astrophysics Data System (ADS)
Paul, Sonja; Ammann, Christof; Alewell, Christine; Leifeld, Jens
2016-04-01
Peatlands serve as important carbon sinks. Globally, more than 30% of the soil organic carbon is stored in organic soils, although they cover only 3% of the land surface. The agricultural use of organic soils usually requires drainage thereby transforming these soils from a net carbon sink into a net source. Currently, about 2 to 3 Gt CO2 are emitted world-wide from degrading organic soils (Joosten 2011; Parish et al. 2008) which is ca. 5% of the total anthropogenic emissions. Besides these CO2 emissions, the resulting subsidence of drained peat soils during agricultural use requires that drainage system are periodically renewed and finally to use pumping systems after progressive subsidence. In Switzerland, the Seeland region is characterised by fens which are intensively used for agriculture since 1900. The organic layer is degrading and subsequently getting shallower and the underlying mineral soil, as lake marl or loam, is approaching the surface. The questions arises for how long and under which land use practises and costs these soils can be cultivated in the near future. The study site was under crop rotation until 2009 when it was converted to extensively used grassland with the water regime still being regulated. The soil is characterised by a degraded organic horizon of 40 to 70 cm. Since December 2014 we are measuring the carbon exchange of this grassland using the Eddy-Covariance method. For 2015, the carbon balance indicates that the degraded fen is a strong carbon source, with approximately 500 g C m-2 a-1. The carbon balance is dominated by CO2 emissions and harvest. Methane emissions are negligible. With the gained emission factors different future scenarios are evaluated for the current cultivation practise of organic soils in central Switzerland. Joosten, H., 2011: Neues Geld aus alten Mooren: Über die Erzeugung von Kohlenstoffzertifikaten aus Moorwiedervernässungen. Telma Beiheft 4, 183-202. Parish, F., A. Sirin, D. Charman, H. Joosten, T
Limitations of selective deltamethrin application for triatomine control in central coastal Ecuador
2011-01-01
Background This year-long study evaluated the effectiveness of a strategy involving selective deltamethrin spraying and community education for control of Chagas disease vectors in domestic units located in rural communities of coastal Ecuador. Results Surveys for triatomines revealed peridomestic infestation with Rhodnius ecuadoriensis and Panstrongylus howardi, with infestation indices remaining high during the study (13%, 17%, and 10%, at initial, 6-month, and 12-month visits, respectively), which indicates a limitation of this strategy for triatomine population control. Infestation was found 6 and 12 months after spraying with deltamethrin. In addition, a large number of previously vector-free domestic units also were found infested at the 6- and 12-month surveys, which indicates new infestations by sylvatic triatomines. The predominance of young nymphs and adults suggests new infestation events, likely from sylvatic foci. In addition, infection with Trypanosoma cruzi was found in 65%, 21% and 29% at initial, 6-month and 12-month visits, respectively. All parasites isolated (n = 20) were identified as TcI. Conclusion New vector control strategies need to be devised and evaluated for reduction of T. cruzi transmission in this region. PMID:21332985
Generalized Bloch theorem and chiral transport phenomena
NASA Astrophysics Data System (ADS)
Yamamoto, Naoki
2015-10-01
Bloch theorem states the impossibility of persistent electric currents in the ground state of nonrelativistic fermion systems. We extend this theorem to generic systems based on the gauged particle number symmetry and study its consequences on the example of chiral transport phenomena. We show that the chiral magnetic effect can be understood as a generalization of the Bloch theorem to a nonequilibrium steady state, similarly to the integer quantum Hall effect. On the other hand, persistent axial currents are not prohibited by the Bloch theorem and they can be regarded as Pauli paramagnetism of relativistic matter. An application of the generalized Bloch theorem to quantum time crystals is also discussed.
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.
Nonuniqueness of optical theorem detectors.
Marengo, Edwin A
2015-11-01
We demonstrate and discuss the multitude of ways in which the extinct power of a scatterer can be measured. To tie some of the developed results to the classical statement of the optical theorem involving the imaginary part of the forward-scattering amplitude, particular attention is given to plane wave excitation. On the other hand, the general results apply to more general probing fields including near fields carrying evanescent components. Novel optical theorem detectors are derived that are based on the Kirchhoff-Helmholtz and Rayleigh-Sommerfeld-based formulations of diffraction, backpropagation, and boundary-value problems as well as on the canonical multipole expansion. The derived detectors also lead to novel expressions for the extinct power in terms of the incident and scattered fields. Applications of the derived results to scattering power sensing with near-field data are also discussed.
NASA Astrophysics Data System (ADS)
Leibovich, N.; Barkai, E.
2015-08-01
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 )⟩˜tγϕEA(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 ϕEA(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.
Pythagoras Theorem and Relativistic Kinematics
NASA Astrophysics Data System (ADS)
Mulaj, Zenun; Dhoqina, Polikron
2010-01-01
In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.
A Miniaturisation of Ramsey's Theorem
NASA Astrophysics Data System (ADS)
de Smet, Michiel; Weiermann, Andreas
We approximate the strength of the infinite Ramsey Theorem by iterating a finitary version. This density principle, in the style of Paris, together with PA will give rise to a first-order theory which achieves a lot of the strength of ACA0 and the original infinitary version. To prove our result, we use a generalisation of the results by Bigorajska and Kotlarski about partitioning α-large sets.
Uniqueness Theorem for Black Objects
Rogatko, Marek
2010-06-23
We shall review the current status of uniqueness theorem for black objects in higher dimensional spacetime. At the beginning we consider static charged asymptotically flat spacelike hypersurface with compact interior with both degenerate and non-degenerate components of the event horizon in n-dimensional spacetime. We gave some remarks concerning partial results in proving uniqueness of stationary axisymmetric multidimensional solutions and winding numbers which can uniquely characterize the topology and symmetry structure of black objects.
A global conformal extension theorem for perfect fluid Bianchi space-times
Luebbe, Christian Tod, Paul
2008-12-15
A global extension theorem is established for isotropic singularities in polytropic perfect fluid Bianchi space-times. When an extension is possible, the limiting behaviour of the physical space-time near the singularity is analysed.
Isothermal-sweep theorems for ultracold quantum gases in a canonical ensemble
Iskin, M.
2011-03-15
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.
The Helmholtz theorem and retarded fields
NASA Astrophysics Data System (ADS)
Heras, Ricardo
2016-11-01
Textbooks frequently use the Helmholtz theorem to derive expressions for electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for time-dependent electric and magnetic fields, even when there is no formal objection to doing so because the proof of the theorem does not involve time derivatives but only spatial derivatives. Here we address the question as to whether the Helmholtz theorem is useful in deriving expressions for the fields of Maxwell’s equations. We show that when this theorem is applied to Maxwell’s equations we obtain instantaneous expressions of the electric and magnetic fields, which are formally correct but of little practical usefulness. We then discuss two generalizations of the theorem which are shown to be useful in deriving the retarded fields.
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.
Cosmological perturbations and the Weinberg theorem
Akhshik, Mohammad; Firouzjahi, Hassan; Jazayeri, Sadra E-mail: firouz@ipm.ir
2015-12-01
The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.
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.
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.
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.
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.
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
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.
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…
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.
TAUBERIAN THEOREMS FOR MATRIX REGULAR VARIATION.
Meerschaert, M M; Scheffler, H-P
2013-04-01
Karamata's Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated.
TAUBERIAN THEOREMS FOR MATRIX REGULAR VARIATION
MEERSCHAERT, M. M.; SCHEFFLER, H.-P.
2013-01-01
Karamata’s Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated. PMID:24644367
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)
A drop theorem without vector topology
NASA Astrophysics Data System (ADS)
Wong, Chi-Wing
2007-05-01
Danes' drop theorem is extended to bornological vector spaces. An immediate application is to establish Ekeland-type variational principle and its equivalence, Caristi fixed point theorem, in bornological vector spaces. Meanwhile, since every locally convex space becomes a convex bornological vector space when equipped with the canonical von Neumann bornology, Qiu's generalization of Danes' work to locally convex spaces is recovered.
Euler and the Fundamental Theorem of Algebra.
ERIC Educational Resources Information Center
Duham, William
1991-01-01
The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)
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 Euler Line and Nine-Point-Circle Theorems.
ERIC Educational Resources Information Center
Eccles, Frank M.
1999-01-01
Introduces the Euler line theorem and the nine-point-circle theorem which emphasize transformations and the power of functions in a geometric concept. Presents definitions and proofs of theorems. (ASK)
Gleason's Theorem for Rectangular JBW-Triples
NASA Astrophysics Data System (ADS)
Edwards, C. Martin; Rüttimann, Gottfried T.
A JBW*-triple B is said to be rectangular if there exists a W*-algebra A and a pair (p,q) of centrally equivalent elements of the complete orthomodular lattice of projections in A such that B is isomorphic to the JBW*-triple pAq. Any weak*-closed injective operator space provides an example of a rectangular JBW*-triple. The principal order ideal of the complete *-lattice of centrally equivalent pairs of projections in a W*-algebra A, generated by (p,q), forms a complete lattice that is order isomorphic to the complete lattice of weak*-closed inner ideals in B and to the complete lattice of structural projections on B. Although not itself, in general, orthomodular, possesses a complementation that allows for definitions of orthogonality, centre, and central orthogonality to be given. A less familiar notion in lattice theory, that is well-known in the theory of Jordan algebras and Jordan triple systems, is that of rigid collinearity of a pair (e2,f2) and (e2,f2) of elements of . This is defined and characterized in terms of properties of . A W*-algebra A is sometimes thought of as providing a model for a statistical physical system. In this case B, or, equivalently, pAq, may be thought of as providing a model for a fixed sub-system of that represented by A. Therefore, may be considered to represent the set consisting of a particular kind of sub-system of that represented by pAq. Central orthogonality and rigid collinearity of pairs of elements of may be regarded as representing two different types of disjointness, the former, classical disjointness, and the latter, decoherence, of the two sub-systems. It is therefore natural to consider bounded measures m on that are additive on centrally orthogonal and rigidly collinear pairs of elements. Using results of J.D.M. Wright, it is shown that, provided that neither of the two hereditary sub-W*-algebras pAp and qAq of A has a weak*-closed ideal of Type I2, such measures are precisely those that are the restrictions of
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
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.
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.
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.
The Scope and Generality of Bell's Theorem
NASA Astrophysics Data System (ADS)
Weatherall, James Owen
2013-09-01
I present what might seem to be a local, deterministic model of the EPR-Bohm experiment, inspired by recent work by Joy Christian, that appears at first blush to be in tension with Bell-type theorems. I argue that the model ultimately fails to do what a hidden variable theory needs to do, but that it is interesting nonetheless because the way it fails helps clarify the scope and generality of Bell-type theorems. I formulate and prove a minor proposition that makes explicit how Bell-type theorems rule out models of the sort I describe here.
Magnetic Corrections to the Soft Photon Theorem.
