Inverting the central limit theorem
Navascues, Miguel; Villanueva, Ignacio
2011-01-01
The central limit theorem states that the sum of N independently distributed n-tuples of real variables (subject to appropriate normalization) tends to a multivariate gaussian distribution for large N. Here we propose to invert this argument: given a set of n correlated gaussian variables, we try to infer information about the structure of the discrete microscopic probability distributions whose convolution generated such a macroscopic behavior. The techniques developed along the article are applied to prove that the classical description of certain macroscopic optical experiments is infinitely more complex than the quantum one.
A History of the Central Limit Theorem
Fischer, Hans
2011-01-01
This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical
Central Limit Theorem for Coloured Hard Dimers
Directory of Open Access Journals (Sweden)
Maria Simonetta Bernabei
2010-01-01
Full Text Available We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs. The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations.
The central limit theorem and chaos
Institute of Scientific and Technical Information of China (English)
NIU Ying-xuan
2009-01-01
Let X be a compact metric space and f : X → X be a continuous map. This paper studies some relationships between stochastic and topological properties of dynamical systems.It is shown that if f satisfies the central limit theorem, then f is topologically ergodic and f is sensitively dependent on initial conditions if and only if f is neither minimal nor equicontinuous.
Central Limit Theorem for Nonlinear Hawkes Processes
Zhu, Lingjiong
2012-01-01
Hawkes process is a self-exciting point process with clustering effect whose jump rate depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. Linear Hawkes process has an immigration-birth representation and can be computed more or less explicitly. It has been extensively studied in the past and the limit theorems are well understood. On the contrary, nonlinear Hawkes process lacks the immigration-birth representation and is much harder to analyze. In this paper, we obtain a functional central limit theorem for nonlinear Hawkes process.
A Central Limit Theorem for Repeating Patterns
Abrams, Aaron; Landau, Henry; Landau, Zeph; Pommersheim, James
2012-01-01
This note gives a central limit theorem for the length of the longest subsequence of a random permutation which follows some repeating pattern. This includes the case of any fixed pattern of ups and downs which has at least one of each, such as the alternating case considered by Stanley in [2] and Widom in [3]. In every case considered the convergence in the limit of long permutations is to normal with mean and variance linear in the length of the permutations.
Central limit theorems under special relativity.
McKeague, Ian W
2015-04-01
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
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.
Improving Conceptions in Analytical Chemistry: The Central Limit Theorem
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.)
Almost Sure Central Limit Theorems for Heavily Trimmed Sums
Institute of Scientific and Technical Information of China (English)
Fang WANG; Shi Hong CHENG
2004-01-01
We obtain an almost sure central limit theorem (ASCLT) for heavily trimmed sums. We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums of i.i.d. random variables with EX1 = 0, EX12 = 1.
Central Limit Theorems for Multicolor Urns with Dominated Colors
Berti, Patrizia; Pratelli, Luca; Rigo, Pietro
2009-01-01
An urn contains balls of d colors. At each time, a ball is drawn and then replaced together with a random number of balls of the same color. Assuming that some colors are dominated by others, we prove central limit theorems. Some statistical applications are discussed.
Central limit theorem of linear regression model under right censorship
Institute of Scientific and Technical Information of China (English)
HE; Shuyuan(何书元); HUANG; Xiang(Heung; Wong)(黄香)
2003-01-01
In this paper, the estimation of joint distribution F(y,z) of (Y, Z) and the estimation in thelinear regression model Y = b′Z + ε for complete data are extended to that of the right censored data. Theregression parameter estimates of b and the variance of ε are weighted least square estimates with randomweights. The central limit theorems of the estimators are obtained under very weak conditions and the derivedasymptotic variance has a very simple form.
Central Limit Theorem for a Stratonovich Integral with Malliavin Calculus
Harnett, Daniel
2011-01-01
The purpose of this paper is to establish the convergence in law of the sequence of "midpoint" Riemann sums for a stochastic process of the form f'(W), where W is a Gaussian process whose covariance function satisfies some technical conditions. As a consequence we derive a change-of-variable formula in law with a second-order correction term which is an It\\^o integral of f"(W) with respect to a Gaussian martingale independent of W. The proof of the convergence in law is based on the techniques of Malliavin calculus and uses a central limit theorem of q-fold Skorohod integrals, which is a multidimensional extension of a result proved by Nourdin and Nualart in [5]. The results proved in this paper are generalizations of previous work by Swanson [10] and Nourdin and R\\'evaillac [7], who found a similar formula for two particular types of fractional Brownian motion. We provide two examples of Gaussian processes W that meet the necessary covariance bounds. The first one is the bifractional Brownian motion with par...
Almost Sure Central Limit Theorem for Partial Sums of Markov Chain
Institute of Scientific and Technical Information of China (English)
Guangming ZHUANG; Zuoxiang PENG; Zhongquan TAN
2012-01-01
The authors prove an almost sure central limit theorem for partial sums based on an irreducible and positive recurrent Markov chain using logarithmic means,which realizes the extension of the almost sure central limit theorem for partial sums from an i.i.d.sequence of random variables to a Markov chain.
An almost Sure Central Limit Theorem for the Weight Function Sequences of NA Random Variables
Indian Academy of Sciences (India)
Qunying Wu
2011-08-01
Consider the weight function sequences of NA random variables. This paper proves that the almost sure central limit theorem holds for the weight function sequences of NA random variables. Our results generalize and improve those on the almost sure central limit theorem previously obtained from the i.i.d. case to NA sequences.
Multidimensional Local Central Limit Theorem of Some Non-uniformly Hyperbolic Systems
Institute of Scientific and Technical Information of China (English)
Hong Qiang XIA
2009-01-01
We consider Young's nonuniformly hyperbolic system (X, T, v) where v is the SRB measure corresponding to the system (X, T), and show that if the components of a Holder observable f : X → Rd are cohomologously independent, then f satisfies the multidimensional central limit theorem. Moreover if f is aperiodic, then f satisfies the local multidimensional central limit theorem.
Pan, Guangming; Zhou, Wang
2010-01-01
A consistent kernel estimator of the limiting spectral distribution of general sample covariance matrices was introduced in Jing, Pan, Shao and Zhou (2010). The central limit theorem of the kernel estimator is proved in this paper.
The functional central limit theorem for strong near-epoch dependent random variables
Institute of Scientific and Technical Information of China (English)
QIU Jin; LIN Zhengyan
2004-01-01
The functional central limit theorem for strong near-epoch dependent sequences of random variables is proved.The conditions given improve on previous results in the literature concerning dependence and heterogeneity.
From Fibonacci Numbers to Central Limit Type Theorems
Miller, Steven J
2010-01-01
A beautiful theorem of Zeckendorf states that every integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $\\{F_n\\}_{n=1}^{\\infty}$. Lekkerkerker proved that the average number of summands for integers in $[F_n, F_{n+1})$ is $n/(\\varphi^2 + 1)$, with $\\varphi$ the golden mean. We prove the following massive generalization: given nonnegative integers $c_1,c_2,\\dots,c_L$ with $c_1,c_L>0$ and recursive sequence $\\{H_n\\}_{n=1}^{\\infty}$ with $H_1=1$, $H_{n+1} =c_1H_n+c_2H_{n-1}+\\cdots +c_nH_1+1$ $(1\\le n< L)$ and $H_{n+1}=c_1H_n+c_2H_{n-1}+\\cdots +c_LH_{n+1-L}$ $(n\\geq L)$, every positive integer can be written uniquely as $\\sum a_iH_i$ under natural constraints on the $a_i$'s, the mean and the variance of the numbers of summands for integers in $[H_{n}, H_{n+1})$ are of size $n$, and the distribution of the numbers of summands converges to a Gaussian as $n$ goes to the infinity. Previous approaches were number theoretic, involving continued fractions, and were limited to results on exis...
A Necessary Moment Condition for the Fractional Central Limit Theorem
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten
2012-01-01
/2) moments are necessary for more general fractional processes. Davidson and de Jong (2000, Econometric Theory 16, 643-- 666) presented a fractional FCLT where onlyq>2 finite moments are assumed. As a corollary to our main theorem we show that their moment condition is not sufficient and hence...
Central limit theorems for smoothed extreme value estimates of Poisson point processes boundaries
Girard, Stéphane
2011-01-01
In this paper, we give sufficient conditions to establish central limit theorems for boundary estimates of Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing leads Gaussian asymptotic distributions and therefore pointwise confidence intervals. Some new unidimensional and multidimensional examples are provided.
A Central Limit Theorem for the Zeroes of the Zeta Function
Rodgers, Brad
2012-01-01
On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's Zeta function that lie in a mesoscopic interval. The result mirrors results of Soshnikov and others in random matrix theory.
A CENTRAL LIMIT THEOREM FOR STRONG NEAR-EPOCH DEPENDENT RANDOM VARIABLES
Institute of Scientific and Technical Information of China (English)
LIN ZHENGYAN; QIU JIN
2004-01-01
In this paper, a central limit theorem for strong near-epoch dependent sequences of random variables introduced in [9] is showed. Under the same moments condition,the authors essentially weaken the "size" requirement mentioned in other papers about near epoch dependence.
A Functional Central Limit Theorem for a Class of Urn Models
Indian Academy of Sciences (India)
Gopal K Basak; Amites Dasgupta
2005-11-01
We construct an independent increments Gaussian process associated to a class of multicolor urn models. The construction uses random variables from the urn model which are different from the random variables for which central limit theorems are available in the two color case.
Central Limit Theorems for a Class of Irreducible Multicolor Urn Models
Indian Academy of Sciences (India)
Gopal K Basak; Amites Dasgupta
2007-11-01
We take a unified approach to central limit theorems for a class of irreducible multicolor urn models with constant replacement matrix. Depending on the eigenvalue, we consider appropriate linear combinations of the number of balls of different colors. Then under appropriate norming the multivariate distribution of the weak limits of these linear combinations is obtained and independence and dependence issues are investigated. Our approach consists of looking at the problem from the viewpoint of recursive equations.
Biskup, M.; Salvi, M.; Wolff, T.
2014-06-01
Given a resistor network on with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central limit theorem holds. The proof is based on the corrector method and the Martingale Central Limit Theorem; a key integrability condition is furnished by the Meyers estimate. More general domains, boundary conditions and ellipticity contrasts will be addressed in a subsequent paper.
Taming systematic uncertainties at the LHC with the central limit theorem
Fichet, Sylvain
2016-01-01
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 occuring in LHC measurements.
Directory of Open Access Journals (Sweden)
Juan Carlos Aquino
2013-06-01
Full Text Available The application of different unit root statistics is by now a standard practice in empirical work. Even when it is a practical issue, these statistics have complex nonstandard distributions depending on functionals of certain stochastic processes, and their derivations represent a barrier even for many theoretical econometricians. These derivations are based on rigorous and fundamental statistical tools which are not (very well known by standard econometricians. This paper aims to fill this gap by explaining in a simple way one of these fundamental tools: namely, the Functional Central Limit Theorem. To this end, this paper analyzes the foundations and applicability of two versions of the Functional Central Limit Theorem within the framework of a unit root with a structural break. Initial attention is focused on the probabilistic structure of the time series to be considered. Thereafter, attention is focused on the asymptotic theory for nonstationary time series proposed by Phillips (1987a, which is applied by Perron (1989 to study the effects of an (assumed exogenous structural break on the power of the augmented Dickey-Fuller test and by Zivot and Andrews (1992 to criticize the exogeneity assumption and propose a method for estimating an endogenous breakpoint. A systematic method for dealing with efficiency issues is introduced by Perron and Rodriguez (2003, which extends the Generalized Least Squares detrending approach due to Elliot et al. (1996. An empirical application is provided.
Sanov and central limit theorems for output statistics of quantum Markov chains
Energy Technology Data Exchange (ETDEWEB)
Horssen, Merlijn van, E-mail: merlijn.vanhorssen@nottingham.ac.uk [School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD (United Kingdom); Guţă, Mădălin, E-mail: madalin.guta@nottingham.ac.uk [School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD (United Kingdom)
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.
Institute of Scientific and Technical Information of China (English)
2009-01-01
This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It?’s type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.
Institute of Scientific and Technical Information of China (English)
Marcin DUDZI(N)SKI; Przemyslaw G(O)RKA
2013-01-01
We prove the almost sure central limit theorems for the maxima of partial sums of r.v.'s under a general condition of dependence due to Doukhan and Louhichi.We will separately consider the centered sequences and the sequences with positive expected values.
Institute of Scientific and Technical Information of China (English)
PENG ShiGe
2009-01-01
This is a survey on normal distributions and the related central limit theorem under sublinear expectation. We also present Brownian motion under sublinear expectations and the related stochastic calculus of Ito's type. The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk, statistics and other industrial problems.
A central limit theorem for the fourth Wick power of the free lattice field
Energy Technology Data Exchange (ETDEWEB)
Albeverio, S. [Bochum Univ. (Germany). Inst. fuer Mathematik]|[Bielefeld Univ. (Germany). Forschungszentrum Bielefeld-Bochum-Stochastik (BiBoS)]|[Centro di Ricerche in Fisica e Matematica (CERFIM), Locarno (Switzerland); Zhou, X.Y. [Bochum Univ. (Germany). Inst. fuer Mathematik]|[Bielefeld Univ. (Germany). Fakultaet fuer Mathematik]|[Beijing Normal Univ., BJ (China). Dept. of Mathematics
1996-11-01
Let G{sub a} be the free lattice field measure of mass m{sub 0} on aZ{sup d}, and :{phi}{sub x}{sup 4}: be the corresponding fourth Wick power of the lattice field {phi}{sub x}. Let g element of C{sub 0}(R{sup d}), g{>=} 0, be a given function and a`=a`(a){>=} a satisfy: lim{sub a{yields}} {sub 0{sup +}}a `=0 and a `Z {sup d} is contained in aZ {sup d}. We prove that if d {>=} 3, or d=2 and lim {sub a{yields}} {sub 0{sup +}}a ` vertical stroke log a vertical stroke {sup 2}= {infinity}, then {l_brace}a `{sup d} sum {sub x} {sub element} {sub of} {sub a`Z{sup d}}g {sub x} : {phi}{sub x}{sup 4}: {r_brace} satisfies the central limit theorem: there is V(a, a `) with lim {sub a{yields}} {sub 0{sup +}}V(a, a `)= {infinity} such that the distribution of V(a, a `) {sup -1}a `{sup d} sum {sub x} {sub element} {sub of} {sub a`Z{sup d}}g {sub x}: {phi}{sub x}{sup 4}: under G {sub a} is convergent to the standard normal distribution, as a {yields} 0 {sup +} (orig.)
A necessary moment condition for the fractional functional central limit theorem
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x_{t}=Delta^{-d}u_{t}, where d in (-1/2,1/2) is the fractional integration parameter and u_{t} is weakly dependent. The classical condition is existence of q>max(2,(d+1/2)^{-1}) moments...... of the innovation sequence. When d is close to -1/2 this moment condition is very strong. Our main result is to show that under some relatively weak conditions on u_{t}, the existence of q≥max(2,(d+1/2)^{-1}) is in fact necessary for the FCLT for fractionally integrated processes and that q>max(2,(d+1....../2)^{-1}) moments are necessary and sufficient for more general fractional processes. Davidson and de Jong (2000) presented a fractional FCLT where only q>2 finite moments are assumed, which is remarkable because it is the only FCLT where the moment condition has been weakened relative to the earlier condition...
A Necessary Moment Condition for the Fractional Functional Central Limit Theorem
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x(t)=¿^(-d)u(t), where d ¿ (-1/2,1/2) is the fractional integration parameter and u(t) is weakly dependent. The classical condition is existence of q>max(2,(d+1/2)-¹) moments...... of the innovation sequence. When d is close to -1/2 this moment condition is very strong. Our main result is to show that under some relatively weak conditions on u(t), the existence of q=max(2,(d+1/2)-¹) is in fact necessary for the FCLT for fractionally integrated processes and that q>max(2,(d+1/2)-¹) moments...... are necessary and sufficient for more general fractional processes. Davidson and de Jong (2000) presented a fractional FCLT where only q>2 finite moments are assumed, which is remarkable because it is the only FCLT where the moment condition has been weakened relative to the earlier condition. As a corollary...
The Star-Forming Main Sequence as a Natural Consequence of the Central Limit Theorem
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 =2/T, and Sig[SFR/M]=. Note that this relative scatter is independent of mass and time. This derived correlation between SFR and stellar mass, and its evolution, matches published data to z=10 with sufficient accuracy to constrain cosmological parameters from the data. This statistical approach to the diversity of star-formation histories reproduces several important observables, including: the scatter in SSFR at fixed mass; the forms of SFHs of nearby dwarf galaxies and the Milky Way. At least one additional process beyond a single one responsible for in situ stellar mass growth will be required to match the evolution of the stellar mass function, and we discuss ways to generalize the framework. The implied dispersion in SFHs, and the SFMS's insensitivity to timescales of stochasticity, thus substantially limits the ability to connect massive galaxies to their progenitors over long cosmic baselines. Such analytical work shows promise for statisically
Limit Theorems For Closed Queuing Networks With Excess Of Servers
Tsitsiashvili, G.
2013-01-01
In this paper limit theorems for closed queuing networks with excess of servers are formulated and proved. First theorem is a variant of the central limit theorem and is proved using classical results of V.I. Romanovskiy for discrete Markov chains. Second theorem considers a convergence to chi square distribution. These theorems are mainly based on an assumption of servers excess in queuing nodes.
Central limit theorem for integrated square error of kernel estimators of spherical density
Institute of Scientific and Technical Information of China (English)
ZHAO; Lincheng
2001-01-01
［1］ Cruzeiro, A. B., Malliavin, P., Renormalized differential geometry on path spaces: Structural equation, curvature, J. Funct. Anal., 1996, 139: 119-181.［2］ Stroock, D. W., Some thoughts about Riemannian structures on path spaces, preprint, 1996.［3］ Driver, B., A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact manifold, J. Funct. Anal., 1992, 109: 272-376.［4］ Enchev, O., Stroock, D. W., Towards a Riemannian geometry on the path space over a Riemannian manifold, J. Funct. Anal., 1995, 134: 392-416.［5］ Hsu, E., Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold, J. Funct. Anal., 1995, 134: 417-450.［6］ Lyons, T. J., Qian, Z. M., A class of vector fields on path space, J.Funct. Anal., 1997, 145: 205-223.［7］ Li, X. D., Existence and uniqueness of geodesics on path spaces, J. Funct. Anal., to be published.［8］ Driver, B., Towards calculus and geometry on path spaces, in Proc. Symp. Pure and Appl. Math. 57 (ed. Cranston, M., Pinsky, M.), Cornell: AMS, 1993, 1995.
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…
Pérez-Rodríguez, F.; Zwietering, M.H.
2012-01-01
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 (¿8), the distribution of the sum (or mean) of those
Central Limit Theorems for Cavity and Local Fields of the Sherrington-Kirkpatrick Model
Chen, Wei-Kuo
2010-01-01
One of the remarkable applications of the cavity method is to prove the Thouless-Anderson-Palmer (TAP) system of equations in the high temperature analysis of the Sherrington-Kirkpatrick (SK) model. This naturally leads us to the important study of the limit laws for cavity and local fields. The first quantitative results for both fields based on Stein's method were studied by Chatterjee. Although Stein's method provides us an efficient search for the limiting distributions, the nature of this method in some way restricts the exploration for optimal and general results. In this paper, our study based on Gaussian interpolation obtains the CLT for cavity fields. With the help of this result, we conclude the CLT for local fields. In both cases, better quantitative results are given.
Kelson, Daniel D
2014-01-01
Star-formation rates (SFR) of disk galaxies strongly correlate with stellar mass, with a small dispersion in SSFR at fixed mass, sigma~0.3 dex. With such small scatter this star-formation main sequence (SFMS) has been interpreted as deterministic and fundamental. Here we demonstrate that it is a simple consequence of the central limit theorem. Our 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). We then derive expectation values for median SSFR of star-forming disks and their scatter over time. We generalize the results for stochastic changes in SFR that are not independent of each other but are correlated over time. For unbiased samples of (disk) galaxies, we derive an expectation that should be independent of mass, decline as 1/T, and have a relative scatter that is independent of mass and time. The derived SFMS and its evolution matches published data to z=10 ...
Limit theorem and uniqueness theorem of backward stochastic differential equations
Institute of Scientific and Technical Information of China (English)
JIANG; Long
2006-01-01
This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0)≡0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectation εg; this paper also proves that if a filtration consistent expectation ε can be represented as a g-expectation εg, then the corresponding generator g must be unique.
An $\\alpha$-stable limit theorem under sublinear expectation
Erhan Bayraktar; Alexander Munk
2014-01-01
For $\\alpha\\in (1,2)$, we present a generalized central limit theorem for $\\alpha$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit theorem is recovered as a special case, provided a mild but natural additional condition holds. Our approach contrasts with previous arguments for the result in the linear setting which have typically relied ...
Some Limit Theorems in Geometric Processes
Institute of Scientific and Technical Information of China (English)
Yeh Lam; Yao-hui Zheng; Yuan-lin Zhang
2003-01-01
Geometric process (GP) was introduced by Lam[4,5], it is defined as a stochastic process {Xn, n =1, 2,...} for which there exists a real number a > 0, such that {an-1Xn, n = 1, 2,...} forms a renewal process (RP). In this paper, we study some limit theorems in GP. We first derive the Wald equation for GP and then obtain the limit theorems of the age, residual life and the total life at t for a GP. A general limit theorem for Sn with a > 1 is also studied. Furthermore, we make a comparison between GP and RP, including the comparison of their limit distributions of the age, residual life and the total life at t.
Limit theorems for fragmentation processes with immigration
Knobloch, Robert
2012-01-01
In this paper we extend two limit theorems which were recently obtained for fragmentation processes to such processes with immigration. More precisely, in the setting with immigration we consider a limit theorem for the process counted with a random characteristic as well as the asymptotic behaviour of an empirical measure associated with the stopping line corresponding to the first blocks, in their respective line of descent, that are smaller than a given size. In addition, we determine the asymptotic decay rate of the size of the largest block in a homogeneous fragmentation process with immigration. The techniques used to proves these results are based on submartingale arguments.
Limit theorems for bifurcating integer-valued autoregressive processes
Blandin, Vassili
2012-01-01
We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with the quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales.
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.
Adiabatic limits,vanishing theorems and the noncommutative residue
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
Limit theorems for bifurcating autoregressive processes with missing data
de Saporta, Benoîte; Marsalle, Laurence
2010-01-01
We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes when some of the data are missing. We model the process of observed data with a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the almost sure convergence of our estimators on the set of non-extinction of the Galton-Watson. We also prove a quadratic strong law and a central limit theorem.
Goedel incompleteness theorems and the limits of their applicability. I
Energy Technology Data Exchange (ETDEWEB)
Beklemishev, Lev D [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-01-25
This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.
Some scaled limit theorems for an immigration super-Brownian motion
Institute of Scientific and Technical Information of China (English)
ZHANG Mei
2008-01-01
In this paper, the small time limit behaviors for an immigration super-Brownian motion are studied, where the immigration is determined by Lebesgue measure. We first prove a functional central limit theorem, and then study the large and moderate deviations associated with this central tendency.
Some scaled limit theorems for an immigration super-Brownian motion
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue measure.We first prove a functional central limit theorem,and then study the large and moderate deviations associated with this central tendency.
Limit theorems for dilute quantum systems leading to quantum poisson processes
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.
Limit theorems for solutions of stochastic differential equation problems
Directory of Open Access Journals (Sweden)
J. Vom Scheidt
1980-01-01
Full Text Available In this paper linear differential equations with random processes as coefficients and as inhomogeneous term are regarded. Limit theorems are proved for the solutions of these equations if the random processes are weakly correlated processes.
POISSON LIMIT THEOREM FOR COUNTABLE MARKOV CHAINS IN MARKOVIAN ENVIRONMENTS
Institute of Scientific and Technical Information of China (English)
方大凡; 王汉兴; 唐矛宁
2003-01-01
A countable Markov chain in a Markovian environment is considered. A Poisson limit theorem for the chain recurring to small cylindrical sets is mainly achieved. In order to prove this theorem, the entropy function h is introduced and the Shannon-McMillan-Breiman theorem for the Markov chain in a Markovian environment is shown. It' s well-known that a Markov process in a Markovian environment is generally not a standard Markov chain, so an example of Poisson approximation for a process which is not a Markov process is given. On the other hand, when the environmental process degenerates to a constant sequence, a Poisson limit theorem for countable Markov chains, which is the generalization of Pitskel's result for finite Markov chains is obtained.
Some functional limit theorems for compound Cox processes
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.
Some Limit Theorems for Negatively Associated Random Variables
Indian Academy of Sciences (India)
Yu Miao; Wenfei Xu; Shanshan Chen; Andre Adler
2014-08-01
Let $\\{X_n,n≥ 1\\}$ be a sequence of negatively associated random variables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the $L^p$-convergence theorem and Marcinkiewicz–Zygmund strong law of large numbers. Furthermore, we consider the strong law of sums of order statistics, which are sampled from negatively associated random variables.
Limit theorems for multi-indexed sums of random variables
Klesov, Oleg
2014-01-01
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...
Limit theorems for vertex-reinforced jump processes on regular trees
Collevecchio, Andrea
2009-01-01
Consider a vertex-reinforced jump process defined on a regular tree, where each vertex has exactly $b$ children, with $b \\ge 3$. We prove the strong law of large numbers and the central limit theorem for the distance of the process from the root. Notice that it is still unknown if vertex-reinforced jump process is transient on the binary tree.
Limit theorems and inequalities via martingale methods
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Chazottes Jean-René
2014-01-01
Full Text Available In these notes, we first give a brief overwiew of martingales methods, from Paul Lévy (1935 untill now, to explain why these methods have become a central tool in probability, statistics and ergodic theory. Next, we present some recent results for/or based on martingales: exponential bounds for super-martingales, concentration inequalities for Lipschitz functionals of dynamical systems, oracle inequalities for the Cox model in a high dimensional setting, and invariance principles for stationary sequences.
Strong Limit Theorems for Arbitrary Fuzzy Stochastic Sequences
Institute of Scientific and Technical Information of China (English)
FEI Wei-yin
2008-01-01
Based on fuzzy random variables, the concept of fuzzy stochastic sequences is defined. Strong limit theorems for fuzzy stochastic sequences are established. Some known results in non-fuzzy stochastic sequences are extended. In order to prove results of this paper, the notion of fuzzy martingale difference sequences is also introduced.
The infrared limit of the SRG evolution and Levinson's theorem
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.
Gkioulekas, Eleftherios
2013-01-01
Many limits, typically taught as examples of applying the "squeeze" theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful…
Order book dynamics in liquid markets: limit theorems and diffusion approximations
Cont, Rama; De Larrard, Adrien
2011-01-01
Revision 2012; We propose a model for the dynamics of a limit order book in a liquid market where buy and sell orders are submitted at high frequency. We derive a functional central limit theorem for the joint dynamics of the bid and ask queues and show that, when the frequency of order arrivals is large, the intraday dynamics of the limit order book may be approximated by a Markovian jump-diffusion process in the positive orthant, whose characteristics are explicitly described in terms of th...
Limit theorems in the imitative monomer-dimer mean-field model via Stein's method
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.
Limit theorems for power variations of ambit fields driven by white noise
DEFF Research Database (Denmark)
Pakkanen, Mikko
We study the asymptotic behavior of lattice power variations of two-parameter ambit fields that are driven by white noise. Our first result is a law of large numbers for such power variations. Under a constraint on the memory of the ambit field, normalized power variations are shown to converge...... to certain integral functionals of the volatility field associated to the ambit field, when the lattice spacing tends to zero. This law of large numbers holds also for thinned power variations that are computed by only including increments that are separated by gaps with a particular asympotic behavior. Our...... second result is a related stable central limit theorem for thinned power variations. Additionally, we provide concrete examples of ambit fields that satisfy the assumptions of our limit theorems....
Fluctuation limit theorems for age-dependent critical binary branching systems
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Murillo-Salas Antonio
2011-03-01
Full Text Available We consider an age-dependent branching particle system in ℝd, where the particles are subject to α-stable migration (0 < α ≤ 2, critical binary branching, and general (non-arithmetic lifetimes distribution. The population starts off from a Poisson random field in ℝd with Lebesgue intensity. We prove functional central limit theorems and strong laws of large numbers under two rescalings: high particle density, and a space-time rescaling that preserves the migration distribution. Properties of the limit processes such as Markov property, almost sure continuity of paths and generalized Langevin equation, are also investigated.
