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Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…
We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36, 11807 (2003)] to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue…
We demonstrate that in constructing asymptotically flat vacuum initial data sets in General Relativity via the conformal method, certain asymptotic structures may be prescribed a priori through the specified seed data, including the ADM…
We propose a formula for finding the horizontal, oblique or curvilinear asymptote of any rational polynomial function of any positive degree, as a sum of matrix determinants formed directly from the coefficients of the terms in the given…
Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…
Asymptotic theories on record values and times, including central limit theorems, make sense only if the sequence of records values (and of record times) is infinite. If not, such theories could not even be an option. In this paper, we give…
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…
An asymptotic theory is developed for general non-integrable boundary quantum field theory in 1+1 dimensions based on the Langrangean description. Reflection matrices are defined to connect asymptotic states and are shown to be related to…
We derive new asymptotic formulae for the norming constants of Sturm-Liouville problem with summable potentials, which generalize and make more precise previously known formulae. Moreover, our formulae take into account the smooth…
We classify the local asymptotic behavior of positive singular solutions to a class of subcritical sixth order equations on the punctured ball. Initially, using a version of the integral moving spheres technique, we prove that solutions are…
The coefficient sequences of multivariate rational functions appear in many areas of combinatorics. Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic properties, and the field of analytic combinatorics in several…
When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
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…
Regularisation allows one to handle ill-posed inverse problems. Here we focus on discrete unfolding problems. The properties of the results are characterised by the consistency between measurements and unfolding result and by the posterior…
We study the asymptotics at zero of continuous functions on (0, 1] by means of their asymptotic ideals, i.e., ideals in the ring of continuous functions on (0, 1] satisfying a polynomial growth condition at 0 modulo rapidly decreasing…
This paper deals with the boundary value problems for the singularly perturbed differential-algebraic system of equations. The case of turning points has been studied. The sufficient conditions for existence and uniqueness of the solution…
Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…
A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various…
We introduce a new approach to the the asymptotic iteration method (AIM) by means of which we establish the standard AIM connection with the continued fractions technique and we develop a novel termination condition in terms of the…