Related papers: Classification of poset-block spaces admitting Mac…
We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group ${T_t}_{t\in\C^n}$ with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also…
The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…
We study a class of nonlinear PDEs that admit the same bi-Hamiltonian structure as WDVV equations: a Ferapontov-type first-order Hamiltonian operator and a homogeneous third-order Hamiltonian operator in a canonical Doyle--Potemin form,…
An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension…
In this paper, for any odd prime $p$ and an integer $m\ge 3$, several classes of linear codes with $t$-weight $(t=3,5,7)$ are obtained based on some defining sets, and then their complete weight enumerators are determined explicitly by…
The weight enumerators (quant-ph/9610040) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher-degree polynomial…
We define combinatorially a partial order on the set partitions and show that it is equivalent to the Bruhat-Chevalley-Renner order on the upper triangular matrices. By considering subposets consisting of set partitions with a fixed number…
We prove the existence of subspace designs with any given parameters, provided that the dimension of the underlying space is sufficiently large in terms of the other parameters of the design and satisfies the obvious necessary divisibility…
Hepworth, Willerton, Leinster and Shulman introduced the magnitude homology groups for enriched categories, in particular, for metric spaces. The purpose of this paper is to describe the magnitude homology group of a metric space in terms…
Shearer and McEliece [1977] showed that there is no MacWilliams identity for the free distance spectra of orthogonal linear convolutional codes. We show that on the other hand there does exist a MacWilliams identity between the generating…
We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial…
We study a few approaches to identify inclusion (up to a shift) between two convex bodies in ${\mathbb R}^n$. To this goal we use mixed volumes and fractional linear maps. We prove that inclusion may be identified by comparing volume or…
Let $G$ be a discrete group. We prove that the category of $G$-posets admits a model structure that is Quillen equivalent to the standard model structure on $G$-spaces. As is already true nonequivariantly, the three classes of maps defining…
In this paper certain $n$-dimensional inequalities are shown to be equivalent to the inequalities in the one-dimensional setting. By this means, embeddings between weighted local Morrey-type spaces are characterized for some ranges of…
In this paper we characterize $m$-isometric and quasi-$m$-isometric weighted conditional type (WCT) operators on the Hilbert space $L^2(\mu)$. Also, we prove that the subclasses of $m$-isometric and quasi-$m$-isometric of normal WCT…
We study the row-space partition and the pivot partition on the matrix space $\mathbb{F}_q^{n \times m}$. We show that both these partitions are reflexive and that the row-space partition is self-dual. Moreover, using various combinatorial…
In this article, we obtain two sets of results. The first set of complete results are exclusively for the case of the bi-disc while the second set of results describe in part, which of these carry over to the general case of the poly-disc:…
The first half of this dissertation reviews the basic notion of vector-valued modular forms and its connection to differential equations. The main purpose of the dissertation is to classify spaces of vector-valued modular forms associated…
The queue number of a poset is the queue number of its cover graph when the vertex order is a linear extension of the poset. Heath and Pemmaraju conjectured that every poset of width $w$ has queue number at most $w$. The conjecture has been…
A poset-stratified space is a pair $(S, S \xrightarrow \pi P)$ of a topological space $S$ and a continuous map $\pi: S \to P$ with a poset $P$ considered as a topological space with its associated Alexandroff topology. In this paper we show…