相关论文: Balanced Colombeau products of the distributions $…

Coulomb gases are special probability distributions, related to potential theory, that appear at many places in pure and applied mathematics and physics. In these short expository notes, we focus on some models, ideas, and structures. We…

Govindan and Klumpp [7] provided a characterization of perfect equilibria using Lexicographic Probability Systems (LPSs). Their characterization was essentially finite in that they showed that there exists a finite bound on the number of…

This paper deals with linear algebraic equations where the global coefficient matrix and constant vector are given respectively, by the summation of the coefficient matrices and constant vectors of the individual agents. Our approach is…

The paper is devoted to regularity theory of generalized solutions to semilinear wave equations with a small nonlinearity. The setting is the one of Colombeau algebras of generalized functions. It is shown that in one space dimension, an…

We define natural topologies on the Colombeau algebras which are compatible with the algebraic structure. These topologies reduces do Scarpalezos sharp topologies when restricted. with this we take a positive step towards topological…

We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of $$\partial_tu-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=g(x,t)\quad\quad\text{in}\quad\quad \mathbb{R}^N\times(0,T),$$ where…

Let $P:\mathbb{C}^n\rightarrow \mathbb{C}$ be an $m$-homogeneous polynomial given by \[P(x)= \sum_{1\leq j_1\leq \ldots \leq j_m \leq n} c_{j_1 \ldots j_m} x_{j_1}\ldots x_{j_m}.\] Defant and Schl\"uters defined a non-symmetric associated…

I present all the details in calculating the posterior distribution of the conjugate Normal-Gamma prior in Bayesian Linear Models (BLM), including correlated observations, prediction, model selection and comments on efficient numeric…

The main result of this paper is the proof that all the symmetric products of a (finite) Galois-Maximal space are also Galois-Maximal spaces. This applies to the special case of real algebraic varieties, solving the problem first stated by…

The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformation of a random variable with the standard normal…

Conway-Maxwell-Poisson (CMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in practice seems to be the inability to…

The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. This problem is very important in applications but there is no systematic study of it. We present here a new technique, which…

We introduce and investigate classes of normed or quasinormed distribution spaces of generalized smoothness that can be obtained by various interpolation methods applied to classical Sobolev, Nikolskii-Besov, and Triebel-Lizorkin spaces. An…

We consider $m\times n$ rectangular matrices formed from Sturmian words with slope $\alpha$, and we fully characterise their balance properties in terms of the Ostrowski representations of $m$ and $n$ with respect to $\alpha$. This…

Let $n_j$ be a lacunary sequence of integers, such that $n_{j+1}/n_j\geq r$. We are interested in linear combinations of the sequence of finite Riesz products $\prod_{j=1}^N(1+\cos(n_j t))$. We prove that, whenever the Riesz products are…

In this note, we characterize the Gompertz distribution in terms of extreme value distributions and point out that it implicitly models the interplay of two antagonistic growth processes. In addition, we derive a closed form expressions for…

We survey some new results regarding a priori regularity estimates for the Boltzmann and Landau equations conditional to the boundedness of the associated macroscopic quantities. We also discuss some open problems in the area. In…

In 1947 Nathan Fine gave a beautiful product for the number of binomial coefficients $\binom{n}{m}$, for $m$ in the range $0 \leq m \leq n$, that are not divisible by $p$. We give a matrix product that generalizes Fine's formula,…

Pointwise estimates for the gradient of solutions to the $p$-Laplace system with right-hand side in divergence form are established. They enable us to develop a nonlinear counterpart of the classical Calder\'on-Zygmund theory in terms of…

Brawley and Carlitz introduced diamond products of elements of finite fields and associated composed products of polynomials in 1987. Composed products yield a method to construct irreducible polynomials of large composite degrees from…