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Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…

Statistics Theory · Mathematics 2019-09-04 Tino Werner

In this article, we study local zeta functions attached to Laurent polynomials over p-adic fields, which are non-degenerate with respect to their Newton polytopes at infinity. As an application we obtain asymptotic expansions for p-adic…

Algebraic Geometry · Mathematics 2015-06-10 E. Leon-Cardenal , W. A. Zuniga-Galindo

Partial differential equations with highly oscillatory input terms are hardly ever solvable analytically and their numerical treatment is difficult. Modulated Fourier expansion used as an {\it ansatz} is a well known and extensively…

Numerical Analysis · Mathematics 2023-11-21 Karolina Kropielnicka , Rafał Perczyński

A system of linear differential equations with oscillatory decreasing coefficients is considered. The coefficients has the form $t^{-\alpha}a(t)$,~$\alpha>0$, where $a(t)$ is trigonometric polynomial with an arbitrary set of frequencies.…

Classical Analysis and ODEs · Mathematics 2015-11-03 V. Sh. Burd , V. A. Karakulin

This paper discusses infill asymptotics for logistic regression estimators for spatio-temporal point processes whose intensity functions are of log-linear form. We establish strong consistency and asymptotic normality for the parameters of…

Statistics Theory · Mathematics 2022-08-26 M. N. M. van Lieshout , C. Lu

Laplace's method is one of the fundamental techniques in the asymptotic approximation of integrals. The coefficients appearing in the resulting asymptotic expansion, arise as the coefficients of a convergent or asymptotic series of a…

Classical Analysis and ODEs · Mathematics 2013-11-05 Gergő Nemes

An asymptotic approach for a Schroedinger type equation with non selfadjoint Hamiltonian of a special type in the case of two close degeneracy (turning) points is developed. Both real and complex degeneracy points are treated by a method of…

Mathematical Physics · Physics 2021-07-20 Ignat Fialkovsky , Maria Perel

Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…

Classical Analysis and ODEs · Mathematics 2021-03-02 T. M. Dunster

A previous paper by the authors found explicit contour integral formulas for certain joint moments of the multi-species q-TAZRP (totally asymmetric zero range process), using algebraic methods. These contour integral formulas have a…

Probability · Mathematics 2024-03-14 Jeffrey Kuan , Zhengye Zhou

A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…

Quantum Physics · Physics 2009-09-25 O. Yu. Shvedov

Let $G$ be a dense graph with good expansion properties and not too close to being bipartite. Let $\boldsymbol d$ be a graphical degree sequence. Under very weak conditions, we find the number of subgraphs of $G$ with degree sequence…

Combinatorics · Mathematics 2025-08-27 Mikhail Isaev , Brendan D. McKay

We consider the asymptotic expansion of the functional series \[S_{\mu}^\pm(a;\lambda)=\sum_{n=0}^\infty \frac{(\pm 1)^n e^{-\lambda n}}{(n^2+a^2)^\mu}\] for $\lambda>0$ and $\mu\geq0$ as $|a|\to \infty$ in the sector $|\arg\,a|<\pi/2$. The…

Classical Analysis and ODEs · Mathematics 2021-12-07 R B Paris

Several important functions, including the gamma function, as well as several infinite sums, admit integral representations involving the Hankel contour. In addition, the large $t$ asymptotic analysis of several recently derived identities…

Classical Analysis and ODEs · Mathematics 2026-05-06 A. S. Fokas , J. Lenells

Let X_i, i\in N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let \Phi be a smooth enough mapping from B into R. An asymptotic evaluation of Z_n=E(\exp (n\Phi (\sum_{i=1}^nX_i/n))), up to a factor (1+o(1)),…

Probability · Mathematics 2007-05-23 Sergio Albeverio , Song Liang

In this note, we are concerned with the asymptotic approximation of a class of double integrals which can be represented as an angular spectrum superposition. These double integrals typically appear in electromagnetic scattering problems.…

Mathematical Physics · Physics 2007-05-23 Fei Wang

We can find in the literature several convergent and/or asymptotic expansions of the Pearcey integral $P(x,y)$ in different regions of the complex variables $x$ and $y$, but they do not cover the whole complex $x$ and $y$ planes. The…

Numerical Analysis · Mathematics 2016-01-15 Jose L. Lopez , Pedro J. Pagola

In this paper, we prove asymptotic expansions of generalized partial theta functions with a nonprincipal Dirichlet character and relate these expansions to certain $L$-series.

Number Theory · Mathematics 2020-08-11 Su Hu , Min-Soo Kim

In this paper we study the dynamics of a holomorphic vector field near a singular point in dimension two using asymptotic expansion techniques. We consider a holomorphic vector field admitting first integrals in small sectors with nonzero…

Dynamical Systems · Mathematics 2018-10-23 F. Reis

A theorem about asymptotic estimation of multiple integral of a special type is proved for the case when the integrand peaks at the integration domain bound, but not at a point of extremum. Using this theorem the asymptotic expansion of the…

Nuclear Theory · Physics 2008-11-26 A. F. Krutov , V. E. Troitsky , N. A. Tsirova

It is shown how to calculate asymptotics of integrals over the positive semi-axis of two functions related to the Degenerate Third Painlev\'e Equation (dP3). As an example, the corresponding results for the meromorphic solution of the dP3…

Classical Analysis and ODEs · Mathematics 2018-11-14 A. V. Kitaev , A. Vartanian