Related papers: The Structure of Submodular Separation Systems
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.
Extending the investigations about the theory of duals, we analyze duals built up with the aid of discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) in order to verify…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
We study the structures of arbitrary split Leibniz triple systems. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of $T$ being of maximal length, the simplicity of the…
This survey note describes a brief systemic view to approaches for evaluation of hierarchical composite (modular) systems. The list of considered issues involves the following: (i) basic assessment scales (quantitative scale, ordinal scale,…
A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite…
The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.
This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…
We study semi-isolation as a binary relation on the locus of a complete type and prove that under some additional assumptions it induces the strict order property.
In this paper, we present an equivalent form of the $\Delta_2 $-condition which allow us to redefine the topological vector space structure of a modular spaces using the filter base. We show also the characterization of closed subsets (in…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…
We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these…
This paper reveals a categorical equivalence connecting two distinct quantum logic structures. The first is the orthomodular lattice, an algebraic system designed to formalize the properties of quantum systems. The second is a finitary…
This paper investigates the interplay between algebraic structure, topology, and differentiability in Clifford semigroups. The study is developed along three main themes. First, in the compact Hausdorff setting, we provide an explicit…
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…
Answering a question by Honsell and Plotkin, we show that there are two equations between lambda terms, the so-called subtractive equations, consistent with lambda calculus but not simultaneously satisfied in any partially ordered model…
A notion of interpretation between arbitrary logics is introduced, and the poset Log of all logics ordered under interpretability is studied. It is shown that in Log infima of arbitrarily large sets exist, but binary suprema in general do…