Strominger, Andrew
2016-01-22
The soft photon theorem, in its standard form, requires corrections when the asymptotic particle states carry magnetic charges. These corrections are deduced using electromagnetic duality and the resulting soft formula conjectured to be exact for all Abelian gauge theories. Recent work has shown that the standard soft theorem implies an infinity of conserved electric charges. The associated symmetries are identified as "large" electric gauge transformations. Here the magnetic corrections to the soft theorem are shown to imply a second infinity of conserved magnetic charges. The associated symmetries are identified as large magnetic gauge transformations. The large magnetic symmetries are naturally subsumed in a complexification of the electric ones. PMID:26849586
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…
There is No Quantum Regression Theorem
Ford, G.W.; OConnell, R.F.
1996-07-01
The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem. {copyright} {ital 1996 The American Physical Society.}
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.
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.
Jebsen-Birkhoff theorem in alternative gravity
Faraoni, Valerio
2010-02-15
We discuss the validity, or lack thereof, of the Jebsen-Birkhoff theorem in scalar-tensor theories by generalizing it and regarding the Brans-Dicke-like scalar as effective matter. Both the Jordan and Einstein frames are discussed and an apparent contradiction between static spherical solutions of scalar-tensor gravity and Hawking's theorem on Brans-Dicke black holes is clarified. The results are applied to metric and Palatini f(R) gravity.
Generalization of Luttinger's Theorem for Fermionic Ladder Systems
NASA Astrophysics Data System (ADS)
Gagliardini, P.; Haas, S.; Rice, T. M.; Sigrist, M.
1998-03-01
Recently Yamanaka et al.(M. Yamanaka, M. Oshikawa, and I. Affleck, PRL 79), 1110 (1997). adapted the Lieb-Schultz-Mattis theorem to obtain a non-perturbative generalization of Luttinger's theorem for 1-dim. fermionic systems. Their method can be extended to ladder systems. The key quantity which enters in a Hubbard or t-J model is the sum of the electron occupation numbers on a rung. At half-filling, this leads at once to a proof that undoped Heisenberg ladders have gapless excitations when the number of legs is odd. Upon doping, the Fermi wavevectors of individual channels are not conserved under interaction, but their sum is. This result does not require a Fermi surface in each channel and is consistent with the recently proposed assignment of 1 el. per rung to gapped insulating even-parity channels, and 1-δ els. to a Luttinger liquid in the odd-parity channel in a lightly doped 3-leg ladder (δ: hole doping). The crossover to 2 dim. occurs in the limit of a large number of legs, and it is the area enclosed by the Fermi surface which enters, consistent with Luttinger's theorem for the case of Landau Fermi liquids.
NASA Astrophysics Data System (ADS)
Baltin, R.
1988-06-01
The differential force law (DFL) and related integral theorems, derived in a previous paper for general geometries, are applied to spherical systems of identical interacting particles, e.g., electrons. From the special functional form of the first-order density matrix, induced solely by symmetry, the DFL occurs as a scalar, pointwise equation relating radial and rotational parts, trad and trot, of the kinetic energy density t to the force density f and to derivatives of the particle density n. Furthermore, an exact connection between the pressure p, trad, and n is established. Finally some theorems are derived which relate integrals, extending over an arbitrary concentric part of the system and involving t, p, and f, to values of p, n, and n' at the surface of the sphere with radius R. One of these theorems is a generalized virial theorem tending to the usual well-known virial theorem in the limit R→∞.
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.
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
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.
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.
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.
Dai-Freed theorem and topological phases of matter
NASA Astrophysics Data System (ADS)
Yonekura, Kazuya
2016-09-01
We describe a physics derivation of theorems due to Dai and Freed about the Atiyah-Patodi-Singer eta-invariant which is important for anomalies and topological phases of matter. This is done by studying a massive fermion. The key role is played by the wave function of the ground state in the Hilbert space of the fermion in the large mass limit. The ground state takes values in the determinant line bundle and has nontrivial Berry phases which characterize the low energy topological phases.
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
Anti-Bell - Refutation of Bell's theorem
NASA Astrophysics Data System (ADS)
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
Generalized fluctuation theorems for classical systems
NASA Astrophysics Data System (ADS)
Agarwal, G. S.; Dattagupta, Sushanta
2015-11-01
The fluctuation theorem has a very special place in the study of nonequilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen fluctuation theorem which is in terms of the distribution of the work p (W )/p (-W )=exp(α W ) . We derive the general form of the fluctuation theorems for an arbitrary multidimensional Gaussian Markov process. Interestingly, the parameter α is by no means universal, hitherto taken for granted in the case of linear Gaussian processes. As a matter of fact, conditions under which α does become a universal parameter 1 /K T are found to be rather restrictive. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is nontrivial. The generalized theorems are equally valid for nonequilibrium steady states and could be especially important in the presence of anisotropic diffusion.
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.
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
Generalizations of the abstract boundary singularity theorem
NASA Astrophysics Data System (ADS)
Whale, Ben E.; Ashley, Michael J. S. L.; Scott, Susan M.
2015-07-01
The abstract boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of abstract boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from C1 curves to locally Lipschitz curves.
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.
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.
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
An invariance theorem in acoustic scattering theory
NASA Astrophysics Data System (ADS)
Ha-Duong, T.
1996-10-01
Karp's theorem states that if the far-field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle is invariant under the group of orthogonal transformations in 0266-5611/12/5/007/img1 (rotations in 0266-5611/12/5/007/img2), then the scatterer is a sphere (circle). The theorem is generalized to the case where the invariant group of the far field pattern is only a subgroup of the orthogonal group, and for a class of mixed boundary conditions.
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.
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.
The flux-summation theorem and the 'evolution of dominance'.
Agutter, Paul S
2008-10-21
The flux-summation theorem (FST) is a central principle of metabolic control analysis. It describes how the control of flux through any metabolic pathway of arbitrary complexity is distributed among the component reaction steps. Two issues concerning the FST are discussed in this paper. First, it has been suggested that the theorem could, in principle, be inapplicable under certain conditions, i.e. the sum of the control coefficients of all the enzymes supporting a pathway could exceed unity. Such conditions have not been found in any species so far studied, so in practice the FST is always applicable. I argue that applicability of the FST is a precondition for phenotypic robustness and therefore for survival. Second, the FST provides a basis for explaining dominance that renders Fisher's 'modifier genes' hypothesis otiose. Some recent misunderstandings of metabolic control analysis have led to the claim that this explanation is flawed and therefore that Fisher's hypothesis can and should be reinstated. Here, these suggestions are refuted.
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.
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).
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.
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.
Answering Junior Ant's "Why" for Pythagoras' Theorem
ERIC Educational Resources Information Center
Pask, Colin
2002-01-01
A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…
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.
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…
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)
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…
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.
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)
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…
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.
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.
Codimension- p Paley-Wiener theorems
NASA Astrophysics Data System (ADS)
Yang, Yan; Qian, Tao; Sommen, Frank
2007-04-01
We obtain the generalized codimension- p Cauchy-Kovalevsky extension of the exponential function e^{i
Reflection theorem for Lorentz-Minkowski spaces
NASA Astrophysics Data System (ADS)
Lee, Nam-Hoon
2016-07-01
We generalize the reflection theorem of the Lorentz-Minkowski plane to that of the Lorentz-Minkowski spaces of higher dimensions. As a result, we show that an isometry of the Lorentz-Minkowski spacetime is a composition of at most 5 reflections.
Local completeness, drop theorem and Ekeland's variational principle
NASA Astrophysics Data System (ADS)
Qiu, Jing-Hui
2005-11-01
By using a very general drop theorem in locally convex spaces we obtain some extended versions of Ekeland's variational principle, which only need assume local completeness of some related sets and improve Hamel's recent results. From this, we derive some new versions of Caristi's fixed points theorems. In the framework of locally convex spaces, we prove that Danes' drop theorem, Ekeland's variational principle, Caristi's fixed points theorem and Phelps lemma are equivalent to each other.
Uniqueness theorem for stationary axisymmetric black holes in Einstein-Maxwell-axion-dilaton gravity
Rogatko, Marek
2010-08-15
We prove the uniqueness theorem for the stationary axisymmetric black hole solution in Einstein-Maxwell-axion-dilaton gravity being the low-energy limit of the heterotic string theory. We consider both the nonextremal and extremal Kerr-Sen black hole solutions.
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
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
Baur, Hannes
2015-01-01
Two new species, Pteromalusbriani sp. n. and Pteromalusjanstai sp. n., with unusual characters are described from the Central Plateau and the Alps in Switzerland, respectively. Pteromalusbriani sp. n. is remarkable in that it has the metatibia quite abruptly expanded before the middle. This type of modification of the hind tibia is unique within the Pteromalidae and probably also the entire Chalcidoidea. It is also very rare in other parasitic wasps, where it is suspected to be associated with pheromone glands. The species is a gregarious endoparasitoid of pupae of Vanessaatalanta (Linnaeus) and Aglaisurticae (Linnaeus), two common butterflies (Lepidoptera: Nymphalidae) in Europe. It is furthermore a koinobiont parasitoid ovipositing in an early larval stage of the host. The other species, Pteromalusjanstai sp. n., shows a flattened mesosoma. A dorsoventrally depressed body is a unique feature within the genus Pteromalus, but known from a number species in unrelated genera and subfamilies. The two records demonstrate that it is possible to discover entirely new species with extraordinary characters even in one of the taxonomically most thoroughly explored parts of the world.
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).
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.
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
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.
NASA Astrophysics Data System (ADS)
Thomas, R. Q.; Kellner, J. R.; Peart, D. R.
2005-12-01
Logistical constraints on sample size and spatial scale limit individual-based field research on tropical trees. With remote sensing data, we may escape these limitations if fates of individuals can be tracked rigorously. We assessed the potential of readily available, commercial satellite data (QuickBird, 0.7 m pixels) obtained in 2003, to track the fate of individual crowns (> 40 m height) in tropical rain forest at La Selva, Costa Rica. The positions and shapes of these crowns in 1997 had been established using small-footprint LiDAR data with field verification. We focused first on a subset (n=180) of trees monitored in the field over the period 1997-2003. For the 60% of those trees whose crown positions and shapes could be tracked with confidence in the satellite image, we correctly recorded all 3 actual deaths. But we also incorrectly assigned 4 additional deaths to living individuals, due to the abundance of dark pixels in their crown areas. For the 40% of field-monitored trees for which our tracking in the satellite data was less confident (due to lack of image clarity), we correctly identified the one real death event, but incorrectly assigned 6 additional deaths to living trees. Thus, for the field-monitored trees, we grossly overestimated mortality in the satellite image (by 350%). Although currently available high resolution satellite imagery was not adequate for reliable monitoring of individuals, even for the largest forest trees, time series satellite data, rather than time series LiDAR to satellite data, might provide unbiased estimates of overall tree mortality rates if errors compensate. Satellite data may be also be useful as a labor and time saving complement to fieldwork on individual forest trees.
