Showing papers on "Asymptotology published in 2011"
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TL;DR: In this paper, the authors define the asymptotic flatness and discuss the symmetry at null infinity in arbitrary dimensions using the Bondi coordinates, and show the symmetry and the mass loss law with the well-defined definition.
Abstract: We define the asymptotic flatness and discuss asymptotic symmetry at null infinity in arbitrary dimensions using the Bondi coordinates. To define the asymptotic flatness, we solve the Einstein equations and look at the asymptotic behavior of gravitational fields. Then we show the asymptotic symmetry and the Bondi mass loss law with the well-defined definition.
90 citations
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14 Oct 2011
TL;DR: The Asymptotic Behavior of Generalized Functions and Integral Transforms Summability of Fourier Series and Integrals and Fourier series and integrals are studied.
Abstract: Asymptotic Behavior of Generalized Functions: S-Asymptotics F'g Quasi-Asymptotics in F' Applications of the Asymptotic Behavior of Generalized Functions: Asymptotic Behavior of Solutions to Partial Differential Equations Asymptotics and Integral Transforms Summability of Fourier Series and Integrals.
63 citations
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TL;DR: The aim of this paper is to improve the Ramanujan formula for approximation the gamma function by constructing a fast asymptotic series.
Abstract: The aim of this paper is to improve the Ramanujan formula for approximation the gamma function. A fast asymptotic series is constructed.
41 citations
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TL;DR: This book is strongly recommended for those interested in the use of asymptotics in statistics and probability problems, and provides a quick and accessible overview of the available results, providing both a basic understanding of their context and references to sources where a more detailed treatment can be found.
Abstract: Asymptotic Theory of Statistics and Probability, by Anirban DasGupta, New York, Springer, 2008, xxvii+722 pp., £55.99 or US$89.95 (hardback), ISBN 978-0-387-75970-8 Unlike many books on asymptotic ...
39 citations
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TL;DR: This note is concerned with the asymptotic stability analysis for nonlinear stochastic differential systems (SDSs) where the systems coefficients are assumed to satisfy local Lipschitz condition and polynomial growth condition.
Abstract: This note is concerned with the asymptotic stability analysis for nonlinear stochastic differential systems (SDSs). The systems coefficients are assumed to satisfy local Lipschitz condition and polynomial growth condition. By applying some novel techniques, some easily verifiable conditions are obtained which ensure the almost sure asymptotic stability and pth moment asymptotic stability for such SDSs. We also provide the range of the order p. A numerical example is provided to illustrate the effectiveness and the benefits of the proposed result.
32 citations
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TL;DR: In this article, an asymptotic expansion for smooth solutions of the Navier-Stokes equations in weighted spaces was derived, which removes previous restrictions on the number of terms of the coefficients, as well as on the range of the polynomial weights.
29 citations
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01 Jan 2011
TL;DR: A survey of asymptotic methods in fluid mechanics and applications is given in this paper, including high Reynolds number flows (interacting boundary layers, marginal separation, turbulence asmptotics), hybrid methods, exponential and multiple scales methods in meteorology.
Abstract: A survey of asymptotic methods in fluid mechanics and applications is given including high Reynolds number flows (interacting boundary layers, marginal separation, turbulence asymptotics) and low Reynolds number flows as an example of hybrid methods, waves as an example of exponential asymptotics and multiple scales methods in meteorology.
19 citations
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TL;DR: In this article, the authors present the exact maximum likelihood estimator of the semi-Markov kernel, which governs the evolution of the SMC, and study its asymptotic properties in the following cases: (i) for one observed trajectory, when the length of the observation tends to infinity, and (ii) for parallel observations of independent copies of an SMC censored at a fixed time.
Abstract: This article concerns maximum-likelihood estimation for discrete time homogeneous nonparametric semi-Markov models with finite state space. In particular, we present the exact maximum-likelihood estimator of the semi-Markov kernel which governs the evolution of the semi-Markov chain (SMC). We study its asymptotic properties in the following cases: (i) for one observed trajectory, when the length of the observation tends to infinity, and (ii) for parallel observations of independent copies of an SMC censored at a fixed time, when the number of copies tends to infinity. In both cases, we obtain strong consistency, asymptotic normality, and asymptotic efficiency for every finite dimensional vector of this estimator. Finally, we obtain explicit forms for the covariance matrices of the asymptotic distributions.
16 citations
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12 citations
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TL;DR: In this paper, an asymptotic perturbation of transfer operators and a method that avoids resolvent's perturbations was proposed to investigate the Hausdorff dimension of a perturbed cookie-cutter set.