Probabilities on the Heisenberg group limit theorems and Brownian motion
Neuenschwander, Daniel
1996-01-01
The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.
Limit theorems for power variations of ambit field driven by white noise
DEFF Research Database (Denmark)
Pakkanen, Mikko S.
2014-01-01
We study the asymptotics of lattice power variations of two-parameter ambit fields driven by white noise. Our first result is a law of large numbers for power variations. Under a constraint on the memory of the ambit field, normalized power variations converge to certain integral functionals...... of the volatility field associated to the ambit field, when the lattice spacing tends to zero. This result holds also for thinned power variations that are computed by only including increments that are separated by gaps with a particular asymptotic behavior. Our second result is a stable central limit theorem...
Strong limit theorems in noncommutative L2-spaces
Jajte, Ryszard
1991-01-01
The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.
A Strong Limit Theorem on Generalized Random Selection for m-valued Random Sequences
Institute of Scientific and Technical Information of China (English)
WANGZhong-zhi; XUFu-xia
2003-01-01
In this paper, a strong limit theorem on gambling strategy for binary Bernoulli sequence, i.e.irregularity theorem, is extended to random selection for dependent m-valued random variables, via using a new method-differentiability on net. Furthermore, by allowing the selection function to take value in finite interval [-M, M], the conception of random selection is generalized.
LIMIT THEOREMS AND OPTIMAL DESIGN WITH ADAPTIVE URN MODELS
Institute of Scientific and Technical Information of China (English)
CHEN Guijing; ZHU Chunhua; WANG Yao-hung
2005-01-01
In this paper we study urn model, using some available estimates of successes probabilities, and adding particle parameter, we establish adaptive models. We obtain some strong convergence theorems, rates of convergence, asymptotic normality of components in the urn, and estimates. With these asymptotical results, we show that the adaptive designs given in this paper are asymptotically optimal designs.
On a new proof of the Lindeberg-Feller classical limit theorem
Formanov, Shakir Kasimovich; Akanbay, Nursadyk; Akhmedov, Askar Bekenovich
2015-09-01
In recent papers researchers describe some of the new types of properties characterization of the normal distribution. This paper gives a new one based on the characterization of these properties, the proof of the classical limit theorem Lindeberg-Feller.
Quasi-sure Limit Theorem of Parabolic Stochastic Partial Differential Equations
Institute of Scientific and Technical Information of China (English)
Xi Cheng ZHANG
2004-01-01
In this paper we prove a quasi-sure limit theorem of parabolic stochastic partial differential equations with smooth coefficients and some initial conditions, by the way, we obtain the quasi-sure continuity of the solution.
Limit theorems for Markov processes indexed by continuous time Galton-Watson trees
Bansaye, Vincent; Marsalle, Laurence; Tran, Viet Chi
2009-01-01
We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton-Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring locations depend on the position of the mother and the number of offspring. We prove a law of large numbers for the empirical measure of individuals alive at time $t$. This relies on a probabilistic interpretation of its intensity by mean of an auxiliary process. This latter has the same generator as the Markov process along the branches plus additional branching events, associated with jumps of accelerated rate and biased distribution. This comes from the fact that choosing an individual uniformly at time $t$ favors lineages with more branching events and larger offspring number. The central limit theorem is considered on a special case. Several examples are developed, including applications to splitting diffusions, cellular aging, branching L\\'evy processes and ancestral line...
Multi-channel sampling theorems for band-limited signals with fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
2008-01-01
Multi-channel sampling for band-limited signals is fundamental in the theory of multi-channel parallel A/D environment and multiplexing wireless communication environment. As the fractional Fourier transform has been found wide applications in signal processing fields, it is necessary to consider the multi-channel sampling theorem based on the fractional Fourier transform. In this paper, the multi-channel sampling theorem for the fractional band-limited signal is firstly proposed, which is the generalization of the well-known sampling theorem for the fractional Fourier transform. Since the periodic nonuniformly sampled signal in the fractional Fourier domain has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived multi-channel sampling theorem and the specific space-shifting and phase-shifting properties of the fractional Fourier transform. Moreover, by designing different fractional Fourier filters, we can obtain reconstruction methods for other sampling strategies.
Limit theorem for a time-dependent coined quantum walk on the line
Machida, Takuya
2010-01-01
We study time-dependent discrete-time quantum walks on the one-dimensional lattice. We compute the limit distribution of a two-period quantum walk defined by two orthogonal matrices. For the symmetric case, the distribution is determined by one of two matrices. Moreover, limit theorems for two special cases are presented.
A Class of Strong Limit Theorems and Moment Generating Function Method
Institute of Scientific and Technical Information of China (English)
Wen Han LI; Gao Rong LI; Nan Bin CAO
2012-01-01
In virtue of the notion of likelihood ratio and moment generating function,the limit properties of the sequences of absolutely continuous random variables are studied,and a class of strong limit theorems represented by inequalities with random bounds are obtained.
A New Type of Limit Theorems for the One-Dimensional Quantum Random Walk
Konno, N
2002-01-01
In this paper we consider the one-dimensional quantum random walk X^{\\phi}_n at time n starting from initial qubit state \\phi determined by 2 \\times 2 unitary matrix U. We give a combinatorial expression for the characteristic function of X^{\\phi}_n. The expression clarifies the dependence of it on components of unitary matrix U and initial qubit state \\phi. As a consequence of the above results, we present a new type of limit theorems for the Hadamard walk. In contrast with the de Moivre-Laplace limit theorem, our symmetric case implies that X^{\\phi}_n/n \\Rightarrow Z^{\\phi} where Z^{\\phi} has a density 1 / \\pi (1-x^2) \\sqrt{1-2x^2} for x \\in (- \\sqrt{2}/2, \\sqrt{2}/2). Moreover we discuss some known simulation results based on our limit theorems.
A scaling limit theorem for the parabolic Anderson model with exponential potential
Lacoin, Hubert
2010-01-01
The parabolic Anderson problem is the Cauchy problem for the heat equation with random potential and localized initial condition. In this paper we consider potentials which are constant in time and independent exponentially distributed in space. We study the growth rate of the total mass of the solution in terms of weak and almost sure limit theorems, and the spatial spread of the mass in terms of a scaling limit theorem. The latter result shows that in this case, just like in the case of heavy tailed potentials, the mass gets trapped in a single relevant island with high probability.
A Fluctuation Type Limit Theorem for Jirina Processes with Immigration
Institute of Scientific and Technical Information of China (English)
Yu Qiang LI
2009-01-01
It is proved by the theory of semigroup that the Ornstein-Uhlenbeck type process with jumps can arise from the fluctuation limit of a sequence of Jirina processes with immigration under suitable moments conditions.
Limit theorems for alternating renewal processes in the infinite mean case
Mitov, K. V.; Yanev, N. M.
2001-01-01
The asymptotic behaviour of an occupation-time process associated with alternating renewal processes is investigated in the infinite mean cycle case. The limit theorems obtained extend some asymptotic results proved by Dynkin (1955), Lamperti (1958) and Erickson (1970) for the classical spent lifetime process. Some new phenomena are also presented.
HEAVY TRAFFIC LIMIT THEOREMS IN FLUID BUFFER MODELS
Institute of Scientific and Technical Information of China (English)
YIN Gang; ZHANG Hanqin
2004-01-01
A fluid buffer model with Markov modulated input-output rates is considered.When traffic intensity is near its critical value, the system is known as in heavy traffic.It is shown that a suitably scaled sequence of the equilibrium buffer contents has a weakor distributional limit under heavy traffic conditionsThis weak limit is a functional of adiffusion process determined by the Markov chain modulating the input and output rates.The first passage time of the reflected process is examinedIt is shown that the mean firstpassage time can be obtained via a solution of a Dirichlet problemThen the transitiondensity of the reflected process is derived by solving the Kolmogorov forward equation witha Neumann boundary conditionFurthermore, when the fast changing part of the generatorof the Markov chain is a constant matrix, the representation of the probability distributionof the reflected process is derivedUpper and lower bounds of the probability distributionare also obtained by means of asymptotic expansions of standard normal distribution.
Limit Theorems for Competitive Density Dependent Population Processes
Parsons, Todd L
2010-01-01
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its extensions have given biologists powerful tools of statistical inference that enabled the quantification of genetic drift and selection. Given the utility of these tools, we often forget that their model - for mathematical, and not biological reasons - makes assumptions that are violated in most real-world populations. In this paper, I consider an alternative framework that merges P. A. P. Moran's continuous-time Markov chain model of allele frequency with the density dependent models of ecological competition proposed by Gause, Lotka and Volterra, that, unlike Moran's model allow for a stochastically varying -- but bounded -- population size. I require that allele numbers vary according to a density-dependent population process, for which the limiting law of large numbers is a...
A weak limit theorem for numerical approximation of Brownian semi-stationary processes
DEFF Research Database (Denmark)
Podolskij, Mark; Thamrongrat, Nopporn
In this paper we present a weak limit theorem for a numerical approximation of Brownian semi-stationary processes studied in [14]. In the original work of [14] the authors propose to use Fourier transformation to embed a given one dimensional (Levy) Brownian semi-stationary process into a two......-parameter stochastic field. For the latter they use a simple iteration procedure and study the strong approximation error of the resulting numerical scheme given that the volatility process is fully observed. In this work we present the corresponding weak limit theorem for the setting, where the volatility....../drift process needs to be numerically simulated. In particular, weak approximation errors for smooth test functions can be obtained from our asymptotic theory....
Mathematical statistics and limit theorems Festschrift in honour of Paul Deheuvels
Mason, David; Pfeifer, Dietmar; Steinebach, Josef
2015-01-01
This Festschrift in honour of Paul Deheuvels’ 65th birthday compiles recent research results in the area between mathematical statistics and probability theory with a special emphasis on limit theorems. The book brings together contributions from invited international experts to provide an up-to-date survey of the field. Written in textbook style, this collection of original material addresses researchers, PhD and advanced Master students with a solid grasp of mathematical statistics and probability theory.
Study of Fixed Point Theorem for Common Limit Range Property and Application to Functional Equations
Directory of Open Access Journals (Sweden)
Nashine Hemant Kumar
2014-06-01
Full Text Available The aim of our paper is to use common limit range property for two pairs of mappings deriving common fixed point results under a generalized altering distance function. Some examples are given to exhibit different type of situation which shows the requirements of conditions of our results. At the end the existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming with the help of a common fixed point theorem is presented.
Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Mohammad Imdad
2013-01-01
Full Text Available The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in metric spaces satisfying an implicit function essentially due to the paper of Ali and Imdad (2008. As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Ali and Imdad (2008. We also furnish some illustrative examples to support our main results.
Day, Troy
2012-04-07
The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century, there have been remarkable advances in the development of theory for this diversification, and the theory's success rests, in part, on the scope of its applicability. A great deal of this theory focuses on a relatively small subset of the space of potential genotypes, chosen largely based on historical or contemporary patterns, and then predicts the evolutionary dynamics within this pre-defined set. To what extent can such an approach be pushed to a broader perspective that accounts for the potential open-endedness of evolutionary diversification? There have been a number of significant theoretical developments along these lines but the question of how far such theory can be pushed has not been addressed. Here a theorem is proven demonstrating that, because of the digital nature of inheritance, there are inherent limits on the kinds of questions that can be answered using such an approach. In particular, even in extremely simple evolutionary systems, a complete theory accounting for the potential open-endedness of evolution is unattainable unless evolution is progressive. The theorem is closely related to Gödel's incompleteness theorem, and to the halting problem from computability theory.
On Almost Sure Max-limit Theorems of Complete and Incomplete Samples from Stationary Sequences
Institute of Scientific and Technical Information of China (English)
Bin TONG; Zuo Xiang PENG
2011-01-01
Let Mn denote the partial maximum of a strictly stationary sequence (Xn). Suppose that some of the random variables of (Xn) can be observed and let (M~)n stand for the maximum of observed random variables from the set {Xi,..., Xn}. In this paper, the almost sure limit theorems related to random vector ((M~),Mn) are considered in terms of i.i.d. case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.
Hybrid Fixed Point Theorems in Symmetric Spaces via Common Limit Range Property
Directory of Open Access Journals (Sweden)
Imdad Mohammad
2014-12-01
Full Text Available In this paper, we point out that some recent results of Vijaywar et al. (Coincidence and common fixed point theorems for hybrid contractions in symmetric spaces, Demonstratio Math. 45 (2012, 611-620 are not true in their present form. With a view to prove corrected and improved versions of such results, we introduce the notion of common limit range property for a hybrid pair of mappings and utilize the same to obtain some coincidence and fixed point results for mappings defined on an arbitrary set with values in symmetric (semi-metric spaces. Our results improve, generalize and extend some results of the existing literature especially due to Imdad et al., Javid and Imdad, Vijaywar et al. and some others. Some illustrative examples to highlight the realized improvements are also furnished.
Heck, Richard G
2011-01-01
Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterlyfundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that a
Institute of Scientific and Technical Information of China (English)
LI Bijing; WANG Guojun
2005-01-01
The concept of truth degrees of formulas in (L)ukasiewicz n-valued proposi tional logic Ln is proposed. A limit theorem is obtained, which says that the truth function (T)n induced by truth degrees converges to the integrated truth function (T) when n converges to infinite. Hence this limit theorem builds a bridge between the discrete valued (L)ukasiewicz logic and the continuous valued (L)ukasiewicz logic. Moreover, the results obrained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic.
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.
Force analysis of pile foundation in rock slope based on upper-bound theorem of limit
Institute of Scientific and Technical Information of China (English)
ZHAO Ming-hua; LIU Jian-hua; LIU Dai-quan; WANG You
2008-01-01
Based on the characteristic that the potential sliding surfaces of rock slope are commonly in the shape of either line or fold line, analysis thought of conventional pile foundation in the flat ground under complex load condition was applied and the upper-bound theorem of limit analysis was used to compute thrust of rock layers with all possible distribution shapes. The interaction of slope and pile was considered design load in terms of slope thrust, and the finite difference method was derived to calculate inner-force and displacement of bridge pile foundation in rock slope under complex load condition. The result of example shows that the distribution model of slope thrust has certain impact on displacement and inner-force of bridge pile foundation. The maximum displacement growth rate reaches 54% and the maximum moment and shear growth rates reach only 15% and 20%, respectively, but the trends of inner-force and displacement of bridge pile foundation are basically the same as those of the conventional pile foundation in the flat ground. When the piles bear the same level lateral thrust, the distribution shapes of slope thrust have different influence on inner-force of pile foundation, especially the rectangle distribution, and the triangle thrust has the smallest displacement and inner-force of pile foundation.
Functional limit theorem for moving average processes generated by dependent random variables
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Let {Xt,t≥1} be a moving average process defined byXt = ∞∑j=0bjξt-j , where {bj,j≥0} is a sequence of real numbers and { ξt, ∞＜ t ＜∞ } is a doubly infinite sequence of strictly stationary φ- mixing random variables. Under conditions on { bj, j ≥0 }which entail that { Xt, t ≥ 1 } is either a long memory process or a linear process, we study asymptotics of Sn ( s ) = [ns]∑t=1 Xt (properly normalized). When { Xt, t≥1 } is a long memory process, we establish a functional limit theorem. When { Xt, t≥1 } is a linear process, we not only obtain the multi-dimensional weak convergence for { Xt, t≥1 }, but also weaken the moment condition on { ξt, - ∞＜ t ＜∞ } and the restriction on { bj,j≥0}. Finally, we give some applications of our results.
Nutrient Limitation in Central Red Sea Mangroves
Almahasheer, Hanan
2016-12-24
As coastal plants that can survive in salt water, mangroves play an essential role in large marine ecosystems (LMEs). The Red Sea, where the growth of mangroves is stunted, is one of the least studied LMEs in the world. Mangroves along the Central Red Sea have characteristic heights of ~2 m, suggesting nutrient limitation. We assessed the nutrient status of mangrove stands in the Central Red Sea and conducted a fertilization experiment (N, P and Fe and various combinations thereof) on 4-week-old seedlings of Avicennia marina to identify limiting nutrients and stoichiometric effects. We measured height, number of leaves, number of nodes and root development at different time periods as well as the leaf content of C, N, P, Fe, and Chl a in the experimental seedlings. Height, number of nodes and number of leaves differed significantly among treatments. Iron treatment resulted in significantly taller plants compared with other nutrients, demonstrating that iron is the primary limiting nutrient in the tested mangrove population and confirming Liebig\\'s law of the minimum: iron addition alone yielded results comparable to those using complete fertilizer. This result is consistent with the biogenic nature of the sediments in the Red Sea, which are dominated by carbonates, and the lack of riverine sources of iron.
Central limit approximations for Markov population processes with countably many types
Barbour, A D
2012-01-01
When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch, this leads to systems in which there are countably infinitely many possible types of entity. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove central limit theorems for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted $\\ell_1$ norm.
Levine, James A
2016-08-01
The Wearable Technology market may increase fivefold by the end of the decade. There is almost no academic investigation as to what drives the investment hypothesis in wearable technologies. This paper seeks to examine this issue from an evidence-based perspective. There is a fundamental disconnect in how consumers view wearable sensors and how companies market them; this is called The Baetylus Theorem where people believe (falsely) that by buying a wearable sensor they will receive health benefit; data suggest that this is not the case. This idea is grounded social constructs, psychological theories and marketing approaches. A marketing proposal that fails to recognize The Baetylus Theorem and how it can be integrated into a business offering has not optimized its competitive advantage. More importantly, consumers should not falsely believe that purchasing a wearable technology, improves health.
Directory of Open Access Journals (Sweden)
Sunny Chauhan
2013-11-01
Full Text Available In this paper, we utilize the notion of common limit range property in Non-Archimedean Menger PM-spaces and prove some fixed point theorems for two pairs of weakly compatible mappings. Some illustrative examples are furnished to support our results. As an application to our main result, we present a common fixed point theorem for four finite families of self mappings. Our results improve and extend several known results existing in the literature.
On the Van Vleck theorem for regular C-fractions with limit-periodic coefficients
Energy Technology Data Exchange (ETDEWEB)
Buslaev, V I [Steklov Mathematical Institute, Russian Academy of Sciences (Russian Federation)
2001-08-31
In this paper we investigate the convergence set of a regular C-fraction with limit-periodic coefficients. This investigation is based on a general assertion concerning the convergence of composites of linear-fractional transformations whose coefficients are limit-periodic functions depending holomorphically on a parameter. We show that the singularity set of such a C-fraction possesses an extremal property stated in terms of the transfinite diameter (capacity) of sets.
Functional limit theorems for generalized variations of the fractional Brownian sheet
DEFF Research Database (Denmark)
Pakkanen, Mikko; Réveillac, Anthony
and on the smallest component of the Hurst parameter vector of the fBs. The limiting process in the former result is another fBs, independent of the original fBs, whereas the limit given by the latter result is an Hermite sheet, which is driven by the same white noise as the original fBs. As an application, we derive...
Functional limit theorems for generalized variations of the fractional Brownian sheet
DEFF Research Database (Denmark)
Pakkanen, Mikko; Réveillac, Anthony
2016-01-01
and on the smallest component of the Hurst parameter vector of the fBs. The limiting process in the former result is another fBs, independent of the original fBs, whereas the limit given by the latter result is an Hermite sheet, which is driven by the same white noise as the original fBs. As an application, we derive...
Some strong limit theorems for nonhomogeneous Markov chains indexed by controlled trees
Directory of Open Access Journals (Sweden)
Weicai Peng
2016-02-01
Full Text Available Abstract In this paper, a kind of infinite, local finite tree T, named a controlled tree, is introduced. Some strong limit properties, such as the strong law of large numbers and the asymptotic equipartition property, for nonhomogeneous Markov chains indexed by T, are established. The outcomes are the generalizations of some well-known results.
A functional limit theorem for partial sums of dependent random variables with infinite variance
Basrak, Bojan; Segers, Johan
2010-01-01
Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version of this is known to be true as well, the limit process being a stable L\\'evy process. The main result in the paper is that for a stationary, regularly varying sequence for which clusters of high-threshold excesses can be broken down into asymptotically independent blocks, the properly centered partial sum process still converges to a stable L\\'evy process. Due to clustering, the L\\'evy triple of the limit process can be different from the one in the independent case. The convergence takes place in the space of c\\`adl\\`ag functions endowed with Skorohod's $M_1$ topology, the more usual $J_1$ topology being inappropriate as the partial sum processes may exhibit rapid successions of jumps within temporal clusters of large values, collapsing in the limit to a single jump. The ...
The Limit Theorems for Maxima of Stationary Gaussian Processes with Random Index
Institute of Scientific and Technical Information of China (English)
Zhong Quan TAN
2014-01-01
Let {X(t), t ≥ 0} be a standard (zero-mean, unit-variance) stationary Gaussian process with correlation function r(·) and continuous sample paths. In this paper, we consider the maxima M (T ) = max{X (t),∀t ∈ [0, T ]} with random index TT , where TT/T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M (TT ) exists under some additional conditions related to the correlation function r(·).
Limit theorems for splitting trees with structured immigration and applications to biogeography
Richard, Mathieu
2010-01-01
We consider a branching process with Poissonian immigration where individuals have inheritable types. At rate $\\theta$, new individuals singly enter the total population and start a new population which evolves like a supercritical, homogeneous, binary Crump-Mode-Jagers process: individuals have i.i.d. lifetimes durations (non necessarily exponential) during which they give birth independently at constant rate b. First, using spine decomposition, we relax previously known assumptions required for a.s. convergence of total population size. Then, we consider three models of structured populations: either all immigrants have a different type, or types are drawn in a discrete spectrum or in a continuous spectrum. In each model, the vector (P_1,P_2,...) of relative abundances of surviving families converges a.s. In the first model, the limit is the GEM distribution with parameter $\\theta/b$.
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
Central limit theorem for biased random walk on multi-type Galton-Watson trees
Dembo, Amir
2010-01-01
Let T be a rooted multi-type Galton-Watson (MGW) tree of finitely many types with at least one offspring at each vertex, and an offspring distribution with exponential tails. The lambda-biased random walk (X_t, t>=0) on T is the nearest-neighbor random walk which, when at a vertex v with d(v) offspring, moves closer to the root with probability lambda/(lambda+d(v)), and to each of the offspring with probability 1/(lambda+d(v)). This walk is recurrent for lambda >= rho and transient for 0 <= lambda < rho, with rho the Perron-Frobenius eigenvalue for the (assumed) irreducible matrix of expected offspring numbers. We prove the following quenched CLT for the critical value lambda = rho: for almost every T, the process |X_{floor(nt)}|/sqrt{n} converges in law as n tends to infinity to a deterministic positive multiple of a reflected Brownian motion. Following the approach of Peres and Zeitouni (2008) for Galton-Watson trees, our proof is based on a new explicit description of a reversing measure for the walk...
Berry-Esseen's central limit theorem for non-causal linear processes in Hilbert space
Machkouri, Mohamed EL
2010-01-01
Let $H$ be a real separable Hilbert space and $(a_k)_{k\\in\\mathbb{Z}}$ a sequence of bounded linear operators from $H$ to $H$. We consider the linear process $X$ defined for any $k$ in $\\mathbb{Z}$ by $X_k=\\sum_{j\\in\\mathbb{Z}}a_j(\\varepsilon_{k-j})$ where $(\\varepsilon_k)_{k\\in\\mathbb{Z}}$ is a sequence of i.i.d. centered $H$-valued random variables. We investigate the rate of convergence in the CLT for $X$ and in particular we obtain the usual Berry-Esseen's bound provided that $\\sum_{j\\in\\mathbb{Z}}\\vert j\\vert\\|a_j\\|_{\\mathcal{L}(H)}<+\\infty$ and $\\varepsilon_0$ belongs to $L_H^{\\infty}$.
A Central Limit Theorem for the Volumes of High Excursions of Stationary Associated Random Fields
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Vadim Demichev
2015-05-01
Full Text Available We prove that under certain conditions the excursion sets volumes of stationary positively associated random fields converge after rescaling to the normal distribution as the excursion level and the size of the observation window grow. In addition, we provide a number of examples.
A Strong Central Limit Theorem for a Class of Random Surfaces
Conlon, Joseph G.; Spencer, Thomas
2014-01-01
This paper is concerned with d = 2 dimensional lattice field models with action , where is a uniformly convex function. The fluctuations of the variable are studied for large | x| via the generating function given by . In two dimensions is proportional to . The main result of this paper is a bound on which is uniform in for a class of convex V. The proof uses integration by parts following Helffer-Sjöstrand and Witten, and relies on estimates of singular integral operators on weighted Hilbert spaces.
A functional central limit theorem for a Markov-modulated infinite-server queue
Anderson, D.F.; Blom, J.G.; Mandjes, M.R.H.; Thorsdottir, H.; deTurck, K.E.E.S
2013-01-01
We consider a model in which the production of new molecules in a chemical reaction network occurs in a seemingly stochastic fashion, and can be modeled as a Poisson process with a varying arrival rate: the rate is $\\lambda_i$ when an external Markov process $J(\\cdot)$ is in state $i$. It is assumed
A Functional Central Limit Theorem for a Markov-Modulated Infinite-Server Queue
Anderson, D.; Blom, J.; Mandjes, M.; Thorsdottir, H.; de Turck, K.
2016-01-01
We consider a model in which the production of new molecules in a chemical reaction network occurs in a seemingly stochastic fashion, and can be modeled as a Poisson process with a varying arrival rate: the rate is λ i when an external Markov process J(⋅) is in state i. It is assumed that molecules
Flatto, Leopold
2009-01-01
Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics. This book stresses the modern appro
Araki, Keisuke
2015-01-01
The dynamics of an incompressible, dissipationless Hall magnetohydrodynamic medium are formulated as a Lagrangian dynamical system on a direct product of two volume-preserving diffeomorphism groups. The hybrid and magnetic helicities are shown to emerge, respectively, from the application of the particle relabeling symmetry for ion and electron flows to Noether's first theorem, while the constant of motion associated with the theorem is generally given by their arbitrary linear combination. Double Beltrami flows, which are obtained here as eigenfunctions of the linear operator that generates the action-preserving perturbation from the generalized velocity, are found to provide a family of orthogonal function bases that yields the spectral representation of the equation of motion with a remarkably simple form. Considering the influence of a uniform background magnetic field and the Hall term effect vanishing limit, the generalized Els\\"asser variables are found to be the most suitable for avoiding problems wit...
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 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
Sustaining Rural Afghanistan under Limited Central Government Influence
Directory of Open Access Journals (Sweden)
John William Groninger
2013-06-01
Full Text Available Land and water access insecurity, land grabbing, and unstable common property status of critical local resources continue to drive conflicts, rural landlessness and environmental problems throughout many areas of Afghanistan where formal government is weak or entirely absent. In contrast to traditional development strategies that favor infrastructure enhancement and backed by enforced national policies, we offer Afghan-specific strategies based on resource conservation and increased capacity of local resource management institutions that can function when and where central government cannot be relied upon to assume or maintain a supportive role. Resource conservation and building local capacity are key components of existing and proposed future efforts to increase stability. However, support for these efforts, whether government or community-based, has been limited in portions of rural Afghanistan , apparently due to low stakeholder confidence in retaining access to improved land, water and other critical resources when international forces withdraw. Powerful individuals and groups, operating outside local community structures, are increasingly impacting land use practices. We suggest a thorough assessment of the present and likely future social environment, including awareness of likely conflicts resulting from agricultural or natural resource improvements, before any tangible actions are taken.
Institute of Scientific and Technical Information of China (English)
Wen Sheng WANG
2002-01-01
Let {W(t); t ≥ 0} be a standard Wiener process and S be the Strassen set of functions.We investigate the exact rates of convergence to zero (as T →∞) of the variables suP0≤t≤T-aT inff∈ssuP0≤x≤1 |Yt,T(x) - f(x)| and inf0≤t≤T-aT suP0≤x≤1 |Yt,T(x) - f(x)| for any given f ∈ S, whereYt,T(x) = (W(t + xaT) - W(t))(2aT(logTa-1T1 + loglog T))-1/2.We establish a relation between how small the increments are and the functional limit resultsof Csorgo-Revesz increments for a Wiener process. Similar results for partial sums of i.i.d. randomvariables are also given.