Leligdowicz, Aleksandra; Katwere, Michael; Piloya, Theresa; Ronald, Allan; Kambugu, Andrew; Katabira, Elly
2006-01-01
Central Nervous System (CNS) infections are associated with significant mortality and morbidity. Accurate diagnosis is necessary for prompt treatment and increased chances of survival. However, there are many challenges to correct diagnoses in resource-limited settings, including the HIV epidemic, late presentation of symptomatic individuals, limited availability of laboratory diagnostic tests as well as treatment, and inadequate access to funds accompanied by lack of financial support from developed countries. This article presents case reports of patients admitted to the Mulago Hospital in Kampala, Uganda that exemplify challenging diagnoses of tuberculous meningitis (TBM), cryptococcal meningitis (CM), toxoplasmosis, and primary CNS lymphoma (PCNSL). Also included is a literature review of the pathology, diagnosis, and treatment of TBM, CM, toxoplasmosis, and PCNSL in immunocompromised patients. PMID:19529809
Bailey, David H.; Misiurewicz, Michal
2005-12-31
A real number alpha is said to be b-normal if every m-long string of digits appears in the base-b expansion of alpha with limiting frequency b-m. We prove that alpha is b-normal if and only if it possesses no base-b ''hot spot''. In other words, alpha is b-normal if and only if there is no real number y such that smaller and smaller neighborhoods of y are visited by the successive shifts of the base-b expansion of alpha with larger and larger frequencies, relative to the lengths of these neighborhoods
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.
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.
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 Θ+ and Ξ--Pentaquarks in 920-GeV pA Collisions
NASA Astrophysics Data System (ADS)
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.; Gorišek, 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.; Križan, 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.; 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.; Starič, 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.; Živko, T.; Zoccoli, A.
2004-11-01
We have searched for Θ+(1540) and Ξ--(1862) pentaquark candidates in proton-induced reactions on C, Ti, and W targets at midrapidity and √(s)=41.6 GeV. In 2×108 inelastic events we find no evidence for narrow (σ≈5 MeV) signals in the Θ+→pK0S and Ξ--→Ξ-π- channels; our 95% C.L. upper limits (UL) for the inclusive production cross section times branching fraction B dσ/dy|y≈0 are (4 16)μb/N for a Θ+ mass between 1521 and 1555MeV, and 2.5μb/N for the Ξ--. The UL of the yield ratio of Θ+/Λ(1520)<(3 12)% is significantly lower than model predictions. Our UL of B Ξ--/Ξ(1530)0<4% is at variance with the results that have provided the first evidence for the Ξ--.
A generalization of averaging theorems for porous medium analysis
NASA Astrophysics Data System (ADS)
Gray, William G.; Miller, Cass T.
2013-12-01
The contributions of Stephen Whitaker to the rigorous analysis of porous medium flow and transport are built on the use of temporal and spatial averaging theorems applied to phases in representative elementary volumes. Here, these theorems are revisited, common point theorems are considered, extensions of existing theorems are developed to include the effects of lower dimensional entities represented as singularities, and a unified form of the theorems for phases, interfaces, common curves, and common points is established for both macroscale and mixed macroscale-megascale systems. The availability of the full set of theorems facilitates detailed analysis of a variety of porous medium systems. Explicit modeling of the physical processes associated with interfaces, common curves, and common points, as well as the kinematics of these entities, can be undertaken at both the macroscale and megascale based on these theorems.
NASA Astrophysics Data System (ADS)
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-09-01
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.
The Bjerknes' Circulation Theorem: A Historical Perspective.
NASA Astrophysics Data System (ADS)
Thorpe, Alan J.; Volkert, Hans; Ziemianski, Micha J.
2003-04-01
Two lines of thinking concerning fluid rotation-using either vorticity or circulation-emerged from the nineteenth-century work of Helmholtz and Thomson (Lord Kelvin), respectively. Vilhelm Bjerknes introduced an extension of Kelvin's ideas on circulation into geophysics. In this essay a historical perspective will be given on what has become known as the "Bjerknes circulation theorem." Bjerknes wrote several papers on this topic, the first being in 1898. As Bjerknes noted, a Polish physicist, Ludwik Silberstein, had previously published an equivalent result concerning vorticity generation in 1896. Silberstein's work had built on an earlier paper by J. R. Schütz in 1895. In his 1898 paper Bjerknes describes many possible applications of the theorem to meteorology and oceanography including to extratropical cyclones, a subject that made his "Bergen School" famous.
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.
Locomotion in complex fluids: Integral theorems
NASA Astrophysics Data System (ADS)
Lauga, Eric
2014-08-01
The biological fluids encountered by self-propelled cells display complex microstructures and rheology. We consider here the general problem of low-Reynolds number locomotion in a complex fluid. Building on classical work on the transport of particles in viscoelastic fluids, we demonstrate how to mathematically derive three integral theorems relating the arbitrary motion of an isolated organism to its swimming kinematics in a non-Newtonian fluid. These theorems correspond to three situations of interest, namely, (1) squirming motion in a linear viscoelastic fluid, (2) arbitrary surface deformation in a weakly non-Newtonian fluid, and (3) small-amplitude deformation in an arbitrarily non-Newtonian fluid. Our final results, valid for a wide-class of swimmer geometry, surface kinematics, and constitutive models, at most require mathematical knowledge of a series of Newtonian flow problems, and will be useful to quantity the locomotion of biological and synthetic swimmers in complex environments.
A Geometrical Approach to Bell's Theorem
NASA Technical Reports Server (NTRS)
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-01-01
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
Thermodynamics of biochemical networks and duality theorems
NASA Astrophysics Data System (ADS)
De Martino, Daniele
2013-05-01
One interesting yet difficult computational issue has recently been posed in biophysics in regard to the implementation of thermodynamic constraints to complex networks. Biochemical networks of enzymes inside cells are among the most efficient, robust, differentiated, and flexible free-energy transducers in nature. How is the second law of thermodynamics encoded for these complex networks? In this article it is demonstrated that for chemical reaction networks in the steady state the exclusion (presence) of closed reaction cycles makes possible (impossible) the definition of a chemical potential vector. Interestingly, this statement is encoded in one of the key results in combinatorial optimization, i.e., the Gordan theorem of the alternatives. From a computational viewpoint, the theorem reveals that calculating a reaction's free energy and identifying infeasible loops in flux states are dual problems whose solutions are mutually exclusive, and this opens the way for efficient and scalable methods to perform the energy balance analysis of large-scale biochemical networks.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
Volume integral theorem for exotic matter
Nandi, Kamal Kanti; Zhang Yuanzhong; Kumar, K.B. Vijaya
2004-12-15
We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well-known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
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.
Amann, Markus; Dempsey, Jerome A
2016-01-01
We recently hypothesized that across the range of normoxia to severe hypoxia the major determinant of central motor drive (CMD) during endurance exercise switches from a predominantly peripheral origin to a hypoxic-sensitive central component of fatigue. We found that peripheral locomotor muscle fatigue (pLMF) is the prevailing factor limiting central motor drive and therefore exercise performance from normoxia to moderate hypoxia (SaO2 > 75 %). In these levels of arterial hypoxemia, the development of pLMF is confined to a certain limit which varies between humans-pLMF does not develop to this limit in more severe hypoxia (SaO2 < 70 %) and exercise is prematurely terminated presumably to protect the brain from insufficient O2 supply. Based on the observations from normoxia to moderate hypoxia, we outlined a model suggesting that group III/IV muscle afferents impose inhibitory influences on the determination of CMD of working humans during high-intensity endurance exercise with the purpose to regulate and restrict the level of exercise-induced pLMF to an "individual critical threshold." To experimentally test this model, we pharmacologically blocked somatosensory pathways originating in the working limbs during cycling exercise in normoxia. After initial difficulties with a local anesthetic (epidural lidocaine, L3-L4) and associated loss of locomotor muscle strength we switched to an intrathecally applied opioid analgesic (fentanyl, L3-L4). These experiments were the first ever to selectively block locomotor muscle afferents during high-intensity cycling exercise without affecting maximal locomotor muscle strength. In the absence of opioid-mediated neural feedback from the working limbs, CMD was increased and end-exercise pLMF substantially exceeded, for the first time, the individual critical threshold of peripheral fatigue. The outcome of these studies confirm our hypothesis claiming that afferent feedback inhibits CMD and restricts the development of
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.
3D Image Reconstructions and the Nyquist-Shannon Theorem
NASA Astrophysics Data System (ADS)
Ficker, T.; Martišek, D.
2015-09-01
Fracture surfaces are occasionally modelled by Fourier's two-dimensional series that can be converted into digital 3D reliefs mapping the morphology of solid surfaces. Such digital replicas may suffer from various artefacts when processed inconveniently. Spatial aliasing is one of those artefacts that may devalue Fourier's replicas. According to the Nyquist-Shannon sampling theorem the spatial aliasing occurs when Fourier's frequencies exceed the Nyquist critical frequency. In the present paper it is shown that the Nyquist frequency is not the only critical limit determining aliasing artefacts but there are some other frequencies that intensify aliasing phenomena and form an infinite set of points at which numerical results abruptly and dramatically change their values. This unusual type of spatial aliasing is explored and some consequences for 3D computer reconstructions are presented.
Madey's theorems for free-electron devices, spontaneous emission, and applications
NASA Astrophysics Data System (ADS)
Becker, W.; McIver, J. K.
1988-12-01
Two theorems due to Madey occupy a central position in free-electron laser physics: one relates the gain to the derivative of the spontaneous emission line shape and the other one relates it to the derivative of the electron energy spread in stimulated emission. We use quantum mechanical perturbation thoery of first order in the radiation field to give a general derivation of the theorems based on (a) the hermiticity of the electronfield interaction, (b) the applicability of lowest order perturbation theory, and (c) the assumption that the emitted photon have a sufficiently low energy. Assumption (b) restricts the validity of the theorems to the small-signal weak-field regime, (c) to the small recoil regime where the gain is classical. We use scalar quantum electrodynamics in the Furry picture in order to keep effects which are nonlinear in the undulator field, e.g. higher harmonic emission. We consider a fairly general one-dimensional (i.e. not having transverse variations) monochromatic undulator field (magnetic or optical undulator, linear or circular polarization, possible presence of a diffractive medium). An appendix considers nonmonochromatic fields. We derive explicit results for the linearly polarized and the helical undulator allowing for an arbitrary orientation of the undulator axis, the electron beam and the emitted radiation with respect to each other. In particular, we discuss the case of Gaussian modes where the applicability of the first theorem has been questioned. It turns out that the theorem is applicable provided that spontaneous emission into the Gaussian mode in question is considered (more generally, into whatever mode is of interest for the gain).
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.
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'.
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)…
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
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.
Stochastic thermodynamics, fluctuation theorems and molecular machines.
Seifert, Udo
2012-12-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
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.
Generalizations of Brandl's theorem on Engel length
NASA Astrophysics Data System (ADS)
Quek, S. G.; Wong, K. B.; Wong, P. C.
