Related papers: Multiple-Order Singularity Expansion Method
While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel…
We introduce a (bi)category $\mathfrak{Sing}$ whose objects can be functorially assigned spaces of distributions and generalized functions. In addition, these spaces of distributions and generalized functions possess intrinsic notions of…
The phase diagrams and transitions of nonequilibrium systems with multiplicative noise are studied theoretically. We show the existence of both strong and weak-coupling critical behavior, of two distinct active phases, and of a nonzero…
All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…
The main issue of this work consists in extracting one or several finite values for the sum of series involved in perturbation theories. It is supposed to work for all cases in which two physical parameters are involved, and makes thorough…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
A new class of regular quaternionic functions, defined by power series in a natural fashion, has been introduced in recent years. Several results of the theory recall the classical complex analysis, whereas other results reflect the…
We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…
Open string amplitudes at tree level have been studied for over fifty years, but there is no known analytic form for general $n$-point amplitudes, and their conventional representation in terms of worldsheet integrals does not make many of…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
We introduce a set of special functions called multiple polyexponential integrals, defined as iterated integrals of the exponential integral $\text{Ei}(z)$. These functions arise in certain perturbative expansions of the local solutions of…
The question how complex systems become more organized and efficient with time is open. Examples are, the formation of elementary particles from pure energy, the formation of atoms from particles, the formation of stars and galaxies, the…
The goal of this note is to extend the result bounding from bellow the minimal possible growth of frequently oscillating subharmonic functions to a larger class of functions that carry similar properties. We refine and find further…
Recent research in light scattering has prompted a re-evaluation of complex quantities, particularly in the context of complex frequency signals, which exhibit exponential growth or decay unlike traditional harmonic signals. We introduce a…
Based on a variant of frequency function, we improve the vanishing order of solutions for Schr\"{o}dinger equations which describes quantitative behavior of strong uniqueness continuation property. For the first time, we investigate the…
We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. We show that for higher orders, it is more efficient to have fields represented in…
This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for…