The relativistic virial theorem and scale invariance
Gaite, Jose
2013-01-01
The virial theorem is related to the dilatation properties of bound states. This is realized, in particular, by the Landau-Lifshitz formulation of the relativistic virial theorem, in terms of the trace of the energy-momentum tensor. We construct a Hamiltonian formulation of dilatations in which the relativistic virial theorem naturally arises as the condition of stability against dilatations. A bound state becomes scale invariant in the ultrarelativistic limit, in which its energy vanishes. However, for very relativistic bound states, scale invariance is broken by quantum effects and the virial theorem must include the energy-momentum tensor trace anomaly. This quantum field theory virial theorem is directly related to the Callan-Symanzik equations. The virial theorem is applied to QED and then to QCD, focusing on the bag model of hadrons. In massless QCD, according to the virial theorem, 3/4 of a hadron mass corresponds to quarks and gluons and 1/4 to the trace anomaly.
Institute of Scientific and Technical Information of China (English)
Wan-yang DAI
2012-01-01
In Internet environment,traffic flow to a link is typically modeled by superposition of ON/OFF based sources.During each ON-period for a particular source,packets arrive according to a Poisson process and packet sizes (hence service times) can be generally distributed.In this paper,we establish heavy traffic limit theorems to provide suitable approximations for the system under first-in first-out (FIFO) and work-conserving service discipline,which state that,wten the lengths of both ON- and OFF-periods are lightly tailed,the sequences of the scaled queue length and workload processes converge weakly to short-range dependent reflecting Gaussian processes,and when the lengths of ON- and/or OFF-periods are heavily tailed with infinite variance,the sequences converge weakly to either reflecting fractional Brownian motions (FBMs) or certain type of longrange dependent reflecting Gaussian processes depending on the choice of scaling as the number of superposed sources tends to infinity.Moreover,the sequences exhibit a state space collapse-like property when the number of sources is large enough,which is a kind of extension of the well-known Little's law for M/M/1 queueing system.Theory to justify the approximations is based on appropriate heavy traffic conditions which essentially mean that the service rate closely approaches the arrival rate when the number of input sources tends to infinity.
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…
Limiting Shapes for Deterministic Centrally Seeded Growth Models
Fey-den Boer, Anne; Redig, Frank
2007-01-01
We study the rotor router model and two deterministic sandpile models. For the rotor router model in ℤ d , Levine and Peres proved that the limiting shape of the growth cluster is a sphere. For the other two models, only bounds in dimension 2 are known. A unified approach for these models with a
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.
Double soft theorem for perturbative gravity
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
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
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.
Improvement of Hartman's linearization theorem
Institute of Scientific and Technical Information of China (English)
SHI; Jinlin(史金麟)
2003-01-01
Hartman's linearization theorem tells us that if matrix A has no zero real part and f(x) isbounded and satisfies Lipchitz condition with small Lipchitzian constant, then there exists a homeomorphismof Rn sending the solutions of nonlinear system x' = Ax + f(x) onto the solutions of linear system x' = Ax.In this paper, some components of the nonlinear item f(x) are permitted to be unbounded and we provethe result of global topological linearization without any special limitation and adding any condition. Thus,Hartman's linearization theorem is improved essentially.
Lagrange Theorem for polygroups
Directory of Open Access Journals (Sweden)
alireza sedighi
2014-12-01
Full Text Available So far?, ?isomorphism theorems in hyperstructure were proved for different structures of polygroups?, ?hyperrings and etc?. ?In this paper?, ?the polygroups properties is studied with the introduction of a suitable equivalence relation?. ?We show that the above relation is strongly regular?. ?Our main purpose in the paper is investigating Lagrang theorem and other expressing of isomorphism theorems for polygroups?.
The asymmetric sandwich theorem
Simons, Stephen
2011-01-01
We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel duality theorem. Most of the results are about affine functions defined on convex subsets of vector spaces, rather than linear functions defined on vector spaces. We consider both results that use a simple boundedness hypothesis (as in Rockafellar's version of the Fenchel duality theorem) and also results that use Baire's theorem (as in the Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper also contains some new results about metrizable topological vector spaces that are not necessarily locally convex.
Martin-Olalla, J M; Martin-Olalla, Jose-Maria; Luna, Alfredo Rey de
2003-01-01
We revisit the relationship between the Nernst theorem and the Kelvin-Planck statement of the second law. We propose that the exchange of entropy uniformly vanishes as the temperature goes to zero. The analysis of this assumption shows that is equivalent to the fact that the compensation of a Carnot engine scales with the absorbed heat so that the Nernst theorem should be embedded in the statement of the second law. ----- Se analiza la relaci{\\'o}n entre el teorema de Nernst y el enunciado de Kelvin-Planck del segundo principio de la termodin{\\'a}mica. Se{\\~n}alamos el hecho de que el cambio de entrop{\\'\\i}a tiende uniformemente a cero cuando la temperatura tiende a cero. El an{\\'a}lisis de esta hip{\\'o}tesis muestra que es equivalente al hecho de que la compensaci{\\'o}n de una m{\\'a}quina de Carnot escala con el calor absorbido del foco caliente, de forma que el teorema de Nernst puede derivarse del enunciado del segundo principio.
Double Soft Theorem for Perturbative Gravity
Saha, Arnab Priya
2016-01-01
Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, 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.
2011-01-01
Arvanitakis established recently a theorem which is a common generalization of Michael's convex selection theorem and Dugundji's extension theorem. In this note we provide a short proof of a more general version of Arvanitakis' result.
If 1+1=2 then the Pythagorean theorem holds, or one more proof of the oldest theorem of mathematics
Directory of Open Access Journals (Sweden)
Alexandru HORVÁTH
2013-06-01
Full Text Available The Pythagorean theorem is one of the oldest theorems of mathematics. It gained during the time a central position and even today it continues to be a source of inspiration. In this note we try to give a proof which is based on a hopefully new approach. Our treatment will be as intuitive as it can be.
To string together six theorems of physics by Pythagoras theorem
Cui, H Y
2002-01-01
In this paper, we point out that there are at lest six theorems in physics sharing common virtue of Pythagoras theorem, so that it is possible to string these theorems together with the Pythagoras theorem for physics teaching, the six theorems are Newton's three laws of motion, universal gravitational force, Coulomb's law, and the formula of relativistic dynamics. Knowing the internal relationships between them, which have never been clearly revealed by other author, will benefit the logic of physics teaching.
On the Equivalence of Weyl Theorem and Generalized Weyl Theorem
Institute of Scientific and Technical Information of China (English)
M. BERKANI
2007-01-01
We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theo rem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a similar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.
Trigonometry, Including Snell's Theorem.
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)
Coincidence Point Theorems, Intersection Theorems and Saddle Point Theorems on FC-spaces
Institute of Scientific and Technical Information of China (English)
PIAO YONG-JIE; YIN ZHE
2009-01-01
In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.
Navier Stokes Theorem in Hydrology
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
STABILITY OF GAS CLOUDS IN GALACTIC NUCLEI: AN EXTENDED VIRIAL THEOREM
Energy Technology Data Exchange (ETDEWEB)
Chen, Xian; Cuadra, Jorge [Instituto de Astrofísica, Facultad de Física, Pontificia Universidad Católica de Chile, 782-0436 Santiago (Chile); Amaro-Seoane, Pau, E-mail: xchen@astro.puc.cl, E-mail: jcuadra@astro.puc.cl, E-mail: Pau.Amaro-Seoane@aei.mpg.de [Max Planck Institut für Gravitationsphysik (Albert-Einstein-Institut), D-14476 Potsdam (Germany)
2016-03-10
Cold gas entering the central 1–10{sup 2} pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH) to turn on an active galactic nucleus (AGN). The conventional criteria to assess the stability of these clouds, such as the Jeans criterion and Roche (or tidal) limit, are insufficient here, because they assume the dominance of self-gravity in binding a cloud, and neglect external agents, such as pressure and tidal forces, which are common in galactic nuclei. We formulate a new scheme for judging this stability. We first revisit the conventional Virial theorem, taking into account an external pressure, to identify the correct range of masses that lead to stable clouds. We then extend the theorem to further include an external tidal field, which is equally crucial for the stability in the region of our interest—in dense star clusters, around SMBHs. We apply our extended Virial theorem to find new solutions to controversial problems, namely, the stability of the gas clumps in AGN tori, the circum-nuclear disk in the Galactic Center, and the central molecular zone of the Milky Way. The masses we derive for these structures are orders of magnitude smaller than the commonly used Virial masses (equivalent to the Jeans mass). Moreover, we prove that these clumps are stable, contrary to what one would naively deduce from the Roche (tidal) limit.
Stability of Gas Clouds in Galactic Nuclei: An Extended Virial Theorem
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.
Maximum principle and convergence of central schemes based on slope limiters
Mehmetoglu, Orhan
2012-01-01
A maximum principle and convergence of second order central schemes is proven for scalar conservation laws in dimension one. It is well known that to establish a maximum principle a nonlinear piecewise linear reconstruction is needed and a typical choice is the minmod limiter. Unfortunately, this implies that the scheme uses a first order reconstruction at local extrema. The novelty here is that we allow local nonlinear reconstructions which do not reduce to first order at local extrema and still prove maximum principle and convergence. © 2011 American Mathematical Society.
ON RANGE DECOMPOSITION THEOREMS
Institute of Scientific and Technical Information of China (English)
吴利生
1990-01-01
We prove the following theorems.Theorem 1.Suppose f:X→Y is a closed map.X is a ωγ and β space,then Y=Y0∪(∪n=1∞Yn),where f-1(y) is countably compact for each y ∈Y0 and Yn is closed discrete in Y for each n≥1,Theorem 2-3:Suppose f:X→Y is a closed map,X is stratifable space,then Y=Y0 ∪(∪n=1∞Yn),where f-1(y) is compact for each y∈Y0 and Yn is closed discrete in Y for each n≥1.
D'Agostini, G
2005-01-01
It is curious to learn that Enrico Fermi knew how to base probabilistic inference on Bayes theorem, and that some influential notes on statistics for physicists stem from what the author calls elsewhere, but never in these notes, {\\it the Bayes Theorem of Fermi}. The fact is curious because the large majority of living physicists, educated in the second half of last century -- a kind of middle age in the statistical reasoning -- never heard of Bayes theorem during their studies, though they have been constantly using an intuitive reasoning quite Bayesian in spirit. This paper is based on recollections and notes by Jay Orear and on Gauss' ``Theoria motus corporum coelestium'', being the {\\it Princeps mathematicorum} remembered by Orear as source of Fermi's Bayesian reasoning.
Kartavtsev, Alexander
2014-01-01
According to the Goldstone theorem a scalar theory with a spontaneously broken global symmetry contains strictly massless states. In this letter we identify a loophole in the current-algebra proof of the theorem. Therefore, the question whether in models with Mexican hat potential the tangential excitations are strictly massless or are just almost massless as compared to the radial ones remains open. We also argue that mass of the tangential excitations approaches zero even if the symmetry is not spontaneously broken but a combination of the field components invariant under the symmetry transformations acquires a large vacuum expectation value.
Pérez-Espigares, Carlos; Redig, Frank; Giardinà, Cristian
2015-08-01
For non-equilibrium systems of interacting particles and for interacting diffusions in d-dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.
Muscle Strength, Physical Activity, and Functional Limitations in Older Adults with Central Obesity
Directory of Open Access Journals (Sweden)
Cassandra M. Germain
2016-01-01
Full Text Available 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.
Virial Theorem and Scale Transformations.
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)
The algal growth-limiting nutrient of lakes located at Mexico’s Mesa Central
Directory of Open Access Journals (Sweden)
Fernando W. Bernal-Brooks
2016-03-01
Full Text Available This paper reports on the algal growth-limiting nutrients of five lakes located on Mexico’s Mesa Central - a topic poorly known in the regional limnology of Mexico. The five case studies involved three contiguous watersheds of Michoacán State and provided a trophic state variation from mesotrophic to hypereutrophic; the case studies included Lakes Zirahuén, Pátzcuaro, Teremendo, Cuitzeo and the Cointzio Reservoir. The fieldwork involved the collection of physical and chemical data (including nutrients from each case study during the dry and rainy seasons of 2010. Additionally, water samples (1 L were obtained and filtered (0.45 µm in the laboratory to keep the nutrient content available for bioassays. The chemical analyses suggested a phosphorus (P limitation in the Cointzio Reservoir, Lake Teremendo and Lake Zirahuén relative to an N:P>16:1. There was a nitrogen (N limitation at three sampling stations of Lake Pátzcuaro, with an N:P<16:1. As result of the bioassays conducted in July 2012, the Cointzio Reservoir and Lake Teremendo appeared to be P-limited and Lake Pátzcuaro appeared to be N-limited at three sampling stations. Lake Zirahuén showed seasonal variation, with an N limitation during the dry season and a P limitation during the wet season. Those cases with similar results from both methods confirmed the limiting nutrient identification. Lake Cuitzeo, Lake Zirahuén (dry season, and the shallowest sampling station in Lake Pátzcuaro produced unclear results because of divergent outcomes. In terms of the algal growth potential, the Cointzio Reservoir remained unaltered from one season to the next. However, for most of the lakes (with the exception of Lake Pátzcuaro sites 2 and 4, the rainy season provided a dilution effect. Effective lake management depends on a clear recognition of such elements that are in control of the aquatic productivity. In the area of Michoacán, both N and P may act as limiting nutrients.
Teleman, Nicolae
2011-01-01
$Local^{3}$ Index Theorem means $Local(Local(Local \\;Index \\; Theorem)))$. $Local \\; Index \\; Theorem$ is the Connes-Moscovici local index theorem \\cite{Connes-Moscovici1}, \\cite{Connes-Moscovici2}. The second "Local" refers to the cyclic homology localised to a certain separable subring of the ground algebra, while the last one refers to Alexander-Spanier type cyclic homology. The Connes-Moscovici work is based on the operator $R(A) = \\mathbf{P} - \\mathbf{e}$ associated to the elliptic pseudo-differential operator $A$ on the smooth manifold $M$, where $\\mathbf{P}$, $\\mathbf{e}$ are idempotents, see \\cite{Connes-Moscovici1}, Pg. 353. The operator $R(A)$ has two main merits: it is a smoothing operator and its distributional kernel is situated in an arbitrarily small neighbourhood of the diagonal in $M \\times M$. The operator $R(A)$ has also two setbacks: -i) it is not an idempotent (and therefore it does not have a genuine Connes-Chern character); -ii) even if it were an idempotent, its Connes-Chern character ...
Multivariate irregular sampling theorem
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.
DEFF Research Database (Denmark)
Törnquist, Asger Dag; Weiss, W.
2009-01-01
We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible. © Instytut Matematyczny PAN, 2009....
Certified Kruskal's Tree Theorem
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Christian Sternagel
2014-07-01
Full Text Available This article presents the first formalization of Kurskal's tree theorem in aproof assistant. The Isabelle/HOL development is along the lines of Nash-Williams' original minimal bad sequence argument for proving the treetheorem. Along the way, proofs of Dickson's lemma and Higman's lemma, as well as some technical details of the formalization are discussed.
Rediscovering Schreinemakers' Theorem.
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…
Multivariate irregular sampling theorem
Institute of Scientific and Technical Information of China (English)
CHEN GuangGui; FANG GenSun
2009-01-01
In this paper, we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result, we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.
DEFF Research Database (Denmark)
Thomassen, Carsten
2004-01-01
We present a short proof of the theorem of Tutte that every planar 3-connected graph has a drawing in the plane such that every vertex which is not on the outer cycle is the barycenter of its neighbors. Moreover, this holds for any prescribed representation of the outer cycle. (C) 2004 Wiley Peri...
Dalen, D. van
2008-01-01
The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next edition
Converse Barrier Certificate Theorems
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2016-01-01
This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither sing...
Automated Discovery of Inductive Theorems
McCasland, Roy; Bundy, Alan; Serge, Autexier
2007-01-01
Inductive mathematical theorems have, as a rule, historically been quite difficult to prove – both for mathematics students and for auto- mated theorem provers. That said, there has been considerable progress over the past several years, within the automated reasoning community, towards proving some of these theorems. However, little work has been done thus far towards automatically discovering them. In this paper we present our methods of discovering (as well as proving) inductive theorems, ...
The Second Noether Theorem on Time Scales
Malinowska, Agnieszka B.; Natália Martins
2013-01-01
We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the $h$ -calculus and the second Noether theorem for the $q$ -calculus.
A Class of Limit Theorems of Moving Averages for END Random Variables%END随机序列滑动平均的若干极限定理
Institute of Scientific and Technical Information of China (English)
胡松; 汪忠志
2013-01-01
利用条件E(exp{t?X1|1/p})＜∞,(p＞1),证明END随机序列滑动平均的极限定理,给出形如(logn)-p(n+(log n)p)∑(k=n+1)Xk的滑动平均的上下界,得到了经典强大数定律.%The classical strong law of large numbers is generalized to the case of END random variables of the form (logn)-p/(n+(logn)p) Σ(k=n+1) Xk with the condition E(exp{t∣X1∣1/p})＜∞,(p>l), by identifying its upper and lower limit.
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.
An Extension of Sobolev's Theorem
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Sobolev's Theorem is the most fundamental theorem in the theory of Invariant Cubature Formulas (ICFs). In this paper, a quantitative structure is established for the classical ICFs. Enlightened by this structure, the author generalizes the concept of ICFs and extends the Sobolev's Theorem to the case of generalized ICFs. Several illustrative examples are given.
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.
Virial theorem and hypervirial theorem in a spherical geometry
Energy Technology Data Exchange (ETDEWEB)
Li Yan; Chen Jingling [Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Zhang Fulin, E-mail: flzhang@tju.edu.cn, E-mail: chenjl@nankai.edu.cn [Physics Department, School of Science, Tianjin University, Tianjin 300072 (China)
2011-09-09
The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)
Directory of Open Access Journals (Sweden)
Peter C. Esselman
2010-03-01
Full Text Available Hydropower dam construction is expanding rapidly in Central America because of the increasing demand for electricity. Although hydropower can provide a low-carbon source of energy, dams can also degrade socially valued riverine and riparian ecosystems and the services they provide. Such degradation can be partially mitigated by the release of environmental flows below dams. However, environmental flows have been applied infrequently to dams in Central America, partly because of the lack of information on the ecological, social, and economic aspects of rivers. This paper presents a case study of how resource and information limitations were addressed in the development of environmental flow recommendations for the Patuca River in Honduras below a proposed hydroelectric dam. To develop flow recommendations, we applied a multistep process that included hydrological analysis and modeling, the collection of traditional ecological knowledge (TEK during field trips, expert consultation, and environmental flow workshops for scientists, water managers, and community members. The final environmental flow recommendation specifies flow ranges for different components of river hydrology, including low flows for each month, high-flow pulses, and floods, in dry, normal, and wet years. The TEK collected from local and indigenous riverine communities was particularly important for forming hypotheses about flow-dependent ecological and social factors that may be vulnerable to disruption from dam-modified river flows. We show that our recommended environmental flows would have a minimal impact on the dam's potential to generate electricity. In light of rapid hydropower development in Central America, we suggest that environmental flows are important at the local scale, but that an integrated landscape perspective is ultimately needed to pursue hydropower development in a manner that is as ecologically sustainable as possible.
Institute of Scientific and Technical Information of China (English)
2012-01-01
At present,there are many factors limiting large area centralized,rapid development,and moderately large-scale land operation in China.These factors include(i) the existing land utilization system is still at adaptation stage,and it lacks universal agreement of people on large-scale land operation;(ii) farmers’ dependence on land is great;(iii) it is difficult to transfer surplus labor;(iv) there is no positive connection between promotion of moderately large-scale land operation and realization of increase of farmers’ income;(v) it remains to be proved whether large-scale operation can become a stable rural occupation and whether big farming households can grow to professional farmers;(vi) large-scale land operation in rural areas may lead to waste of resources;(vii) the promotion of large-scale land operation may cause other social contradictions.
Taylor, Marika
2016-01-01
The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension $3/2 < \\Delta < 5/2$. Therefore the strongest version of the F theorem is in general violated.
Indian Academy of Sciences (India)
N V Rao
2003-02-01
The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose is a compact set in the complex plane and 0 belongs to the boundary . Let $\\mathcal{A}(K)$ denote the space of all functions on such that is holomorphic in a neighborhood of and (0) = 0. Also for any given positive integer , let $\\mathcal{A}(m, K)$ denote the space of all such that is holomorphic in a neighborhood of and $f(0) = f'(0) = \\cdots = f^{(m)}(0) = 0$. Then $\\mathcal{A}(m, K)$ is dense in $\\mathcal{A}(K)$ under the supremum norm on provided that there exists a sector $W = \\{re^{i}; 0 ≤ r ≤ , ≤ ≤ \\}$ such that $W \\cap K = \\{0\\}$. (This is the well-known Poincare's external cone condition).} We present various generalizations of this result in the context of higher dimensions replacing holomorphic with harmonic.
Gouin, Henri
2015-01-01
Comments on Archimedes' theorem about sphere and cylinder; In his treatise addressed to Dositheus of Pelusium, Archimedes of Syracuse obtained the result of which he was the most proud: a sphere has two-thirds the volume of its circumscribing cylinder. At his request a sculpted sphere and cylinder were placed on his tomb near Syracuse. Usually, it is admitted that to find this formula, Archimedes used a half polygon inscribed in a semicircle; then he performed rotations of these two figures t...
1987-03-20
with standard expressions of spherical trigonometry is sinr)0 = cos0 sini//0 (4.37) which is consistent with the results obtained previously with...theorems for discrete transforms. However, sampling questions inlroduce difficult obstacles in the develop- ment of a discrete theory. First, sampling...additional obstacle to discrete represen- tations of the CT. An example of qualitative predication of the shape of silhouettes with the Silhouette-Slice
Convergence theorems for lattice group-valued measures
Boccuto, Antonio
2015-01-01
Convergence Theorems for Lattice Group-valued Measures explains limit and boundedness theorems for measures taking values in abstract structures. The eBook begins with a historical survey about these topics since the beginning of the last century, moving on to basic notions and preliminaries on filters/ideals, lattice groups, measures and tools which are featured in the rest of this text. Readers will also find a survey on recent classical results about limit, boundedness and extension theorems for lattice group-valued measures followed by information about recent developments on these kinds o
THREE SOLUTIONS THEOREMS FOR NONLINEAR OPERATOR EQUATIONS AND APPLICATIONS
Institute of Scientific and Technical Information of China (English)
SUN Jingxian; XU Xi'an
2005-01-01
In this paper, some three solutions theorems about a class of operators which are said to be limit-increasing are obtained. Some applications to the second order differential equations boundary value problems are given.
Tau leaping of stiff stochastic chemical systems via local central limit approximation
Energy Technology Data Exchange (ETDEWEB)
Yang, Yushu, E-mail: yushuyang7@gmail.com [Department of Mathematics and Statistics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250 (United States); Rathinam, Muruhan, E-mail: muruhan@umbc.edu [Department of Mathematics and Statistics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250 (United States)
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.
Sandwich classification theorem
Directory of Open Access Journals (Sweden)
Alexey Stepanov
2015-09-01
Full Text Available The present note arises from the author's talk at the conference ``Ischia Group Theory 2014''. For subgroups FleN of a group G denote by Lat(F,N the set of all subgroups of N , containing F . Let D be a subgroup of G . In this note we study the lattice LL=Lat(D,G and the lattice LL ′ of subgroups of G , normalized by D . We say that LL satisfies sandwich classification theorem if LL splits into a disjoint union of sandwiches Lat(F,N G (F over all subgroups F such that the normal closure of D in F coincides with F . Here N G (F denotes the normalizer of F in G . A similar notion of sandwich classification is introduced for the lattice LL ′ . If D is perfect, i.,e. coincides with its commutator subgroup, then it turns out that sandwich classification theorem for LL and LL ′ are equivalent. We also show how to find basic subroup F of sandwiches for LL ′ and review sandwich classification theorems in algebraic groups over rings.
Soft Photon and Graviton Theorems in Effective Field Theory
Elvang, Henriette; Naculich, Stephen G
2016-01-01
Extensions of the photon and graviton soft theorems are derived in 4d local effective field theories with massless particles of arbitrary spin. We prove that effective operators can result in new terms in the soft theorems at subleading order for photons and subsubleading order for gravitons. The new soft terms are unique and we provide a complete classification of all local operators responsible for such modifications. We show that no local operators can modify the subleading soft graviton theorem. The soft limits are taken in a manifestly on-locus manner using a complex double deformation of the external momenta. In addition to the new soft theorems, the resulting master formula yields consistency conditions such as the conservation of electric charge, the Einstein equivalence principle, supergravity Ward identities, and the Weinberg-Witten theorem.
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.
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-12-01
From 1996, the Norwegian and Swedish power markets were joined and a common power exchange was established. The two countries deal differently with bottlenecks (transmission obstruction) in their central networks. This report compares methods for dealing with such bottlenecks and looks at the alternatives. It emphasises the efficiency of pricing and incentives and the possibility of exercising market power under the different methods. Norway uses a method of price regions, or bottleneck tax. Prices are determined for the various price regions so as to keep the power flow below specified bounds. A surplus region is assigned a lower price than a deficit region and the bottleneck tax is the difference in price between two such price regions. The Swedish system is based on a counter purchase concept. In his offer to the spotmarket, the supplier has bound himself to provide a certain amount to the current system price regardless of network limitations. Up-regulation means that he produces more than this amount. Down-regulation means that he is paid for supplying less than he had offered to the current system price. In up- or down-regulation, compensation is given as the difference between the system price and the price on the counter purchase market. The main conclusions are: (1) Counter purchase is unsuitable as the main strategy for Norway. (2) Counter purchase may be suitable with short-lived and unpredicted bottlenecks; price regions may be suitable for long-lasting and predicted bottlenecks. Time is a central factor. (3) Present-day models for bottleneck management in Norway and Sweden do not give the optimum short-term load distribution on the network. In general, the current Norwegian system works fairly well, although it might be worthwhile to consider a system that approaches node pricing. 3 refs., 34 figs., 3 tabs.
A new VLA/e-MERLIN limit on central images in the gravitational lens system CLASS B1030+074
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.
Limitations and potentials of dual-purpose cow herds in Central Coastal Veracruz, Mexico.
Absalón-Medina, Victor Antonio; Blake, Robert W; Fox, Danny Gene; Juárez-Lagunes, Francisco I; Nicholson, Charles F; Canudas-Lara, Eduardo G; Rueda-Maldonado, Bertha L
2012-08-01
Feed chemical and kinetic composition and animal performance information was used to evaluate productivity limitations and potentials of dual-purpose member herds of the Genesis farmer organization of central coastal Veracruz, Mexico. The Cornell Net Carbohydrate and Protein System model (Version 6.0) was systematically applied to specific groups of cows in structured simulations to establish probable input-output relationships for typical management, and to estimate probable outcomes from alternative management based on forage-based dietary improvements. Key herd vulnerabilities were pinpointed: chronic energy deficits among dry cows of all ages in late gestation and impeded growth for immature cows. Regardless of the forage season of calving, most cows, if not all, incur energy deficits in the final trimester of gestation; thus reducing the pool of tissue energy and constraining milking performance. Under typical management, cows are smaller and underweight for their age, which limits feed intake capacity, milk production and the probability of early postpartum return to ovarian cyclicity. The substitution of good-quality harvested forage for grazing increased predicted yields by about one-third over typical scenarios for underweight cows. When diets from first parturition properly supported growth and tissue repletion, milk production in second and third lactations was predicted to improve about 60%. Judiciously supplemented diets based on good quality grass and legume forages from first calving were predicted to further increase productivity by about 80% across a three-lactation cow lifetime. These dual-purpose herd owners have large incentives to increase sales income by implementing nutritional strategies like those considered in this study.
Limits to physiological plasticity of the coral Pocillopora verrucosa from the central Red Sea
Ziegler, M.
2014-07-26
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
Cateter Venoso Central de Inserção Periférica: limites e possibilidades
Directory of Open Access Journals (Sweden)
Jaqueline Petry
2012-12-01
Full Text Available O presente estudo objetivou identificar limites e possibilidades de expansão do uso do Peripherally Inserted Central Catheters (PICC em unidades neonatais e pediátricas para outras unidades de internação. Trata-se de uma pesquisa exploratório-descritiva de abordagem qualitativa. A coleta de dados ocorreu em agosto e setembro de 2010, por meio de entrevista semiestruturada, com dez enfermeiros de um hospital do Rio Grande do Sul. A análise dos dados resultou em duas categorias: fatores limitadores da expansão do uso do PICC – falta de conhecimento técnico de profissionais de saúde, elevado custo do procedimento, enfrentamento dessa inovação tecnológica e a especificidade desse recurso – e fatores facilitadores para a expansão do PICC – benefícios para o paciente, diminuição do estresse da equipe e a otimização do tempo de trabalho. Conclui-se que a produção de boas evidências sobre o uso do PICC podem auxiliar os profissionais e as instituições utilizarem melhor esse recurso, beneficiando a qualidade da atenção.
