Related papers: How singular are moment generating functions?
In this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here the related special numbers are Stirling numbers of the…
We study functions on isolated singularities and prove some results of type Milnor number = Tjurina number. We use them to endow the base space of their miniversal deformation with the structure of F-manifold.
Let $\mu$ be a probability measure (or corresponding random variable) such that all moments $\mu_n$ exist. Knowledge of the moments is not sufficient to determine infinite divisibility of the measure; we show also that infinitely divisible,…
We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…
In Functional Analysis, certain conclusions apply to sequences, but they cannot be carried over when we consider nets. In fact, some nets, including sequences, can behave unexpectedly. In this paper we are interested in exploring the…
P\'olya in 1926 showed that the hypergeometric function $F(z)=\null_2F_1(a,b;c;z)$ has a totally monotone sequence as its coefficients; that is, $F$ is the generating function of a Hausdorff moment sequence, when $0\le a\le 1$ and $0\le…
Any nonlinear equation of the form y''=\sum_{n=0}^N a_n(z)y^n has a (generally branched) solution with leading order behaviour proportional to (z-z_0)^{-2/(N-1)} about a point z_0, where the coefficients a_n are analytic at z_0 and…
Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase--space. In this…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of absolutely monotonic components, or reflections of…
We characterize infinitesimal generators of semigroups of holomorphic self-maps of strongly convex domains using the pluricomplex Green function and the pluricomplex Poisson kernel. Moreover, we study boundary regular fixed points of…
Using some knowledge of multiplicity disributions for high energy reactions, it is possible to propose a simple analytical model of particle production by strong external sources. The model describes qualitatively most peculiar properties…
In this article, we set up the continuous maximal regularity theory for a class of linear differential operators on manifolds with singularities. These operators exhibit degenerate or singular behaviors while approaching the singular ends.…
We give an arithmetic criterion which is sufficient to imply the discreteness of various two-generator subgroups of $PSL(2,{\bold C})$. We then examine certain two-generator groups which arise as extremals in various geometric problems in…
We study the limit behaviour of solutions of a class of solutions of nonlinear parabolic equations with a degenerate strong absorption. We prove that two types of phenomena can occur: the pointwise singularity or the formation of razor…
We investigate the statistics of selected rare events in a (1+1)-dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or…
We shed some new light to the problem of characterizing those functions of several arguments that have a unique identification minor. The 2-set-transitive functions are known to have this property. We describe another class of functions…
Beginning in 2006, G. Gentili and D.C. Struppa developed a theory of regular quaternionic functions with properties that recall classical results in complex analysis. For instance, in each Euclidean ball centered at 0 the set of regular…
Singular perturbations have been used to select solutions of (non-convex) variational problems with a multiplicity of minimizers. The prototype of such an approach is the gradient theory of phase transitions by L. Modica, who specialized…
We consider sequences of random variables whose probability generating functions are polynomials all of whose roots lie on the unit circle. The distribution of such random variables has only been sporadically studied in the literature. We…