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There are investigated such cosmological models which instead of the usual spatial homogeneity property only fulfil the condition that in a certain synchronized system of reference all spacelike sections t = const. are homogeneous…
We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological…
We introduce a notion of p-orthogonality in a general Banach space $1 \le p \le \infty$. We use this concept to characterize $\ell_p$-spaces among Banach spaces and also among complete order smooth p-normed spaces. We further introduce a…
It is known that a Banach space contains an isomorphic copy of $c_0$ if, and only if, it can be equivalently renormed to be almost square. We introduce and study transfinite versions of almost square Banach spaces with the purpose to relate…
This note aims to clarify the interrelations of certain inequivalently defined Banach spaces denoted by C^i(\bar\Omega) for a natural number i and a bounded open set \Omega. We give some sufficient conditions for the equality of these…
We deal with a mechanism of generating distributional chaos in planar nonautonomous ODEs and try to measure chaosity in terms of topological entropy. It is based on the interplay between simple periodic solutions. We prove the existence of…
We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of a strictly stationary orthomartingale random field. These inequalities can be used to establish complete convergence of…
We derive moment and tail estimates for Gaussian chaoses of arbitrary order with values in Banach spaces. We formulate a conjecture regarding two-sided estimates and show that it holds in a certain class of Banach spaces including L_q…
We construct a nonseparable Banach space $\mathcal X$ (actually, of density continuum) such that any uncountable subset $\mathcal Y$ of the unit sphere of $\mathcal X$ contains uncountably many points distant by less than $1$ (in fact, by…
We study properties of continuous semi-homogeneous operators of degree $k$ via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space. We prove necessary and sufficient conditions for these functions to…
We study the arithmetical ranks and the cohomological dimensions of an infinite class of Cohen-Macaulay varieties of minimal degree. Among these we find, on the one hand, infinitely many set-theoretic complete intersections, on the other…
Categories of locally ordered spaces are especially well-adapted to the realization of most precubical sets, though their colimits are not so easy to determine (in comparison with colimits in the category of d-spaces for example). We use…
For each $d\geq 0$, we prove decoupling inequalities in $\mathbb R^3$ for the graphs of all bivariate polynomials of degree at most $d$ with bounded coefficients, with the decoupling constant depending uniformly in $d$ but not the…
Banagl's method of intersection spaces allows to modify certain types of stratified pseudomanifolds near the singular set in such a way that the rational Betti numbers of the modified spaces satisfy generalized Poincar\'{e} duality in…
The main purpose of this article is to introduce some new binomial difference sequence spaces of fractional order ${\tilde{\alpha}} $ along with infinite matrices. Some topological properties of these spaces are considered along with the…
A Banach lattice E is called p-disjointly homogeneous, 1< p< infty, when every sequence of pairwise disjoint normalized elements in E has a subsequence equivalent to the unit vector basis of l_p. Employing methods from interpolation theory,…
Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random…
We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges.
We present an infinite dimensional Banach space in which the set of hyperbolic linear isomorphisms in that space is not dense (in the norm topology) in the set of linear isomorphisms.
The effect of quenched disorder in the one-dimensional asymmetric exclusion process is reviewed. Both particlewise and sitewise disorder generically induces phase separation in a range of densities. In the particlewise case the existence of…