Related papers: Factorization, majorization, and domination for li…
A necessary and sufficient condition for an element of an algebra (in the sense of Universal Algebra) to be in the dominion of a subalgebra is given, in terms of transferable sets. This criterion is then used to formulate a more wieldy…
In this article, we present a new method to study uniqueness of form extensions in a rather general setting. The method is based on the theory of ordered Hilbert spaces and the concept of domination of semigroups. Our main abstract result…
We study a factorization of bounded linear maps from an operator space $A$ to its dual space $A^*$. It is shown that $T : A \longrightarrow A^*$ factors through a pair of a column Hilbert spaces $\mathcal{H}_c$ and its dual space if and…
In a graph $G$, a vertex dominates itself and its neighbours. A subset $S\subseteq V(G)$ is said to be a double dominating set of $G$ if $S$ dominates every vertex of $G$ at least twice. The minimum cardinality among all double dominating…
We initiate a study of the homomorphism domination exponent of a pair of graphs F and G, defined as the maximum real number c such that |Hom(F,T)| \geq |Hom(G,T)|^c for every graph T. The problem of determining whether HDE(F,G) \geq 1 is…
This article is devoted to a study of majorization based on semi-doubly stochastic operators (denoted by $S\mathcal{D}(L^1)$) on $L^1(X)$ when $X$ is a $\sigma$-finite measure space. We answered Mirsky's question and characterized the…
Majorization is a basic concept in matrix theory that has found applications in numerous settings over the past century. Power majorization is a more specialized notion that has been studied in the theory of inequalities. On the other hand,…
We consider "Taylor domination" property for an analytic function $f(z)=\sum_{k=0}^{\infty}a_{k}z^{k},$ in the complex disk $D_R$, which is an inequality of the form \[ |a_{k}|R^{k}\leq C\ \max_{i=0,\dots,N}\ |a_{i}|R^{i}, \ k \geq N+1. \]…
In this paper we study combinatorial and algorithmic resp. complexity questions of upper domination, i.e., the maximum cardinality of a minimal dominating set in a graph. We give a full classification of the related maximisation and…
In this series of papers we study subspaces of de Branges spaces of entire functions which are generated by majorization on subsets $D$ of the closed upper half-plane. The present, first, part is addressed to the question which subspaces of…
This article is concerned with finite rank stability theory, and more precisely two classical ways to decompose a type using minimal types. The first is its domination equivalence to a Morley power of minimal types, and the second its…
In this paper we begin an exploration of several domination-related parameters (among which are the total, restrained, total restrained, paired, outer connected and total outer connected domination numbers) in the generalized lexicographic…
Motivated by the theory of domination for types, we introduce a notion of domination for Keisler measures called extension domination. We argue that this variant of domination behaves similarly to its type setting counterpart. We prove that…
The domination number $\gamma(G)$ of a graph $G$, its exponential domination number $\gamma_e(G)$, and its porous exponential domination number $\gamma_e^*(G)$ satisfy $\gamma_e^*(G)\leq \gamma_e(G)\leq \gamma(G)$. We contribute results…
The density operator is usually defined starting from a set of kets in the Hilbert space and a probability distribution. From this definition it is easy to obtain a factorization of a given density operator, here called density factor (DF).…
Write $\mathrm{ord}_p(\cdot)$ for the multiplicative order in $\mathbb{F}_p^{\times}$. Recently, Matthew Just and the second author investigated the problem of classifying pairs $\alpha, \beta \in \mathbb{Q}^{\times}\setminus\{\pm 1\}$ for…
We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This…
We show that the factorization problem $\theta (z)=\theta_2(z)\theta_1(z)$ is solvable in the class of Hilbert space operator-valued functions holomorphic on some neighbourhood of $z=0$ in $\nspace{C}{N}$ and having a zero at $z=0$ (here…
We compare three approaches to studying the behavior of an analytic function $f(z)=\sum_{k=0}^\infty a_kz^k$ from its Taylor coefficients. The first is "Taylor domination" property for $f(z)$ in the complex disk $D_R$, which is an…
A family of regularization functionals is said to admit a linear representer theorem if every member of the family admits minimizers that lie in a fixed finite dimensional subspace. A recent characterization states that a general class of…