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The theory of the basic statistical concept of (Lehmann-Scheff\'e-)completeness is perfected by providing the theorem indicated in the title and previously overlooked for several decades. Relations to earlier results are discussed and…
In a broad sense, positivstellens\"atze are results about representations of polynomials which are strictly positive on a given set. We give constructive and, to a large extent, elementary proofs of some known positivstellens\"atze for…
In this work we present a new class of numerical semigroups called GSI-semigroups. We see the relations between them and others families of semigroups and we give explicitly their set of gaps. Moreover, an algorithm to obtain all the…
This article is partly a survey and partly a research paper. It tackles the use of Groebner bases for addressing problems of numerical semigroups, which is a topic that has been around for some years, but it does it in a systematic way…
In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…
The purpose of this paper is to revisit the proof of the Gearhardt-Pr\"uss-Hwang-Greiner theorem for a semigroup $S(t)$, following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on $\Vert…
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly general criteria for the geometric convergence of normalized unbounded semigroups.
We shall prove an extension of the semipositivity theorem for the case of reducible algebraic fiber spaces.
We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expansions for a class of permutation statistics including the…
We give some explicit calculations for stable distributions and convergence to them, mainly based on less explicit results in Feller (1971). The main purpose is to provide ourselves with easy reference to explicit formulas and examples.…
In this paper, we propose two new classes of tensors: double B-tensors and quasi-double B-tensors, give some properties of double B-tensors and quasi-double B-tensors, discuss their relationships with B-tensors and positive definite tensors…
The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general values of positive semidefinite rank we provide a conjecture…
In 1995, Reznick showed an important variant of the obvious fact that any positive semidefinite (real) quadratic form is a sum of squares of linear forms: If a form (of arbitrary even degree) is positive definite then it becomes a sum of…
We prove that a non-elementary relatively hyperbolic group is statistically hyperbolic with respect to every finite generating set. We also establish statistical hyperbolicity for certain direct products of two groups, one of which is…
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
A survey of recent results in elementary number theory is presented in this paper. Special attention is given to structure and asymptotic properties of certain families of positive integers.
In this work, we establish new analytical results which are required for the derivation of subtle properties of the members of two classes of the generalized Feller--Spitzer distributions introduced in our forthcoming paper.
In a recent paper by L. Fel two new identities for the degree of syzygies are given. We present an algebraic proof of them, using only basic homological algebra tools. We also extend these results.