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During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be…

Optimization and Control · Mathematics 2023-02-10 Matúš Benko , Patrick Mehlitz

We establish sharp large deviation asymptotics for the maximum order statistic of independent and identically distributed heavy-tailed random variables, valid for all Borel subsets of the right tail. This result yields exact decay rates for…

Probability · Mathematics 2026-01-09 José M. Zapata

Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear…

Classical Analysis and ODEs · Mathematics 2007-05-23 Angelo B. Mingarelli , Kishin Sadarangani

Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree $n$ and real parameter $a$. It is assumed that $-\Delta_{1} n+\frac{3}{2} \leq a \leq \Delta_{2} n$ for fixed arbitrary…

Classical Analysis and ODEs · Mathematics 2025-11-04 T. M. Dunster , Amparo Gil , Diego Ruiz-Antolin , Javier Segura

We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of $S$-matrix elements, in arbitrary spacetime dimensions and with…

High Energy Physics - Theory · Physics 2021-05-19 Tom Melia , Sridip Pal

The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper…

Functional Analysis · Mathematics 2020-06-23 M. O. Aibinu , S. C. Thakur , S. Moyo

This paper is devoted to the asymptotic behavior of global solutions to the convection-diffusion equation in the Fujita-subcritical case. We improve the result by Zuazua (1993) and establish higher order asymptotic expansions with decay…

Analysis of PDEs · Mathematics 2024-11-05 Ryunosuke Kusaba

We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean…

Statistics Theory · Mathematics 2022-11-30 Mayya Zhilova

In this paper we derive a new representation for the incomplete gamma function, exploiting the reformulation of the method of steepest descents by C. J. Howls (Howls, Proc. R. Soc. Lond. A 439 (1992) 373--396). Using this representation, we…

Classical Analysis and ODEs · Mathematics 2015-07-28 Gergő Nemes

Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and expicitly list asymptotic expressions for the points and weights of Gaussian…

Numerical Analysis · Mathematics 2022-08-25 Peter Opsomer , Daan Huybrechs

The value of a highly oscillatory integral is typically determined asymptotically by the behaviour of the integrand near a small number of critical points. These include the endpoints of the integration domain and the so-called stationary…

Numerical Analysis · Mathematics 2022-07-06 Daan Huybrechs , Arno B. J. Kuijlaars , Nele Lejon

The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of semilinear parabolic partial differential…

Numerical Analysis · Mathematics 2018-02-16 Kristian Debrabant , Jens Lang

Although the Hardy inequality corresponding to one quadratic singularity, with optimal constant, does not admit any extremal function, it is well known that such a potential can be improved, in the sense that a positive term can be added to…

Analysis of PDEs · Mathematics 2012-12-06 Jean Dolbeault , Bruno Volzone

Enumeration of walks with small steps in the quadrant has been a topic of great interest in combinatorics over the last few years. In this article, it is shown how to compute exact asymptotics of the number of such walks with fixed start-…

Combinatorics · Mathematics 2024-05-28 Andreas Nessmann

In this note, we present an abstract approach to study asymptotic orders for adaptive approximations with respect to a monotone set function $\mathfrak{J}$ defined on dyadic cubes. We determine the exact upper order in terms of the critical…

Optimization and Control · Mathematics 2025-03-18 Marc Kesseböhmer , Aljoscha Niemann

We construct a one-dimensional first-order theory for functionally graded elastic beams using the variational-asymptotic method. This approach ensures an asymptotically exact one-dimensional equations, allowing for the precise determination…

Classical Physics · Physics 2025-01-22 Khanh Chau Le , Tuan Minh Tran

We study asymptotics of fiber integrals depending on a large parameter. When the critical fiber is singular, full-asymptotic expansions are established in two different cases : local extremum and isolated real principal type singularities.…

General Mathematics · Mathematics 2007-05-23 Brice Camus

The asymptotic expansion of the Touchard polynomials $T_n(z)$ (also known as the exponential polynomials) for large $n$ and complex values of the variable $z$, where $|z|$ may be finite or allowed to be large like $O(n)$, has been recently…

Classical Analysis and ODEs · Mathematics 2016-06-29 R B Paris

This paper aims to study the asymptotic expansion of analytic torsion forms associated with a certain series of flat bundles. We prove the existence of the full expansion and give a formula for the sub-leading term, while Bismut-Ma-Zhang…

Differential Geometry · Mathematics 2023-01-11 Qiaochu Ma

Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the…

Classical Analysis and ODEs · Mathematics 2020-09-11 T. M. Dunster , A. Gil , J. Segura