Related papers: On the extrapolation of perturbation series
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 describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by…
Let $ \mathbb{Q}\mathcal{E}_{\mathbb{Z}} $ be the set of power sums whose characteristic roots belong to $ \mathbb{Z} $ and whose coefficients belong to $ \mathbb{Q} $, i.e. $ G : \mathbb{N} \rightarrow \mathbb{Q} $ satisfies…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
In this article the solution of the special problem of the conditional extremum for the conjugate trigonometric polynomials is given. A possibility to apply this result to the problems of optimal stabilization of quasidynamic chaos in…
We prove a factorization formula for the Taylor series coefficients of a zero of a polynomial as a function of the polynomial's coefficients. This result extends to more general functions which we call "complex-exponent polynomials". To…
We obtain several Cauchy-like and Pellet-like results for the zeros of a general complex polynomial by considering similarity transformations of the squared companion matrix and the reformulation of the zeros of a scalar polynomial as the…
The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion.…
We study the outliers for two models which have an interesting connection. On the one hand, we study a specific class of planar Coulomb gases which are determinantal. It corresponds to the case where the confining potential is the…
We describe a classification of degree n complex coefficient polynomials with respect to combinatorial patterns that arise from the two real algebraic curves obtained as the zero sets for their real and imaginary part. In particular, we…
In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In…
This article is a survey of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of Analysis. Some new properties are included and several Analysis-related applications are mentioned.
In many cases of interest, the perturbative series based on conventional Feynman diagrams have a zero radius of convergence. Series with a finite radius of convergence can be obtained by either introducing a large field cutoff or by…
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…
We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
In the study of the cyclicity of a function $f$ in reproducing kernel Hilbert spaces an important role is played by sequences of polynomials $\{p_n\}_{n\in \mathbb{N}}$ called \emph{optimal polynomial approximants} (o.p.a.). For many such…
Methods of summation of power series relevant to applications in quantum theory are reviewed, with particular attention to expansions in powers of the coupling constant and in inverse powers of an energy variable. Alternatives to the Borel…
We study an infinite class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. This generalizes a sequence of sparse polynomials which arises in a natural way as graph theoretic…
For a homogenization problem associated to a linear elliptic operator, we prove the existence of a distributional corrector and we find an approximation scheme for the homogenized coefficients. We also study the convergence rates in the…