2013-04-01
Let n < m be positive integers such that [g,nh] = [g,mh] and assume that n and m are chosen minimal with respect to this property. Let gi = [g,n+ih] where i = 1,2,…,m-n. Then π(g,h) = (g1,…,gm-n) is called the Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.
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
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.``
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.
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.
AdS/BCFT correspondence, holographic g-theorem and Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Najian, Bahman
2014-09-01
We investigate some aspects of holographic dual of boundary conformal field theories for higher derivative Gauss-Bonnet (GB) gravity. We explore the holographic g-theorem for GB gravity and introduce holographic g-functions in five and six dimensions. Focusing on the coefficients of the logarithmic terms in the partition functions of BCFTs holographically, and in the presence of higher derivative terms, in even dimensions we show that these are associated with corrected A-type trace anomaly. Building on this, in odd dimensions, we present supporting evidence for monotonicity property of boundary central charge in BCFT5 in Einstein gravity. However, in the GB gravity case, we find that the monotonicity behavior is violated. This invalidates the holographic g-theorem for the GB gravity.
Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics
NASA Astrophysics Data System (ADS)
Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.
2008-11-01
In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.
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.
Flores, Noemí; Olvera, Maricela; Sigala, Juan Carlos; Gosset, Guillermo; Morett, Enrique; Bolívar, Francisco
2009-01-01
The phosphoenolpyruvate: carbohydrate transferase system (PTS) transports glucose in Escherichia coli. Previous work demonstrated that strains lacking PTS, such as PB11, grow slow on glucose. PB11 has a reduced expression of glycolytic, and upregulates poxB and acs genes as compared to the parental strain JM101, when growing on glucose. The products of the latter genes are involved in the production of AcetylCoA. Inactivation of rpoS that codes for the RNA polymerase σ38 subunit, reduces further (50%) growth of PB11, indicating that σ38 plays a central role in the expression of central metabolism genes in slowly growing cells. In fact, transcription levels of glycolytic genes is reduced in strain PB11rpoS− as compared to PB11. In this report we studied the role of σ70 and σ38 in the expression of the complete glycolytic pathway and poxB and acs genes in certain PTS− strains and their rpoS− derivatives. We determined the transcription start sites (TSSs) and the corresponding promoters, in strains JM101, PB11, its derivative PB12 that recovered its growth capacity, and in their rpoS− derivatives, by 5′RACE and pyrosequencing. In all these genes the presence of sequences resembling σ38 recognition sites allowed the proposition that they could be transcribed by both sigma factors, from overlapping putative promoters that initiate transcription at the same site. Fourteen new TSSs were identified in seventeen genes. Besides, more than 30 putative promoters were proposed and we confirmed ten previously reported. In vitro transcription experiments support the functionality of putative dual promoters. Alternatives that could also explain lower transcription levels of the rpoS− derivatives are discussed. We propose that the presence if real, of both σ70 and σ38 dependent promoters in all glycolytic genes and operons could allow a differential transcription of these central metabolism genes by both sigma subunits as an adaptation response to carbon
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.
Bell's theorem on arbitrary causal structures
NASA Astrophysics Data System (ADS)
Fritz, Tobias
2014-03-01
Bell's theorem is a gedankenexperiment with an underlying causal structure in the form of the letter ``M.'' I will describe how such a Bell scenario is a special case of a vastly larger class of scenarios, in which the causal structure of the ``M'' is replaced by an arbitrary directed acyclic graph (or, equivalently, by a causal set). In this formalism, the apparent difference between the notions of ``choice of setting,'' ``source,'' and ``measurement'' disappears completely and all of these become special cases of the general notion of ``event.'' I will explain how this relieves Bell's theorem of the philosophical baggage associated with free will and also present several mathematical results about these more general scenarios obtained by various people. This formalism is expected to have applications in many other areas of science: it is relevant whenever a system is probed at certain points in space and time, and at each of these points there may be hidden information not observed by the probes.
On the inversion of Fueter's theorem
NASA Astrophysics Data System (ADS)
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2016-10-01
The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space R n + 1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension n. The present work extends the result to all dimensions n by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function f defined in a suitable open set in R n + 1, where n is a positive integer, we can find a slice hyperholomorphic function f → such that f =Δ (n - 1) / 2 f →. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.
NASA Astrophysics Data System (ADS)
Kamann, S.; Wisotzki, L.; Roth, M. M.; Gerssen, J.; Husser, T.-O.; Sandin, C.; Weilbacher, P.
2014-06-01
We used the PMAS integral field spectrograph to obtain large sets of radial velocities in the central regions of three northern Galactic globular clusters: M3, M13, and M92. By applying the novel technique of crowded field 3D spectroscopy, we measured radial velocities for about 80 stars within the central ~10″ of each cluster. These are by far the largest spectroscopic datasets obtained in the innermost parts of these clusters up to now. To obtain kinematical data across the whole extent of the clusters, we complement our data with measurements available in the literature. We combine our velocity measurements with surface brightness profiles to analyse the internal dynamics of each cluster using spherical Jeans models, and investigate whether our data provide evidence for an intermediate-mass black hole in any of the clusters. The surface brightness profiles reveal that all three clusters are consistent with a core profile, although shallow cusps cannot be excluded. We find that spherical Jeans models with a constant mass-to-light ratio provide a good overall representation of the kinematical data. A massive black hole is required in none of the three clusters to explain the observed kinematics. Our 1σ (3σ) upper limits are 5300 M⊙ (12 000 M⊙) for M3, 8600 M⊙ (13 000 M⊙) for M13, and 980 M⊙ (2700 M⊙) for M92. A puzzling circumstance is the existence of several potential high velocity stars in M3 and M13, as their presence can account for the majority of the discrepancies that we find in our mass limits compared to M92. Based on observations collected at the Centro Astronómico Hispano-Alemán (CAHA) at Calar Alto, operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC).Appendices are available in electronic form at http://www.aanda.orgTables D.1 to D.6 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc
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.
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
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
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.)
Group Theoretical Interpretation of von Neumann's Theorem on Composite Systems.
ERIC Educational Resources Information Center
Bergia, S.; And Others
1979-01-01
Shows that von Neumann's mathematical theorem on composite systems acquires a transparent physical meaning with reference to a suitable physical example; a composite system in a state of definite angular momentum. Gives an outline of the theorem, and the results are restated in Dirac's notation, thus generalizing von Neumann's results which were…
Generalizations of Karp's theorem to elastic scattering theory
NASA Astrophysics Data System (ADS)
Tuong, Ha-Duong
Karp's theorem states that if the far field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle in R2 is invariant under the group of rotations, then the scatterer is a circle. The theorem is generalized to the elastic scattering problems and the axisymmetric scatterers in R3.
Note on two theorems in nonequilibrium statistical mechanics
Cohen, E.G.D.; Gallavotti, G.
1999-09-01
An attempt is made to clarify the difference between a theorem derived by Evans and Searles in 1994 on the statistics of trajectories in phase space and a theorem proved by the authors in 1995 on the statistics of fluctuations on phase space trajectory segments in a nonequilibrium stationary state.
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.
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…
The logical status of thermodynamic proofs of mathematical theorems
NASA Astrophysics Data System (ADS)
Deakin, M. A. B.; Troup, G. J.
1981-06-01
The logical status of such thermodynamic proofs of mathematical theorems as Landsberg's derivation of the inequality of arithmetic and geometric means is considered. The status is not as absolute as the rigorous demonstration of a mathematical theorem. Many axiomatic accounts of thermodynamics use this inequality to reduce the number of physical assumptions required.
On Euler's Theorem for Homogeneous Functions and Proofs Thereof.
ERIC Educational Resources Information Center
Tykodi, R. J.
1982-01-01
Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)
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…
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 +…
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…
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…
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.
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.
Quantum-thermodynamic treatment of intrinsic anharmonicity; Wallace's theorem revisited
NASA Astrophysics Data System (ADS)
Jacobs, Michel H. G.; de Jong, Bernard H. W. S.
2005-12-01
Wallace (in Thermodynamics of crystals, 1972) developed a theorem, rooted in rigid lattice dynamics, which incorporates intrinsic anharmonic effects in solids. The practical application of this theorem in mineral physics is computationally involved and this is the main reason for the theorem not getting the attention it deserves. Because intrinsic anharmonicity is an important issue at the extreme conditions in planetary mantles, we derived a method which removes the computational obstacles in applying this theorem. We extended the theorem to incorporate details of the phonon spectrum and tested our algorithm on forsterite (Mg2SiO4). Using a least squares inversion technique applied to all available experimental data, we show that it results in an accurate representation of thermodynamic properties and sound wave velocities of Mg2SiO4 in its complete pressure-temperature stability range. We also show that the accuracy of our results is not significantly affected by the use of a different equation of state.
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
The virial theorem for the polarizable continuum model
Cammi, R.
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.
Precise Calibration of the Virial Theorem from Hubble Volume Cluster Catalogs
NASA Astrophysics Data System (ADS)
Evrard, A. E.; Horikawa, T.; Virgo Consortium Collaboration
2000-10-01
The Hubble Volume project of the Virgo Consortium has created 109 particle N-body simulations of large-scale structure formation in ΛCDM and τCDM cosmologies with resolution sufficient to define a virtual Coma cluster with 500 particles. Light-cone survey output from the simulations provide synthetic sky surveys of the dark matter distribution in very large cosmic volumes, ~ 1010 h-3 Mpc3. Cluster catalogs derived from the surveys contain 100,000 to 500,000 clusters with masses exceeding 5 x 1013 h-1 Msun and redshifts extending to z ~ 2. We analyse in detail the virial relation between dark matter mass MΔ c and velocity dispersion σ . We find a unified calibration of the relation in the form H(z) MΔ c = A σ p for which the amplitude A and slope p are independent of cosmology and/or epoch (H(z) is the Hubble parameter at redshift z). This holds for clusters whose properties are defined within a spherical region encompassing a fixed density contrast Δ c (typically 200) with respect to the critical density. Other definitions of clusters require a redshift dependent amplitude A(z). The scatter in σ at fixed H(z) M about the mean relation is small ( ~ 6%) and positively skewed. Subdividing the population into two classes --- `parents' and `children' --- we identify the minority child component as the source of the skewness and infer that the children are merger debris that has not yet been fully incorporated into the parent population. For the parents alone, the probability distribution function of the velocity dispersion residuals is very well modeled by a Gaussian distribution, suggesting a central limit theorem interpretation. The accuracy of the calibration will be addressed by examining Virgo simulations with higher mass resolution and smaller volumes. Connections to obervable measures --- cluster X-ray temperature and galaxy velocity dispersion --- will be briefly discussed.
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.
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.
The Birkhoff theorem and string clouds
NASA Astrophysics Data System (ADS)
Bronnikov, K. A.; Kim, S.-W.; Skvortsova, M. V.
