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A modification of perturbation theory, known as delta-expansion (variationally improved perturbation), gave rigorously convergent series in some D=1 models (oscillator energy levels) with factorially divergent ordinary perturbative…
We consider a model for a polymer interacting with an attractive wall through a random sequence of charges. We focus on the so-called diluted limit, when the charges are very rare but have strong intensity. In this regime, we determine the…
After reviewing basic facts about large-order behaviour of perturbation expansions in various fields of physics, I consider several alternatives to the Borel summation method and discuss their relevance to different physical situations.…
A method for the resummation of nonalternating divergent perturbation series is described. The procedure constitutes a generalization of the Borel-Pad\'{e} method. Of crucial importance is a special integration contour in the complex plane.…
The renormalization method based on the Taylor expansion for asymptotic analysis of differential equations is generalized to difference equations. The proposed renormalization method is based on the Newton-Maclaurin expansion. Several basic…
We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data on the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of…
We present a new prescription for the resummation of the divergent series of perturbative corrections, due to soft gluon emission, to hard processes near threshold in perturbative QCD (threshold resummation). This prescription is based on…
In this work, we address the problem of polynomial interpolation of non-pointwise data. More specifically, we assume that our input information comes from measurements obtained on diffuse compact domains. Although the nodal and the diffused…
We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…
We determine the density expansion of the radius of gyration, of the hydrodynamic radius, and of the end-to-end distance for a monodisperse polymer solution in good-solvent conditions. We consider the scaling limit (large degree of…
This paper studies, for the first time, a bilevel polynomial program whose constraints involve uncertain linear constraints and another uncertain linear optimization problem. In the case of box data uncertainty, we present a sum of squares…
We determine the second, third, and fourth virial coefficients appearing in the density expansion of the osmotic pressure of a monodisperse polymer solution in good-solvent conditions. Using the expected large-concentration behavior, we…
We study scaling properties of self avoiding polymer stars and networks of arbitrary given but fixed topology. We use massive field theoretical renormalization group framework to calculate critical exponents governing their universal…
The low-energy scattering of two charged particles is analyzed using a renormalization group approach based on dimensional regularization with power-divergence subtraction. A nontrivial solution with a marginally unstable direction is…
In this work, we introduce new families of nonconforming approximation methods for reconstructing functions on general polygonal meshes. These methods are defined using degrees of freedom based on weighted moments of orthogonal polynomials…
The constraint of a progressive decrease in residual renormalization scale dependence with increasing loop order is developed as a method for obtaining bounds on unknown higher-order perturbative corrections to renormalization-group…
We propose to study the infrared behaviour of polymerised (or tethered) random manifolds of dimension D interacting via an exclusion condition with a fixed impurity in d-dimensional Euclidean space in which the manifold is embedded. We…
Recent progresses in the understanding of the scaling behavior of self-avoiding flexible polymerized membranes (tethered manifolds) are reviewed. They rely on a new general renormalization group approach for a class of models with non-local…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
Mueller polarimetry involves a variety of instruments and technologies whose importance and scope of applications are rapidly increasing. The exploitation of these powerful resources depends strongly on the mathematical models that underlie…