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We explore the dynamical behaviour of cosmological models involving a scalar field (with an exponential potential and a canonical kinetic term) and a matter fluid with spatial curvature included in the equations of motion. Using…
We summarize an explicit construction of a duality cycle for geometric transitions in type II and heterotic theories. We emphasize that the manifolds with torsion constructed with this duality cycle are crucial for understanding different…
We study period integrals of CY hypersurfaces in a partial flag variety. We construct a holonomic system of differential equations which govern the period integrals. By means of representation theory, a set of generators of the system can…
We take the abstract basis approach to classical domain theory and extend it to quantitative domains. In doing so, we provide dual characterisations of distance domains (some new even in the classical case) as well as unifying and extending…
We construct a version of Hamiltonian Floer Homology based on the notion of a semi-infinite cycle. As an application, we provide a new proof for the existence of critical points of the action functional.
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
The force fields of interior boundaries of matters are calculated as superposition of fields of modified Sierpinski carpet. The long-range effect interaction in irradiated crystals is introduced as various manifestations of second order…
This article examines the dynamic phase transitions and pattern formations attributed to binary systems modeled by the Cahn-Hilliard equation. In particular, we consider a two-dimensional lattice structure and determine how different…
The purpose of this paper is twofold. Firstly, the new matrix domains are constructed with the new infinite matrices and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix…
We introduce multi-sheeted versions of algebraic domains and quadrature domains, allowing them to be branched covering surfaces over the Riemann sphere. The two classes of domains turn out to be the same, and the main result states that the…
Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…
In this survey we present several results concerning various topologies that were introduced in recent years on spaces of valuation domains.
An introduction to geography of log models with applications to positive cones of FT varieties and to geometry of minimal models and Mori fibrations.
In this paper, we study certain applications of sphericalization in Gromov hyperbolic metric spaces. We first show that the doubling property regarding two classes of metrics on the Gromov boundary of hyperbolic spaces are coincided. Next,…
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled…
The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties…
The article provides a brief survey of the mathematics of some of the newly being developed so called "hybrid" (also called "multi-physics" or "multi-wave") imaging techniques.
We investigate the presence of domain walls in models described by three real scalar fields. We search for stable defect structures which minimize the energy of the static field configurations. We work out explict orbits in field space and…
Light scalar fields, with double well potentials and direct matter couplings, undergo density driven phase transitions, leading to the formation of domain walls. Such theories could explain dark energy, dark matter or source the nanoHz…