2016-10-01
We consider spherically symmetric space-times in GR under the unconventional assumptions that the spherical radius r is either a constant or has a null gradient in the (t, x) subspace orthogonal to the symmetry spheres (i.e., {(\\partial r)}2 = 0). It is shown that solutions to the Einstein equations with r={const} contain an extra (fourth) spatial or temporal Killing vector and thus satisfy the Birkhoff theorem under an additional physically motivated condition that the tangential pressure is functionally related to the energy density. This leads to solutions that directly generalize the Bertotti-Robinson, Nariai and Plebanski-Hacyan solutions. Under similar conditions, solutions with {(\\partial r)}2 = 0 but r\
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
Globally optimal impulsive transfers via Green's theorem
NASA Astrophysics Data System (ADS)
Hazelrigg, G. A., Jr.
1984-08-01
For certain classes of trajectories the cost function (characteristic velocity) can be written as a 'quasilinear' function of the change in state. In the case presented, impulsive transfers between coplanar, coaxial orbits with transfer time and angle unrestricted, Green's theorem can be used to determine the optimal transfer between given terminal states. This is done in a manner which places no restrictions on the number of impulses used and leads to globally optimal results. These results are used to show that the Hohmann transfer and the biparabolic transfer provide global minima in their respective regions. The regions in which monoelliptic and biparabolic trajectories are globally optimal are also defined for elliptic terminal states. The results are applicable to the case in which restrictions are placed on the radius of closest approach or greatest recession from the center of the force field.
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
2014-12-01
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.
Caprioli, Riccardo; Cargini, Daniele; Marcacci, Maurilia; Cammà, Cesare; Giansante, Carla; Ferri, Nicola
2013-03-26
Crayfish plague, caused by the oomycete Aphanomyces astaci, is a serious disease of European freshwater crayfish and has eliminated entire populations in several European countries. In September 2011, mortality was observed among the Austropotamobius pallipes population of a river basin in the Abruzzi region (central Italy), and A. astaci DNA was detected by PCR in dead crayfish. A systematic survey was carried out to evaluate the spread and the effects of the plague in the river basin. The source of the outbreak remained unknown since North American crayfish species, which frequently act as subclinical carriers of the infection, were not detected in the area. The A. pallipes population disappeared from a river stretch of ~1 km, where A. astaci infection was detected in dead crayfish. However, apparently unaffected crayfish were still present upstream of that area as well as in a tributary that joined the brook in the apparently depopulated stretch. A. astaci infection was not detected in dead individuals collected in the upstream area and tributary. A follow-up visit conducted in the following season showed the presence of A. pallipes in the river stretch hit by the plague. In this outbreak, the spread of the infection could have been limited by a low density of the crayfish population and by the geographic conformation of the river basin, which includes a dense network of small tributaries, characterized by high flow velocity and low water temperature. In this particular setting, crayfish plague outbreaks can remain undetected. This underlines the importance of active monitoring programs aimed at the prompt recognition of both episodes of mortality and the presence of non-indigenous crayfish species.
NASA Astrophysics Data System (ADS)
Gaines, K.; Meinzer, F. C.; Duffy, C.; Thomas, E.; Eissenstat, D. M.
2014-12-01
Water uptake and retention by trees affects their ability to cope with drought, as well as influences ground water recharge and stream flow. Historically, water has not often been limiting in Eastern U.S. forests. As a result, very little work has been done to understand the basics of timing of water use by vegetation in these systems. As droughts are projected to increase in length and severity in future decades, this focus is increasingly important, particularly for informing hydrologic models. We used deuterium tracer and sap flux techniques to study tree water transport on a forested ridge top with shallow soil in central Pennsylvania. Three trees of each of the species, Acer saccharum, Carya tomentosa, Quercus prinus, and Quercus rubrum were accessed by tree climbing and scaffolding towers. We hypothesized that contrasting vessel size of the tree species would affect the efficiency of water transport (tracer velocity) and contrasting tree size would affect tracer storage as estimated by tracer residence times. Trees were injected with deuterated water in July 2012. Leaves were sampled 15 times over 35 days, initially daily for the first week, then at regular intervals afterwards. The tracer arrived in the canopy of the study trees between 1 and 7 days after injection, traveling at a velocity of 2 to 19 m d-1. The tracer residence time was between 7 and 33 days. Although there was variation in tracer velocity and residence time in individual trees, there were no significant differences among wood types or species (P>0.05). The general patterns in timing of water use were similar to other studies on angiosperm trees in tropical and arid ecosystems. There was no evidence of longer residence times in the larger trees. Sap flux-based estimates of sap velocity were much lower than tracer estimates, which was consistent with other studies. Levels of sap flux and midday water potential measurements suggested that the trees were water-stressed. We observed relatively
The dead-end elimination theorem and its use in protein side-chain positioning
NASA Astrophysics Data System (ADS)
Desmet, Johan; Maeyer, Marc De; Hazes, Bart; Lasters, Ignace
1992-04-01
THE prediction of a protein's tertiary structure is still a considerable problem because the huge amount of possible conformational space1 makes it computationally difficult. With regard to side-chain modelling, a solution has been attempted by the grouping of side-chain conformations into representative sets of rotamers2-5. Nonetheless, an exhaustive combinatorial search is still limited to carefully identified packing units5,6containing a limited number of residues. For larger systems other strategies had to be develop-ped, such as the Monte Carlo Procedure6,7 and the genetic algorithm and clustering approach8. Here we present a theorem, referred to as the 'dead-end elimination' theorem, which imposes a suitable condition to identify rotamers that cannot be members of the global minimum energy conformation. Application of this theorem effectively controls the computational explosion of the rotamer combinatorial problem, thereby allowing the determination of the global minimum energy conformation of a large collection of side chains.
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.
On Pythagoras Theorem for Products of Spectral Triples
NASA Astrophysics Data System (ADS)
D'Andrea, Francesco; Martinetti, Pierre
2013-05-01
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.
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.
Fluctuation theorem for Hamiltonian systems: Le Chatelier's principle.
Evans, D J; Searles, D J; Mittag, E
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields. PMID:11414885
Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle
NASA Astrophysics Data System (ADS)
Evans, Denis J.; Searles, Debra J.; Mittag, Emil
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
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.
Noncommutative topology and the world's simplest index theorem.
van Erp, Erik
2010-05-11
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.
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
On the Spin-Statistics Theorem
NASA Astrophysics Data System (ADS)
Peshkin, Murray
2002-05-01
M.V. Berry and J.M. Robbins* (B) have explained the spin-statistics theorem (SST) within nonrelativistic quantum mechanics (QM), without using relativity or field theory. For two identical spinless particles, their starting point is a coordinate space which consists of unordered pairs r,r' where r and r' represent two points in space, not particle labels. The point r,r' is the point r',r\\. That has topological consequences for the 6D configuration space and for the wave functions |r,r'>. More generally, spin variables are appended and there are N vectors. B gave a beautiful mathematical analysis to go from there to the usual SST under stated assumptions of QM. They also explored alternative assumptions that give unusual results but that may not be physical. I seek additional insight by recasting B's analysis into a form that emphasizes the relative orbital angular momenta of pairs of particles. I report here on the spinless case, where boson statistics emerges in a transparent way. This approach appears to exclude unusual possibilities. Work supported by U.S. DOE contract W-31-109-ENG-38. *Proc. R. Soc. Lond. A 453, 1771 (1997).
A stem cell niche dominance theorem
2011-01-01
Background Multilevelness is a defining characteristic of complex systems. For example, in the intestinal tissue the epithelial lining is organized into crypts that are maintained by a niche of stem cells. The behavior of the system 'as a whole' is considered to emerge from the functioning and interactions of its parts. What we are seeking here is a conceptual framework to demonstrate how the "fate" of intestinal crypts is an emergent property that inherently arises from the complex yet robust underlying biology of stem cells. Results We establish a conceptual framework in which to formalize cross-level principles in the context of tissue organization. To this end we provide a definition for stemness, which is the propensity of a cell lineage to contribute to a tissue fate. We do not consider stemness a property of a cell but link it to the process in which a cell lineage contributes towards tissue (mal)function. We furthermore show that the only logically feasible relationship between the stemness of cell lineages and the emergent fate of their tissue, which satisfies the given criteria, is one of dominance from a particular lineage. Conclusions The dominance theorem, conceived and proven in this paper, provides support for the concepts of niche succession and monoclonal conversion in intestinal crypts as bottom-up relations, while crypt fission is postulated to be a top-down principle. PMID:21214945
Digital superresolution and the generalized sampling theorem
NASA Astrophysics Data System (ADS)
Prasad, Sudhakar
2007-02-01
The technique of reconstructing a higher-resolution (HR) image of size ML×ML by digitally processing L×L subpixel-shifted lower-resolution (LR) copies of it, each of size M×M, has now become well established. This particular digital superresolution problem is analyzed from the standpoint of the generalized sampling theorem. It is shown both theoretically and by computer simulation that the choice of regularly spaced subpixel shifts for the LR images tends to maximize the robustness and minimize the error of reconstruction of the HR image. In practice, since subpixel-level control of LR image shifts may be nearly impossible to achieve, however, a more likely scenario, which is also discussed, is one involving random subpixel shifts. It is shown that without reasonably tight bounds on the range of random shifts, the reconstruction is likely to fail in the presence of even small amounts of noise unless either reliable prior information or additional data are available.
On the 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.
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.
Information-disturbance theorem for mutually unbiased observables
Miyadera, Takayuki; Imai, Hideki
2006-04-15
We derive a version of information-disturbance theorems for mutually unbiased observables. We show that the information gain by Eve inevitably makes the outcomes by Bob in the conjugate basis not only erroneous but random.
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.
Generalized Optical Theorem Detection in Random and Complex Media
NASA Astrophysics Data System (ADS)
Tu, Jing
The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar
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
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.
a New Look at GOLDSTONE’S Theorem
NASA Astrophysics Data System (ADS)
Buchholz, Detlev; Doplicher, Sergio; Longo, Roberto; Roberts, John E.
The appearance of spontaneously broken symmetries and its bearing on the physical mass spectrum are analyzed in the algebraic setting of local quantum field theory. Within this setting, a generalization of Goldstone’s Theorem is established which does not rely on the existence of conserved currents. Continuous symmetries not satisfying the premises of the theorem can be spontaneously broken even in the presence of a mass gap.
No-broadcasting theorem and its classical counterpart.
Kalev, Amir; Hen, Itay
2008-05-30
Although it is widely accepted that "no-broadcasting"-the nonclonability of quantum information-is a fundamental principle of quantum mechanics, an impossibility theorem for the broadcasting of general density matrices has not yet been formulated. In this Letter, we present a general proof for the no-broadcasting theorem, which applies to arbitrary density matrices. The proof relies on entropic considerations, and as such can also be directly linked to its classical counterpart, which applies to probabilistic distributions of statistical ensembles.
Liouville`s theorem and phase-space cooling
Mills, R.L.; Sessler, A.M.
1993-09-28
A discussion is presented of Liouville`s theorem and its consequences for conservative dynamical systems. A formal proof of Liouville`s theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur.
