Related papers: A Hybrid of Darboux's Method and Singularity Analy…
We study enumeration functions for unimodal sequences of positive integers, where the size of a sequence is the sum of its terms. We survey known results for a number of natural variants of unimodal sequences, including Auluck's generalized…
We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solubility of some equations and distribution of sequences in small intervals. We obtain classic and…
Search trees are fundamental data structures in computer science. We study functionals on random search trees that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…
We conclude our work [arXiv:2403.07628, arXiv:2503.12644] on asymptotic expansions at the soft edge for the classical $n$-dimensional Gaussian and Laguerre ensembles, now studying the gap-probability generating functions. We show that the…
We present a hybrid asymptotic/numerical method for the accurate computation of single and double layer heat potentials in two dimensions. It has been shown in previous work that simple quadrature schemes suffer from a phenomenon called…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…
In this paper, we study the asymptotic behavior of Jacobi biorthogonal polynomials. A Darboux-type formula is established using the method of steepest descent. In the proof, we construct an appropriate contour to apply the Rodrigues…
In this paper, we combine the method of multiple scales and the method of matched asymptotic expansions to construct uniformly-valid asymptotic solutions to autonomous and non-autonomous difference equations in the neighbourhood of a…
The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of…
We give asymptotic expansions for the moments of the $M_2$-rank generating function and for the $M_2$-rank generating function at roots of unity. For this we apply the Hardy-Ramanujan circle method extended to mock modular forms. Our…
We describe a method to evaluate integrals that arise in the asymptotic analysis when two saddle points may be close together. These integrals, which appear in problems from optics, acoustics or quantum mechanics as well as in a wide class…
We examine the behavior of the coefficients of powers of polynomials over a finite field of prime order. Extending the work of Allouche-Berthe, 1997, we study a(n), the number of occurring strings of length n among coefficients of any power…
Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral…
In the paper we discuss two questions about smooth expanding dynamical systems on the circle. (i) We characterize the sequences of asymptotic length ratios which occur for systems with H\"older continuous derivative. The sequences of…
An asymptotic expansion with respect to a small parameter of the solution of the Cauchy problem is constructed for a system of three transfer equations, two of which are singularly perturbed by the degeneracy of the entire senior part of…
This study concerns with singularly perturbed systems of second-order reaction-diffusion equations in ODE's. To handle this type of problems, a numerical-asymptotic hybrid method is employed. In this hybrid method, an efficient asymptotic…
The problem of computing quantum mechanical propagators can be recast as a computation of a Wilson line operator for parallel transport by a flat connection acting on a vector bundle of wavefunctions. In this picture the base manifold is an…
Is studied asymptotic expansion for solution of singularly perturbed equation for functional of Markovian evolution in Rd. The view of regular and singular parts of solution is found.