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A recently developed linear algebraic method for the computation of perturbation expansion coefficients to large order is applied to the problem of a hydrogenic atom in a magnetic field. We take as the zeroth order approximation the $D…
This paper is the first in a series of three which attempt to resolve the difficulties that have plagued the $NN-\pi NN$ problem for the past ten years. Various theoretical inconsistencies in the current formulation have been pointed out…
An introduction to the methods and ideas of Chiral Perturbation Theory is presented in this talk. The discussion is illustrated with some phenomenological predictions that can be compared with available experimental results.
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
We study perturbations around the generalized Kazakov multicritical one-matrix model. The multicritical matrix model has a potential where the coefficients of $z^n$ only fall off as a power $1/n^{s+1}$. This implies that the potential and…
We prove several statements about arithmetic hyperbolicity of certain blow-up varieties. As a corollary we obtain multiple examples of simply connected quasi-projective varieties that are pseudo-arithmetically hyperbolic. This generalizes…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
We study continuity of the roots of nonmonic polynomials as a function of their coefficients using only the most elementary results from an introductory course in real analysis and the theory of single variable polynomials. Our approach…
Je retracerai l'histoire des conjectures de Weil sur le nombre de solutions d'\'equations polynomiales dans un corps fini et quelques unes des approches qui ont \'et\'e propos\'ees pour les r\'esoudre. The Weil conjectures: origins,…
We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
MAP perturbation models have emerged as a powerful framework for inference in structured prediction. Such models provide a way to efficiently sample from the Gibbs distribution and facilitate predictions that are robust to random noise. In…
We compare, for the static potential and at short distances, perturbation theory with the results of lattice simulations. We show that a renormalon-dominance picture explains why in the literature sometimes agreement, and another…
Perturbative approaches have often been used to include the effects of ground-state correlations in extended theories of the random-phase approximation. Validity of such approaches is investigated for a solvable model where comparison with…
At the light of recent results in literature we review a conjecture formulated in Math. Phys. Electron. J. 1 (1995), paper 5, 1--13, about the mechanism of breakdown of invariant sets in KAM problems and the identification of the dominant…
A class of scalar models with non-polynomial interaction, which naturally admits an analytical resummation of the series of tadpole diagrams is studied in perturbation theory. In particular, we focus on a model containing only one…
The difficulties of perturbation theory associated with unstable fundamental fields (such as the lack of exact gauge invariance in each order) are cured if one constructs perturbative expansion directly for probabilities interpreted as…
We investigate the effects of the regularization procedure used in the J-Matrix method. We show that it influences the convergence, and propose an alternative regularization approach. We explicitly perform some model calculations to…
The interaction between two particles with shape or interaction anisotropy can be modeled using a pairwise potential energy function that depends on their relative position and orientation; however, this function is often challenging to…
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.