Related papers: Development of complexity induced frameworks for c…
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two and three mode systems of differential equations coupled via quadratic $\chi_2$ type nonlinearity as well as two mode…
The static, charged, spherically symmetric matter distribution have been studied by considering polytropic equation of state. Two polytropic indices have been considered for study. The plots of density, radial pressure, tangential pressure,…
For certain shapes of inclusions embedded in a body, the field inside the inclusion is uniform for some boundary condition. We provide a construction scheme for inclusions of general shapes having such a uniformity property in two…
Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing…
In this paper we give a generalization of the normal holomorphic frames in the symplectic manifolds and find conditions for the integrability of complex structures.
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
A general formalism recently proposed to study Newtonian polytropes for anisotropic fluids is here extended to the relativistic regime. Thus, it is assumed that a polytropic equation of state is satisfied by, both, the radial and the…
We develop a rigidity theory for frameworks in $\mathbb{R}^3$ which have two coincident points but are otherwise generic and only infinitesimal motions which are tangential to a family of cylinders induced by the realisation are considered.…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
A generalized anisotropic-diffusion framework is developed for transport problem in media described by a tensorial scattering coefficient and a scalar Henyey--Greenstein asymmetry factor. In this regime the classical similarity relation…
We present a new algorithmic framework which utilizes tropical geometry and homotopy continuation for solving systems of polynomial equations where some of the polynomials are generic elements in linear subspaces of the polynomial ring.…
We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…
In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For…
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…
We solve the integration problem for generalized complex manifolds, obtaining as the natural integrating object a weakly holomorphic symplectic groupoid, which is a real symplectic groupoid with a compatible complex structure defined only…
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in…
We investigate the impact of an external pressure on the structure of self-gravitating polytropes for axially symmetric ellipsoids and rings. The confinement of the fluid by photons is accounted for through a boundary condition on the…
In this paper, we investigate complexity of anisotropic cylindrical object under the influence of electromagnetic field in $f(G,T)$ theory, where $G$ and $T$ indicate the Gauss-Bonnet term and trace of the stress-energy tensor,…
In this note, we describe a procedure to construct generalized complex structures with an arbitrarily large number of type change loci on products of the circle with a connected sum of closed 3-manifolds. The loci need not be isotopic.