Related papers: Beyond polarities: Generalizing Maxwell's reciproc…
We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered…
This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished circle. This provides a completely…
In this paper we explore the link between the theory of sheaves on graphs and noncommutative geometry showing that many concepts and constructions in the latter can be generalized and enhanced using methods coming from the former. They…
We associate curves of isotropic, Lagrangian and coisotropic subspaces to higher order, one parameter variational problems. Minimality and conjugacy properties of extremals are described in terms of these curves.
We use contact geometry to describe the monoid of projectively equivariant meromorphic differential operators on a complex curve, quantization of which generalizes known constructions of classical equivariants to non-commutative function…
Motivated by recent work of Au, C{\'e}bron, Dahlqvist, Gabriel, and Male, we study regularity properties of the distribution of a sum of two selfad-joint random variables in a tracial noncommutative probability space which are free over a…
We compute the differential geometric invariants of cuspidal edges on flat surfaces in hyperbolic $3$-space and in de Sitter space. Several dualities of invariants are pointed out.
We study intersections of projective convex sets in the sense of Steinitz. In a projective space, an intersection of a nonempty family of convex sets splits into multiple connected components each of which is a convex set. Hence, such an…
The analytical structure of some generalizations of the circle map is given. Also a generalization of off centre reflection is studied. The stability of Ito-Glass coupled map lattice is studied.
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
This study is motivated by the researches in the field of invariants of geodesic and conformal mappings presented in (T. Y. Thomas, [22]) and (H. Weyl, [25]). The Thomas projective parameter and the Weyl projective tensor are generalized in…
We survey some algebraic geometric aspects of mirror symmetry and duality in string theory. Some applications of computer algebra to algebraic geometry and string theory are shortly reviewed.
This book contains the material of my research on stereotype duality theories in geometry. It was intended as a continuation of my recently published monograph in De Gruyter on stereotype spaces and algebras.
Problem of global integration of geometric structures arising in the theory of dynamical systems admitting the normal shift is considered. In the case when such integration is possible the problem of globalization for shift maps is studied.
A review of author's work on cyclic inequalities of Shapiro-Diananda type and related optimization problems is presented.
On the simultaneous edge coloring of graphs
We introduce and study the basic notion of polarized Poisson manifolds generalizing the classical case of Poisson manifolds and extend this last notion for the ${k-}$% symplectic stuctures. And also, we show that for any polarized…
A geometric formulation which describes extended supergravities in any dimension in presence of electric and magnetic sources is presented. In this framework the underlying duality symmetries of the theories are manifest. Particular…
Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…
The tools developed in a preceding article for interpreting spacetime geometry in terms of all possible space-plus-time splitting approaches are applied to circular orbits in some familiar stationary axisymmetric spacetimes. This helps give…