相关论文: Exponential dichotomy and $(L^p,L^q)$-admissibilit…
We review and analyse techniques from the literature for extending a normed algebra, A to a normed algebra, B, so that B has interesting or desirable properties which A may lack. For example, B might include roots of monic polynomials over…
We prove a definable version of Matou\v{s}ek's $(p,q)$-theorem in NIP theories. This answers a question of Chernikov and Simon. We also prove a uniform version. The proof builds on a proof of Boxall and Kestner who proved this theorem in…
Generalizing results of our earlier paper, we investigate the following question. Let $\pi(\lambda) : A \to B$ be an analytic family of surjective homomorphisms between two Banach algebras, and $q(\lambda)$ an analytic family of idempotents…
Free exponential families have been previously introduced as a special case of the q-exponential family. We show that free exponential families arise also from a procedure analogous to the definition of exponential families by using the…
In this paper we study the polynomial version of Pillai's conjecture on the exponential Diophantine equation \begin{equation*} p^n - q^m = f. \end{equation*} We prove that for any non-constant polynomial $ f $ there are only finitely many…
We propose a number of concepts and properties related to `weighted' statistical inference where the observed data are classified in accordance with a `value' of a sample string. The motivation comes from the concepts of weighted…
We show that $\ell_p$ norms are characterized as the unique norms which are both invariant under coordinate permutation and multiplicative with respect to tensor products. Similarly, the $L_p$ norms are the unique rearrangement-invariant…
We introduce polynomially weighted $\ell^p$-norms on the bar complex of a finitely generated group. We prove that, for groups of polynomial or exponential growth, the homology of the completed complex does not depend on the value of $p$ in…
Exponential families are a particular class of statistical manifolds which are particularly important in statistical inference, and which appear very frequently in statistics. For example, the set of normal distributions, with mean {\mu}…
We define the notion of couple density $(D, \mathbf b)$ where $D$ is a non-empty subset of $\mathbb Z^{m}$ and $ \mathbf b$ a fixed element in $\{0, \cdots, q-2\}^{m};$ We determine a minimum in terms of the density of the couple…
The aim of this paper is to emphasize various concepts of dichotomies for evolution equations in Banach spaces, due to the important role they play in the approach of stable, instable and central manifolds. The asymptotic properties of the…
In this paper we compute the exact divisibility of exponential sums associated to binomials $F(X)=aX^{d_1} +b X^{d_2}$. In particular, for the case where $\max\{d_1,d_2\}\leq\sqrt{p-1}$, the exact divisibility is computed. As a byproduct of…
A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…
In this paper we give necessary and sufficient conditions for the norm on an infinite dimensional Banach space to be sub differentiable, for various classes of Bananch spaces.
For linear random dynamical systems in a separable Banach space $X$, we derived a series of Krein-Rutman type Theorems with respect to co-invariant cone family with rank-$k$, which present a (quasi)-equivalence relation between the…
We study the class of $(p,q)$-regular operators between quasi-Banach lattices. In particular, a representation of this class as the dual of a certain tensor norm for Banach lattices is given. We also provide some factorization results for…
This paper describes the Elliptical Quartic Exponential distribution in $\mathbb{R}^D$, obtained via a maximum entropy construction by imposing second and fourth moment constraints. I discuss relationships to related work, analytical…
This paper deals with the exponential separation of type II, an important concept for random systems of differential equations with delay, introduced in \JM\ et al.~\cite{MiNoOb1}. Two different approaches to its existence are presented.…
This paper aims to establish the norm properties of the variable mixed space $ \ell^{q(\cdot)}(L^{p(\cdot)}) $ when $ 1<q_-,p_-,q_+,p_+<\infty $. In this way, we address the open problem raised by Almeida and H\"{a}st\"{o}.
We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate priors. In each case, the transition…