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Showing papers on "Asymptotology published in 2014"


Book
29 Sep 2014
TL;DR: The basic concepts of asymptotic expansions, Mellin transform techniques, and the distributional approach are explained.
Abstract: Preface 1. Fundamental concepts of asymptotics 2. Classical procedures 3. Mellin transform techniques 4. The summability method 5. Elementary theory of distributions 6. The distributional approach 7. Uniform asymptotic expansions 8. Double integrals 9. Higher dimensional integrals Bibliography Symbol Index Author index Subject index.

1,061 citations


Book
29 Sep 2014

145 citations


Book
18 Feb 2014
TL;DR: In this paper, the authors introduce a theory of asymptotic expansion of generalized functions, which is a generalization of the theory of distributional expansion of Dirac delta functions.
Abstract: Basic results in asymptotics introduction to the theory of distributions a distributional theory of asymptotic expansions the asymptotic expansion of multi-dimensional generalized functions the asymptotic expansion of certain series considered by Ramamujan series of dirac delta functions.

74 citations


Book
29 Jan 2014
TL;DR: In this article, the authors present a broad overview of local asymptotics for statistical experiments in the sense of mixed normality or local Asymptotic quadraticity.
Abstract: This textbook is devoted to the general asymptotic theory of statistical experiments. Local asymptotics for statistical models in the sense of local asymptotic (mixed) normality or local asymptotic quadraticity make up the core of the book. Numerous examples deal with classical independent and identically distributed models and with stochastic processes.

22 citations


Journal ArticleDOI
TL;DR: In this article, asymptotic behavior of a class of fourth-order neutral delay dynamic equations with a noncanonical operator on an arbitrary time scale is studied, and an illustrative example is provided.
Abstract: This paper is concerned with asymptotic behavior of a class of fourth-order neutral delay dynamic equations with a noncanonical operator on an arbitrary time scale. A new asymptotic criterion and an illustrative example are included.

19 citations


Journal ArticleDOI
TL;DR: A new equivalent sufficient condition is given for the neutral delay differential-algebraic equations to be delay-independent asymptotically stable and theAsymptotic stability of the numerical solutions generated by the Runge--Kutta methods combined with Lagrange interpolation is investigated.
Abstract: This paper is concerned with asymptotic stability of linear neutral delay differential-algebraic equations and Runge--Kutta methods. First, we give a new equivalent sufficient condition for the neutral delay differential-algebraic equations to be delay-independent asymptotically stable. Then we investigate the asymptotic stability of the numerical solutions generated by the Runge--Kutta methods combined with Lagrange interpolation. Some results on the asymptotic stability of Runge--Kutta methods of high order are given. Finally, numerical examples of index 1 and 2 are conducted to confirm our numerical stability result.

13 citations



Journal ArticleDOI
TL;DR: The exactification of the Poincaré asymptotic expansion (PAE) of the Hankel integral is obtained, using the distributional approach of McClure & Wong, and it is found that, for half-integer orders of the Bessel function, the exactification terminates, so that it gives an exact finite sum representation of theHankel integral.
Abstract: We obtain an exactification of the Poincare asymptotic expansion (PAE) of the Hankel integral, as , using the distributional approach of McClure & Wong. We find that, for half-integer orders of the Bessel function, the exactified asymptotic series terminates, so that it gives an exact finite sum representation of the Hankel integral. For other orders, the asymptotic series does not terminate and is generally divergent, but is amenable to superasymptotic summation, i.e. by optimal truncation. For specific examples, we compare the accuracy of the optimally truncated asymptotic series owing to the McClure–Wong distributional method with owing to the Mellin–Barnes integral method. We find that the former is spectacularly more accurate than the latter, by, in some cases, more than 70 orders of magnitude for the same moderate value of b. Moreover, the exactification can lead to a resummation of the PAE when it is exact, with the resummed Poincare series exhibiting again the same spectacular accuracy. More importantly, the distributional method may yield meaningful resummations that involve scales that are not asymptotic sequences.

6 citations



Journal ArticleDOI
TL;DR: In this paper, the authors revisited the asymptotic convergence properties of the 3D-shell model with respect to the thickness parameter and established strong convergence results for the model in bending-and membrane-dominated behavior.
Abstract: We revisit the asymptotic convergence properties—with respect to the thickness parameter—of the earlier-proposed 3D-shell model. This shell model is very attractive for engineering applications, in particular due to the possibility of directly using a general 3D constitutive law in the corresponding finite element formulations. We establish strong convergence results for the 3D-shell model in the two main types of asymptotic regimes, namely, bending- and membrane-dominated behavior. This is an important achievement, as it completely substantiates the asymptotic consistency of the 3D-shell model with 3D linearized isotropic elasticity.