Stability of Gas Clouds in Galactic Nuclei: An Extended Virial Theorem
Chen, Xian; Cuadra, Jorge
2015-01-01
Cold gas entering the central $1$ to $10^2$ pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH) to turn on an active galactic nucleus (AGN). The conventional criteria to assess the stability of these clouds, such as the Jeans criterion and Roche (or tidal) limit, are insufficient here, because they assume the dominance of self-gravity in binding a cloud, and neglect external agents, such as pressure and tidal forces, which are common in galactic nuclei. We formulate a new scheme for judging this stability. We first revisit the conventional Virial theorem, taking into account an external pressure, to identify the correct range of masses that lead to stable clouds. We then extend the theorem to include an external tidal field, crucial for the stability in the region of interest -- in dense star clusters, around SMBHs. We apply our extended Virial theorem to find the cor...
Transfinite Approximation of Hindman's Theorem
Beiglböck, Mathias
2010-01-01
Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring of the integers there are arbitrarily long finite sets with the same property. We extend the finite form of Hindman's Theorem to a "transfinite" version for each countable ordinal, and show that Hindman's Theorem is equivalent to the appropriate transfinite approximation holding for every countable ordinal. We then give a proof of Hindman's Theorem by directly proving these transfinite approximations.
Mlakar, Jernej; Zorman, Jerneja Videčnik; Matičič, Mojca; Vrabec, Matej; Alibegović, Armin; Popović, Mara
2016-02-01
Primary angiitis of the central nervous system is a rare condition, usually with an insidious onset. There is a wide variety of histological types (granulomatous, lymphocytic or necrotizing vasculitis) and types of vessel involved (arteries, veins or both). Most cases are idiopathic. We describe a first case of idiopathic granulomatous central nervous system phlebitis with additional limited involvement of the heart and lung, exclusively affecting small and medium sized veins in a 22-year-old woman, presenting as a sub acute headache. The reasons for this peculiar limitation of inflammation to the veins and the involvement of the heart and lungs are unknown.
Theorems on Positive Data: On the Uniqueness of NMF
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Hans Laurberg
2008-01-01
Full Text Available 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.
Experimental studies of the transient fluctuation theorem using liquid crystals
Indian Academy of Sciences (India)
Soma Datta; Arun Roy
2009-05-01
In a thermodynamical process, the dissipation or production of entropy can only be positive or zero, according to the second law of thermodynamics. However, the laws of thermodynamics are applicable to large systems in the thermodynamic limit. Recently a fluctuation theorem, known as the transient fluctuation theorem (TFT), which generalizes the second law of thermodynamics to small systems has been proposed. This theorem has been tested in small systems such as a colloidal particle in an optical trap. We report for the first time an analogous experimental study of TFT in a spatially extended system using liquid crystals.
Wigner-Araki-Yanase theorem beyond conservation laws
Tukiainen, Mikko
2017-01-01
The ability to measure every quantum observable is ensured by a fundamental result in quantum measurement theory. Nevertheless, additive conservation laws associated with physical symmetries, such as the angular momentum conservation, may lead to restrictions on the measurability of the observables. Such limitations are imposed by the theorem of Wigner, Araki, and Yanase (WAY). In this paper a formulation of the WAY theorem is presented rephrasing the measurability limitations in terms of quantum incompatibility. This broader mathematical basis enables us to both capture and generalize the WAY theorem by allowing us to drop the assumptions of additivity and even conservation of the involved quantities. Moreover, we extend the WAY theorem to the general level of positive operator-valued measures.
The Non-Signalling theorem in generalizations of Bell's theorem
Walleczek, J.; Grössing, G.
2014-04-01
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational
Abelian theorems for Whittaker transforms
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Richard D. Carmichael
1987-01-01
Full Text Available Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ∞ in absolute value inside a wedge region in the right half plane.
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Coghetto Roland
2015-06-01
Full Text Available Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
A Time scales Noether's theorem
Anerot, Baptiste; Cresson, Jacky; Pierret, Frédéric
2016-01-01
We prove a time scales version of the Noether's theorem relating group of symmetries and conservation laws. Our result extends the continuous version of the Noether's theorem as well as the discrete one and corrects a previous statement of Bartosiewicz and Torres in \\cite{BT}.
Geometry of the Adiabatic Theorem
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.…
Lopez-Real, Francis
2008-01-01
While the author was searching the web, he came across an article by Michael Keyton of IMSA (Illinois Mathematics and Science Academy) called "Theorems of mystery". The phrase is Keyton's own, and he defines such a theorem as "a result that has considerable structure with minimal hypotheses." The simplest of his 10 examples is one that many…
Some Theorems on Generalized Basic Hypergeometric Series
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A. D. Wadhwa
1972-07-01
Full Text Available In an earlier paper the author has established two theorems on generalized hypergeometric functions. In each theorem a numerator differs from a denominator by a positive integer. These theorems were further used to prove some theorems on the sums of Kampe de Feriet functions. Here, we have established the theorems which are the basic analogues of the theorems proved in the earlier paper.
Combinatorial Reciprocity Theorems
Beck, Matthias
2012-01-01
A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families of such counting functions connected to hyperplane arrangements, lattice points in polyhedra, proper colorings of graphs, and $P$-partitions. We will see that in each instance we get interesting information out of a counting function when we evaluate it at a \\emph{negative} integer (and so, a priori the counting function does not make sense at this number). Our goals are to convey some of the charm these "alternative" evaluations of counting functions exhibit, and to weave a unifying thread through various combinatorial reciprocity theorems by looking at them through the lens of geometry, which will include some scenic detours through other combinatorial concepts.
Towards the Carpenter's Theorem
Argerami, Martin
2008-01-01
Let M be a II_1 factor, A a masa in M and E the unique conditional expectation on A. Under some technical assumptions on the inclusion of A in M, which hold true for any semiregular masa of a separable factor, we show that for every discrete a in the positive part of the unit ball of A it is possible to find a projection p in M such that E(p)=a$. We also show an example of a diffuse operator x in A such that there exists a projection q in M with E(q)=x. These results show a new family of instances of a conjecture by Kadison, the so-called ``Carpenter's Theorem''.
POTENTIAL AND LIMITS OF RENEWABLE ENERGY IN THE CENTRAL AND SOUTH-EAST EUROPE REGION
CIRLEA Filip; Iancu, Iulian
2012-01-01
Renewable energy sources (solar power, wind power, hydroenergy, biomass, biofuels) with energy efficiency contribute to increasing security of electricity supply, competitiveness and sustainable development. The countries of the Central and South-East Europe region must to develop a focus on alternative energy sources and on energy efficiency and energy saving. Developing the renewable energy sector in a sustainable manner in the Central and South-East Europe region would enhance security of ...
An Equivalent Gauge and the Equivalence Theorem
Wulzer, Andrea
2014-01-01
I describe a novel covariant formulation of massive gauge theories in which the longitudinal polarization vectors do not grow with the energy. Therefore in the present formalism, differently from the ordinary one, the energy and coupling power-counting is completely transparent at the level of individual Feynman diagrams, with obvious advantages both at the conceptual and practical level. Since power-counting is transparent, the high-energy limit of the amplitudes involving longitudinal particles is immediately taken, and the Equivalence Theorem is easily demonstrated at all orders in perturbation theory. Since the formalism makes the Equivalence Theorem self-evident, and because it is based on a suitable choice of the gauge, we can call it an "Equivalent Gauge".
Generalized Sampling Theorem for Bandpass Signals
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Prokes Ales
2006-01-01
Full Text Available The reconstruction of an unknown continuously defined function from the samples of the responses of linear time-invariant (LTI systems sampled by the th Nyquist rate is the aim of the generalized sampling. Papoulis (1977 provided an elegant solution for the case where is a band-limited function with finite energy and the sampling rate is equal to times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.
Generalized Sampling Theorem for Bandpass Signals
Prokes, Ales
2006-12-01
The reconstruction of an unknown continuously defined function[InlineEquation not available: see fulltext.] from the samples of the responses of[InlineEquation not available: see fulltext.] linear time-invariant (LTI) systems sampled by the[InlineEquation not available: see fulltext.]th Nyquist rate is the aim of the generalized sampling. Papoulis (1977) provided an elegant solution for the case where[InlineEquation not available: see fulltext.] is a band-limited function with finite energy and the sampling rate is equal to[InlineEquation not available: see fulltext.] times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST) for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.
Aurora B suppresses microtubule dynamics and limits central spindle size by locally activating KIF4A
Nunes Bastos, Ricardo; Gandhi, Sapan R.; Baron, Ryan D.; Gruneberg, Ulrike; Nigg, Erich A.
2013-01-01
Anaphase central spindle formation is controlled by the microtubule-stabilizing factor PRC1 and the kinesin KIF4A. We show that an MKlp2-dependent pool of Aurora B at the central spindle, rather than global Aurora B activity, regulates KIF4A accumulation at the central spindle. KIF4A phosphorylation by Aurora B stimulates the maximal microtubule-dependent ATPase activity of KIF4A and promotes its interaction with PRC1. In the presence of phosphorylated KIF4A, microtubules grew more slowly and showed long pauses in growth, resulting in the generation of shorter PRC1-stabilized microtubule overlaps in vitro. Cells expressing only mutant forms of KIF4A lacking the Aurora B phosphorylation site overextended the anaphase central spindle, demonstrating that this regulation is crucial for microtubule length control in vivo. Aurora B therefore ensures that suppression of microtubule dynamic instability by KIF4A is restricted to a specific subset of microtubules and thereby contributes to central spindle size control in anaphase. PMID:23940115
Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem
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Juliana Bueno-Soler
2016-09-01
Full Text Available This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs. We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.
A Generalized Carpenter's Rule Theorem for Self-Touching Linkages
Abbott, Timothy G; Gassend, Blaise
2009-01-01
The Carpenter's Rule Theorem states that any chain linkage in the plane can be folded continuously between any two configurations while preserving the bar lengths and without the bars crossing. However, this theorem applies only to strictly simple configurations, where bars intersect only at their common endpoints. We generalize the theorem to self-touching configurations, where bars can touch but not properly cross. At the heart of our proof is a new definition of self-touching configurations of planar linkages, based on an annotated configuration space and limits of nontouching configurations. We show that this definition is equivalent to the previously proposed definition of self-touching configurations, which is based on a combinatorial description of overlapping features. Using our new definition, we prove the generalized Carpenter's Rule Theorem using a topological argument. We believe that our topological methodology provides a powerful tool for manipulating many kinds of self-touching objects, such as...
-Dimensional Fractional Lagrange's Inversion Theorem
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F. A. Abd El-Salam
2013-01-01
Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.
Complex integration and Cauchy's theorem
Watson, GN
2012-01-01
This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the
DEFF Research Database (Denmark)
Bangsø Nielsen, Henrik; Angelidaki, Irini
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...
A low upper mass limit for the central black hole in the late-type galaxy NGC 4414
Thater, S.; Krajnović, D.; Bourne, M. A.; Cappellari, M.; de Zeeuw, T.; Emsellem, E.; Magorrian, J.; McDermid, R. M.; Sarzi, M.; van de Ven, G.
2017-01-01
We present our mass estimate of the central black hole in the isolated spiral galaxy NGC 4414. Using natural guide star adaptive optics assisted observations with the Gemini Near-Infrared Integral Field Spectrometer (NIFS) and the natural seeing Gemini Multi-Object Spectrographs-North (GMOS), we derived two-dimensional stellar kinematic maps of NGC 4414 covering the central 1.5 arcsec and 10 arcsec, respectively, at a NIFS spatial resolution of 0.13 arcsec. The kinematic maps reveal a regular rotation pattern and a central velocity dispersion dip down to around 105 km s-1. We constructed dynamical models using two different methods: Jeans anisotropic dynamical modeling and axisymmetric Schwarzschild modeling. Both modeling methods give consistent results, but we cannot constrain the lower mass limit and only measure an upper limit for the black hole mass of MBH = 1.56 × 106M⊙ (at 3σ level) which is at least 1σ below the recent MBH-σe relations. Further tests with dark matter, mass-to-light ratio variation and different light models confirm that our results are not dominated by uncertainties. The derived upper limit mass is not only below the MBH-σe relation, but is also five times lower than the lower limit black hole mass anticipated from the resolution limit of the sphere of influence. This proves that via high quality integral field data we are now able to push black hole measurements down to at least five times less than the resolution limit. The reduced data cubes (FITS files) are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/597/A18
Cardioids and Morley's Trisector Theorem
J. Brinkhuis (Jan); van de Craats, J.
2017-01-01
textabstractA self-contained account of Morley's own proof of his celebrated trisector theorem is given. This makes this elegant and almost forgotten fragment of analytic Euclidean geometry more accessible to modern readers
Statistics, Causality and Bell's theorem
Gill, Richard D
2012-01-01
Bell's (1964) theorem is popularly supposed to establish the non-locality of quantum physics as a mathematical-physical theory. Building from this, observed violation of Bell's inequality in experiments such as that of Aspect and coworkers (1982) is popularly supposed to provide empirical proof of non-locality in the real world. This paper reviews recent work on Bell's theorem, linking it to issues in causality as understood by statisticians. The paper starts with a new proof of a strong (finite sample) version of Bell's theorem which relies only on elementary arithmetic and (counting) probability. This proof underscores the fact that Bell's theorem tells us that quantum theory is incompatible with the conjunction of three cherished and formerly uncontroversial physical principles, nicknamed here locality, realism, and freedom. The first, locality, is obviously connected to causality: causal influences need time to propagate spatially. Less obviously, the other two principles, realism and freedom, are also fo...
The Second Noether Theorem on Time Scales
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Agnieszka B. Malinowska
2013-01-01
Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.
The second Noether theorem on time scale
Malinowska, Agnieszka B.; Martins, Natália
2014-01-01
We extend the second Noether theorem to variational problems on time scales. Our result provides as corollaries the classical second Noether theorem, the second Noether theorem for the $h$-calculus and the second Noether theorem for the $q$-calculus.
The Kolmogorov-Riesz compactness theorem
Hanche-Olsen, Harald
2009-01-01
We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.
Upper Limit of D0 Production in Central Pb-Pb Collisions at 158A GeV
Alt, C; Baatar, B; Barna, D; Bartke, Jerzy; Betev, L; Bialkowska, H; Blume, C; Boimska, B; Botje, M; Bracinik, J; Bramm, R; Buncic, P; Cerny, V; Christakoglou, P; Chvala, O; Cramer, J G; Csató, P; Dinkelaker, P; Eckardt, V; Flierl, D; Fodor, Z; Foka, P; Friese, V; Gál, J; Gazdzicki, M; Genchev, V; Georgopoulos, G; Gladysz-Dziadus, E; Grebieszkow, K; Hegyi, S; Höhne, C; Kadija, K; Karev, A; Kliemant, M; Kniege, S; Kolesnikov, V I; Kornas, E; Korus, R; Kowalski, M; Kraus, I; Kreps, M; Van Leeuwen, M; Lévai, Peter; Litov, L; Lungwitz, B; Makariev, M; Malakhov, A I; Mateev, M; Melkumov, G L; Mischke, A; Mitrovski, M; Molnár, J; Mrówczynski, S; Nicolic, V; Pálla, G; Panagiotou, A D; Panayotov, D; Petridis, A; Pikna, M; Prindle, D; Pühlhofer, F; Renfordt, R; Roland, C; Roland, G; Rybczynski, M; Rybicki, A; Sandoval, A; Schmitz, N; Schuster, T; Seyboth, P; Siklér, F; Sitár, B; Skrzypczak, E; Stefanek, G; Stock, R; Ströbele, H; Susa, T; Szentpétery, I; Sziklai, J; Szymanski, P; Trubnikov, V; Varga, D; Vassiliou, Maria; Veres, G I; Vesztergombi, G; Vranic, D; Wetzler, A; Wlodarczyk, Z; Yoo, I K; Zimányi, J
2006-01-01
Results are presented from a search for the decays D0 -> Kmin piplus and D0bar -> Kplus pimin in a sample of 3.8x10^6 central Pb-Pb events collected with a beam energy of 158A GeV by NA49 at the CERN SPS. No signal is observed. An upper limit on D0 production is derived and compared to predictions from several models.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
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.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
Energy Technology Data Exchange (ETDEWEB)
Woolgar, Eric, E-mail: ewoolgar@ualberta.ca [Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 (Canada); Wylie, William, E-mail: wwylie@syr.edu [215 Carnegie Building, Department of Mathematics, Syracuse University, Syracuse, New York 13244 (United States)
2016-02-15
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
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.
A new VLA/e-MERLIN limit on central images in the gravitational lens system CLASS B1030+074
Quinn, Jonathan; Tagore, Amitpal; Biggs, Andrew; Birkinshaw, Mark; Chapman, Scott; De Zotti, Gianfranco; McKean, John; Perez-Fournon, Ismael; Scott, Douglas; Serjeant, Stephen
2016-01-01
We present new VLA 22-GHz and e-MERLIN 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 microJy/beam 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, or an inner power law slope very close to isothermal, in order to suppress the central i...
The Limits of Friendship: US Security Cooperation in Central Asia (Walker Paper, Number 9)
2007-10-01
ward Black, Lt Col Taft Blackburn, Jeannie Borden , Barbara Braese, Col Matt Brand, Lt Col David Brigham, Maj kent Broome, Maj Mark Campbell...collapse of the Soviet Union in December 1991, Pres. George H . W. Bush sought to develop an aid program for the newly independent states in Eurasia...September 1995, 4. 43. Neil MacFarlane, Western Engagement in the Caucasus and Central Asia (London: Royal Institute of International Affairs, 1999
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.
Fixed-point-like theorems on subspaces
Directory of Open Access Journals (Sweden)
Bernard Cornet
2004-08-01
Full Text Available We prove a fixed-point-like theorem for multivalued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems: the fixed-point-like theorem by Hirsch et al. (1990 or Husseini et al. (1990 and the fixed-point theorem by Gale and Mas-Colell (1975 (which generalizes Kakutani's theorem (1941.
A remark on a Theorem by Ekeland-Hofer
Albers, Peter
2010-01-01
In [EH89, Theorem 1] Ekeland-Hofer prove that for a centrally symmetric, restricted contact type hypersurface in R^{2n} and for any global, centrally symmetric Hamiltonian perturbation there exists a leaf-wise intersection point. In this note we show that if we replace restricted contact type by star-shaped there exists infinitely many leaf-wise intersection points or a leaf-wise intersection point on a closed characteristic.
Distributed Online Judge System for Interactive Theorem Provers
Directory of Open Access Journals (Sweden)
Mizuno Takahisa
2014-03-01
Full Text Available 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.
Distributed Online Judge System for Interactive Theorem Provers
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.
Limited irrigation of corn-based no-till crop rotations in west central Great Plains.
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...
A low upper mass limit for the central black hole in the late-type galaxy NGC 4414
Thater, Sabine; Bourne, Martin A; Cappellari, Michele; de Zeeuw, Tim; Emsellem, Eric; Magorrian, John; McDermid, Richard M; Sarzi, Marc; van de Ven, Glenn
2016-01-01
We present our mass estimate of the central black hole in the isolated spiral galaxy NGC 4414. Using natural guide star adaptive optics assisted observations with the Gemini Near-Infrared Integral Field Spectrometer (NIFS) and the natural seeing Gemini Multi-Object Spectrographs-North (GMOS), we derived two-dimensional stellar kinematic maps of NGC 4414 covering the central 1.5 arcsec and 10 arcsec, respectively, at a NIFS spatial resolution of 0.13 arcsec. The kinematic maps reveal a regular rotation pattern and a central velocity dispersion dip down to around 105 km/s. We constructed dynamical methods using two different methods: Jeans anisotropic dynamical modeling and axisymmetric Schwarzschild modeling. Both modeling methods give consistent results, but we cannot constrain the lower mass limit and only measure an upper limit for the black hole mass of Mbh= 1.56 x 10^6 Msun(at 3 sigma level) which is at least 1 sigma below the recent Mbh-sigma_e relations. Further tests with dark matter, mass-to-light rat...
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
Ferromagnetism beyond Lieb's theorem
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
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
Four theorems on the psychometric function.
Directory of Open Access Journals (Sweden)
Keith A May
Full Text Available In a 2-alternative forced-choice (2AFC discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise x β(Transducer, where β(Noise is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer depends on the transducer. We derive general expressions for β(Noise and β(Transducer, from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx(b, β ≈ β(Noise x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is
Izmailov, Ramil; Filippov, Alexander I; Ghosh, Mithun; Nandi, Kamal K
2015-01-01
We investigate the stability of circular material orbits in the analytic galactic metric recently derived by Harko \\textit{et al.} (2014). It turnsout that stability depends more strongly on the dark matter central density $%\\rho_{0}$ than on other parameters of the solution. This property then yields an upper limit on $\\rho _{0}$ for each individual galaxy, which we call here $\\rho _{0}^{\\text{upper}}$, such that stable circular orbits are possible \\textit{only} when the constraint $\\rho _{0}\\leq \\rho _{0}^{\\text{upper}}$ is satisfied. This is our new result. To approximately quantify the upper limit, we consider as a familiar example our Milky Way galaxy that has a projected dark matter radius $R_{\\text{DM}}\\sim 180$ kpc and find that $\\rho _{0}^{\\text{upper}}\\sim 2.37\\times 10^{11}$ $M_{\\odot }$kpc$^{-3}$. This limit turns out to be about four orders of magnitude larger than the latest data on central density $\\rho _{0}$ arising from the fit to the Navarro-Frenk-White (NFW) and Burkert density profiles. Su...
A novel sampling theorem on the rotation group
McEwen, J D; Leistedt, B; Peiris, H V; Wiaux, Y
2015-01-01
We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by associating the rotation group with the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to capture all of the information content of a signal band-limited at $L$, reducing the number of required samples by a factor of two compared to other equiangular sampling theorems. We present fast algorithms to compute the associated Fourier transform on the rotation group, the so-called Wigner transform, which scale as $O(L^4)$, compared to the naive scaling of $O(L^6)$. For the common case of a low directional band-limit $N$, complexity is reduced to $O(N L^3)$. Our fast algorithms will be of direct use in speeding up the computation of directional wavelet transforms on the sphere. We make our SO3 code implementing these algorithms publicly available.
Restriction limits and main drivers of fruit production in palm in central Amazonia
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 theorems for quantum processes
Albash, Tameem; Marvian, Milad; Zanardi, Paolo
2013-01-01
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that unitality replaces micro-reversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.
The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project
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)
Pasicki, Lech
2011-01-01
Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty general, as we assume the differential form to be continuous on a compact set F(A) and C1 "inside" while F(A) is built of "bricks" and its inner part is a C1 manifold. There is no problem of orientability and the integrals under consideration are convergent. The proof is based on integration by parts and inner approximation.
Noether theorems and higher derivatives
Townsend, Paul K
2016-01-01
A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\\epsilon$ to an arbitrary function of time; the Noether charge $Q$ is then the coefficient of $\\dot\\epsilon$ in the variation of the action. Here we examine the validity of this proof for Lagrangian mechanics with arbitrarily-high time derivatives, in which context "higher-level" analogs of Noether's theorem can be similarly proved, and "Noetherian charges" read off from, e.g. the coefficient of $\\ddot \\epsilon$ in the variation of the action. While $Q=0$ implies a restricted gauge invariance, an unrestricted gauge invariance requires zero Noetherian charges too. Some illustrative examples are considered.
Louis M. Houston
2012-01-01
Sign data are the signs of signal added to noise. It is well known that a constant signal can be recovered from sign data. In this paper, we show that an integral over variant signal can be recovered from an integral over sign data based on the variant signal. We refer to this as a generalized sign data average. We use this result to derive a Green's theorem for sign data. Green's theorem is important to various seismic processing methods, including seismic migration. Results in this paper ge...
The truncated Second Main Theorem and uniqueness theorems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we first establish a truncated Second Main Theorem for algebraically nondegenerate holomorphic mappings from the complex plane into a complex projective variety V intersecting hypersurfaces. We then prove some uniqueness results for meromorphic mappings. The result of Demailly about a partial solution to the Fujita’s conjecture is used.
Carbon balance indicates a time limit for cultivation of organic soils in central Switzerland
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
Directory of Open Access Journals (Sweden)
Yumiseva César A
2011-02-01
Full Text Available Abstract 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.
The Classical Version of Stokes' Theorem Revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2005-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...
Von Laue's theorem and its applications
Wang, Changbiao
2012-01-01
Von Laue's theorem is strictly proved in detail to clarify confusions in textbook and literature. This theorem is used to analyze the classical electron and the static electric field confined in a finite region of space.
A normal form theorem around symplectic leaves
Crainic, M.N.; Marcut, I.T.
2012-01-01
We prove the Poisson geometric version of the Local Reeb Stability (from foliation theory) and of the Slice Theorem (from equivariant geometry), which is also a generalization of Conn’s linearization theorem.
Angle Defect and Descartes' Theorem
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.)
JACKSON'S THEOREM FOR COMPACT GROUPS
Institute of Scientific and Technical Information of China (English)
H. Vaezi; S. F. Rzaev
2002-01-01
In this article we consider the generalized shift operator defined by(Sh.f)(g) = ∫Gf (tut-1g)dton compact group G and by help of this operator we define "Spherical" modulus of continuity. So we proveStechkin and Jackson type theorems.
LUROTH'S THEOREM IN DIFFERENTIAL FIELDS
Institute of Scientific and Technical Information of China (English)
GAO Xiaoshan; XU Tao
2002-01-01
In this paper, we present a constructive proof of Liroth's theorem in differentialcase. We also give a method to find the inversion maps for general differential rationalparametric equations. As a consequence, we prove that a differential rational curve alwayshas a set of proper parametric equations.
Shell theorem for spontaneous emission
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Mortensen, Jakob Egeberg; Lodahl, Peter;
2013-01-01
and therefore is given exactly by the dipole approximation theory. This surprising result is a spontaneous emission counterpart to the shell theorems of classical mechanics and electrostatics and provides insights into the physics of mesoscopic emitters as well as great simplifications in practical calculations....
GENERALIZED RECIPROCAL THEOREMS AND THEIR APPLICATIONS
Institute of Scientific and Technical Information of China (English)
付宝连
2002-01-01
Generalized reciprocal theorems of non-coupled and coupled systems , which are valid for two deformed bodies with different constitutive relations are established by generalizing the idea of Betti ' s reciprocal theorem. When the constitutive relations of the two deformed bodies are all alike and linear elastic, the generalized reciprocal theorem of non-coupled systems just becomes Betti' s . Meanwhile, the generalized reciprocal theorems are applied to simulate calculations in elasticity.
Raychaudhuri equation and singularity theorems in Finsler spacetimes
Minguzzi, E
2015-01-01
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that all the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain, e.g. Hawking's, Penrose's, Hawking and Penrose's, Geroch's, Gannon's, Tipler's, Kriele's, Topological Censorship's, and so on. It is argued that all the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance, geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure and horizons differentiability are also included.
Noether-Like Theorems for Causal Variational Principles
Finster, Felix
2015-01-01
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is proven that these symmetries give rise to corresponding conserved quantities, expressed in terms of so-called surface layer integrals. In a suitable limiting case, the Noether-like theorems for causal fermion systems reproduce charge conservation and the conservation of energy and momentum in Minkowski space. Thus the conservation of charge and energy-momentum are found to be special cases of general conservation laws which are intrinsic to causal fermion systems.
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).
Ordering in mechanical geometry theorem proving
Institute of Scientific and Technical Information of China (English)
李洪波￥
1997-01-01
Ordering in mechanical geometry theorem proving is studied from geometric viewpoint and some new ideas are proposed. For Thebault’s theorem which is the most difficult theorem that has ever been proved by Wu’ s method, a very simple proof using Wu’s method under a linear order is discovered.
A definability theorem for first order logic
Butz, C.; Moerdijk, I.
2001-01-01
In this paper we will present a definability theorem for first order logic This theorem is very easy to state and its proof only uses elementary tools To explain the theorem let us first observe that if M is a model of a theory T in a language L then clearly any definable subset S M ie a subset S
A note on generalized Weyl's theorem
Zguitti, H.
