Related papers: Self-similar continued root approximants
We introduce a concept of asymptotic principal values which enables us to handle rigorously singular integrals of higher-order poles encountered in the computation of various quantities based on correlation functions of a vacuum. Several…
We obtain asymptotics for sums of the form $$ \sum_{n=1}^P e(\alpha_kn^k + \alpha_1n), $$ involving lower order main terms. As an application, we show that for almost all $\alpha_2 \in [0,1)$ one has $$ \sup_{\alpha_1 \in [0,1)} \Big|…
In this paper, we derive an asymptotic error expansion for the eigenvalue approximations by the lowest order Raviart-Thomas mixed finite element method for the general second order elliptic eigenvalue problems. Extrapolation based on such…
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 paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
An algorithm is proposed for determining asymptotics of the sum of a perturbative series in the strong coupling limit using given values of the expansion coefficients. Operation of the algorithm is illustrated by test examples, method for…
This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial conditions. The class of…
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
Summation methods play a very important role in quantum field theory because all perturbation series are divergent and the expansion parameter is not always small. A number of methods have been tried in this context, most notably Pade…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
Asymptotic analysis for related inference problems often involves similar steps and proofs. These intermediate results could be shared across problems if each of them is made self-contained and easily identified. However, asymptotic…
We study the applicability of Pade Approximants (PA) to estimate a "sum" of asymptotic series of the type appearing in QCD. We indicate that one should not expect PA to converge for positive values of the coupling constant and propose to…
The investigation asymptotic limits on associated data mainly focused on limit theorems of summands of associated data and on the related invariance principles. In a series of papers, we are going to set the general frame of the theory by…
Resummation methods using continued functions are implemented to converge divergent series appearing in perturbation problems related to continuous phase transitions in field theories. In some cases, better convergence properties are…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…
In thermal field theory selfconsistent (Phi-derivable) approximations are used to improve (resum) propagators at the level of two-particle irreducible diagrams. At the same time vertices are treated at the bare level. Therefore such…
The article addresses the problem of image sampling with minimal possible sampling rates and reviews the recent advances in sampling theory and methods: modern formulations of the sampling theorems, potentials and limitations of Compressed…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and…
An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in $\ln S$ and analytically continuing its divergent power series solution such that…