Related papers: Distributive Mereotopology: Extended distributive …
Contact algebra is one of the main tools in region-based theory of space. In \cite{dmvw1, dmvw2,iv,i1} it is generalized by dropping the operation Boolean complement. Furthermore we can generalize contact algebra by dropping also the…
Contact Boolean algebras are one of the main algebraic tools in region-based theory of space. T. Ivanova provided strong motivations for the study of merely semilattices with a contact relation. Another significant motivation for…
We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact…
The aim of this paper is to give new representation theorems for extended contact algebras. These representation theorems are based on equivalence relations.
The ternary extended contact relation was introduced in (Ivanova, 2020) as a more expressive counterpart of the standard binary contact relation. The class of Boolean algebras expanded with the relation was named Extended Contact Algebras…
This paper is mainly concerned with the relation-algebraical aspects of the well-known Region Connection Calculus (RCC). We show that the contact relation algebra (CRA) of certain RCC model is not atomic complete and hence infinite. So in…
Cardiac myocytes are the fundamental cells composing the heart muscle. The propagation of electric signals and chemical quantities through them is responsible for their nonlinear contraction and dilatation. In this study, a theoretical…
The paper is in the field of Region Based Theory of Space (RBTS), sometimes called mereotopology. RBTS is a kind of point-free theory of space based on the notion of region. Its origin goes back to some ideas of Whitehead, De Laguna and…
The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…
Applying a general categorical construction for the extension of dualities, we present a new proof of the Fedorchuk duality between the category of compact Hausdorff spaces with their quasi-open mappings and the category of complete normal…
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…
On contact manifolds we describe a notion of (contact) finite-type for linear partial differential operators satisfying a natural condition on their leading terms. A large class of linear differential operators are of finite-type in this…
One of the standard axioms for Boolean Contact Algebras says that if a region x is in contact with the join of y and z, then x is in contact with at least one of the two regions. Our intention is to examine a stronger version of this axiom…
The notions of a {\em 2-precontact space}\/ and a {\em 2-contact space}\/ are introduced. Using them, new representation theorems for precontact and contact algebras are proved. It is shown that there are bijective correspondences between…
A general definition of mathematical morphology has been defined within the algebraic framework of complete lattice theory. In this framework, dealing with deterministic and increasing operators, a dilation (respectively an erosion) is an…
In this paper we consider symplectic and contact Lie algebras. We define contactization and symplectization procedures and describe its main properties. We also give classification of such algebras in dimensions 3 and 4. The classification…
We propose a new contact relation between polytopes. Intuitively, we say that two polytopes are in strong contact if a small enough object can pass from one of them to the other while remaining in their union. In the first half of the paper…
I define higher codimensional versions of contact structures on manifolds as maximally non-integrable distributions. I call them multicontact structures. Cartan distributions on jet spaces provide canonical examples. More generally, I…
For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated Teichmueller space of the surface. On the geometric…
k-Contact geometry is a generalisation of contact geometry to analyse field theories. We develop an approach to k-contact geometry based on distributions that are distributionally maximally non-integrable and admit, locally, k commuting…