2006-04-01
We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.
On Brayton and Moser's missing stability theorem
Jeltsema, D.; Scherpen, J. M. A.
2005-01-01
In the early 1960s, Brayton and Moser proved three theorems concerning the stability of nonlinear electrical circuits. The applicability of each theorem depends on three different conditions on the type of admissible nonlinearities in circuit. Roughly speaking, this means that the theorems apply to
The F-Theorem and F-Maximization
Pufu, Silviu S
2016-01-01
This contribution contains a review of the role of the three-sphere free energy F in recent developments related to the F-theorem and F-maximization. The F-theorem states that for any Lorentz-invariant RG trajectory connecting a conformal field theory CFT_UV in the ultraviolet to a conformal field theory CFT_IR, the F-coefficient decreases: F_UV > F_IR. I provide many examples of CFTs where one can compute F, approximately or exactly, and discuss various checks of the F-theorem. F-maximization is the principle that in an N=2 SCFT, viewed as the deep IR limit of an RG trajectory preserving N=2 supersymmetry, the superconformal R-symmetry maximizes F within the set of all R-symmetries preserved by the RG trajectory. I review the derivation of this result and provide examples.
Convolution theorems for the linear canonical transform and their applications
Institute of Scientific and Technical Information of China (English)
DENG Bing; TAO Ran; WANG Yue
2006-01-01
As generalization of the fractional Fourier transform (FRFT), the linear canonical transform (LCT) has been used in several areas, including optics and signal processing. Many properties for this transform are already known, but the convolution theorems, similar to the version of the Fourier transform, are still to be determined. In this paper, the authors derive the convolution theorems for the LCT, and explore the sampling theorem and multiplicative filter for the band limited signal in the linear canonical domain. Finally, the sampling and reconstruction formulas are deduced, together with the construction methodology for the above mentioned multiplicative filter in the time domain based on fast Fourier transform (FFT), which has much lower computational load than the construction method in the linear canonical domain.
Primitive Near-rings-Some Structure Theorems
Institute of Scientific and Technical Information of China (English)
Gerhard Wendt
2007-01-01
We show that any zero symmetric 1-primitive near-ring with descending chain condition on left ideals can be described as a centralizer near-ring in which the multipli-cation is not the function composition but sandwich multiplication.This result follows from a more general structure theorem on 1-primitive near-rings with multiplicative right identity,not necessarily having a chain condition on left ideals.We then use our results to investigate more closely the multiplicative semigroup of a 1-primitive near-ring.In par-ticular,we show that the set of regular elements forms a right ideal of the multiplicative semigroup of the near-ring.
Level reduction and the quantum threshold theorem
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
The de Finetti theorem for test spaces
Barrett, Jonathan; Leifer, Matthew
2009-03-01
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
The de Finetti theorem for test spaces
Energy Technology Data Exchange (ETDEWEB)
Barrett, Jonathan [H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL (United Kingdom); Leifer, Matthew [Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1 (Canada)], E-mail: j.barrett@bristol.ac.uk, E-mail: matt@mattleifer.info
2009-03-15
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
Time dependent electromagnetic fields and 4-dimensional Stokes' theorem
Andosca, Ryan
2016-01-01
Stokes' theorem is central to many aspects of physics -- electromagnetism, the Aharonov-Bohm effect, and Wilson loops to name a few. However, the pedagogical examples and research work almost exclusively focus on situations where the fields are time-independent so that one need only deal with purely spatial line integrals ({\\it e.g.} $\\oint {\\bf A} \\cdot d{\\bf x}$) and purely spatial area integrals ({\\it e.g.} $\\int (\
The no-ghost theorem for string theory in curved backgrounds with a flat timelike direction
Asano, M; Asano, Masako; Natsuume, Makoto
2000-01-01
It is well-known that the standard no-ghost theorem can be extended to the general c=26 CFT with d-dimensional Minkowski spacetime M^{(1,d-1)} and a compact unitary CFT K of central charge c_{K} = 26-d. The theorem has been established under the assumption d \\geq 2 so far. We prove the no-ghost theorem for d=1, i.e., when only the timelike direction is flat. This is done using the technique of Frenkel, Garland and Zuckerman.
Multiwavelet sampling theorem in Sobolev spaces
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper is to establish the multiwavelet sampling theorem in Sobolev spaces. Sampling theorem plays a very important role in digital signal communication. The most classical sampling theorem is Shannon sampling theorem, which works for bandlimited signals. Recently, sampling theorems in wavelets or multiwavelets subspaces are extensively studied in the literature. In this paper, we firstly propose the concept of dual multiwavelet frames in dual Sobolev spaces (H s (R) , H-s (R)). Then we construct a special class of dual multiwavelet frames, from which the multiwavelet sampling theorem in Sobolev spaces is obtained. That is, for any f ∈ H s (R) with s > 1/2, it can be exactly recovered by its samples. Especially, the sampling theorem works for continuous signals in L 2 (R), whose Sobolev exponents are greater than 1 /2.
Pythagoras Theorem and Relativistic Kinematics
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.
ANDRAGOGY OF DEVELOPMENT: BASIC THEOREMS
Directory of Open Access Journals (Sweden)
A. G. Teslinov
2016-01-01
Full Text Available The article presents criticism of the state of scientific knowledge about adult education and provides the reasons for the choice of directions of its development.Methods. The approach to the substantiation of directions of development of andragogy includes aspectual analysis of scientific rhetoric of adult education; summarizing the symptoms and causes of the problems of educational practice examples of education managers; the analysis of the status of andragogy as a scientific paradigm; a conceptual analysis of the key theses of the modern synthesis of andragogy and the provisions for developmental adult education.Results and scientific novelty. Four theorems are formulated that specify the complete set of propositions about a developmental approach to adult education. These theorems are presented as a scientific hypothesis about the features of the approach. The theorems are proved, and the substantiation of the conditions of emergence of the adult education of educational properties is described. The idea of adult education as a developing culture is in the centre of reasoning. It is shown that the assertions of theorems form the conceptual core of the scientific branches in adult education – andragogy of development. The effect of the practical interpretation of its provisions is disclosed.Practical significance. Disclosed meanings and recommendations may be oriented to developers of educational systems and media for adults while creating the developmental components. These references will help to overcome the evident trend information of adult education to the "pulling" them up to continually outdated standards, and to give it the look of a truly developing technology.
An improvement of Papadakis' theorem
Institute of Scientific and Technical Information of China (English)
ZHANG Zhihua; MU Lehua; ZHANG Peixuan
2004-01-01
There exist many orthonormal wavelets which cannot be derived by multiresolution analysis (MRA) with a single scaling function.In 2000,Papadakis announced that any orthonormal wavelet is derived by a generalized MRA with countable scaling functions at most.We improve Papadakis' theorem and find that for any othonormal wavelet,the least number of the corresponding scaling functions is just the essential supremum of the dimension function of the orthonormal wavelet.Moreover,we construct directly the fewest scaling functions.
A Miniaturisation of Ramsey's Theorem
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.
Compactness theorems of fuzzy semantics
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically. The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.
Expectation Value in Bell's Theorem
Wang, Zheng-Chuan
2006-01-01
We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell's inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experiments to show the violation of Bell's inequality and then further deny the local hidden-variables theor...
An exactly solvable model for Brownian motion : IV. Susceptibility and Nyquist's theorem
Ullersma, P.
1966-01-01
By means of an exactly solvable model, treated in a previous paper1), the relation between the microscopic and macroscopic susceptibility is discussed. Furthermore, the limits of the validity of Nyquist's theorem are given.
Reflections on the PBR Theorem: Reality Criteria & Preparation Independence
Directory of Open Access Journals (Sweden)
Shane Mansfield
2014-12-01
Full Text Available This paper contains initial work on attempting to bring recent developments in the foundations of quantum mechanics concerning the nature of the wavefunction within the scope of more logical and structural methods. A first step involves dualising a criterion for the reality of the wavefunction proposed by Harrigan & Spekkens, which was central to the Pusey-Barrett-Rudolph theorem. The resulting criterion has several advantages, including the avoidance of certain technical difficulties relating to sets of measure zero. By considering the 'reality' not of the wavefunction but of the observable properties of any ontological physical theory a new characterisation of non-locality and contextuality is found. Secondly, a careful analysis of preparation independence, one of the key assumptions of the PBR theorem, leads to a precise analogy with the kind of locality prohibited by Bell's theorem. Motivated by this, we propose a weakening of the assumption to something analogous to no-signalling. This amounts to allowing global or non-local correlations in the joint ontic state, which nevertheless do not allow for superluminal signalling. This is, at least, consistent with the Bell and Kochen-Specker theorems. We find a counter-example to the PBR argument, which violates preparation independence, but does satisfy this physically motivated assumption. The question of whether the PBR result can be strengthened to hold under the relaxed assumption is therefore posed.
2017-01-01
Seed dispersal permits the colonization of favorable habitats and generation of new populations, facilitating escape from habitats that are in decline. There is little experimental evidence of the factors that limit epiphyte dispersion towards their hosts. In a tropical dry forest in central Mexico, we monitored the phenology of dispersion of epiphyte species of the genus Tillandsia; we tested experimentally whether precipitation could cause failures in seed dispersal and whether seed capture differs among vertical strata and between host species with high (Bursera copallifera) and low (Conzattia multiflora) epiphyte loads. With the exception of one species that presents late dispersion and low abundance, all of the species disperse prior to the onset of the rainy season. However, early rains immobilize the seeds, affecting up to 24% of the fruits in species with late dispersion. We observed that Tillandsia seeds reach both Bursera and Conzattia hosts, but found that adherence to the host is 4–5 times higher in Bursera. Furthermore, seeds liberated from Bursera travel shorter distances and up to half may remain within the same crown, while the highest seed capture takes place in the upper strata of the trees. We conclude that dispersion of Tillandsia seeds is limited by early rains and by the capture of seeds within the trees where populations concentrate. This pattern of capture also helps to explain the high concentrations of epiphytes in certain hosts, while trees with few epiphytes can be simultaneously considered deficient receivers and efficient exporters of seeds. PMID:28158320
Victoriano-Romero, Elizabeth; Valencia-Díaz, Susana; Toledo-Hernández, Víctor Hugo; Flores-Palacios, Alejandro
2017-01-01
Seed dispersal permits the colonization of favorable habitats and generation of new populations, facilitating escape from habitats that are in decline. There is little experimental evidence of the factors that limit epiphyte dispersion towards their hosts. In a tropical dry forest in central Mexico, we monitored the phenology of dispersion of epiphyte species of the genus Tillandsia; we tested experimentally whether precipitation could cause failures in seed dispersal and whether seed capture differs among vertical strata and between host species with high (Bursera copallifera) and low (Conzattia multiflora) epiphyte loads. With the exception of one species that presents late dispersion and low abundance, all of the species disperse prior to the onset of the rainy season. However, early rains immobilize the seeds, affecting up to 24% of the fruits in species with late dispersion. We observed that Tillandsia seeds reach both Bursera and Conzattia hosts, but found that adherence to the host is 4-5 times higher in Bursera. Furthermore, seeds liberated from Bursera travel shorter distances and up to half may remain within the same crown, while the highest seed capture takes place in the upper strata of the trees. We conclude that dispersion of Tillandsia seeds is limited by early rains and by the capture of seeds within the trees where populations concentrate. This pattern of capture also helps to explain the high concentrations of epiphytes in certain hosts, while trees with few epiphytes can be simultaneously considered deficient receivers and efficient exporters of seeds.
Software Reliability through Theorem Proving
Directory of Open Access Journals (Sweden)
S.G.K. Murthy
2009-05-01
Full Text Available Improving software reliability of mission-critical systems is widely recognised as one of the major challenges. Early detection of errors in software requirements, designs and implementation, need rigorous verification and validation techniques. Several techniques comprising static and dynamic testing approaches are used to improve reliability of mission critical software; however it is hard to balance development time and budget with software reliability. Particularly using dynamic testing techniques, it is hard to ensure software reliability, as exhaustive testing is not possible. On the other hand, formal verification techniques utilise mathematical logic to prove correctness of the software based on given specifications, which in turn improves the reliability of the software. Theorem proving is a powerful formal verification technique that enhances the software reliability for missioncritical aerospace applications. This paper discusses the issues related to software reliability and theorem proving used to enhance software reliability through formal verification technique, based on the experiences with STeP tool, using the conventional and internationally accepted methodologies, models, theorem proving techniques available in the tool without proposing a new model.Defence Science Journal, 2009, 59(3, pp.314-317, DOI:http://dx.doi.org/10.14429/dsj.59.1527
ON LIMITING PROPERTIES OF BERNSTEIN-TROTTER TYPE OPERATOR
Institute of Scientific and Technical Information of China (English)
ZengXiaoming; LinLu
1994-01-01
In this paper ,a class of Bernstein-Trotter type operator and its limiting properties are studied. By using both the limiting theorem and P. Le' vy continuity theorem on probability theory, a theorem of convergence is obtained. The result in [1] is included.
On a curvature-statistics theorem
Energy Technology Data Exchange (ETDEWEB)
Calixto, M [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de Astrofisica de Andalucia, Apartado Postal 3004, 18080 Granada (Spain)], E-mail: Manuel.Calixto@upct.es
2008-08-15
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature ({kappa} = {+-}1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
On Krasnoselskii's Cone Fixed Point Theorem
Directory of Open Access Journals (Sweden)
Man Kam Kwong
2008-04-01
Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.
The classical version of Stokes' Theorem revisited
DEFF Research Database (Denmark)
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 $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly...... exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together with a 'fattening' technique for surfaces and the inverse function theorem....
The Helmholtz theorem and retarded fields
Heras, Ricardo
2016-01-01
Textbooks frequently use the Helmholtz theorem to derive expressions for the electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for the 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 to derive 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 to derive the retarded fields.
The Helmholtz theorem and retarded fields
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.
Directory of Open Access Journals (Sweden)
Jacques C. Tardif
2016-09-01
Full Text Available In central Canada, long fire history reconstructions are rare. In a context where both anthropogenic and climate influences on fire regime have changed, Parks Canada has a mandate to maintain ecological integrity. Here we present a fire history derived from fire-scarred jack pine (Pinus banksiana Lamb. trees growing at their southern distribution limit in Riding Mountain National Park (RMNP. In Lake Katherine Fire Management Unit (LKFMU, a subregion within the park, fire history was reconstructed from archival records, tree-ring records, and charcoal in lake sediment. From about 1450 to 1850 common era (CE the fire return intervals varied from 37 to 125 years, according to models. During the period 1864–1930 the study area burned frequently (Weibull Mean Fire Intervals between 2.66 and 5.62 years; this period coincided with the end of First Nations occupation and the start of European settlement. Major recruitment pulses were associated with the stand-replacing 1864 and 1894 fires. This period nevertheless corresponded to a reduction in charcoal accumulation. The current fire-free period in LKFMU (1930–today coincides with RMNP establishment, exclusion of First Nations land use and increased fire suppression. Charcoal accumulation further decreased during this period. In the absence of fire, jack pine exclusion in LKFMU is foreseeable and the use of prescribed burning is advocated to conserve this protected jack pine ecosystem, at the southern margins of its range, and in the face of potential climate change.
Symbolic logic and mechanical theorem proving
Chang, Chin-Liang
1969-01-01
This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
Brownian limits, local limits, extreme value and variance asymptotics for convex hulls in the ball
Calka, Pierre; Yukich, J E
2009-01-01
The paper of Schreiber and Yukich [40] establishes an asymptotic representation for random convex polytope geometry in the unit ball $\\B_d, d \\geq 2,$ in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of the so-called generalized paraboloid growth process. This paper further exploits this connection, introducing also a dual object termed the paraboloid hull process. Via these growth processes we establish local functional and measure-level limit theorems for the properly scaled radius-vector and support functions as well as for curvature measures and $k$-face empirical measures of convex polytopes generated by high density Poisson samples. We use general techniques of stabilization theory to establish Brownian sheet limits for the defect volume and mean width functionals, and we provide explicit variance asymptotics and central limit theorems for the $k$-face and intrinsic volume functionals. We establish extreme value theorems for radius-vector and suppo...
A generalised Sylvester-Gallai Theorem
Directory of Open Access Journals (Sweden)
L. M. Pretorius
2007-09-01
Full Text Available We give an algorithmic proof for the contrapositive of the following theorem that has recently been proved by the authors:Let S be a ﬁnite set of points in the plane, with each point coloured red, blue or with both colours. Suppose that for any two distinct points A and B in S sharing a colour k, there is a third point in S which has (inter alia the colour different from k and is collinear with A and B. Then all the points in S are collinear.This theorem is a generalization of both the Sylvester-Gallai Theorem and the Motzkin-Rabin Theorem.
Directory of Open Access Journals (Sweden)
Sol Swords
2011-10-01
Full Text Available Interactive theorem proving requires a lot of human guidance. Proving a property involves (1 figuring out why it holds, then (2 coaxing the theorem prover into believing it. Both steps can take a long time. We explain how to use GL, a framework for proving finite ACL2 theorems with BDD- or SAT-based reasoning. This approach makes it unnecessary to deeply understand why a property is true, and automates the process of admitting it as a theorem. We use GL at Centaur Technology to verify execution units for x86 integer, MMX, SSE, and floating-point arithmetic.
A generalized preimage theorem in global analysis
Institute of Scientific and Technical Information of China (English)
MA; Jipu
2001-01-01
［1］Ma Jipu, (1.2) inverses of operators between Banach spaces and conjugacy theorem, Chinese Annals of Math., B, 1999, 20(1): 57.［2］Ma Jipu, Rank theorem of operators between Banach spaces, Science in China, Ser. A, 2000, 43(1): 1.［3］Ma Jipu, Local conjugacy theorem, rank theorems in advenced calculus and a generalized principle constructing Banach manifolds, Science in China, Ser. A, 2000, 43(12): 1233.［4］Zeidler, A. E., Nonlinear Function Analysis and Its Applications, IV: Applications to Mathematical Physics, New York: Springer-Verlag, 1988.
The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces
Huang, Jianhua
2005-12-01
In this paper we present some new matching theorems with open cover and closed cover by using the generalized R-KKM theorems [L. Deng, X. Xia, Generalized R-KKM theorem in topological space and their applications, J. Math. Anal. Appl. 285 (2003) 679-690] in the topological spaces with property (H). As applications, some coincidence theorems are established in topological spaces. Our results extend and generalize some known results.
Limit theory for planar Gilbert tessellations
Schreiber, Tomasz
2010-01-01
A Gilbert tessellation arises by letting linear segments (cracks) in the plane unfold in time with constant speed, starting from a homogeneous Poisson point process of germs in randomly chosen directions. Whenever a growing edge hits an already existing one, it stops growing in this direction. The resulting process tessellates the plane. The purpose of the present paper is to establish law of large numbers, variance asymptotics and a central limit theorem for geometric functionals of such tessellations. The main tool applied is the stabilization theory for geometric functionals.
An elementary derivation of the quantum virial theorem from Hellmann-Feynman theorem
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.
A simple characteristic-free proof of the Brill-Noether theorem
Osserman, Brian
2011-01-01
We describe how the use of a different degeneration from that considered by Eisenbud and Harris leads to a simple and characteristic-independent proof of the Brill-Noether theorem using limit linear series. As suggested by the degeneration, we prove an extended version of the theorem allowing for imposed ramification at up to two points. Although experts in the field have long been aware of the main ideas, we address some technical issues which arise in proving the full version of theorem.
The virial theorem and the ground state problem in polaron theory
Energy Technology Data Exchange (ETDEWEB)
Kashirina, N. I., E-mail: n_kashirina@mail.ru [National Academy of Sciences of Ukraine, Institute of Semiconductor Physics (Ukraine); Lakhno, V. D., E-mail: lak@impb.psn.ru [Russian Academy of Sciences, Institute of Mathematical Problems of Biology (Russian Federation); Tulub, A. V., E-mail: tulub@NK7099.Spb.edu [St. Petersburg State University (Russian Federation)
2012-05-15
The virial theorem for the translation-invariant theory of a polaron [3] is discussed. It is shown that, in [3], Tulub made a nonoptimal choice of variational parameters in the strong-coupling limit, which led to the violation of the virial relations. The introduction of an additional variational parameter to the test function reduces the polaron energy and makes it possible to satisfy the relations of the virial theorem for a strong-coupling polaron (the Pekar 1: 2: 3: 4 theorem).
The Virial Theorem and the Ground State Problem in Polaron Theory
2013-01-01
The virial theorem for the translation-invariant theory of a polaron [3] is discussed. It is shown that, in [3], Tulub made a nonoptimal choice of variational parameters in the strong-coupling limit, which led to the violation of the virial relations. The introduction of an additional variational parameter to the test function reduces the polaron energy and makes it possible to satisfy the relations of the virial theorem for a strong-coupling polaron (the Pekar 1 : 2 : 3 : 4 theorem).
Vallès, Jean
2012-01-01
Our aim is to prove a Poncelet type theorem for a line configuration on the complex projective. More precisely, we say that a polygon with 2n sides joining 2n vertices A1, A2,..., A2n is well inscribed in a configuration Ln of n lines if each line of the configuration contains exactly two points among A1, A2, ..., A2n. Then we prove : "Let Ln be a configuration of n lines and D a smooth conic in the complex projective plane. If it exists one polygon with 2n sides well inscribed in Ln and circumscribed around D then there are infinitely many such polygons. In particular a general point in Ln is a vertex of such a polygon." We propose an elementary proof based on Fr\\'egier's involution. We begin by recalling some facts about these involutions. Then we explore the following question : When does the product of involutions correspond to an involution? It leads to Pascal theorem, to its dual version proved by Brianchon, and to its generalization proved by M\\"obius.
Brudnyi, A
2011-01-01
We develop the elements of complex function theory within certain algebras of holomorphic functions on coverings of complex manifolds (including holomorphic extension from complex submanifolds, properties of divisors, corona type theorem, holomorphic analogue of Peter-Weyl approximation theorem, Hartogs type theorem, characterization of the uniqueness sets, etc). Our model examples are: (1) algebra of Bohr's holomorphic almost periodic functions on tube domains (i.e. the uniform limits of exponential polynomials) (2) algebra of all fibrewise bounded holomorphic functions (arising in corona problem for H^\\infty) (3) algebra of holomorphic functions having fibrewise limits. Our proofs are based on the analogues of Cartan theorems A and B for coherent type sheaves on the maximal ideal spaces of these subalgebras.
A New Type of Singularity Theorem
Senovilla, José M M
2007-01-01
A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive observational difference between singular and non-singular, globally hyperbolic, open cosmological models.
Abel's theorem in the noncommutative case
Leitenberger, Frank
2004-03-01
We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel's theorem.
Interpolation theorems on weighted Lorentz martingale spaces
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator.
A note on the tolerated Tverberg theorem
2016-01-01
In this paper we give an asymptotically tight bound for the tolerated Tverberg Theorem when the dimension and the size of the partition are fixed. To achieve this we study certain partitions of order-type homogeneous sets and use a generalization of the Erd\\H{o}s-Szekeres theorem.
A New Fixed Point Theorem and Applications
Directory of Open Access Journals (Sweden)
Min Fang
2013-01-01
Full Text Available A new fixed point theorem is established under the setting of a generalized finitely continuous topological space (GFC-space without the convexity structure. As applications, a weak KKM theorem and a minimax inequalities of Ky Fan type are also obtained under suitable conditions. Our results are different from known results in the literature.
THE EXISTENCE THEOREM OF OPTIMAL GROWTH MODEL
Institute of Scientific and Technical Information of China (English)
Gong Liutang; Peng Xianze
2005-01-01
This paper proves a general existence theorem of optimal growth theory. This theorem is neither restricted to the case of a constant technology progress, nor stated in terms of mathematical conditions which have no direct economic interpretation and moreover, are difficult to apply.
On the Hausdorff-Young theorem
Nasserddine, W
2005-01-01
Let $G_{mn}=ax + b$ be the matricial group of a local field. The Hausdorff-Young theorem for $G_{11}$ was proved by Eymard-Terp in 1978. We will establish here the Hausdorff-Young theorem for $G_{nn}$ for all $n \\in \\mathbb{N}$.
Euler and the Fundamental Theorem of Algebra.
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)
The Euler Line and Nine-Point-Circle Theorems.
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)
Generalized fluctuation theorems for classical systems
Agarwal, G S
2015-01-01
Fluctuation theorems have a very special place in the study of non equilibrium 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 $p(W)/p(-W)=\\exp(\\alpha W)$. We derive the general form of the fluctuation theorems for an arbitrary Gaussian Markov process and find conditions when the parameter $\\alpha$ becomes a universal parameter $1/kT$. 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 non-trivial. The generalized theorems are equally valid for non-equilibrium steady states.
Pointwise ergodic theorems beyond amenable groups
Bowen, Lewis
2011-01-01
We prove pointwise and maximal ergodic theorems for probability measure preserving actions of any countable group, provided it admits an essentially free, weakly mixing amenable action of stable type III_r for some r >0. Our approach is based on the following two principles. First, it is possible to generalize the ergodic theory of measure-preserving actions of amenable groups to include probability-measure-preserving amenable equivalence relations. Second, it is possible to reduce the proof of ergodic theorems for actions of a general group to the proof of ergodic theorems in an associated measure-preserving amenable equivalence relation, provided the group admits an amenable action with the properties stated above. The general ergodic theorems established here are used in a sequel paper to prove mean and pointwise ergodic theorems for arbitrary Gromov-hyperbolic groups.
Gleason's Theorem for Rectangular JBW-Triples
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
Isotropy theorem for cosmological vector fields
Cembranos, J A R; Maroto, A L; Jareño, S J Núñez
2012-01-01
We consider homogeneous abelian vector fields in an expanding universe. We find a mechanical analogy in which the system behaves as a particle moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of the virial theorem that for arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. For simple power-law potentials of the form V=\\lambda (A^\\mu A_\\mu)^n, the average equation of state is found to be w=(n-1)/(n+1). This implies that vector coherent oscillations could act as natural dark matter or dark energy candidates. Finally, we show that under very general conditions, the average energy-momentum tensor of a rapidly evolving bounded vector field in any background geometry is always isotropic and has the perfect fluid form for any locally inertial observer.
Uniqueness theorems in linear elasticity
Knops, Robin John
1971-01-01
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...
Posterior Probability and Fluctuation Theorem in Stochastic Processes
Ohkubo, Jun
2009-12-01
A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via Bayes’ theorem. In conventional fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when suitable assumptions are employed.
Sampling Theorem in Terms of the Bandwidth and Sampling Interval
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.
Moving mirrors and the fluctuation-dissipation theorem
Stargen, D Jaffino; Sriramkumar, L
2016-01-01
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 a...
Zero modes of various graphene configurations from the index theorem
Pachos, J K; Stone, M; Hatzinikitas, Agapitos; Pachos, Jiannis K.; Stone, Michael
2007-01-01
In this article we consider a graphene sheet that is folded in various compact geometries with arbitrary topology described by a certain genus, $g$. While the Hamiltonian of these systems is defined on a lattice one can take the continuous limit. The obtained Dirac-like Hamiltonian describes well the low energy modes of the initial system. Starting from first principles we derive an index theorem that corresponds to this Hamiltonian. This theorem relates the zero energy modes of the graphene sheet with the topology of the compact lattice. For $g=0$ and $g=1$ these results coincide with the analytical and numerical studies performed for fullerene molecules and carbon nanotubes while for higher values of $g$ they give predictions for more complicated molecules.
Newton's Theorem of Revolving Orbits in General Relativity
Christian, Pierre
2016-01-01
Newton's theorem of revolving orbits states that one can multiply the angular speed of a Keplerian orbit by a factor $k$ by applying a radial inverse cubed force proportional to $(1-k^2)$. In this paper we derive two generalizations of this theorem in general relativity, valid for the motion of massive particles in any static, spherically symmetric metrics. The first generalization, which we named the "force" picture, generalizes Newton's radial inverse cubed force by a corresponding four-force. The second generalization, which we named the "metric" picture, instead modifies the metric of the system to produce the multiplication in angular speed. Further, we verify the Newtonian limits of both generalizations and demonstrate that there is no such generalization for rotating metrics.
Fan beam image reconstruction with generalized Fourier slice theorem.
Zhao, Shuangren; Yang, Kang; Yang, Kevin
2014-01-01
For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.