Localising Dehn's lemma and the loop theorem in 3-manifolds
NASA Astrophysics Data System (ADS)
Aitchison, I. R.; Hyam Rubinstein, J.
2004-09-01
We give a new proof of Dehn's lemma and the loop theorem. This is a fundamental tool in the topology of 3-manifolds. Dehn's lemma was originally formulated by Dehn, where an incorrect proof was given. A proof was finally given by Papakyriakopolous in his famous 1957 paper where the fundamental idea of towers of coverings was introduced. This was later extended to the loop theorem, and the version used most frequently was given by Stallings.
Generalized Panofsky-Wenzel theorem and hybrid coupling
NASA Astrophysics Data System (ADS)
Smirnov, A. V.
2001-08-01
The Panofsky-Wenzel theorem is reformulated for the case in which phase slippage between the wave and beam is not negligible. The extended theorem can be applied in analysis of detuned waveguides, RF injectors, bunchers, some tapered waveguides or high-power sources and multi-cell cavities for dipole and higher order modes. As an example, the relative contribution of the Lorentz' component of the deflecting force is calculated for a conventional circular disk-loaded waveguide.
Levinson theorem for Aharonov-Bohm scattering in two dimensions
Sheka, Denis D.; Mertens, Franz G.
2006-11-15
We apply the recently generalized Levinson theorem for potentials with inverse-square singularities [Sheka et al., Phys. Rev. A 68, 012707 (2003)] to Aharonov-Bohm systems in two dimensions (2D). By this theorem, the number of bound states in a given mth partial wave is related to the phase shift and the magnetic flux. The results are applied to 2D soliton-magnon scattering.
The Hartogs extension theorem for holomorphic vector bundles and sprays
NASA Astrophysics Data System (ADS)
Andrist, Rafael B.; Shcherbina, Nikolay; Wold, Erlend F.
2016-10-01
We give a detailed proof of Siu's theorem on extendibility of holomorphic vector bundles of rank larger than one, and prove a corresponding extension theorem for holomorphic sprays. We apply this result to study ellipticity properties of complements of compact subsets in Stein manifolds. In particular we show that the complement of a closed ball in {C}n, n ≥3, is not subelliptic.
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.
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.
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.
Quantum duality, unbounded operators, and inductive limits
NASA Astrophysics Data System (ADS)
Dosi, Anar
2010-06-01
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.
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.
Simulation of biological evolution and the NFL theorems.
Meester, Ronald
2009-09-01
William Dembski (No free lunch: why specified complexity cannot be purchased without intelligence, 2002) claimed that the NFL theorems from optimization theory render darwinian biological evolution impossible. Häggström (Biology and Philosophy 22:217-230, 2007) argued that the NFL theorems are not relevant for biological evolution at all, since the assumptions of the NFL theorems are not met. Although I agree with Häggström (Biology and Philosophy 22:217-230, 2007), in this article I argue that the NFL theorems should be interpreted as dealing with an extreme case within a much broader context. This broader context is in fact relevant for scientific research of certain evolutionary processes; not in the sense that the theorems can be used to draw conclusions about any intelligent design inference, but in the sense that it helps us to interpret computer simulations of evolutionary processes. As a result of this discussion, I will argue that from simulations, we do not learn much about how complexity arises in the universe. This position is in contrast with certain claims in the literature that I will discuss.
On local-hidden-variable no-go theorems
NASA Astrophysics Data System (ADS)
Methot, A. A.
2006-06-01
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow.
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.
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.
NASA Astrophysics Data System (ADS)
Beck, C.; Campos, C.; Eriş, K. K.; Çağatay, N.; Mercier de Lepinay, B.; Jouanne, F.
2015-02-01
In the deep part of the Sea of Marmara (Turkey), the sedimentation developing upon the North Anatolian Fault is strongly influenced by the associated seismic activity, through gravity reworking (fluidized landslides) and tsunamis. Specific layers (homogenites + turbidites, HmTu), representing individual sedimentary events, have been characterized along three giant piston cores retrieved from the Çinarcik and Central (or Orta) basins. Pre-Holocene, nonmarine sediments, were analyzed, representing the last 12-17 kyr BP (before present). For a 2 kyr long interval, 11 events could be precisely correlated on both sides of the Central Basin's southwestern scarp. For each of them, based on the specific depositional process, the thickness difference between the two sites was considered as a direct estimation of the vertical component of a coeval coseismic offset. The homogenite (upper) component accounts for the major part of the thickness difference (ranging from 36 to 144 cm). These offsets were considered as likely representing dominantly vertical throws, along the transtensional southwestern boundary of the inner, pull-apart Central Basin. In terms of natural hazards, further investigations on this local behavior should rather be directed to tsunami genesis.
Attractive Hubbard model with disorder and the generalized Anderson theorem
Kuchinskii, E. Z. Kuleeva, N. A. Sadovskii, M. V.
2015-06-15
Using the generalized DMFT+Σ approach, we study the influence of disorder on single-particle properties of the normal phase and the superconducting transition temperature in the attractive Hubbard model. A wide range of attractive potentials U is studied, from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong-coupling region, where the superconducting transition is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures much higher than the superconducting transition temperature. We study two typical models of the conduction band with semi-elliptic and flat densities of states, respectively appropriate for three-dimensional and two-dimensional systems. For the semi-elliptic density of states, the disorder influence on all single-particle properties (e.g., density of states) is universal for an arbitrary strength of electronic correlations and disorder and is due to only the general disorder widening of the conduction band. In the case of a flat density of states, universality is absent in the general case, but still the disorder influence is mainly due to band widening, and the universal behavior is restored for large enough disorder. Using the combination of DMFT+Σ and Nozieres-Schmitt-Rink approximations, we study the disorder influence on the superconducting transition temperature T{sub c} for a range of characteristic values of U and disorder, including the BCS-BEC crossover region and the limit of strong-coupling. Disorder can either suppress T{sub c} (in the weak-coupling region) or significantly increase T{sub c} (in the strong-coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of the superconducting critical temperature are essentially due to only the general disorder widening of the conduction band.
Towards a novel no-hair theorem for black holes
Hertog, Thomas
2006-10-15
We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four-dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.
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.
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
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.
Noncommutative topology and the world's simplest index theorem.
van Erp, Erik
2010-05-11
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
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.
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
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)
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.
Refinement of Representation Theorems for Context-Free Languages
NASA Astrophysics Data System (ADS)
Fujioka, Kaoru
In this paper, we obtain some refinement of representation theorems for context-free languages by using Dyck languages, insertion systems, strictly locally testable languages, and morphisms. For instance, we improved the Chomsky-Schützenberger representation theorem and show that each context-free language L can be represented in the form L = h (D ∩ R), where D is a Dyck language, R is a strictly 3-testable language, and h is a morphism. A similar representation for context-free languages can be obtained, using insertion systems of weight (3, 0) and strictly 4-testable languages.
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.
A cartoon-assisted proof of Sarkowskii's theorem
NASA Astrophysics Data System (ADS)
Kaplan, Harvey
1987-11-01
Much of the present article serves as an introduction to a set of ideas familiar in dynamical systems theory. No familiarity with these ideas is assumed on the part of the reader. The ideas are then combined in simple, geometric arguments to prove Sarkowskii's theorem. This theorem is important in the study of one-dimensional, deterministic, dissipative dynamical systems. It provides a unified framework for the occurrences of both orderly and chaotic motions. The relationship of the mathematical models discussed here to real physical and biological systems is discussed briefly and the reader is referred to the literature for descriptions of diverse, beautiful, relevant experiments.
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.
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…
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…
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.
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.
An Experiment on a Physical Pendulum and Steiner's Theorem
ERIC Educational Resources Information Center
Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.
2010-01-01
Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…
A 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.
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.…
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.
Ambarzumyan's theorem for the quasi-periodic boundary conditions
NASA Astrophysics Data System (ADS)
Kıraç, Alp Arslan
2016-09-01
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.
Virial theorem and Gibbs thermodynamic potential for Coulomb systems
Bobrov, V. B. E-mail: satron@mail.ru; Trigger, S. A. E-mail: satron@mail.ru
2014-10-15
Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction.
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.
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…
On Feynman's Triangle Problem and the Routh Theorem
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2009-01-01
In this article, we give a brief history of the Feynman's Triangle problem and describe a simple method to solve a general version of this problem, which is called the Routh Theorem. This method could be found useful to school teachers, instructors or lecturers who are involved in teaching geometry.
A 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).
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.
The Hartman-Grobman theorem for semilinear hyperbolic evolution equations
NASA Astrophysics Data System (ADS)
Hein, Marie-Luise; Prüss, Jan
2016-10-01
The famous Hartman-Grobman theorem for ordinary differential equations is extended to abstract semilinear hyperbolic evolution equations in Banach spaces by means of simple direct proof. It is also shown that the linearising map is Hölder continuous. Several applications to abstract and specific damped wave equations are given, to demonstrate the strength of our results.
Rotationally invariant proof of Bell's theorem without inequalities
Cabello, Adan
2003-03-01
The singlet state of two spin-(3/2) particles allows a proof of Bell's theorem without inequalities with two distinguishing features: any local observable can be regarded as an Einstein-Podolsky-Rosen element of reality, and the contradiction with local realism occurs not only for some specific local observables but for any rotation whereof.
Kochen-Specker Theorem as a Precondition for Quantum Computing
NASA Astrophysics Data System (ADS)
Nagata, Koji; Nakamura, Tadao
2016-08-01
We study the relation between the Kochen-Specker theorem (the KS theorem) and quantum computing. The KS theorem rules out a realistic theory of the KS type. We consider the realistic theory of the KS type that the results of measurements are either +1 or -1. We discuss an inconsistency between the realistic theory of the KS type and the controllability of quantum computing. We have to give up the controllability if we accept the realistic theory of the KS type. We discuss an inconsistency between the realistic theory of the KS type and the observability of quantum computing. We discuss the inconsistency by using the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be for an easy detector to a Pauli observable. We cannot accept the realistic theory of the KS type to simulate the double-slit experiment in a significant specific case. The realistic theory of the KS type can not depicture quantum detector. In short, we have to give up both the observability and the controllability if we accept the realistic theory of the KS type. Therefore, the KS theorem is a precondition for quantum computing, i.e., the realistic theory of the KS type should be ruled out.
The No-Hair Theorem for the Abelian Higgs Model
NASA Astrophysics Data System (ADS)
Lahiri, Amitabha
We consider the general procedure for proving no-hair theorems for static, spherically symmetric black holes. We apply this method to the Abelian Higgs model and find a proof of the no-hair conjecture that circumvents the objections raised against the original proof due to Adler and Pearson.
An Extension of the Mean Value Theorem for Integrals
ERIC Educational Resources Information Center
Khalili, Parviz; Vasiliu, Daniel
2010-01-01
In this note we present an extension of the mean value theorem for integrals. The extension we consider is motivated by an older result (here referred as Corollary 2), which is quite classical for the literature of Mathematical Analysis or Calculus. We also show an interesting application for computing the sum of a harmonic series.