5 citations


Journal ArticleDOI
TL;DR: In this paper, exact efficient asymptotic stability criteria for two-parameter systems of two autonomous delay differential equations were established, and exact efficient stability criteria were established for twoparameter system with two differentiable differential equations.
Abstract: We establish exact efficient asymptotic stability criteria for two-parameter systems of two autonomous delay differential equations


Journal ArticleDOI
TL;DR: In this paper, an integro-differential kinetic equation coupled with a Gaussian isokinetic thermostat is used for modeling complex systems in the applied sciences under the action of an external force field.
Abstract: This paper is devoted to the asymptotic analysis of a mathematical framework that has recently been proposed for modelling complex systems in the applied sciences under the action of an external force field. This framework consists in an integro-differential kinetic equation coupled with a Gaussian isokinetic thermostat. The asymptotic limit obtained here using low-field scaling shows the emergence of diffusive behaviour on a macroscopic scale.


Journal ArticleDOI
TL;DR: The direct scheme, consisting of an immediate substitution of a postulated asymptotic expansion of a solution into the problem condition and finding a family of control problems to define the terms of the asymPTotic expansion, results in the asylptotic solution of the considered problem.

Journal ArticleDOI
TL;DR: The existence of a solution to a generalized Kolmogorov-Petrovskii-Piskunov equation is proved and its asymptotic expansion of the internal transition layer type is constructed as discussed by the authors.
Abstract: The existence of a solution to a generalized Kolmogorov-Petrovskii-Piskunov equation is proved and its asymptotic expansion of the internal transition layer type is constructed The convergence of the asymptotics is proved by applying the asymptotic comparison principle developed for a new class of problems

Posted Content
TL;DR: In this paper, the authors review recent results on the existence of asymptotic observables in algebraic QFT and discuss the problem of completeness of observables from this perspective.
Abstract: We review recent results on the existence of asymptotic observables in algebraic QFT. The problem of asymptotic completeness is discussed from this perspective.

Journal ArticleDOI
TL;DR: In this article, an asymptotic solution for two-, three-and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD, in terms of glueball and meson propagators, was found.
Abstract: We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic $S$-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic $S$-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the $LSZ$ reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-$N$ $QCD$, and in particular on any string solution.

Journal ArticleDOI
TL;DR: In this article, the authors developed asymptotic properties for a parabolic system with two-time scales associated with a transient switching diffusion, which is motivated by stochastic systems.
Abstract: This work develops asymptotic properties for a parabolic system with two-time scales associated with a transient switching diffusion. Although the problem is motivated by stochastic systems, the techniques that we are using are purely analytic. Asymptotic expansions are constructed; their validity is justified.

Journal ArticleDOI
TL;DR: In this paper, the error estimate is given in terms of the characteristic (Riccati) functions which are constructed from the phase functions of an asymptotic solution, which means that the improvement of the approximation depends essentially on the Riccati functions.
Abstract: We investigate the asymptotic solutions of the planar dynamic systems and the second order equations on a time scale by using a new version of Levinson's asymptotic theorem. In this version the error estimate is given in terms of the characteristic (Riccati) functions which are constructed from the phase functions of an asymptotic solution. It means that the improvement of the approximation depends essentially on the asymptotic behavior of the Riccati functions. We describe many different approximations using the flexibility of this approach. As an application we derive the analogue of D'Alembert's formula for the one dimensional wave equation in a discrete time.

OtherDOI
29 Sep 2014
TL;DR: In this paper, two asymptotic distributions of quadratic form in Gaussian random variables were proposed for the case when the number of random variables n is larger than n.
Abstract: In the reliability analysis of safety-critical complex engineering structures, a very large number of the system parameters can be considered to be random variables. The difficulty in computing the failure probability using the classical first and second-order reliability methods (FORM and SORM) increases rapidly with the number of variables or “dimension”. On the basis of the asymptotic distribution of quadratic form in Gaussian random variables, two formulations, for the case when the number of random variables n ∞, are provided. The first is called strict asymptotic formulation and the second is called weak asymptotic formulation. Both approximations result in simple closed-form expressions for the probability of failure of an engineering structure. The proposed asymptotic approximations are compared with existing approximations and Monte Carlo simulations using numerical examples. Keywords: reliability analysis; asymptotic methods; SORM

Book ChapterDOI
01 Jan 2014
TL;DR: In this paper, the authors compare results of non-asymptotic, local theory of random matrices (Chap. 5.1) with results of asymptotic and global theory of matrices.
Abstract: The chapter contains standard results for asymptotic, global theory of random matrices. The goal is for readers to compare these results with results of non-asymptotic, local theory of random matrices (Chap. 5. A recent treatment of this subject is given by Qiu et al. [5].