The pointwise Hellmann-Feynman theorem
Directory of Open Access Journals (Sweden)
David Carfì
2010-02-01
Full Text Available In this paper we study from a topological point of view the Hellmann-Feynman theorem of Quantum Mechanics. The goal of the paper is twofold: On one hand we emphasize the role of the strong topology in the classic version of the theorem in Hilbert spaces, for what concerns the kind of convergence required on the space of continuous linear endomorphisms, which contains the space of (continuous observables.On the other hand we state and prove a new pointwise version of the classic Hellmann-Feynman theorem. This new version is not yet present in the literature and follows the idea of A. Bohm concerning the topology which is desiderable to use in Quantum Mechanics. It is indeed out of question that this non-trivial new version of the Hellmann-Feynman theorem is the ideal one - for what concerns the continuous observables on Hilbert spaces, both from a theoretical point of view, since it is the strongest version obtainable in this context - we recall that the pointwise topology is the coarsest one compatible with the linear structure of the space of continuous observables -, and from a practical point of view, because the pointwise topology is the easiest to use among topologies: it brings back the problems to the Hilbert space topology. Moreover, we desire to remark that this basic theorem of Quantum Mechanics, in his most desiderable form, is deeply interlaced with two cornerstones of Functional Analysis: the Banach-Steinhaus theorem and the Baire theorem.
DEFF Research Database (Denmark)
Damkilde, Lars
2007-01-01
Limit State analysis has a long history and many prominent researchers have contributed. The theoretical foundation is based on the upper- and lower-bound theorems which give a very comprehensive and elegant formulation on complicated physical problems. In the pre-computer age Limit State analysis...
Existence theorems for ordinary differential equations
Murray, Francis J
2007-01-01
Theorems stating the existence of an object-such as the solution to a problem or equation-are known as existence theorems. This text examines fundamental and general existence theorems, along with the Picard iterants, and applies them to properties of solutions and linear differential equations.The authors assume a basic knowledge of real function theory, and for certain specialized results, of elementary functions of a complex variable. They do not consider the elementary methods for solving certain special differential equations, nor advanced specialized topics; within these restrictions, th
Haag's theorem in renormalised quantum field theories
Klaczynski, Lutz
2016-01-01
We review a package of no-go results in axiomatic quantum field theory with Haag's theorem at its centre. Since the concept of operator-valued distributions in this framework comes very close to what we believe canonical quantum fields are about, these results are of consequence to quantum field theory: they suggest the seeming absurdity that this highly victorious theory is incapable of describing interactions. We single out unitarity of the interaction picture's intertwiner as the most salient provision of Haag's theorem and critique canonical perturbation theory to argue that renormalisation bypasses Haag's theorem by violating this very assumption.
Effective randomness, strong reductions and Demuth's theorem
Bienvenu, Laurent
2011-01-01
We study generalizations of Demuth's Theorem, which states that the image of a Martin-L\\"of random real under a tt-reduction is either computable or Turing equivalent to a Martin-L\\"of random real. We show that Demuth's Theorem holds for Schnorr randomness and computable randomness (answering a question of Franklin), but that it cannot be strengthened by replacing the Turing equivalence in the statement of the theorem with wtt-equivalence. We also provide some additional results about the Turing and tt-degrees of reals that are random with respect to some computable measure.
Index Theorem and Random Matrix Theory for Improved Staggered Quarks
Energy Technology Data Exchange (ETDEWEB)
Follana, E. [Department of Physics and Astronomy, University of Glasgow (United Kingdom); Hart, A. [School of Physics, University of Edinburgh (United Kingdom); Davies, C.T.H. [Department of Physics and Astronomy, University of Glasgow (United Kingdom)
2006-03-15
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD. We find a clear separation of the spectrum of eigenvalues into high chirality, would-be zero modes and others, in accordance with the Index Theorem. We find the expected clustering of the non-zero modes into quartets as we approach the continuum limit. The predictions of random matrix theory for the epsilon regime are well reproduced. We conclude that improved staggered quarks near the continuum limit respond correctly to QCD topology.
Stojak, Joanna; McDevitt, Allan D.; Herman, Jeremy S.; Kryštufek, Boris; Uhlíková, Jitka; Purger, Jenő J.; Lavrenchenko, Leonid A.; Searle, Jeremy B.; Wójcik, Jan M.
2016-01-01
The common vole (Microtus arvalis) has been a model species of small mammal for studying end-glacial colonization history. In the present study we expanded the sampling from central and eastern Europe, analyzing contemporary genetic structure to identify the role of a potential ‘northern glacial refugium’, i.e. a refugium at a higher latitude than the traditional Mediterranean refugia. Altogether we analyzed 786 cytochrome b (cytb) sequences (representing mitochondrial DNA; mtDNA) from the whole of Europe, adding 177 new sequences from central and eastern Europe, and we conducted analyses on eight microsatellite loci for 499 individuals (representing nuclear DNA) from central and eastern Europe, adding data on 311 new specimens. Our new data fill gaps in the vicinity of the Carpathian Mountains, the potential northern refugium, such that there is now dense sampling from the Balkans to the Baltic Sea. Here we present evidence that the Eastern mtDNA lineage of the common vole was present in the vicinity of this Carpathian refugium during the Last Glacial Maximum and the Younger Dryas. The Eastern lineage expanded from this refugium to the Baltic and shows low cytb nucleotide diversity in those most northerly parts of the distribution. Analyses of microsatellites revealed a similar pattern but also showed little differentiation between all of the populations sampled in central and eastern Europe. PMID:27992546
The Michaelis-Menten-Stueckelberg Theorem
Directory of Open Access Journals (Sweden)
Alexander N. Gorban
2011-05-01
Full Text Available We study chemical reactions with complex mechanisms under two assumptions: (i intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS and (ii they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE. Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events. This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.
Security Theorems via Model Theory
Directory of Open Access Journals (Sweden)
Joshua Guttman
2009-11-01
Full Text Available A model-theoretic approach can establish security theorems for cryptographic protocols. Formulas expressing authentication and non-disclosure properties of protocols have a special form. They are quantified implications for all xs . (phi implies for some ys . psi. Models (interpretations for these formulas are *skeletons*, partially ordered structures consisting of a number of local protocol behaviors. *Realized* skeletons contain enough local sessions to explain all the behavior, when combined with some possible adversary behaviors. We show two results. (1 If phi is the antecedent of a security goal, then there is a skeleton A_phi such that, for every skeleton B, phi is satisfied in B iff there is a homomorphism from A_phi to B. (2 A protocol enforces for all xs . (phi implies for some ys . psi iff every realized homomorphic image of A_phi satisfies psi. Hence, to verify a security goal, one can use the Cryptographic Protocol Shapes Analyzer CPSA (TACAS, 2007 to identify minimal realized skeletons, or "shapes," that are homomorphic images of A_phi. If psi holds in each of these shapes, then the goal holds.
Index theorems for quantum graphs
Fulling, S A; Wilson, J H
2007-01-01
In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order differential operators as an intermediary. In this paper, the case of quantum graphs is addressed. A quantum graph is a graph considered as a (singular) one-dimensional variety and equipped with a second-order differential Hamiltonian H (a "Laplacian") with suitable conditions at vertices. For the case of scale-invariant vertex conditions (i.e., conditions that do not mix the values of functions and of their derivatives), the constant term of the heat-kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph. This observation is placed into the index-theory context by factoring the Laplacian into two first-order operators, H =A*A, and relating the constant term to the index of A. An independent consideration provides an index f...
A generalized preimage theorem in global analysis
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The concept of locally fine point and generalized regular valueof a C1 map between Banach spaces were carried over C1 map between Banach manifolds. Hence the preimage theorem, a principle constructing Banach manifolds in global analysis, is generalized.
The virial theorem for nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: paolo.amore@gmail.com, E-mail: fernande@quimica.unlp.edu.ar
2009-09-15
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular, we consider conservative nonlinear oscillators and obtain the same main result derived earlier from the expansion in Chebyshev polynomials. (letters and comments)
Transformation groups and the virial theorem
Kampen, N.G. van
1972-01-01
A generalization of Noether's result for classical mechanics is given, which shows that the virial theorem is related to an invariance property of the Lagrange function. Two examples are discussed in detail.
Rank theorems of operators between Banach spaces
Institute of Scientific and Technical Information of China (English)
2000-01-01
Let E and F be Banach spaces, and B( E, F) all of bounded linear operators on E into F. Let T0 ∈ B( E, F) with an outer inverse T0# ∈ B( F, E). Then a characteristic condition of S= (I + T0# ( T- T0))-1 T0# with T∈ B( E, F) and || T0# ( T- T0) || < 1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.
Rank theorems of operators between Banach spaces
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Let E and F be Banach spaces, and B(E,F) all of bounded linear operators on E into F. Let T0∈B(E,F) with an outer inverse T#0∈B(F,E). Then a characteristic condition of S=(I+T#0(T-T0))-1T#0 with T∈B(E,F) and ‖T#0(T-T0)‖<1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.
Affine and Projective Tree Metric Theorems
Harel, Matan; Pachter, Lior
2011-01-01
The tree metric theorem provides a combinatorial four point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A similar (but weaker) four point condition characterizes dissimilarity maps derived from circular split systems (Kalmanson metrics). The tree metric theorem was first discovered in the context of phylogenetics and forms the basis of many tree reconstruction algorithms, whereas Kalmanson metrics were first considered by computer scientists, and are notable in that they are a non-trivial class of metrics for which the traveling salesman problem is tractable. We present a unifying framework for these theorems based on combinatorial structures that are used for graph planarity testing. These are (projective) PC-trees, and their affine analogs, PQ-trees. In the projective case, we generalize a number of concepts from clustering theory, including hierarchies, pyramids, ultrametrics and Robinsonian matrices, and the theorems that relate them. As with tree metric...
Dimensional analysis beyond the Pi theorem
Zohuri, Bahman
2017-01-01
Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First ...
Two No-Go Theorems on Superconductivity
Tada, Yasuhiro
2016-01-01
We study lattice superconductors such as attractive Hubbard models. As is well known, Bloch's theorem asserts absence of persistent current in ground states and equilibrium states for general fermion systems. While the statement of the theorem is true, we can show that the theorem cannot exclude possibility of a surface persistent current. Such a current can be stabilized by boundary magnetic fields which do not penetrate into the bulk region of a superconductor, provided emergence of massive photons, i.e., Meissner effect. Therefore, we can expect that a surface persistent current is realized for a ground/equilibrium state in the sense of stability against local perturbations. We also apply Elitzur's theorem to superconductors at finite temperatures. As a result, we prove absence of symmetry breaking of the global U(1) phase of electrons for almost all gauge fixings. These observations suggest that the nature of superconductivity is the emergence of massive photons rather than the symmetry breaking of the U(...
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered o...... we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem....
Sahoo- and Wayment-Type Integral Mean Value Theorems
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…
A New GLKKM Theorem and Its Application to Abstract Economies
Institute of Scientific and Technical Information of China (English)
WEN Kai-ting
2012-01-01
In this paper,a new GLKKM theorem in L-convex spaces is established.As applications,a new fixed point theorem and a maximal element theorem are obtained in Lconvex spaces.Finally,equilibrium existence theorems for abstract economies and qualitative games in L-convex spaces are yielded.
Energy Technology Data Exchange (ETDEWEB)
Ventura, M. [Autoridad Regulatoria Nuclear, Av. Libertador 8250 (1429), Capital Federal (Argentina)]. e-mail: mventura@sede.arn.gov.ar
2006-07-01
In the mark of the modification of the Atucha-I Nuclear Central Installation (CNA-I) as consequence of the Introduction of the System 'Second Drain of Heat' (SSC), the Entity Responsible for the CNA-I (NASA) requested authorization to the Nuclear Regulatory Authority (ARN) to modify the value of the minimum level of water in the secondary side in the Steam generators (GVs) to activate the signal 'shoot of the Cut of the Reactor' (RESA-LLV). As the level in the GVs is one of those parameters that are used to shoot the Emergency Feeding System (RX), component of the SSC System, also was analyzed the change in the activation of the shoot signal of the 'Second Drain of Heat' (2SSC-LLV). The ARN uses for the study of the nuclear safety of nuclear power plants, the series of prediction programs RELAP5/MOD3.X. It participates of the evaluation and maintenance activities of these codes through specific agreements with the U.S. Nuclear Regulatory Commission (US-NRC). It is necessary to account with programs of this type since the ARN it licenses the construction and operation of Nuclear Power Plants (NPPs) and other outstanding facilities and it inquires its operation according to its own standards. With these tools its are auditing the calculations that the Responsible Entities of the operation make to guarantee the operability of the NPPs assisting the mentioned standards. The analysis with computational codes is used as a tool to achieve the best understanding in the behavior of the plant in union with the engineering approach, the manual calculations, the data analysis and the experience in the operation of the machine. (Author)
Herbrand's theorem and non-Euclidean geometry
Beeson, Michael; Boutry, Pierre; Narboux, Julien
2014-01-01
International audience; We use Herbrand's theorem to give a new proof that Eu- clid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non- Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing proof.
Type Theory, Computation and Interactive Theorem Proving
2015-09-01
in type theory . Harper and student Kuen-Bang Hou developed a machine-checked proof of the equivalence of group actions and cov- ering spaces in...Track 2: Interactive theorem proving and au- tomated reasoning 3.1 Homotopy type theory Avigad participated in the Univalent Foundations Program at IAS...AFRL-AFOSR-VA-TR-2016-0071 TYPE THEORY , COMPUTATION AND INTERACTIVE THEOREM PROVING Jeremy Avigad CARNEGIE MELLON UNIVERSITY Final Report 09/01/2015
Transversality theorems for the weak topology
2011-01-01
In his 1979 paper Trotman proves, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the strong (Whitney) topology implies that the stratification is $(a)$-regular. Here we first discuss the Thom transversality theorem for the weak topology and then give a similiar kind of result for the weak topology, under very weak hypotheses. Recently sever...
The large deviations theorem and ergodicity
Energy Technology Data Exchange (ETDEWEB)
Gu Rongbao [School of Finance, Nanjing University of Finance and Economics, Nanjing 210046 (China)
2007-12-15
In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions.
Quantum De Moivre-Laplace theorem for noninteracting indistinguishable particles
Shchesnovich, V S
2016-01-01
The De Moivre-Laplace theorem applied to a Galton board says that probability distribution of $N$ balls over output bins takes a Gaussian form as $N\\to \\infty$. A quantum version of the theorem for $N$ noninteracting indistinguishable bosons (fermions) in a unitary $M$-mode network is discovered: the average probability distribution of particles over bins in a random network converges to a Gaussian law as $N\\to\\infty$, where their quantum statistics enters through the particle density $N/M$. The quantum De Moivre-Laplace theorem applies to an arbitrary partition of output modes into small number of bins and, moreover, for a given network with averaging over allowed input configurations. For $N\\gg 1$ the Gaussian law is a good approximation for an exact probability distribution over bins in a network without symmetries. In the thermodynamic limit $N\\to\\infty$ a finite difference in probability in a random network between indistinguishable bosons, fermions, and distinguishable particles is possible only at a no...
Khare, A; Paranjape, M B; Khare, Avinash; MacKenzie, R; Paranjape, M B
1994-01-01
The Coleman-Hill theorem prohibits the appearance of radiative corrections to the topological mass (more precisely, to the parity-odd part of the vacuum polarization tensor at zero momentum) in a wide class of abelian gauge theories in 2+1 dimensions. We re-express the theorem in terms of the effective action rather than in terms of the vacuum polarization tensor. The theorem so restated becomes somewhat stronger: a known exception to the theorem, spontaneously broken scalar Chern-Simons electrodynamics, obeys the new non-renormalization theorem. Whereas the vacuum polarization {\\sl does} receive a one-loop, parity-odd correction, this does not translate to a radiative contribution to the Chern-Simons term in the effective action. We also point out a new situation, involving scalar fields and parity-odd couplings, which was overlooked in the original analysis, where the conditions of the theorem are satisfied and where the topological mass does, in fact, get a radiative correction.
Mental Constructions for The Group Isomorphism Theorem
Directory of Open Access Journals (Sweden)
Arturo Mena-Lorca
2016-03-01
Full Text Available The group isomorphism theorem is an important subject in any abstract algebra undergraduate course; nevertheless, research shows that it is seldom understood by students. We use APOS theory and propose a genetic decomposition that separates it into two statements: the first one for sets and the second with added structure. We administered a questionnaire to students from top Chilean universities and selected some of these students for interviews to gather information about the viability of our genetic decomposition. The students interviewed were divided in two groups based on their familiarity with equivalence relations and partitions. Students who were able to draw on their intuition of partitions were able to reconstruct the group theorem from the set theorem, while those who stayed on the purely algebraic side could not. Since our approach to learning this theorem was successful, it may be worthwhile to gather data while teaching it the way we propose here in order to check how much the learning of the group isomorphism theorem is improved. This approach could be expanded to other group homomorphism theorems provided further analysis is conducted: going from the general (e.g., sets to the particular (e.g., groups might not always the best strategy, but in some cases we may just be turning to more familiar settings.
The modified Poynting theorem and the concept of mutual energy
Zhao, Shuang-ren; Yang, Kang; Yang, Xingang; Yang, Xintie
2015-01-01
The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting theorem the electromagnetic field is superimposition of different electromagnetic fields including the field of retarded potential and advanced potential. The media epsilon (permittivity) and mu (permeability) can also be different in the different fields. The concept of mutual energy is introduced which is the difference between the total energy and self-energy. Using the modified Poynting theorem with the concept of the mutual energy the modified mutual energy theorem is derived. Applying time-offset transform and time integral to the modified mutual energy theorem, the time-correlation modified mutual energy theorem is obtained. Assume there are only two fields which are retarded potential, and there is only one media, the modified time-correlation energy theorem becomes the time-correlation energy theorem, which is also referred as the time-correlation reciprocity theorem. Assume there are two electromagnetic fi...
Institute of Scientific and Technical Information of China (English)
Lei DENG; Ming Ge YANG
2006-01-01
Some new coincidence theorems involving admissible set-valued mappings are proved in general noncompact topological spaces. As applications, some new minimax inequalities, section theorem, best approximation theorem, existence theorems of weighted Nash equilibria and Pareto equilibria for multiobjective games are given in general topological spaces.
The nekhoroshev theorem and long-term stabilities in the solar system
Directory of Open Access Journals (Sweden)
Guzzo M.
2015-01-01
Full Text Available The Nekhoroshev theorem has been often indicated in the last decades as the reference theorem for explaining the dynamics of several systems which are stable in the long-term. The Solar System dynamics provides a wide range of possible and useful applications. In fact, despite the complicated models which are used to numerically integrate realistic Solar System dynamics as accurately as possible, when the integrated solutions are chaotic the reliability of the numerical integrations is limited, and a theoretical long-term stability analysis is required. After the first formulation of Nekhoroshev’s theorem in 1977, many theoretical improvements have been achieved. On the one hand, alternative proofs of the theorem itself led to consistent improvements of the stability estimates; on the other hand, the extensions which were necessary to apply the theorem to the systems of interest for Solar System Dynamics, in particular concerning the removal of degeneracies and the implementation of computer assisted proofs, have been developed. In this review paper we discuss some of the motivations and the results which have made Nekhoroshev’s theorem a reference stability result for many applications in the Solar System dynamics.
Completely Monotone Multisequences, Symmetric Probabilities and a Normal Limit Theorem
Indian Academy of Sciences (India)
J C Gupta
2000-11-01
Let G, be the set of all partial completely monotone multisequences of order and degree , i.e., multisequences (1, 2,$\\ldots$ ,k), 1, 2,$\\ldots$ , = 0, 1, 2,$\\ldots$ ,1 + 2 + \\$cdots$ + ≤ n, (0,0,$\\ldots$ ,0) = 1 and $(-1)^{_0}^{_0}$ (1, 2,$\\ldots$ ,)≥ 0 whenever 0 ≤ -(1 + 2 +$\\cdots$ +) where (1, 2,$\\ldots$ ,)=(1+1, 2,$\\ldots$ ,)+ (1,2+1,$\\ldots$ ,)+$\\cdots$ + (1, 2,$\\ldots$ ,+1)-(1,2,$\\ldots$ ,)$. Further, let $\\prod_{n,k}$ be the set of all symmetric probabilities on ${0, 1, 2,\\ldots ,k}^{n}$. We establish a one-to-one correspondence between the sets G, and $\\prod_{n, k}$ and use it to formulate and answer interesting questions about both. Assigning to G, the uniform probability measure, we show that, as → ∞ , any fixed section {(1, 2,$\\ldots$ ,), 1 ≤ $\\sum ≤ }, properly centered and normalized, is asymptotically multivariate normal. That is, $\\left\\{\\sqrt{\\left(\\binom{n+k}{k}\\right)}((1, 2,\\ldots ,)-c_0(1, 2,\\ldots ,), 1≤ _1+2+\\cdots +_k≤ m\\right\\}$ converges weakly to MVN[0,]; the centering constants 0(1, 2,$\\ldots$ ,) and the asymptotic covariances depend on the moments of the Dirichlet $(1, 1,\\ldots ,1; 1)$ distribution on the standard simplex in .
Limiting theorems for the nodes in binary search trees
Institute of Scientific and Technical Information of China (English)
2008-01-01
We consider three random variables X_n, Y_n and Z_n, which represent the numbers of the nodes with 0, 1, and 2 children, in the binary search trees of size n. The expectation and variance of the three above random variables are got, and it is also shown that X_n, Y_n and Z_n are all asymptotically normal as n→∞by applying the contraction method.
Limit Theorems for some Branching Measure-Valued Processes
Cloez, Bertrand
2011-01-01
We consider a particles system, where, the particles move independently according to a Markov process and branching event occurs at an inhomogeneous time. The offspring locations and their number may depend on the position of the mother. Our setting capture, for instance, the processes indexed by Galton-Watson tree. We first determine the asymptotic behaviour of the empirical measure. The proof is based on an expression of the empirical measure using an auxiliary process. This latter is not distributed as a one cell lineage, there is a biased phenomenon. Our model is a microscopic description of a random (discrete) population of individuals. We then obtain a large population approximation as weak solution of a growth- fragmentation equation. We illustrate our result with two examples. The first one is a size-structured population model which describes the mitosis and the second one can model a parasite infection.
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.
Maximum entropy as a consequence of Bayes' theorem in differentiable manifolds
Davis, Sergio
2015-01-01
Bayesian inference and the principle of maximum entropy (PME) are usually presented as separate but complementary branches of inference, the latter playing a central role in the foundations of Statistical Mechanics. In this work it is shown that the PME can be derived from Bayes' theorem and the divergence theorem for systems whose states can be mapped to points in a differentiable manifold. In this view, entropy must be interpreted as the invariant measure (non-informative prior) on the space of probability densities.
The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory
Directory of Open Access Journals (Sweden)
Claude Semay
2015-01-01
Full Text Available The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: be C1 nonlinear map, where U (x0) is an open set containing point x0∈E. With the locally fine property for Frechet derivatives f′(x) and generalized rank theorem for f′(x), a local conjugacy theorem, i.e. a characteristic condition for f being conjugate to f′(x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
Institute of Scientific and Technical Information of China (English)
马吉溥
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
Dai-Freed theorem and topological phases of matter
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.
Dai-Freed theorem and topological phases of matter
Yonekura, Kazuya
2016-01-01
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.
Goldstone's Theorem on a Light-Like Plane
Beane, Silas R
2015-01-01
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(2N), recovering a result originally found by Weinberg using different methods.
Generalized fluctuation theorems for classical systems
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.
Ergodic theorem, ergodic theory, and statistical mechanics.
Moore, Calvin C
2015-02-17
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics.
WEYL'S TYPE THEOREMS AND HYPERCYCLIC OPERATORS
Institute of Scientific and Technical Information of China (English)
M.H. M. Rashid
2012-01-01
For a bounded operator T acting on an infinite dimensional separable Hilbert space H,we prove the following assertions: (i) If T or T* ∈ SC,then generalized aBrowder's theorem holds for f(T) for every f ∈ Hol(σ(T)).(ii) If T or T* ∈ HC has topological uniform descent at all λ ∈ iso(σ(T)),then generalized Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)).(iii) If T ∈ HC has topological uniform descent at all λ ∈ E(T),then T satisfies generalized Weyl's theorem.(iv) Let T ∈ HC.If T satisfies the growth condition Gd(d ≥ 1),then generalized Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)).(v) If T ∈ SC,then,f(σSBF-+ (T)) =σSBF-+ (f(T)) for all f ∈ Hol(σ(T)).(vi) Let T be a-isoloid such that T* ∈ HC.If T - λI has finite ascent at every λ ∈ Ea(T)and if F is of finite rank on H such that TF =FT,then T + F obeys generalized a-Weyl's theorem.
Anti-Bell - Refutation of Bell's theorem
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.
Directory of Open Access Journals (Sweden)
Marwan Amin Kutbi
2014-01-01
weakly compatible mappings in symmetric spaces satisfying generalized (ψ,φ-contractive conditions employing the common limit range property. We furnish some interesting examples which support our main theorems. Our results generalize and extend some recent results contained in Imdad et al. (2013 to symmetric spaces. Consequently, a host of metrical common fixed theorems are generalized and improved. In the process, we also derive a fixed point theorem for four finite families of mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings.
Institute of Scientific and Technical Information of China (English)
周如瑞; 卢迪; 王本德; 周惠成
2016-01-01
The development of hydrometeorological forecast technology offers important opportunities for reservoir dynamic control of flood limited water level. Economic benefits can be improved by raising the flood limited water level, but there is certain flood control risk. The purpose of this study was to propose a risk analysis method of upper bound of dynamic control of flood limited water level in order to provide the support for the development of dynamic control of flood limited water level. The proposed risk analysis method was based on Bayes theorem and flood forecast error characteristics. Qinghe reservoir, located in the northeast of China, was taken as an example. 21 flood events of actual and forecast runoff from the year 1964 to 2013 were used. For large reservoirs that has the ability for multi-year regulation, decision makers of flood control operation concern a lot about runoff forecast accuracy because the design flood is controlled by the flood volume. First, maximum entropy method was selected to simulate the runoff prediction error probability density function of 21 flood events, also forecast error range was calculated. According to the actual need of runoff forecast error in Qinghe reservoir, the range was divided into 6 zones, and distribution probabilities of runoff forecast errors in each zone, namely the prior probability distributions of flood forecasting errors were obtained by integrating the density function. Then, the probabilities of the highest water levels being higher than corresponding designed levels within different flood forecast error bounds were studied, and the risks of different flood forecast errors were inferred by Bayes theorem when the highest water level in flood regulation met with the design flood frequency. Based on the risk analysis method, risks of each design water level considering flood forecast information were compared with risks of conventional mode. The proposed risk analysis method of upper bound of dynamic
Statistical properties of the universal limit map of grazing bifurcations
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.
STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE
Institute of Scientific and Technical Information of China (English)
杨卫国; 刘文
2001-01-01
This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove thc Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.
Causality, Bell's theorem, and Ontic Definiteness
Henson, Joe
2011-01-01
Bell's theorem shows that the reasonable relativistic causal principle known as "local causality" is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while dropping any of the better-known assumptions of Bell's theorem. However, another assumption of Bell's theorem is the use of classical logic. One part of this assumption is the principle of "ontic definiteness", that is, that it must in principle be possible to assign definite truth values to all propositions treated in the theory. Once the logical setting is clarified somewhat, it can be seen that rejecting this principle does not in any way undermine the type of causal principle used by Bell. Without ontic definiteness, the deterministic causal condition known as Einstein Locality succeeds in banning superluminal influence (including signalling) whilst allowing correlations that violate Bell's inequalities. Objections to altering logic, and the consequences for operational and...
Bayes' theorem: scientific assessment of experience
Directory of Open Access Journals (Sweden)
Lex Rutten
2010-10-01
Full Text Available Homeopathy is based on experience and this is a scientific procedure if we follow Bayes' theorem. Unfortunately this is not the case at the moment. Symptoms are added to our materia medica based on absolute occurrence, while Bayes theorem tells us that this should be based on relative occurrence. Bayes theorem can be applied on prospective research, but also on retrospective research and consensus based on a large number of cases. Confirmation bias is an important source of false data in experience based systems like homeopathy. Homeopathic doctors should become more aware of this and longer follow-up of cases could remedy this. The existing system of adding symptoms to our materia medica is obsolete.
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.
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
The Heisenberg Uncertainty Principle and the Nyquist-Shannon Sampling Theorem
Directory of Open Access Journals (Sweden)
Millette P. A.