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…
Shock waves and Birkhoff's theorem in Lovelock gravity
Gravanis, E.
2010-11-15
Spherically symmetric shock waves are shown to exist in Lovelock gravity. They amount to a change of branch of the spherically symmetric solutions across a null hypersurface. The implications of their existence for the status of Birkhoff's theorem in the theory is discussed.
Stochastic functionals and fluctuation theorem for multikangaroo processes.
Van den Broeck, C; Toral, R
2014-06-01
We introduce multikangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functional. We calculate analytically the large deviation properties. We apply our results to zero-crossing statistics and to stochastic thermodynamics, including the derivation of the fluctuation theorem and the large deviation properties for the stochastic entropy production in a typical solid state device. PMID:25019742
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…
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.
Fixed point theorems for generalized contractions in ordered metric spaces
NASA Astrophysics Data System (ADS)
O'Regan, Donal; Petrusel, Adrian
2008-05-01
The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, MEC. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petrusel, I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.
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.
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).
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.
Torres-Peralta, Rafael; Morales-Alamo, David; González-Izal, Miriam; Losa-Reyna, José; Pérez-Suárez, Ismael; Izquierdo, Mikel; Calbet, José A L
2015-01-01
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
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
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
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.
Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes
Remmen, Grant N.; Bao, Ning; Pollack, Jason
2016-07-11
We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throatmore » separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. In conclusion, this theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.« less
Algebraic functions of complexity one, a Weierstrass theorem, and three arithmetic operations
NASA Astrophysics Data System (ADS)
Beloshapka, V. K.
2016-07-01
The Weierstrass theorem concerning functions admitting an algebraic addition theorem enables us to give an explicit description of algebraic functions of two variables of analytical complexity one. Their description is divided into three cases: the general case, which is elliptic, and two special ones, a multiplicative and an additive one. All cases have a unified description; they are the orbits of an action of the gauge pseudogroup. The first case is a 1-parameter family of orbits of "elliptic addition," the second is the orbit of multiplication, and the third of addition. Here the multiplication and addition can be derived from the "elliptic addition" by passages to a limit. On the other hand, the elliptic orbits correspond to complex structures on the torus, the multiplicative orbit corresponds to the complex structure on the cylinder, and the additive one to that on the complex plane. This work was financially supported by the Russian Foundation for Basic Research under grants nos. 14-00709-a and 13-01-12417-ofi-m2.
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.
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.
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.
Teaching temporal coherence and the Wiener Khintchin theorem at a senior/graduate level
NASA Astrophysics Data System (ADS)
Chavel, Pierre H.; Jonathan, Jean-Michel C.
2002-05-01
One important issue in teaching interferences is that two separate wavelengths usually do not interfere: any interference pattern is the spectral integral of all interference patterns of all monochromatic components. Although optical detectors are quadratic in nature, crossed terms involving two different frequencies in the expression of an interference pattern vanish. More precisely, while in non stationary signals such as ultrashort pulses two wavelengths can give rise to beating phenomena, this does not happen with the usual thermal light beams. The phenomenon is directly connected with the Wiener Khintchin theorem, and therefore with the principle of Fourier transform spectroscopy. In an introductory course, oversimplification leading to frustrating physical and mathematical deficiencies is hardly avoidable. In this communication, we suggest an introduction of this question at a senior/graduate level. Numerical simulations are used to provide an intuitive understanding of the phenomena. If the Wiener Khintchin theorem is introduced by defining the power spectrum from the infinite time limit of the ordinary Fourier transform of a Gaussian windowed version of the signal, the mathematics are simple and the method offers a clear connection with the operation of real (i.e. finite time) detectors analyzing interference fringes.
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
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.
Bell's Theorem and the Issue of Determinism and Indeterminism
NASA Astrophysics Data System (ADS)
Esfeld, Michael
2015-05-01
The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell's theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for the derivation of Bell's theorem. Determinism as such does not undermine that independence (unless there are particular initial conditions of the universe that would amount to conspiracy). Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave-function can go together with effective wave-functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave-functions are sufficient for the mentioned independence premise to hold.
Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper
NASA Technical Reports Server (NTRS)
Schumann, Johann; Koga, Dennis (Technical Monitor)
1999-01-01
In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).
A 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.
Weinberg's proof of the spin-statistics theorem
NASA Astrophysics Data System (ADS)
Massimi, Michela; Redhead, Michael
The aim of this paper is to offer a conceptual analysis of Weinberg's proof of the spin-statistics theorem by comparing it with Pauli's original proof and with the subsequent textbook tradition, which typically resorts to the dichotomy positive energy for half-integral spin particles/microcausality for integral-spin particles. In contrast to this tradition, Weinberg's proof does not directly invoke the positivity of the energy, but derives the theorem from the single relativistic requirement of microcausality. This seemingly innocuous difference marks an important change in the conceptual basis of quantum physics. Its historical, theoretical, and conceptual roots are here reconstructed. The link between Weinberg's proof and Pauli's original is highlighted: Weinberg's proof turns out to do justice to Pauli's anti-Dirac lines of thought. The work of Furry and Oppenheimer is also surveyed as a "third way" between the textbook tradition established by Pauli and Weinberg's approach.
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
Diffusive Magnetohydrodynamic Instabilities beyond the Chandrasekhar Theorem
NASA Astrophysics Data System (ADS)
Rüdiger, Günther; Schultz, Manfred; Stefani, Frank; Mond, Michael
2015-10-01
We consider the stability of axially unbounded cylindrical flows that contain a toroidal magnetic background field with the same radial profile as their azimuthal velocity. For ideal fluids, Chandrasekhar had shown the stability of this configuration if the Alfvén velocity of the field equals the velocity of the background flow, i.e., if the magnetic Mach number {Mm}=1. We demonstrate that magnetized Taylor-Couette flows with such profiles become unstable against non-axisymmetric perturbations if at least one of the diffusivities is finite. We also find that for small magnetic Prandtl numbers {Pm} the lines of marginal instability scale with the Reynolds number and the Hartmann number. In the limit {Pm}\\to 0 the lines of marginal instability completely lie below the line for {Mm}=1 and for {Pm}\\to ∞ they completely lie above this line. For any finite value of {Pm}, however, the lines of marginal instability cross the line {Mm}=1, which separates slow from fast rotation. The minimum values of the field strength and the rotation rate that are needed for the instability (slightly) grow if the rotation law becomes flat. In this case, the electric current of the background field becomes so strong that the current-driven Tayler instability (which also exists without rotation) appears in the bifurcation map at low Hartmann numbers.
Applications of the theorem of Pythagoras in R3
NASA Astrophysics Data System (ADS)
Srinivasan, V. K.
2010-01-01
Three distinct points ? and ? with ? are taken, respectively on the x, y and the z-axes of a rectangular coordinate system in ? Using the converse of the theorem of Pythagoras, it is shown that the triangle ? can never be a right-angled triangle. The result seems to be intuitive, but nevertheless requires a proof. As an application, some intuitive results about a tetrahedron are confirmed.
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.
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.
Reciprocity theorem and perturbation theory for photonic crystal waveguides.
Michaelis, D; Peschel, U; Wächter, C; Bräuer, A
2003-12-01
Starting from Maxwell's equations we derive a reciprocity theorem for photonic crystal waveguides. A set of strongly coupled discrete equations results, which can be applied to the simulation of perturbed photonic crystal waveguides. As an example we analytically study the influence of the dispersion of a two level system on the band structure of a photonic crystal waveguide. In particular, the formation of polariton gaps is discussed.
Uniqueness theorems for some inverse heat-conduction problems
NASA Astrophysics Data System (ADS)
Muzylev, N. V.
1980-04-01
Heat treatment of metals, involving rapid thermal processes, is an example of situations where the mathematical determination of thermal characteristics makes it necessary to solve a certain inverse problem, i.e., from some information on the temperature field, obtained from direct measurements. The present paper deals with the uniqueness of inverse problems of this type. Uniqueness theorems are proven for the determination of the coefficients of a nonlinear parabolic equation from the boundary conditions.
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.
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.
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.
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.
Interpretation of the quantum formalism and Bell's theorem
Santos, E. )
1991-02-01
It is argued that quantum mechanics must be interpreted according to the Copenhagen interpretation. Consequently the formalism must be used in a purely operational way. The relation between realism, hidden variables, and the Bell inequalities is discussed. The proof of impossibility of local hidden-variables theories (Bell theorem) is criticized on the basis that the quantum mechanical states violating local realism are not physically realizable states.
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.
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
Klein's theorem and the proof of E0 = mc2
NASA Astrophysics Data System (ADS)
Ohanian, Hans C.
2012-12-01
Despite repeated attempts, Einstein failed to give us a general and rigorous proof of his E0=mc2 relation. A completely general proof emerged in 1918 from a theorem on the four-vector character of energy-momentum of extended systems by the mathematician Felix Klein, but this proof is not well known, rarely seen in textbooks, and sometimes misunderstood. A simple version of this proof is presented here, with discussion of the crucial role of the energy-momentum tensor.
Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields
Pan, Xiao-Yin; Sahni, Viraht
2015-11-07
The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momenta. The proofs differ from the original HK proof and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function. A Percus-Levy-Lieb constrained-search proof expanding the domain of validity to N-representable functions, and to degenerate states, again for fixed electron number and angular momentum, is also provided.
Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields.
Pan, Xiao-Yin; Sahni, Viraht
2015-11-01
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.
An analogue of Wagner's theorem for decompositions of matrix algebras
NASA Astrophysics Data System (ADS)
Ivanov, D. N.
2004-12-01
Wagner's celebrated theorem states that a finite affine plane whose collineation group is transitive on lines is a translation plane. The notion of an orthogonal decomposition (OD) of a classically semisimple associative algebra introduced by the author allows one to draw an analogy between finite affine planes of order n and ODs of the matrix algebra M_n(\\mathbb C) into a sum of subalgebras conjugate to the diagonal subalgebra. These ODs are called WP-decompositions and are equivalent to the well-known ODs of simple Lie algebras of type A_{n-1} into a sum of Cartan subalgebras. In this paper we give a detailed and improved proof of the analogue of Wagner's theorem for WP-decompositions of the matrix algebra of odd non-square order an outline of which was earlier published in a short note in "Russian Math. Surveys" in 1994. In addition, in the framework of the theory of ODs of associative algebras, based on the method of idempotent bases, we obtain an elementary proof of the well-known Kostrikin-Tiep theorem on irreducible ODs of Lie algebras of type A_{n-1} in the case where n is a prime-power.
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.
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.
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.
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.
Index theorem and universality properties of the low-lying eigenvalues of improved staggered quarks.
Follana, E; Hart, A; Davies, C T H
2004-12-10
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as expected from the index theorem, and their chirality expectation value is large ( approximately 0.7). The remaining modes have low chirality and show clear signs of clustering into quartets and approaching the random matrix theory predictions for all topological charge sectors. We conclude that improvement of the fermionic and gauge actions moves the staggered quarks closer to the continuum limit where they respond correctly to QCD topology.