Abstract: We consider an asymptotic behaviour of the topological pressure, the Gibbs measure and the measure-theoretic entropy concerning a potential defined on a subshift. Our results are obtained by considering asymptotic perturbation of transfer operators and by using a method that avoids resolvent’s perturbation. In application, we investigate an asymptotic behaviour of the Hausdorff dimension of a perturbed cookie-cutter set.
7 citations
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TL;DR: For asymptotically bounded holomorphic functions defined in a poly-sector in this article, the existence of a strong asymPTotic expansion in Majima's sense following a single multidirectional direction towards the vertex implies (global) expansion in the whole polysector.
Abstract: In this paper we prove that, for asymptotically bounded holomorphic functions defined in a polysector in ${\mathbb C}^n$, the existence of a strong asymptotic expansion in Majima's sense following a single multidirection towards the vertex entails (global) asymptotic expansion in the whole polysector. Moreover, we specialize this result for Gevrey strong asymptotic expansions. This is a generalization of a result proved by A. Fruchard and C. Zhang for asymptotic expansions in one variable, but the proof, mainly in the Gevrey case, involves different techniques of a functional-analytic nature.
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01 Jan 2011TL;DR: In this article, the authors pointed out that an estimator, though asymptotically much less efficient than another, may still have much greater probability concentration than the latter.
Abstract: Partly of an expository nature this note brings out the fact that an estimator, though asymptotically much less efficient (in the classical sense) than another, may yet have much greater probability concentration (as defined in this article) than the latter.
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TL;DR: A new heuristic technique of ''meta-expansions'', which is both simple and efficient in practice, even though the answers are not guaranteed to be correct in general.
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TL;DR: In this article, a double asymptotic limit theory for the persistent parameter in explosive continuous time models driven by Levy processes with a large number of time span (N) and a small number of sampling interval (h) is presented.
Abstract: This paper develops a double asymptotic limit theory for the persistent parameter (k) in explosive continuous time models driven by Levy processes with a large number of time span (N) and a small number of sampling interval (h). The simultaneous double asymptotic theory is derived using a technique in the same spirit as in Phillips and Magdalinos (2007) for the mildly explosive discrete time model. Both the intercept term and the initial condition appear in the limiting distribution. In the special case of explosive continuous time models driven by the Brownian motion, we develop the limit theory that allows for the joint limits where N -> infinity and h -> 0 simultaneously, the sequential limits where N -> infinity is followed by h -> 0, and the sequential limits where h -> 0 is followed by N -> infinity. All three asymptotic distributions are the same.
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TL;DR: In this paper, a uniform asymptotic approximation of the solution of a boundary-value problem is constructed and justified up to an arbitrary power of a small parameter, where the parameter is a collection of two-dimensional elliptic equations in 2D domains depending on one parameter.
Abstract: A second order elliptic equation with a small parameter at one of the highest order derivatives is considered in a three-dimensional domain. The limiting equation is a collection of two-dimensional elliptic equations in two-dimensional domains depending on one parameter. By the method of matching of asymptotic expansions, a uniform asymptotic approximation of the solution of a boundary-value problem is constructed and justified up to an arbitrary power of a small parameter. §
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14 Apr 2011TL;DR: In this article, a simplified procedure for finding such expansions is presented for the relation (n+ 1)(16n − 15)qn+1 = (128n + 40n − 82n − 45) qn − n − n(256n − 240n + 64n − 7), qn−1 + (16n + 1)n(n − 1)/qn−2.
Abstract: Any solution of Eq. (1) can be extended in the real direction, but under the passage to a different domain, its asymptotics generally changes. A general procedure for finding such expansions is fairly complicated, but in most cases, a simplified procedure is sufficient; we describe its application for the example of the relation (n+ 1)(16n − 15)qn+1 = (128n + 40n − 82n − 45)qn − n(256n − 240n + 64n − 7)qn−1 + (16n + 1)n(n − 1)qn−2. (3)
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19 Jan 2011TL;DR: Using an expansion for analytic functions of operators, the asymptotic distribution of an estimator of the functional regression parameter is obtained in a rather simple way; the result is applied to testing linear hypotheses.
Abstract: Exploiting an expansion for analytic functions of operators, the asymptotic distribution of an estimator of the functional regression parameter is obtained in a rather simple way; the result is applied to testing linear hypotheses. The expansion is also used to obtain a quick proof for the asymptotic optimality of a functional classification rule, given Gaussian populations.
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TL;DR: In this paper, various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. But they do not consider the non-local interaction between variables of the discrete media into account.
Abstract: In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. While applying asymptotic methods as a rule the following situation appears: the existence of asymptotics for $\ve\rightarrow 0$ implies an existence of the asymptotics for $\ve\rightarrow\infty$. Therefore, the idea to construct one function valid for the whole parameter interval for $\ve$ is very attractive. The construction of asymptotically equivalent functions possessing a known asymptotic behaviour for $\ve\rightarrow 0$ and $\ve\rightarrow \infty$ will be discussed. Using summation and interpolation procedures we focus on continuous models derived from a discrete micro-structure. Various continualization procedures that take the non-local interaction between variables of the discrete media into account are analysed.