2013-07-01
Full Text Available The derivation of the Heisenberg Uncertainty Principle (HUP from the Uncertainty Theorem of Fourier Transform theory demonstrates that the HUP arises from the dependency of momentum on a wave number that exists at the quantum level. It also establishes that the HUP is purely a relationship between the eﬀective widths of Fourier transform pairs of variables (i.e. conjugate variables. We note that the HUP is not a quantum mechanical measurement principle per se. We introduce the Quantum Mechanical equivalent of the Nyquist-Shannon Sampling Theorem of Fourier Transform theory, and show that it is a better principle to describe the measurement limitations of Quantum Mechanics. We show that Brillouin zones in Solid State Physics are a manifestation of the Nyquist-Shannon Sampling Theorem at the quantum level. By comparison with other ﬁelds where Fourier Transform theory is used, we propose that we need todiscern between measurement limitations and inherent limitations when interpreting the impact of the HUP on the nature of the quantum level. We further propose that while measurement limitations result in our perception of indeterminism at the quantum level, there is no evidence that there are any inherent limitations at the quantum level, based on the Nyquist-Shannon Sampling Theorem
Generalizations of the Abstract Boundary singularity theorem
Whale, Ben E; Scott, Susan M
2015-01-01
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 $C^1$ curves to locally Lipschitz curves.
A Noether Theorem for Markov Processes
Baez, John C
2012-01-01
Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the Hamiltonian if and only if its expected value remains constant in time for every state. For Markov processes that no longer holds, but an observable commutes with the Hamiltonian if and only if both its expected value and standard deviation are constant in time for every state.
Spectral mapping theorems a bluffer's guide
Harte, Robin
2014-01-01
Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.
Pauli and the spin-statistics theorem
Duck, Ian M
1997-01-01
This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties. Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that
Jarzynski's theorem for lattice gauge theory
Caselle, Michele; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-01-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium states. In this article, we extend Jarzynski's theorem to lattice gauge theory, and present examples of applications for two 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 Schroedinger functional and for simulations at finite density using reweighting techniques.
Limits for the central production of Theta^+ and Xi^{--} pentaquarks in 920 GeV pA collisions
Abt, I; Agari, M; Albrecht, H; Aleksandrov, A; Amaral, V S; Amorim, A; Aplin, S J; Aushev, V; Bagaturia, Yu S; Balagura, V; Bargiotti, M; Barsukova, O; Bastos, J; Batista, J; Bauer, C; Bauer, T S; Belkov, A; Belotelov, I; Bertin, A; Bobchenko, B M; Böcker, M; Bogatyrev, A; Böhm, G; Brauer, M; Bruinsma, M; Bruschi, M; Buchholz, P; Buran, T; Carvalho, J; Conde, P; Cruse, C; Dam, M; Danielsen, K M; Danilov, M; De Castro, S; Deppe, H; Dong, X; Dreis, H B; Egorytchev, V; Ehret, K; Eisele, F; Emeliyanov, D; Essenov, S; Fabbri, Franco Luigi; Faccioli, P; Feuerstack-Raible, M; Flammer, J; Fominykh, B A; Funcke, M; Garrido, L; Giacobbe, B; Glass, J; Goloubkov, D; Golubkov, Yu A; Golutvin, A; Golutvin, I A; Gorbounov, I; Gorisek, A; Gouchtchine, O; Goulart, D C; Gradl, S; Gradl, W; Grimaldi, F; Guilitsky, Yu; Hansen, J D; Hernández, J M; Hofmann, W; Hott, T; Hulsbergen, W D; Husemann, U; Igonkina, O; Ispiryan, M; Jagla, T; Jiang, C; Kapitza, H; Karabekyan, S; Karpenko, N; Keller, S; Kessler, J; Khasanov, F M; Kiryushin, Yu T; Knöpfle, K T; Kolanoski, H; Korpar, S; Krauss, C; Kreuzer, P; Krizan, P; Krücker, D; Kupper, S; Kvaratskheliia, T; Lanyov, A V; Lau, K; Lewendel, B; Lohse, T; Lomonosov, B N; 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 A; Nörenberg, M; Nowak, S; Núñez-Pardo de Vera, M T; Ouchrif, M; Ould-Saada, F; Padilla, C; Peralta, D; Pernack, R; Pestotnik, R; Piccinini, M; Pleier, M A; Poli, M; Popov, V; Pose, A; Pose, D; Prystupa, S; Pugatch, V; Pylypchenko, Y; Pyrlik, J; Reeves, K; Ressing, D; Rick, H; Riu, I; Robmann, P; Rostovtseva, I; Rybnikov, V; Sánchez, F; Sbrizzi, A; Schmelling, M; Schmidt, B; Schreiner, A; Schröder, H; Schwartz, A J; Schwarz, A S; Schwenninger, B; Schwingenheuer, B; Sciacca, F; Semprini-Cesari, N; Shuvalov, S; Silva, L; Smirnov, K V; Sozuer, L; Solunin, S; Somov, A; Somov, S; Spengler, J; Spighi, R; Spiridonov, A A; Stanovnik, A; Staric, M; Stegmann, C; Subramanian, H S; Symalla, M; Tikhomirov, I; Titov, M; Tsakov, I; Uwer, U; Van Eldik, C; Vasilev, Yu; Villa, M; Vitale, A; Vukotic, I; Wahlberg, H; Walenta, Albert H; Walter, M; Wang, J J; Wegener, D; Werthenbach, U; Wolters, H; Wurth, R; Wurz, A; Zaitsev, Yu; Zavertyaev, M V; Zech, G; Zeuner, T; Zhelezov, A; Zheng, Z; Zimmermann, R; Zivko, T; Zoccoli, A
2004-01-01
We have searched for Theta^+(1540) and Xi^{--}(1862) pentaquark candidates in proton-induced reactions on C, Ti and W targets at mid-rapidity and \\sqrt{s} = 41.6 GeV. In 2x10^8 inelastic events we find no evidence for narrow (sigma~5 MeV) signals in the Theta^+ -> pK_s and Xi^{--} -> Xi^-pi^- channels; our 95% CL upper limits (UL) for the inclusive production cross section times branching fraction Bx(dsigma/dy)|_{y~0} are 3.7 and 2.5 microb/N. The UL of the yield ratio of [Theta^+ / Lambda(1520)] < 2.7% is significantly lower than model predictions. Our UL of [BxXi^{--} / Xi(1530)^0] < 4% is at variance with the results that have provided first evidence for the Xi^{--} signal.
Towards a No-Lose Theorem for Naturalness
Curtin, David
2015-01-01
We derive a phenomenological no-lose theorem for naturalness up to the TeV scale, which applies when quantum corrections to the Higgs mass from top quarks are canceled by perturbative BSM particles (top partners) of similar multiplicity due to to some symmetry. Null results from LHC searches already seem to disfavor such partners if they are colored. Any partners with SM charges and ~TeV masses will be exhaustively probed by the LHC and a future 100 TeV collider. Therefore, we focus on neutral top partners. While these arise in Twin Higgs theories, we analyze neutral top partners as model-independently as possible using EFT and Simplified Model methods. We classify all perturbative neutral top partner structures in order to compute their irreducible low-energy signatures at proposed future lepton and hadron colliders, as well as the irreducible tunings suffered in each scenario. Central to our theorem is the assumption that SM-charged BSM states appear in the UV completion of neutral naturalness, which is the...
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.
Lp-inverse theorem for modified beta operators
Directory of Open Access Journals (Sweden)
V. K. Jain
2003-04-01
Full Text Available We obtain a converse theorem for the linear combinations of modified beta operators whose weight function is the Baskakov operators. To prove our inverse theorem, we use the technique of linear approximating method, namely, Steklov mean.
Application of the residue theorem to bilateral hypergeometric series
Directory of Open Access Journals (Sweden)
Wenchang Chu
2007-12-01
Full Text Available The application of the residue theorem to bilateral hypergeometric series identities is systematically reviewed by exemplifying three classes of summation theorems due to Dougall (1907, Jackson (1949, 1952 and Slater-Lakin (1953.
A duality theorem of crossed coproduct for Hopf algebras
Institute of Scientific and Technical Information of China (English)
王栓宏
1995-01-01
A duality theorem for Hopf crossed coproduct is proved. This theorem plays a role similar to that appearing in the work of Koppinen (which generalized the corresponding results of group grraded ring).
An existence theorem for Volterra integrodifferential equations with infinite delay
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Ferenc Izsak
2003-01-01
Full Text Available Using Schauder's fixed point theorem, we prove an existence theorem for Volterra integrodifferential equations with infinite delay. As an appplication, we consider an $n$ species Lotka-Volterra competitive system.
A Note on a Broken-Cycle Theorem for Hypergraphs
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Trinks Martin
2014-08-01
Full Text Available Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there
A Dual of the Compression-Expansion Fixed Point Theorems
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Henderson Johnny
2007-01-01
Full Text Available This paper presents a dual of the fixed point theorems of compression and expansion of functional type as well as the original Leggett-Williams fixed point theorem. The multi-valued situation is also discussed.
The Application of Mutual Energy Theorem in Expansion of Radiation Field in Spherical Waves
Zhao, Shuang-Ren
2016-01-01
In recent years the shperical wave expansion method has been widely applied to the theory and calculation of electromagnetic fields. But the inner product exist in reference[1] is defined on the Banach space[2]. Through redefining the inner product this article limits the wave expansion method to Hibert space[3]. For this reason the mutual energy theorem is introduced.
Fluctuation theorem applied to the Nosé-Hoover thermostated Lorentz gas
Gilbert, Thomas
2006-03-01
We present numerical evidence supporting the validity of the Gallavotti-Cohen fluctuation theorem applied to the driven Lorentz gas with Nosé-Hoover thermostating. It is moreover argued that the asymptotic form of the fluctuation formula is independent of the amplitude of the driving force in the limit where it is small.
Student Research Project: Goursat's Other Theorem
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
Answering Junior Ant's "Why" for Pythagoras' Theorem
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.…
Crum's Theorem for `Discrete' Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2009-01-01
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\\"odinger equation is a difference equation.
Stokes' theorem, volume growth and parabolicity
Valtorta, Daniele
2010-01-01
We present some new Stokes'type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced.
Generalized Friedland's theorem for C0-semigroups
Cichon, Dariusz; Jung, Il Bong; Stochel, Jan
2008-07-01
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
An extension theorem for conformal gauge singularities
Tod, Paul
2007-01-01
We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem.
Agreement Theorems in Dynamic-Epistemic Logic
Degremont, Cedric; Roy, Oliver
2012-01-01
This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structure
Lagrange’s Four-Square Theorem
Directory of Open Access Journals (Sweden)
Watase Yasushige
2015-02-01
Full Text Available This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23].
1/4-pinched contact sphere theorem
DEFF Research Database (Denmark)
Ge, Jian; Huang, Yang
2016-01-01
Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness res...
Average sampling theorems for shift invariant subspaces
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.
On the Hardy-Littlewood maximal theorem
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Shinji Yamashita
1982-01-01
Full Text Available The Hardy-Littlewood maximal theorem is extended to functions of class PL in the sense of E. F. Beckenbach and T. Radó, with a more precise expression of the absolute constant in the inequality. As applications we deduce some results on hyperbolic Hardy classes in terms of the non-Euclidean hyperbolic distance in the unit disk.
A Generalized Krein-Rutman Theorem
Zhang, Lei
2016-01-01
A generalized Krein-Rutman theorem for a strongly positive bounded linear operator whose spectral radius is larger than essential spectral radius is established: the spectral radius of the operator is an algebraically simple eigenvalue with strongly positive eigenvector and other eigenvalues are less than the spectral radius.
A non-archimedean Montel's theorem
Favre, Charles; Trucco, Eugenio
2011-01-01
We prove a version of Montel's theorem for analytic functions over a non-archimedean complete valued field. We propose a definition of normal family in this context, and give applications of our results to the dynamics of non-archimedean entire functions.
The Fundamental Theorems of Interval Analysis
van Emden, M. H.; Moa, B.
2007-01-01
Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements and proofs of the fundamental theorems of interval arithmetic and interval analysis. Revision Feb. 10, 2009: added reference to and acknowledgement of P. Taylor.
A cosmological no-hair theorem
Chambers, C M; Chris M Chambers; Ian G Moss
1994-01-01
A generalisation of Price's theorem is given for application to Inflationary Cosmologies. Namely, we show that on a Schwarzschild--de Sitter background there are no static solutions to the wave or gravitational perturbation equations for modes with angular momentum greater than their intrinsic spin.
Multiplier theorems for special Hermite expansions on
Institute of Scientific and Technical Information of China (English)
张震球; 郑维行
2000-01-01
The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calderon-Zygmund decomposition. Then the multiplier theorem in Lp(1 < p < ω ) is obtained. The special Hermite expansions in twisted Hardy space are also considered. As an application, the multipli-ers for a certain kind of Laguerre expansions are given in Lp space.
JACKSON‘S THEOREM FOR COMPACT GROUPS
Institute of Scientific and Technical Information of China (English)
H.Vaezi; S.F.Rzaev
2002-01-01
In this article we consider the generalized shift operator defined by (Shuf)(g)=∫Gf(tut-1g)dt on compact group G and by help of this operator we define “Spherical” modulus of continuity.So we prove Stechkin and Jackson type theorems.
Green's Theorem for Generalized Fractional Derivatives
Odzijewicz, Tatiana; Torres, Delfim F M
2012-01-01
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case when the generalized operators are reduced to the standard partial fractional derivatives and fractional integrals in the sense of Riemann-Liouville or Caputo.
SOME REFINEMENTS OF ENESTROM-KAKEYA THEOREM
Institute of Scientific and Technical Information of China (English)
A.Aziz; B.A.Zargar
2007-01-01
In this paper we present certain interesting refinements of a well-known Enestrom-Kakeya theorem in the theory of distribution of zeros of polynomials which among other things also improve upon some results of Aziz and Mohammad, Govil and Rehman and others.
Nash-Williams’ cycle-decomposition theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2016-01-01
We give an elementary proof of the theorem of Nash-Williams that a graph has an edge-decomposition into cycles if and only if it does not contain an odd cut. We also prove that every bridgeless graph has a collection of cycles covering each edge at least once and at most 7 times. The two results...
Tennis Rackets and the Parallel Axis Theorem
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.
Automated theorem proving theory and practice
Newborn, Monty
2001-01-01
As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate. Computers that perform billions of operations per second are now commonplace. Multiprocessors with thousands of little computers - relatively little! -can now carry out parallel computations and solve problems in seconds that only a few years ago took days or months. Chess-playing programs are on an even footing with the world's best players. IBM's Deep Blue defeated world champion Garry Kasparov in a match several years ago. Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from given facts, or abstractly, to prove theorems-the subject of this book. Specifically, this book is about two theorem-proving programs, THEO and HERBY. The first four chapters contain introductory material about automated theorem proving and the two programs. This includes material on the language used to express theorems, predicate calculus, and the rules of...
A non-differentiable Noether's theorem
Cresson, Jacky; Greff, Isabelle
2011-02-01
In the framework of the nondifferentiable embedding of Lagrangian systems, defined by Cresson and Greff [non-dierentiable embedding of lagrangian systems and partial dierential equations. Preprint Max-Plank-Institut für Mathematik in den Naturwissenschaften, Leipzig 16, 26 (2010)], we prove a Noether's theorem based on the lifting of one-parameter groups of diffeomorphisms.
Some Generalizations of Jungck's Fixed Point Theorem
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J. R. Morales
2012-01-01
Full Text Available We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.
Generalization of the Hellmann-Feynman theorem
Energy Technology Data Exchange (ETDEWEB)
Esteve, J.G., E-mail: esteve@unizar.e [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Falceto, Fernando [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Garcia Canal, C. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata and IFLP-CONICET (Argentina)
2010-01-25
The well-known Hellmann-Feynman theorem of quantum mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition of the Hamiltonian of the system also depends on that parameter.
Generalizations of Brandl's theorem on Engel length
Quek, S. G.; Wong, K. B.; Wong, P. C.
2013-04-01
Let n 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.
A simpler derivation of the coding theorem
Lomnitz, Yuval
2012-01-01
A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information follow naturally in the proof. It may also be applicable to situations where typicality is not natural.
Norton's theorem for batch routing queueing networks
Bause, Falko; Boucherie, Richard J.; Buchholz, Peter
2001-01-01
This paper shows that the aggregation and decomposition result known as Norton’s theorem for queueing networks can be extended to a general class of batch routing queueing networks with product-form solution that allows for multiple components to simultaneously release and receive (batches of) custo
Nonempty intersection theorems in topological spaces with applications
Institute of Scientific and Technical Information of China (English)
Min FANG; Nan-jing HUANG
2009-01-01
In this paper,we establish some new nonempty intersection theorems for generalized L-KKM mappings and prove some new fixed point theorems for set-valued mappings under suitable conditions in topological spaces.As applications,an existence theorem for an equilibrium problem with lower and upper bounds and two existence theorems for a quasi-equilibrium problem with lower and upper bounds are obtained in topological spaces.Our results generalize some known results in the literature.
Two Theorems on Calculating the Relative Entropy of Entanglement
Institute of Scientific and Technical Information of China (English)
WU Sheng-Jun; ZHANG Yong-De; WU Qiang
2001-01-01
We present two theorems on calculating the relative entropy of entanglement. Theorem 1 is an extension of Vedral and Plenio's theorem (Phys. Rev. A 57 (1998) 1619) for pure states, which is useful for calculating the relative entropy of entanglement for all pure states as well as for a class of mixed states. Theorem 2 gives the relative entropy of entanglement for any bipartite state whose tripartite purification has two separable reduced bipartite states.
Ehrenfest theorem, Galilean invariance and nonlinear Schr"odinger equations
Kälbermann, G
2003-01-01
Galilean invariant Schr"odinger equations possessing nonlinear terms coupling the amplitude and the phase of the wave function can violate the Ehrenfest theorem. An example of this kind is provided. The example leads to the proof of the theorem: A Galilean invariant Schr"odinger equation derived from a lagrangian density obeys the Ehrenfest theorem. The theorem holds for any linear or nonlinear lagrangian.
A Complement to the Valiron-Titchmarsh Theorem for Subharmonic Functions
Institute of Scientific and Technical Information of China (English)
Alexander I.Kheyfits
2014-01-01
The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n≥3. Here we extend the Drasin complement to the Valiron-Titchmarsh theorem and show that if u is a subharmonic function of this class and of order 0<ρ<1, then the existence of the limit limr→∞logu(r)/N(r), where N(r) is the integrated counting function of the masses of u, implies the regular asymptotic behavior for both u and its associated measure.
Quantum Effects on the Deflection of Light and the Gauss-Bonnet Theorem
Jusufi, Kimet
2016-01-01
In this letter we apply the Gauss--Bonnet theorem to calculate the deflection angle by a quantum corrected Schwarzschild black hole in the weak limit approximation. In particular, we calculate the light deflection by two types of quantum corrected black holes: the renormalization group improved Schwarzschild solution and the quantum corrected Schwarzschild solution in Bohmian quantum mechanics. We start from the corresponding optical metrics to use then the Gauss--Bonnet theorem and calculate the Gaussian curvature in both cases. Finally, we calculate the leading terms of the deflection angle and show that quantum corrections modifies the deflection angle in both solutions.
Applications of square-related theorems
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.
Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
von Neumann, John
2010-01-01
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.
A Simple Geometrical Derivation of the Spatial Averaging Theorem.
Whitaker, Stephen
1985-01-01
The connection between single phase transport phenomena and multiphase transport phenomena is easily accomplished by means of the spatial averaging theorem. Although different routes to the theorem have been used, this paper provides a route to the averaging theorem that can be used in undergraduate classes. (JN)
A remark on Kov\\'acs' vanishing theorem
Fujino, Osamu
2012-01-01
We give an alternative proof of Kov\\'acs' vanishing theorem. Our proof is based on the standard arguments of the minimal model theory. We do not need the notion of Du Bois pairs. We reduce Kov\\'acs' vanishing theorem to the well-known relative Kawamata--Viehweg--Nadel vanishing theorem.
ON COLLECTIVELY FIXED POINT THEOREMS ON FC-SPACES
Institute of Scientific and Technical Information of China (English)
Yongjie Piao
2010-01-01
Based on a KKM type theorem on FC-space,some new fixed point theorems for Fan-Browder type are established,and then some collectively fixed point theorems for a family of Φ-maps defined on product space of FC-spaees are given.These results generalize and improve many corresponding results.
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
2014-01-01
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
Shargel, Benjamin Hertz
2009-01-01
Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-rever...
Bringing Bell's theorem back to the domain of Particle Physics & Cosmology
Hiesmayr, Beatrix C
2015-01-01
John St. Bell was a physicist working most of his time at CERN and contributing intensively and sustainably to the development of Particle Physics and Collider Physics. As a hobby he worked on so-called "foundations of quantum theory", that was that time very unpopular, even considered to be scientifically taboo. His 1964-theorem, showing that predictions of local realistic theories are different to those of quantum theory, initiated a new field in quantum physics: quantum information theory. The violation of Bell's theorem, for instance, is a necessary and sufficient criterion for generating a secure key for cryptography at two distant locations. This contribution shows how Bell's theorem can be brought to the realm of high energy physics and presents the first conclusive experimental feasible test for weakly decaying neutral mesons on the market. Strong experimental and theoretical limitations make a Bell test in weakly decaying systems such as mesons and hyperons very challenging, however, these systems sh...
On weakly periodic-like rings and commutativity theorems
Directory of Open Access Journals (Sweden)
Abu-Khuzam Hazar
2006-12-01
Full Text Available A ring $R$ is called periodic if, for every $x$ in $R$, there exist distinct positive integers $m$ and $n$ such that $x^m=x^n$. An element $x$ of $R$ is called potent if $x^k=x$ for some integer $k>1$. A ring $R$ is called weakly periodic if every $x$ in $R$ can be written in the form $x=a+b$ for some nilpotent element $a$ and some potent element $b$ in $R$. A ring $R$ is called weakly periodic-like if every element $x$ in $R$ which is not in the center $C$ of $R$ can be written in the form $x=a+b$, with $a$ nilpotent and $b$ potent. Some structure and commutativity theorems are established for weakly periodic-like rings $R$ satisfying certain torsion-freeness hypotheses along with conditions involving some elements being central.
Soft theorems from string theory
Energy Technology Data Exchange (ETDEWEB)
Di Vecchia, Paolo [The Niels Bohr Institute, University of Copenhagen (Denmark); Nordita, KTH Royal Institute of Technology and Stockholm University (Sweden); Marotta, Raffaele [Istituto Nazionale di Fisica Nucleare, Sezione di Napoli (Italy); Complesso Universitario di Monte S. Angelo, Napoli (Italy); Mojaza, Matin [Nordita, KTH Royal Institute of Technology and Stockholm University (Sweden)
2016-04-15
Soft behaviour of closed string amplitudes involving dilatons, gravitons and anti-symmetric tensors, is studied in the framework of bosonic string theory. The leading double soft limit of gluons is analysed as well, starting from scattering amplitudes computed in the open bosonic string. Field theory expressions are then obtained by sending the string tension to infinity. The presented results have been derived in the papers of Ref [1]. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Non-Gaussian Limiting Laws for the Entries of Regular Functions of the Wigner Matrices
Pastur, L
2011-01-01
This paper is a continuation of our paper "Fluctuations of Matrix Elements of Regular Functions of Gaussian Random Matrices", J. Stat. Phys. (134), 147--159 (2009), in which we proved the Central Limit Theorem for the matrix elements of differential functions of the real symmetric random Gaussian matrices (GOE). Here we consider the real symmetric random Wigner matrices having independent (modulo symmetry conditions) but not necessarily Gaussian entries. We show that in this case the matrix elements of sufficiently smooth functions of these random matrices have in general another limiting law which coincides essentially with the probability law of matrix entries.
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.
Intermediate convergents and a metric theorem of Khinchin
Haynes, Alan K
2009-01-01
A landmark theorem in the metric theory of continued fractions begins this way: Select a non-negative real function $f$ defined on the positive integers and a real number $x$, and form the partial sums $s_n$ of $f$ evaluated at the partial quotients $a_1,..., a_n$ in the continued fraction expansion for $x$. Does the sequence $\\{s_n/n\\}$ have a limit as $n\\rar\\infty$? In 1935 A. Y. Khinchin proved that the answer is yes for almost every $x$, provided that the function $f$ does not grow too quickly. In this paper we are going to explore a natural reformulation of this problem in which the function $f$ is defined on the rationals and the partial sums in question are over the intermediate convergents to $x$ with denominators less than a prescribed amount. By using some of Khinchin's ideas together with more modern results we are able to provide a quantitative asymptotic theorem analogous to the classical one mentioned above.
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.
Boyce, H; van der Marel, R P; Baumgardt, H; Kissler-Patig, M; Neumayer, N; de Zeeuw, P T
2016-01-01
We constrain the possible presence of a central black hole (BH) in the center of the Large Magellanic Cloud (LMC). This requires spectroscopic measurements over an area of order a square degree, due to the poorly known position of the kinematic center. Such measurements are now possible with the impressive field of view of the Multi Unit Spectroscopic Explorer (MUSE) on the ESO Very Large Telescope. We used the Calcium Triplet (~850nm) spectral lines in many short-exposure MUSE pointings to create a two-dimensional integrated-light line-of-sight velocity map from the ~$10^8$ individual spectra, taking care to identify and remove Galactic foreground populations. The data reveal a clear velocity gradient at an unprecedented spatial resolution of 1 arcmin$^{2}$. We fit kinematic models to arrive at a $3\\sigma$ upper-mass-limit of $9\\times10^{6}$ M$_{Sun}$ for any central BH - consistent with the known scaling relations for supermassive black holes and their host systems. This adds to the growing body of knowledg...
Causarum Investigatio and the Two Bell's Theorems of John Bell
Wiseman, Howard M
2015-01-01
"Bell's theorem" can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination. His 1976 theorem is their incompatibility with the single property of Local Causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with the assumption of Local Causality, even if not by that name. Although the two Bell's theorems are logically equivalent, their assumptions are not. Hence, the earlier and later theorems suggest quite different conclusions, embraced by operationalists and realists, respectively. The key issue is whether Locality or Local Causality is the appropriate notion emanating from Relativistic Causality, and this rests on one's basic notion of causation. For operationalists the appropriate notion is what is here called the Principle of Agent-Causation, while for realists it is Reichenbach's Principle of common cause. By...
Parameterized quantum field theory without Haag's theorem
Seidewitz, Ed
2015-01-01
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that quantum field theory can be formulated, using an invariant, fifth path parameter in addition to the usual four position parameters, in such a way that Haag's theorem no longer applies, but such that the Dyson perturbation expansion for the sc...
De Finetti theorems for easy quantum groups
Banica, Teodor; Speicher, Roland
2009-01-01
We study sequences of noncommutative random variables which are invariant under "quantum transformations" coming from an orthogonal quantum group satisfying the "easiness" condition axiomatized in our previous paper. For 10 easy quantum groups, we obtain de Finetti type theorems characterizing the joint distribution of any infinite, quantum invariant sequence. In particular, we give a new and unified proof of the classical results of de Finetti and Freedman for the easy groups S_n, O_n, which is based on the combinatorial theory of cumulants. We also recover the free de Finetti theorem of K\\"ostler and Speicher, and the characterization of operator-valued free semicircular families due to Curran. We consider also finite sequences, and prove an approximation result in the spirit of Diaconis and Freedman.
A noncommutative extended de Finetti theorem
Köstler, Claus
2008-01-01
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is a noncommutative version of this theorem. In contrast to the classical result of Ryll-Nadzewski, exchangeability turns out to be stronger than spreadability for infinite noncommutative random sequences. Out of our investigations emerges noncommutative conditional independence in terms of a von Neumann algebraic structure closely related to Popa's notion of commuting squares and K\\"ummerer's generalized Bernoulli shifts. Our main result is applicable to classical probability, quantum probability, in particular free probability, braid group representations and Jones subfactors.
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.
Noether theorem for {mu}-symmetries
Energy Technology Data Exchange (ETDEWEB)
Cicogna, Giampaolo [Dipartimento di Fisica, Universita di Pisa and INFN, Sezione di Pisa, Largo B Pontecorvo 3, 50127 Pisa (Italy); Gaeta, Giuseppe [Dipartimento di Matematica, Universita di Milano, via Saldini 50, 20133 Milano (Italy)
2007-09-28
We give a version of Noether theorem adapted to the framework of {mu}-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of {lambda}-symmetries, and connects {mu}-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this '{mu}-conservation law' actually reduces to a standard one; we also note a relation between {mu}-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under {mu}-prolonged variation fields, leading to modified Euler-Lagrange equations. In this setting, {mu}-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples.