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.
Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas
NASA Astrophysics Data System (ADS)
Hameiri, Elie
2013-10-01
Based on an extension to plasmas of Ertel's classical vorticity theorem in fluid dynamics, it is shown that for each species in a multi-fluid plasma there exists a set of nested surfaces that have this species' fluid particles confined within them. Variational formulations for the plasma evolution and its equilibrium states are developed, based on the new surfaces and all of the dynamical conservation laws associated with them. It is shown that in the general equilibrium case, the energy principle lacks a minimum and cannot be used as a stability criterion. A special limit of the variational principle yields single-fluid magnetohydrodynamic plasma equilibria and can be used to approximate the equilibrium state of a two-fluid plasma in a perturbative way. Work supported by USDOE under grant no. DE-FG02-86ER53223.
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.
NASA Astrophysics Data System (ADS)
von Neumann, J.
2010-11-01
It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way, the ergodic theorem and the H-theorem are formulated and proven (without “assumptions of disorder”), followed by a discussion of the physical meaning of the mathematical conditions characterizing their domain of validity. The German original was published in Zeitschrift für Physik 57, 30-70 (1929) [paper received on May 10th, 1929] and is available as electronic supplementary material at www.epj.org. Translated by Roderich Tumulka, Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA; e-mail: tumulka@math.rutgers.edu. Additions in the text by the translator are put in square brackets. Footnotes are also footnotes in the original unless otherwise marked. Footnotes in the original containing only citations have been moved to the main text. In the original, equations and references are not numbered. The notation agrees essentially with the original, with the following exceptions: h/2π has been replaced with ħ; the notation [a,b] for intervals has been introduced to simplify some sentences. In a few cases, misprints and other mistakes in formulas have been identified by the translator, corrected in the text, and mentioned in a footnote. The translator is grateful to Wolf Beiglböck for suggesting improvements and librarian Mei Ling Lo of Rutgers University for help with the bibliography.
A Maximal Element Theorem in FWC-Spaces and Its Applications
Hu, Qingwen; Miao, Yulin
2014-01-01
A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672
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.
On equivalence of generalized multi-valued contractions and Nadler's fixed point theorem
NASA Astrophysics Data System (ADS)
Eldred, A. Anthony; Anuradha, J.; Veeramani, P.
2007-12-01
We consider two generalizations of Nadler's theorem, one proved by Mizoguchi and Takahashi in response to the Reich conjecture and another theorem proved by Kaneko. We show that due to the additional conditions of these theorems the given multi-valued map reduces to a multi-valued contraction mapE We prove this result by showing that the orbit of the multi-valued map is bounded under the contractive conditions of the two generalizations.
A Limit Theorem on the Cores of Large Standard Exchange Economies
Brown, Donald J.; Robinson, Abraham
1972-01-01
This note introduces a new mathematical tool, nonstandard analysis, for the analysis of an important class of problems in mathematical economics—the relation between bargaining and the competitive price system. PMID:16591988
Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem.
Burnecki, Krzysztof; Wylomanska, Agnieszka; 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
NASA Astrophysics Data System (ADS)
Grigelionis, B. I.; Kubilyus, K.; Mikulyavichyus, R. A.
1982-12-01
CONTENTSIntroduction § 1. The stably weak convergence of probability measures in metric spaces § 2. A martingale characterization, and convergence of measures corresponding to semimartingales § 3. The stably weak convergence of point processes § 4. Necessary and sufficient conditions for the convergence of semimartingales and point processes References
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
No Fine Theorem for Macrorealism: Limitations of the Leggett-Garg Inequality
NASA Astrophysics Data System (ADS)
Clemente, Lucas; Kofler, Johannes
2016-04-01
Tests of local realism and macrorealism have historically been discussed in very similar terms: Leggett-Garg inequalities follow Bell inequalities as necessary conditions for classical behavior. Here, we compare the probability polytopes spanned by all measurable probability distributions for both scenarios and show that their structure differs strongly between spatially and temporally separated measurements. We arrive at the conclusion that, in contrast to tests of local realism where Bell inequalities form a necessary and sufficient set of conditions, no set of inequalities can ever be necessary and sufficient for a macrorealistic description. Fine's famous proof that Bell inequalities are necessary and sufficient for the existence of a local realistic model, therefore, cannot be transferred to macrorealism. A recently proposed condition, no-signaling in time, fulfills this criterion, and we show why it is better suited for future experimental tests and theoretical studies of macrorealism. Our work thereby identifies a major difference between the mathematical structures of local realism and macrorealism.
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.
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.
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.
On the matching method and the Goldstone theorem in holography
NASA Astrophysics Data System (ADS)
Bajc, Borut; Lugo, Adrián R.
2013-07-01
We study the transition of a scalar field in a fixed AdS d+1 background between an extremum and a minimum of a potential. We compute analytically the solution to the perturbation equation for the vev deformation case by generalizing the usual matching method to higher orders and find the propagator of the boundary theory operator defined through the AdS-CFT correspondence. We show that, contrary to what happens at the leading order of the matching method, the next-to-leading order presents a simple pole at q 2 = 0 in accordance with the Goldstone theorem applied to a spontaneously broken dilatation invariance.
Extinction and the optical theorem. Part I. Single particles.
Berg, Matthew J; Sorensen, Christopher M; Chakrabarti, Amitabha
2008-07-01
We study the extinction caused by a single particle and present a conceptual phase-based explanation for the related optical theorem. Simulations of the energy flow caused by a particle's presence in a collimated beam of light demonstrate how the extinction process occurs. It is shown that extinction does not necessarily cause a reduction of the energy flow along the exact forward direction. Implications regarding the measurement of the single-particle extinction cross section are discussed. This work is extended to noninteracting and interacting multiparticle groups in Part II [J. Opt. Soc. Am. A25, pp. 1514 (2008)].
Faithful quantum broadcast beyond the no-go theorem
NASA Astrophysics Data System (ADS)
Luo, Ming-Xing; Deng, Yun; Chen, Xiu-Bo; Yang, Yi-Xian; Li, Hong-Heng
2013-05-01
The main superiority of the quantum remote preparation over quantum teleportation lies the classical resource saving. This situation may be changed from the following constructions. Our purpose in this paper is to find some special differences between these two quantum tasks besides the classical resource costs. Some novel schemes show that the first one is useful to simultaneously broadcast arbitrary quantum states, while the second one cannot because of the quantum no-cloning theorem. Moreover, these broadcast schemes may be adapted to satisfying the different receivers' requirements or distributing the classical information, which are important in various quantum applications such as the quantum secret distribution or the quantum network communication.
Factorization Theorems for Exclusive Heavy-Quarkonium Production
NASA Astrophysics Data System (ADS)
Bodwin, Geoffrey T.; Garcia I Tormo, Xavier; Lee, Jungil
2008-09-01
We outline the proofs of the factorization theorems for exclusive two-body charmonium production in B-meson decay and e+e- annihilation to all orders in perturbation theory in quantum chromodynamics. We find that factorized expressions hold up to corrections of order mc/mb in B-meson decay and corrections of order mc2/s in e+e- annihilation, where mc is the charm-quark mass, mb is the bottom-quark mass, and s is the e+e- center-of-momentum energy.
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.
Research in advanced formal theorem-proving techniques
NASA Technical Reports Server (NTRS)
Rulifson, J. F.
1971-01-01
The present status is summarized of a continuing research program aimed at the design and implementation of a language for expressing problem-solving procedures in several areas of artificial intelligence, including program synthesis, robot planning, and theorem proving. Notations, concepts, and procedures common to the representation and solution of many of these problems were abstracted and incorporated as features into the language. The areas of research covered are described, and abstracts of six papers that contain extensive description and technical detail of the work are presented.
No-local-broadcasting theorem for multipartite quantum correlations.
Piani, Marco; Horodecki, Paweł; Horodecki, Ryszard
2008-03-01
We prove that the correlations present in a multipartite quantum state have an operational quantum character even if the state is unentangled, as long as it does not simply encode a multipartite classical probability distribution. Said quantumness is revealed by the new task of local broadcasting, i.e., of locally sharing preestablished correlations, which is feasible if and only if correlations are stricly classical. Our operational approach leads to natural definitions of measures for quantumness of correlations. It also reproduces the standard no-broadcasting theorem as a special case.
The epidemic threshold theorem with social and contact heterogeneity
NASA Astrophysics Data System (ADS)
Hincapié Palacio, Doracelly; Ospina Giraldo, Juan; Gómez Arias, Rubén Darío
2008-03-01
The threshold theorem of an epidemic SIR model was compared when infectious and susceptible individuals have homogeneous mixing and heterogeneous social status and when individuals of random networks have contact heterogeneity. Particularly the effect of vaccination in such models is considered when: individuals or nodes are exposed to impoverished, vaccination and loss of immunity. An equilibrium analysis and local stability of small perturbations about the equilibrium values were implemented using computer algebra. Numerical simulations were executed in order to describe the dynamic of transmission of diseases and changes of the basic reproductive rate. The implications of these results are examined around the threats to the global public health security.
Reynolds transport theorem for a two-phase flow
NASA Astrophysics Data System (ADS)
Collado, Francisco J.
2007-01-01
Transport equations for one-dimensional (1d), steady, two-phase flow have been proposed based on the fact that if the phases have different velocities, they cannot cover the same distance (the control volume length) in the same time. Thus, working in the same control volume for the two phases, the time scales of the phases have to be different. From this approach, transport balances for 1D, steady, two-phase flow have been already derived, supplying acceptable correlations for two-phase flow. Here, based on the strict application of the Reynolds transport theorem, general transport balances for two-phase flow are suggested.
Application of the complex Poynting theorem to metamaterial multilayered nanostructures
NASA Astrophysics Data System (ADS)
Aylo, Rola; Nehmetallah, George; Banerjee, Partha
2012-10-01
In earlier work, the transfer matrix method (TMM) and the angular plane wave spectrum method (APWS) have been used to analyze plane wave and beam propagation in a multilayer structure consisting of positive index and negative index materials. In this paper, we demonstrate the use the complex Poynting theorem (CPT) to validate numerical calculations by the TMM and APWS methods. Application of CPT also gives physical insight into the power balance inside such structures which may possess complex permittivities and permeabilities, and have propagating and nonpropagating waves.
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.
On the Fundamental Theorem of the Theory of Relativity
NASA Astrophysics Data System (ADS)
Mamone-Capria, Marco
2016-08-01
A new formulation of what may be called the "fundamental theorem of the theory of relativity" is presented and proved in (3 + 1)-space-time, based on the full classification of special transformations and the corresponding velocity addition laws. A system of axioms is introduced and discussed leading to the result, and a study is made of several variants of that system. In particular the status of the group axiom is investigated with respect to the condition of the two-way isotropy of light. Several issues which are ignored or misunderstood in the literature are emphasized.
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.
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.
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.