Related papers: A note on the connectedness property of union-free…
Many of the structural characteristics of a network depend on the connectivity with and within the hubs. These dependencies can be related to the degree of a node and the number of links that a node shares with nodes of higher degree. In…
We investigate the set of partial partitions of a finite set, ordered by inclusion. With this ordering the set of partial partitions can be studied as an abstract simplicial complex. We use the theory of shellable nonpure complexes to find…
Uniqueness and independence are two fundamental properties of data. Their enforcement in database systems can lead to higher quality data, faster data service response time, better data-driven decision making and knowledge discovery from…
By virtue of Balmer's celebrated theorem, the classification of thick tensor ideals of a tensor triangulated category $\T$ is equivalent to the topological structure of its Balmer spectrum $\spc \T$. Motivated by this theorem, we discuss…
An axiomatic theory of operator connections and operator means was investigated by Kubo and Ando in 1980. A connection is a binary operation for positive operators satisfying the monotonicity, the transformer inequality and the…
We present a property satisfied by a large variety of complex continued fraction algorithms (the "finite building property") and use it to explore the structure of bijectivity domains for natural extensions of Gauss maps. Specifically, we…
This is a survey of some of the consequences of the recently introduced congruences on the theory of connectednesses (radical classes) and disconnectednesses (semisimple classes) of graphs and topological spaces. In particular, it is shown…
Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…
We introduce a natural concept of positive definiteness for bundle maps between Fell bundles over (possibly different) discrete groups and describe several examples. Such maps induce completely positive maps between the associated full…
The proper parts of face lattices of convex polytopes are shown to satisfy a strong form of the Cohen--Macaulay property, namely that removing from their Hasse diagram all edges in any closed interval results in a Cohen--Macaulay poset of…
We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity…
We present a unified rule format for structural operational semantics with terms as labels that guarantees that the associated labelled transition system has some bounded-nondeterminism property. The properties we consider include finite…
We associate a rational number $\chi(\mathcal{A})$ to every category $\mathcal{A}$ whose object and morphism sets are finite. We show that the assignment $\chi$ is additive under disjoint union and it preserves products. Hence we consider…
Generating a huge number of association rules reduces their utility in the decision making process, done by domain experts. In this context, based on the theory of Formal Concept Analysis, we propose to extend the notion of Formal Concept…
We describe a new logical data model, called the concept-oriented model (COM). It uses mathematical functions as first-class constructs for data representation and data processing as opposed to using exclusively sets in conventional…
We prove some new properties of fidelity (transition probability) and concurrence, the latter defined by straightforward extension of Wootters notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on…
In this note we extend connectedness results to formal properties of inverse images under proper maps of Schubert varieties and of the diagonal in products of projective rational homogeneous spaces
In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].
The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to…
The operator monotone functions defined in the positive half-line are of particular importance. We give a version of the theory in which integral representations for these functions can be established directly without invoking L\"owner's…