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.
Wigner-Eckart theorem for induced symmetries
Energy Technology Data Exchange (ETDEWEB)
Klein, D.J. (Texas A and M University, Galveston (USA). Department of Marine Sciences); Seligman, T.H. (Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Fisica)
1982-01-01
A unified treatment is given for all group-theoretic problems arising from the evaluation of matrix elements involving operators and states of induced symmetries. To achieve this general treatment two group-theoretic theorems are proven, the first characterizing recoupling coefficients between different symmetry adaptation schemes, and the second making a double coset factorization of a group algebraic matrix basis element. A number of problems previously discussed in the literature, including the conventional Wigner-Eckart theorem and more recent double coset expansions of matrix elements, are realized as special cases in the present treatment. These results entail two new types of recoupling coefficients, namely DC coefficients and 3-symmetry symbols, so that some of their properties are indicated.
Locomotion in complex fluids: Integral theorems
Lauga, Eric
2014-01-01
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.
Multideviations: The hidden structure of Bell's theorems
Fogel, Brandon
2015-01-01
Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open problem. Here I provide a new set of tools, which I refer to as "multideviations", for finding and analyzing these inequalities for the fully general case. In Part I, I introduce the multideviation framework and then use it to prove an important theorem: the Bell distributions can be generated from the set of joint distributions over all observables by deeming specific degrees of freedom unobservable. In Part II, I show how the theorem provides a new method for finding tight Bell inequalities. I then specify a set of new tight Bell inequalities for arbitrary event spaces -- the "even/odd" inequalities -- which have a straightforward interpretation when expressed in terms of multideviations. The even/odd inequalities concern degrees of freedom that are independent of those invol...
Fluctuation theorem for constrained equilibrium systems
Gilbert, Thomas; Dorfman, J. Robert
2006-02-01
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
Simultaneous DOA estimation based on Kolmogorov's theorem
Nájar Martón, Montserrat; Lagunas Hernandez, Miguel A.
1993-01-01
The design of a new architecture for signal processing, based on the Kolmogorov's theorem (1957), is addressed. This architecture is applied to solve the problem of source separation. Particularly, an adaptive algorithm is proposed to separate simultaneously all the unknown impinging sources on an aperture of sensors. The implemented framework is composed of two different stages: the first one is the inhibition stage, which turns the problem of estimating simultaneous DOAs (directions of arri...
Hildebrandt's theorem for the essential spectrum
Directory of Open Access Journals (Sweden)
Janko Bračič
2015-01-01
Full Text Available We prove a variant of Hildebrandt's theorem which asserts that the convex hull of the essential spectrum of an operator \\(A\\ on a complex Hilbert space is equal to the intersection of the essential numerical ranges of operators which are similar to \\(A\\. As a consequence, it is given a necessary and sufficient condition for zero not being in the convex hull of the essential spectrum of \\(A\\.
Theorems for Asymptotic Safety of Gauge Theories
Bond, Andrew D
2016-01-01
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.
Resource Adaptive Agents in Interactive Theorem Proving
Benzmueller, Christoph
2009-01-01
We introduce a resource adaptive agent mechanism which supports the user in interactive theorem proving. The mechanism uses a two layered architecture of agent societies to suggest appropriate commands together with possible command argument instantiations. Experiments with this approach show that its effectiveness can be further improved by introducing a resource concept. In this paper we provide an abstract view on the overall mechanism, motivate the necessity of an appropriate resource concept and discuss its realization within the agent architecture.
Reciprocity Theorems for Ab Initio Force Calculations
Wei, C; Mele, E J; Rappe, A M; Lewis, Steven P.; Rappe, Andrew M.
1996-01-01
We present a method for calculating ab initio interatomic forces which scales quadratically with the size of the system and provides a physically transparent representation of the force in terms of the spatial variation of the electronic charge density. The method is based on a reciprocity theorem for evaluating an effective potential acting on a charged ion in the core of each atom. We illustrate the method with calculations for diatomic molecules.
Bell's theorem without inequalities and without alignments
Cabello, A
2003-01-01
A proof of Bell's theorem without inequalities is presented which exhibits three remarkable properties: (a) reduced local states are immune to collective decoherence, (b) local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups, and (c) local measurements require only individual measurements on the qubits. Indeed, it is shown that this proof is essentially the only one which fulfils (a), (b), and (c).
On the equivalence theorem for integrable systems
Melikyan, A; Rivelles, V O
2014-01-01
We investigate the equivalence theorem for integrable systems using two formulations of the Alday-Arutyunov-Frolov model. We show that the S-matrix is invariant under the field transformation which reduces the non-linear Dirac brackets of one formulation into the standard commutation relations in the second formulation. We also explain how to perform the direct diagonalization of the transformed Hamiltonian by constructing the states corresponding to self-adjoint extensions.
Hyperplane arrangements and Lefschetz's hyperplane section theorem
Yoshinaga, Masahiko
2005-01-01
The Lefschetz hyperplane section theorem asserts that a complex affine variety is homotopy equivalent to a space obtained from its generic hyperplane section by attaching some cells. The purpose of this paper is to give an explicit description of attaching maps of these cells for the complement of a complex hyperplane arrangement defined over real numbers. The cells and attaching maps are described in combinatorial terms of chambers. We also discuss the cellular chain complex with coefficient...
Bezout's theorem and Cohen-Macaulay modules
1999-01-01
We define very proper intersections of modules and projective subschemes. It turns out that equidimensional locally Cohen-Macaulay modules intersect very properly if and only if they intersect properly. We prove a Bezout theorem for modules which meet very properly. Furthermore, we show for equidimensional subschemes $X$ and $Y$: If they intersect properly in an arithmetically Cohen-Macaulay subscheme of positive dimension then $X$ and $Y$ are arithmetically Cohen-Macaulay. The module version...
Carnot's theorem and Szil\\'ard engine
Shu, Liangsuo; Huang, Suyi; Jin, Shiping
2016-01-01
In this work, the relationship between Carnot engine and Szil\\'ard engine was discussed. By defining the available information about the temperature difference between two heat reservoirs, the Carnot engine was found to have a same physical essence with Szil\\'ard engine: lossless conversion of available information. Thus, a generalized Carnot's theorem for wider scope of application can be described as "all the available information is 100% coded into work".
Volume Integral Theorem for Exotic Matter
Nandi, Kamal Kanti; Zhang, Yuan-Zhong; Kumar, K. B. Vijaya
2004-01-01
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 ...
The "Nernst Theorem" and Black Hole Thermodynamics
Wald, R M
1997-01-01
The Nernst formulation of the third law of ordinary thermodynamics (often referred to as the ``Nernst theorem'') asserts that the entropy, $S$, of a system must go to zero (or a ``universal constant'') as its temperature, $T$, goes to zero. This assertion is commonly considered to be a fundamental law of thermodynamics. As such, it seems to spoil the otherwise perfect analogy between the ordinary laws of thermodynamics and the laws of black hole mechanics, since rotating black holes in general relativity do not satisfy the analog of the ``Nernst theorem''. The main purpose of this paper is to attempt to lay to rest the ``Nernst theorem'' as a law of thermodynamics. We consider a boson (or fermion) ideal gas with its total angular momentum, $J$, as an additional state parameter, and we analyze the conditions on the single particle density of states, $g(\\epsilon,j)$, needed for the Nernst formulation of the third law to hold. (Here, $\\epsilon$ and $j$ denote the single particle energy and angular momentum.) Alt...
Haag's Theorem and Parameterized Quantum Field Theory
Seidewitz, Edwin
2017-01-01
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
Cueto-Rojas, H F; Maleki Seifar, R; Ten Pierick, A; van Helmond, W; Pieterse M, M; Heijnen, J J; Wahl, S A
2016-09-16
Ammonium is the most common N-source for yeast fermentations. Although, its transport and assimilation mechanisms are well documented, there have been only few attempts to measure the in vivo intracellular concentration of ammonium and assess its impact on gene expression. Using an isotope dilution mass spectrometry (IDMS)-based method we were able to measure the intracellular ammonium concentration in N-limited aerobic chemostat cultivations using three different N-sources (ammonium, urea and glutamate) at the same growth rate (0.05 h(-1)). The experimental results suggest that, at this growth rate, a similar concentration of intracellular ammonium, about 3.6 mmol NH4(+)/LIC, is required to supply the reactions in the central N-metabolism independent of the N-source. Based on the experimental results and different assumptions, the vacuolar and cytosolic ammonium concentrations were estimated. Furthermore, we identified a futile cycle caused by NH3 leakage to the extracellular space, which can cost up to 30% of the ATP production of the cell under N-limited conditions, and a futile redox cycle between reactions Gdh1 and Gdh2. Finally, using shotgun proteomics with labeled reference-relative protein expression, differences between the various environmental conditions were identified and correlated with previously identified N-compound sensing mechanisms.
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.
The limit shape problem for ensembles of Young diagrams
Hora, Akihito
2016-01-01
This book treats ensembles of Young diagrams originating from group-theoretical contexts and investigates what statistical properties are observed there in a large-scale limit. The focus is mainly on analyzing the interesting phenomenon that specific curves appear in the appropriate scaling limit for the profiles of Young diagrams. This problem is regarded as an important origin of recent vital studies on harmonic analysis of huge symmetry structures. As mathematics, an asymptotic theory of representations is developed of the symmetric groups of degree n as n goes to infinity. The framework of rigorous limit theorems (especially the law of large numbers) in probability theory is employed as well as combinatorial analysis of group characters of symmetric groups and applications of Voiculescu's free probability. The central destination here is a clear description of the asymptotic behavior of rescaled profiles of Young diagrams in the Plancherel ensemble from both static and dynamic points of view.
Institute of Scientific and Technical Information of China (English)
岑松; 周培蕾
2016-01-01
为了提高有限元的性能,弹性力学的解析解(齐次方程的通解)常常可用作有限元的试探函数。然而单元自由度数与完备的直角坐标解析解个数并不匹配,不完备的试函数会导致单元有方向依赖性。利用新型局部自然坐标———第二类四边形面积坐标 QACM-II (S,T),给出了平面问题对应任意方向纯弯曲状态的应力函数解析解,即S 3和T3的线性组合,并推导出了这两组应力函数对应的应力、应变和位移解析解。之后,利用QACM-II表示的解析解构造了非对称的平面4节点8自由度单元 USQ4,该单元可以同时通过常应力/应变分片检验和纯弯测试,从而破解了 MacNeal局限定理对平面低阶单元的限制。%In order to improve the performance of finite element models,analytical solutions of problems in theory of elasticity (the general solutions of the homogeneous equations )were often used as the element trial functions.However,the number of the element DOFs usually does not match the number of the complete analytical solutions,and such incomplete trial functions may lead to direction dependence of the finite elements.In this paper,a new local natural coordinate method,i.e.,the second form of the quadrilateral area coordinate method QACM-II (S,T),was employed to formulate the analytical solutions (the linear combination of S3 and T3 )of the Airy stress function for pure bending state along arbitrary directions.And corresponding analytical solutions for stresses,strains or displacements were also derived out.Then,by utilizing above solutions,a new unsymmetric 4-node,8-DOF plane quadrilate-ral element,denoted by USQ4,was successfully created.The new element can pass both the constant strain/stress patch test and the pure bending test,which means that the limitation defined by the MacNeal’s theorem is overcome.
Index Theorem and Random Matrix Theory for Improved Staggered Quarks
Energy Technology Data Exchange (ETDEWEB)
Follana, E. [Department of Physics and Astronomy, University of Glasgow, G12 8QQ Glasgow (United Kingdom)
2005-03-15
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 of eigenvalues 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. 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.
Inheritance principle and Non-renormalization theorems at finite temperature
Brigante, M; Liu, H; Brigante, Mauro; Festuccia, Guido; Liu, Hong
2006-01-01
We show that in the large $N$ limit, a weakly coupled SU(N) gauge theory with adjoint matter on a class of compact manifolds (like $S^3$) satisfies an ``inheritance principle'' in the low temperature phase. Finite temperature correlation functions of gauge invariant single-trace operators are related to those at zero temperature by summing over images of each operator in the Euclidean time direction. This implies that the corresponding finite temperature string theory dual can be formulated as a sigma model with Euclidean time direction periodically compactified. As a consequence, various non-renormalization theorems of $\\NN=4$ Super-Yang-Mills theory survive at finite temperature despite the fact that the conformal and supersymmetries are both broken.
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
Fluctuation theorem for out-of-time-ordered correlator
Halpern, Nicole Yunger
2016-01-01
The out-of-time-ordered correlator (OTOC) diagnoses quantum chaos and the scrambling of quantum information via the spread of entanglement. The OTOC encodes forward and reverse evolutions and has deep connections with the flow of time. So do fluctuation theorems such as Jarzynski's Equality, derived in nonequilibrium statistical mechanics. I unite these two powerful, seemingly disparate tools by deriving a fluctuation theorem for the OTOC. The fluctuation theorem is analogous to Jarzynski's Equality. The theorem's left-hand side equals the OTOC. The right-hand side implies a platform-nonspecific protocol for experimentally measuring the OTOC in an indirect manner fundamentally different from existing proposals. Time evolution need not be reversed in any trial. The theorem opens holography, condensed matter, and quantum information to new insights from fluctuation theorems and vice versa.
The implicit function theorem history, theory, and applications
Krantz, Steven G
2003-01-01
The implicit function theorem is part of the bedrock of mathematics analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth function, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash-Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex store, and intimately bound up with the development of fundamental ideas in a...
Inconsistency of Carnot's theorem's proof by R. Clausius
Ihnatovych, V
2013-01-01
R. Clausius proved Carnot's theorem basing on postulate "Heat cannot, of itself, pass from a colder to a hotter body". Alexander Gukhman demonstrated that Carnot's theorem can be proved based on the postulate "Heat cannot, of itself, pass from a hotter to a colder body". He concluded that Carnot's theorem does not follow from Clausius' postulate. The following paper gives a detailed justification of Gukhman's derivation.
Logic for computer science foundations of automatic theorem proving
Gallier, Jean H
2015-01-01
This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in fir
Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators
Institute of Scientific and Technical Information of China (English)
王雪红; 郭军义; 李艳
2012-01-01
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ?/?λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
On the linearization theorem for proper Lie groupoids
Crainic, Marius
2011-01-01
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the the fixed point case (known as Zung's theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passing to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise conditions needed for the theorem to hold (which often have been misstated in the literature).
Gerlach, Moritz
2011-01-01
We prove that every bounded, positive, irreducible, stochastically continuous semigroup on the space of bounded, measurable functions which is strong Feller, consists of kernel operators and possesses an invariant measure converges pointwise. This differs from Doob's theorem in that we do not require the semigroup to be Markovian and request a fairly weak kind of irreducibility. In addition, we elaborate on the various notions of kernel operators in this context, show the stronger result that the adjoint semigroup converges strongly and discuss as an example diffusion equations on rough domains. The proofs are based on the theory of positive semigroups and do not use probability theory.
Lifespan theorem for constrained surface diffusion flows
McCoy, James; Williams, Graham; 10.1007/s00209-010-0720-7
2012-01-01
We consider closed immersed hypersurfaces in $\\R^{3}$ and $\\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.
Stone's representation theorem in fuzzy topology
Institute of Scientific and Technical Information of China (English)
LIU; Yingming(刘应明); ZHANG; Dexue(张德学)
2003-01-01
In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces.
Jackson's Theorem on Bounded Symmetric Domains
Institute of Scientific and Technical Information of China (English)
Ming Zhi WANG; Guang Bin REN
2007-01-01
Polynomial approximation is studied on bounded symmetric domain Ω in C n for holo-morphic function spaces X ,such as Bloch-type spaces,Bergman-type spaces,Hardy spaces,Ω algebra and Lipschitz space.We extend the classical Jackson ’s theorem to several complex variables:E k f,X ) ω (1 /k,f,X ),where E k f,X )is the deviation of the best approximation of f ∈X by polynomials of degree at mostk with respect to the X -metric and ω (1/k,f,X )is the corresponding modulus of continuity.
Adiabatic theorems for generators of contracting evolutions
Avron, J E; Graf, G M; Grech, P
2011-01-01
We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems generated by Lindbladians all the way to classically driven stochastic systems. In all these cases the adiabatic evolution approximates, to lowest order, the natural notion of parallel transport in the manifold of instantaneous stationary states. The dynamics in the manifold of instantaneous stationary states and transversal to it have distinct characteristics: The former is irreversible and the latter is transient in a sense that we explain. Both the gapped and gapless cases are considered. Some applications are discussed.
Godel's Incompleteness Theorems and Platonic Metaphysics
Mikovic, Aleksandar
2015-01-01
We argue by using Godel's incompletness theorems in logic that platonism is the best metaphysics for science. This is based on the fact that a natural law in a platonic metaphysics represents a timeless order in the motion of matter, while a natural law in a materialistic metaphysics can be only defined as a temporary order which appears at random in the chaotic motion of matter. Although a logical possibility, one can argue that this type of metaphysics is highly implausible. Given that mathematics fits naturally within platonism, we conclude that a platonic metaphysics is more preferable than a materialistic metaphysics.
Fixed point theorems in spaces and -trees
Directory of Open Access Journals (Sweden)
Kirk WA
2004-01-01
Full Text Available We show that if is a bounded open set in a complete space , and if is nonexpansive, then always has a fixed point if there exists such that for all . It is also shown that if is a geodesically bounded closed convex subset of a complete -tree with , and if is a continuous mapping for which for some and all , then has a fixed point. It is also noted that a geodesically bounded complete -tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.
On Clifford's theorem for singular curves
Franciosi, Marco
2011-01-01
Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H^0(C, I_S K_C) contains a generically invertible section). Under some general assumptions on S or C we show that h^0(C, I_S K_C) <= p_a(C) - deg (S)/2 and if equality holds then either S is trivial, or C is honestly hyperelliptic or 3-disconnected. As a corollary we give a generalization of Clifford's theorem for reduced curves.
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
J M M Senovilla
2007-07-01
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies.
Number systems and the Chinese Remainder Theorem
van de Woestijne, Christiaan E
2011-01-01
A well-known generalisation of positional numeration systems is the case where the base is the residue class of $x$ modulo a given polynomial $f(x)$ with coefficients in (for example) the integers, and where we try to construct finite expansions for all residue classes modulo $f(x)$, using a suitably chosen digit set. We give precise conditions under which direct or fibred products of two such polynomial number systems are again of the same form. The main tool is a general form of the Chinese Remainder Theorem. We give applications to simultaneous number systems in the integers.
APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION
Institute of Scientific and Technical Information of China (English)
杨守志; 程正兴; 唐远炎
2003-01-01
An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution. The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation, a piece-wise linear function, and posseses an explicit computation formula. Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function.
Theorem proving support in programming language semantics
Bertot, Yves
2007-01-01
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational semantics, axiomatic semantics, and abstract interpretation. Descriptions as recursive functions are also provided whenever suitable, thus yielding a a verification condition generator and a static analyser that can be run inside the theorem prover for use in reflective proofs. Extraction of an interpreter from the denotational semantics is also described. All different aspects are formally proved sound with respect to the natural semantics specification.
Adiabatic theorem for non-hermitian time-dependent open systems
Fleischer, A; Fleischer, Avner; Moiseyev, Nimrod
2005-01-01
In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone, R. Ketzmerik, and W. Kohn, Phys. Rev. A 56, 4045 (1997)]. Here with the help of the (t,t') formalism combined with the complex scaling method we derive an adiabatic theorem for open systems and provide an analytical criteria for the validity of the adiabatic limit. The use of the complex scaling transformation plays a key role in our derivation. As a numerical example we apply the adiabatic theorem we derived to a 1D model Hamiltonian of Xe atom which interacts with strong, monochromatic sine-square laser pulses. We show that the gener- ation of odd-order harmonics and the absence of hyper-Raman lines, even when the pulses are extremely short, can be explained with the help of the adiabatic theorem we derived.
A Formal Proof Of The Riesz Representation Theorem
Directory of Open Access Journals (Sweden)
Anthony Narkawicz
2011-01-01
Full Text Available This paper presents a formal proof of the Riesz representation theorem in the PVS theorem prover. The Riemann Stieltjes integral was defined in PVS, and the theorem relies on this integral. In order to prove the Riesz representation theorem, it was necessary to prove that continuous functions on a closed interval are Riemann Stieltjes integrable with respect to any function of bounded variation. This result follows from the equivalence of the Riemann Stieltjes and Darboux Stieltjes integrals, which would have been a lengthy result to prove in PVS, so a simpler lemma was proved that captures the underlying concept of this integral equivalence. In order to prove the Riesz theorem, the Hahn Banach theorem was proved in the case where the normed linear spaces are the continuous and bounded functions on a closed interval. The proof of the Riesz theorem follows the proof in Haaser and Sullivan's book Real Analysis. The formal proof of this result in PVS revealed an error in textbook's proof. Indeed, the proof of the Riesz representation theorem is constructive, and the function constructed in the textbook does not satisfy a key property. This error illustrates the ability of formal verification to find logical errors. A specific counterexample is given to the proof in the textbook. Finally, a corrected proof of the Riesz representation theorem is presented.
Fluctuation-dissipation theorem and quantum tunneling with dissipation
Fujikawa, K
1998-01-01
We suggest to take the fluctuation-dissipation theorem of Callen and Welton as a basis to study quantum dissipative phenomena (such as macroscopic quantum tunneling) in a manner analogous to the Nambu-Goldstone theorem for spontaneous symmetry breakdown. It is shown that the essential physical contents of the Caldeira-Leggett model such as the suppression of quantum coherence by Ohmic dissipation are derived from general principles only, namely, the fluctuation-dissipation theorem and unitarity and causality (i.e., dispersion relations), without referring to an explicit form of the Lagrangian. An interesting connection between quantum tunneling with Ohmic dissipation and the Anderson's orthogonality theorem is also noted.
Generalizations of the Nash Equilibrium Theorem in the KKM Theory
Directory of Open Access Journals (Sweden)
Park Sehie
2010-01-01
Full Text Available The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection theorem, the Fan-type analytic alternative, and the Nash equilibrium theorem for abstract convex spaces satisfying the partial KKM principle. These results are compared with previously known cases for -convex spaces. Consequently, our results unify and generalize most of previously known particular cases of the same nature. Finally, we add some detailed historical remarks on related topics.
Generalizations of the Nash Equilibrium Theorem in the KKM Theory
Directory of Open Access Journals (Sweden)
Sehie Park
2010-01-01
Full Text Available The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection theorem, the Fan-type analytic alternative, and the Nash equilibrium theorem for abstract convex spaces satisfying the partial KKM principle. These results are compared with previously known cases for G-convex spaces. Consequently, our results unify and generalize most of previously known particular cases of the same nature. Finally, we add some detailed historical remarks on related topics.
Fluctuation theorem in dynamical systems with quenched disorder
Drocco, Jeffrey; Olson Reichhardt, Cynthia; Reichhardt, Charles
2010-03-01
We demonstrate that the fluctuation theorem of Gallavotti and Cohen can be used to characterize far from equilibrium dynamical nonthermal systems in the presence of quenched disorder where strong fluctuations or crackling noise occur. By observing the frequency of entropy-destroying trajectories, we show that the theorem holds in specific dynamical regimes near the threshold for motion, indicating that these systems might be ideal candidates for understanding what types of nonthermal fluctuations could be used in constructing generalized fluctuation theorems. We also discuss how the theorem could be tested with global or local probes in systems such as superconducting vortices, magnetic domain walls, stripe phases, Coulomb glasses and earthquake models.
Directory of Open Access Journals (Sweden)
Ronghua He
2012-04-01
Full Text Available Let $I$ be any index set. By using some existence theorems of maximal elements for a family of set-valued mappings involving a better admissible set-valued mapping under noncompact setting of $FC$-spaces, we first present some nonempty intersection theorems for a family $\\{G_{i}\\}_{i\\in I}$ in a product space of $FC$-spaces. Next we give a coincidence theorem and a Fan-Browder type fixed point theorem. Finally, as applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems are proved in product $FC$-space, some existence theorems of solutions for a system of Ky Fan type minimax inequalities involving a family of $G_{\\cal B}$-majorized mappings defined on the product space of $FC$-space are also obtained. Our results improve and generalize some recent results.
Birth of a theorem a mathematical adventure
Villani, Cédric
2015-01-01
This man could plainly do for mathematics what Brian Cox has done for physics" (Sunday Times). What goes on inside the mind of a rock-star mathematician? Where does inspiration come from? With a storyteller's gift, Cedric Villani takes us on a mesmerising journey as he wrestles with a new theorem that will win him the most coveted prize in mathematics. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, doubt and anxiety, elation and despair. We discover how it feels to be obsessed by a theorem during your child's cello practise and throughout your dreams, why appreciating maths is a bit like watching an episode of Columbo, and how sometimes inspiration only comes from locking yourself away in a dark room to think. Blending science with history, biography with myth, Villani conjures up an inimitable cast of characters including the omnipresent Einstein, mad genius Kurt Godel, and Villani's personal hero, John Nash. Bir...
De Finetti Theorem on the CAR Algebra
Crismale, Vitonofrio; Fidaleo, Francesco
2012-10-01
The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend the De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self-containing interest.
De Finetti theorem on the CAR algebra
Crismale, Vito
2012-01-01
The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self--containing interest.
Bell's theorem, inference, and quantum transactions
Garrett, A. J. M.
1990-04-01
Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, “local”) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's new transactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the “delayed choice” experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theorem reinforces arguments in favor of hidden variables.
A vector bundle proof of Poncelet theorem
Vallès, Jean
2012-01-01
In the town of Saratov where he was prisonner, Poncelet, continuing the work of Euler and Steiner on polygons simultaneously inscribed in a circle and circumscribed around an other circle, proved the following generalization : "Let C and D be two smooth conics in the projective complex plane. If D passes through the n(n-1)/2 vertices of a complete polygon with n sides tangent to C then D passes through the vertices of infinitely many such polygons." According to Marcel Berger this theorem is the nicest result about the geometry of conics. Even if it is, there are few proofs of it. To my knowledge there are only three. The first proof, published in 1822 and based on infinitesimal deformations, is due to Poncelet. Later, Jacobi proposed a new proof based on finite order points on elliptic curves; his proof, certainly the most famous, is explained in a modern way and in detail by Griffiths and Harris. In 1870 Weyr proved a Poncelet theorem in space (more precisely for two quadrics) that implies the one above whe...
On the inversion of Fueter's theorem
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.
Directory of Open Access Journals (Sweden)
Thomas Fürst
Full Text Available BACKGROUND: Schistosomiasis and soil-transmitted helminthiasis are two high-burden neglected tropical diseases. In highly endemic areas, control efforts emphasize preventive chemotherapy. However, as morbidity, infection, and transmission begin to decrease, more targeted treatment is likely to become more cost-effective, provided that comparatively cheap diagnostic methods with reasonable accuracy are available. METHODOLOGY: Adults were administered an anamnestic questionnaire in mid-2010 during a cross-sectional epidemiological survey in the Taabo health demographic surveillance system in south-central Côte d'Ivoire. Questions pertaining to risk factors and signs and symptoms for schistosomiasis and soil-transmitted helminthiasis were included. The individuals' helminth infection status and their belonging to three different anthelmintic treatment groups were compared with the questionnaire results (i to inform the local health authorities about the epidemiological and clinical footprint of locally prevailing helminthiases, and (ii to explore the scope and limits of an anamnestic questionnaire as monitoring tool, which eventually could help guiding the control of neglected tropical diseases in control-induced low-endemicity settings. PRINCIPAL FINDINGS: Our study sample consisted of 195 adults (101 males, 94 females. We found prevalences of hookworm, Trichuris trichiura, Schistosoma haematobium, and Schistosoma mansoni of 39.0%, 2.7%, 2.1%, and 2.1%, respectively. No Ascaris lumbricoides infection was found. Helminth infection intensities were generally very low. Seven, 74 and 79 participants belonged to three different treatment groups. Multivariable logistic regression models revealed statistically significant (p<0.05 associations between some risk factors, signs, and symptoms, and the different helminth infections and treatment groups. However, the risk factors, signs, and symptoms showed weak diagnostic properties. CONCLUSIONS