Related papers: How singular are moment generating functions?
We prove a recursion formula for generating functions of certain renormalizations of *-moments of the DT(\delta_0,1)-operator T, involving an operation \odot on formal power series and a transformation E that converts \odot to usual…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
We develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems. We introduce and study the notion of the Schur generating function of a random discrete configuration. Our main result provides a…
We investigate meandric systems with a large number of loops using tools inspired by free probability. For any fixed integer $r$, we express the generating function of meandric systems on $2n$ points with $n-r$ loops in terms of a finite…
An elementary, at the undergraduate level derivation is given of precise upper bounds of the number of various RNA secondary structures. The method works when the generating function has multiple singularities at the circle of convergence,…
We construct Lipschitz $Q$-valued functions which approximate carefully integral currents when their cylindrical excess is small and they are almost minimizing in a suitable sense. This result is used in two subsequent works to prove the…
We demonstrate that individual behaviors directed at the attainment of distinctiveness can in fact produce complete social conformity. We thus offer an unexpected generative mechanism for this central social phenomenon. Specifically, we…
Two results concerning the number of threshold functions $P(2, n)$ and the probability ${\mathbb P}_n$ that a random $n\times n$ Bernoulli matrix is singular are established. We introduce a supermodular function $\eta^{\bigstar}_n : 2^{{\bf…
The analysis of singular regions in the NUT solutions carried out in the recent paper (Manko and Ruiz, 2005 Class. Quantum Grav. 22, p.3555) is now extended to the Demianski-Newman vacuum and electrovacuum spacetimes. We show that the…
The constancy of the Milnor number has several characterizations which were summarized by Greuel in 1986. This paper presents a study of these characterizations in the case of families of functions with isolated singularities defined on an…
The study of the singularities and zeros of the generating functions of multiplicity distributions is advocated. Some hints from well known probability distributions and experimental data are given. The statistical mechanics analogies…
This note is the third part of our work devoted to uniqueness sets for spaces of entire functions. Given a discrete set $\Lambda$ with angular density $\Delta$ with respect to the order $\rho$, satisfying some regularity condition, we show…
We define two-parameter generalizations of Andrews' $(k+1)$-marked odd Durfee symbols and $2k$th symmetrized odd rank moments, and study the automorphic properties of some of their generating functions. When $k=0$ we obtain families of…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
Our paper is devoted to several problems from the field of modified divisors: namely exponential and infinitary divisors. We study the behaviour of modified divisors, sum-of-divisors and totient functions. Main results concern with the…
We consider nonlinear dispersive equations of Schr\"odinger-type involving fractional powers $0<s\le 1$ of the Laplacian and a defocusing power-law nonlinearity. We conduct numerical simulations in the case of small, energy supercritical…
We investigate in this work the spectrum of singularities of super-Brownian motion with stable branching. The main purpose is to provide a uniform description of the latter in high dimension $d\geq\tfrac{2}{\gamma-1}$, presenting the…
In this paper, we show generation and propagation of polynomial and exponential moments, as well as global well-posedness of the homogeneous binary-ternary Boltzmann equation. We also show that the co-existence of binary and ternary…
Understanding how singularities behave under small perturbations is a central theme in singularity theory. In this paper we establish sufficient conditions for families of analytic function-germs on a germ of a complex analytic space to…
In this paper we are interested in moments of Minkowski question mark function ?(x). It appears that, to certain extent, the results are analogous to the results obtained for objects associated with Maass wave forms: period functions,…