01 Jan 2011
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TL;DR: This special issue consists mainly of a collection of presentations at the 3rd International Symposium on Nonlinear Dynamics, Shanghai, China, conveying a strong, reliable, efficient, and promising development of various asymptotic methods.
Abstract: where the unknown constants a, b and ω can be determined by substituting (4) into (1). For practical problems, we can not obtain such a good initial condition like Eq. (3), sometimes the measured initial/boundary conditions have to be expressed in approximate forms, and sometimes only some point values on boundaries can be measured, we call these problems as approximate initial/boundary conditions and point boundary conditions, respectively, such problems can not be solved exactly but asymptotically. Asymptotical approach to nonlinear equations, fractional differential equations, and problemswith approximate initial/boundary conditions or point boundary conditions is the next frontier towards nonlinear science [1]. The oldest asymptotic method is the Ying Buzu Shu, which appeared in an ancient Chinese classic called Jiu Zhang Suan Shu (Nine Chapters on the Art of Mathematics), for solving algebraic equations, and the method has been widely used to solve nonlinear differential equations, especially nonlinear oscillators and with great success as shown in this special issue by Hui-Li Zhang and Zhong-fu Ren, respectively. In Ref. [2] many asymptotic methods were systematically reviewed, and their potential applications were outlined. This special issue consists mainly of a collection of presentations at the 3rd International Symposium on Nonlinear Dynamics, September 25–28, 2010, Shanghai, China, conveying a strong, reliable, efficient, and promising development of various asymptotic methods. Included herein is a collection of original refereed research papers by well-established researchers in the field of nonlinear science. We hope that these papers will prove to be a timely and valuable reference for researchers in this area. In this special issue, various asymptotic methods (e.g. Hamiltonian approach, Adomian method, variational iteration method, homotopy perturbation method, exp-function method, differential transformation method and ancient Chinese algorithm) for real-life nonlinear problems are given and can be used as paradigms for many other applications. The aim of this special issue is to bring to the fore themany new and exciting applications of the asymptoticmethods, thereby capturing both the interest and imagination of the wider communities in various fields. Finally I would like to express my appreciation to the editor-in-chief of Computers & Mathematics with Applications, Prof. Ervin Y. Rodin, and all reviewers who took the time to review articles in a very short time.
01 Jan 2011
TL;DR: The Autobiographical Statement as mentioned in this paper is a collection of essays written by the author of the book "Autobiography of a man: A Personal Essay" (1998).
Abstract: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Autobiographical Statement . . . . . . . . . . . . . . . . . . . . . . . . . . 100
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TL;DR: In this article, the large jump asymptotic method for parabolic interface problems is presented, and the derivation and proof of the error estimates for their approximation is shown to be of order two.
Abstract: To approximate some problems with strongly discontinuous coefficients, we present the large jump asymptotic method for parabolic interface problems, focus on the derivation and proof of the asymptotic error estimates for our approximation, and show it is of order two. Numerical experiments verify the theoretical results.
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01 Jan 2011TL;DR: In this article, an asymptotic paraxial approximation to model ultrarelativistic particles is derived based on data mining methods that directly deal with numerical results of simulations, to understand what each order of the expansion brings to the simulation results.
Abstract: This paper proposed a new approach based on data mining to evaluate the e_ciency of numerical asymptotic models. Indeed, data mining has proved to be an e_cient tool of analysis in several domains. In this work, we first derive an asymptotic paraxial approximation to model ultrarelativistic particles. Then, we use data mining methods that directly deal with numerical results of simulations, to understand what each order of the asymptotic expansion brings to the simulation results. This new approach o_ers the possibility to understand, on the numerical results themselves, the precision level of a numercial asymptotic model.
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TL;DR: The asymptotic limit of the nonlinear Schrodinger-Poisson system with general WKB initial data is studied in this article, where it is proved that the current converges to the strong solution of the incompressible Euler.
Abstract: The asymptotic limit of the nonlinear
Schrodinger-Poisson system with general WKB initial data is
studied in this paper. It is proved that the current, defined by
the smooth solution of the nonlinear Schrodinger-Poisson system,
converges to the strong solution of the incompressible Euler
equations plus a term of fast singular oscillating gradient vector
fields
when both the Planck constant $\hbar$ and the Debye
length $\lambda$ tend to zero. The proof involves homogenization
techniques, theories of symmetric quasilinear hyperbolic system
and elliptic estimates, and the key point is to establish the
uniformly bounded estimates with respect to both the Planck
constant and the Debye length.