Related papers: Complex functions as lumps of energy
It is shown, that extended particle-like objects should infinitely long collapse into some discontinuous configurations of the same topology, but vanishing mass. Analytic results concerning the general properties and asymptotic rates of…
We outline here a simple mathematical introduction to the notions of multipoles for a general extensive property $\Pi$ from the point of view of continuum mechanics. Classically, $\Pi$ is the electric charge, but the theory is not limited…
We describe a class of theories of dielectric polarization and a species of solitons in these theories. The solitons, made entirely out of the polarization field, have quantized values of the electric charge and can be interpreted as…
We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the…
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…
This is a survey of some recent results concerning polynomial inequalities and polynomial approximation of functions in the complex plane. The results are achieved by the application of methods and techniques of modern geometric function…
This paper is a survey about recent developments in the local entropy theory for topological dynamical systems and continuous group actions, with particular emphasis on the connections with other areas of dynamical systems and mathematics.
The proposition that photon is a topological object (J. Math. Phys. 49, 032303, 2008) is given rigorous foundation based on pure vector field theory independent of the electromagnetic fields. Holomorphy of 4-dimensional space-time and the…
This work formulates and gives grounds for general principles and theorems that question the energy function doctrine and its quantum version as a genuine law of nature without borders of adequacy. The emphasis is on the domain where the…
In the 1950s Morse defined the analogue of Morse functions for topological manifolds. In many instances, when mathematicians are using techniques on topological manifolds that appear to be Morse-theoretic in nature, there is a topological…
Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.
We review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations. We also discuss a few open problems.
The dynamical model on 3+1 dimensional spacetime admitting soliton solutions is discussed. The proposal soliton is localized in the vicinity of a closed contour, which could be linked and/or knotted. The topological charge is Hopf…
Special functions have always played a central role in physics and in mathematics, arising as solutions of particular differential equations, or integrals, during the study of particular important physical models and theories in Quantum…
The necessity of computing integrals with complex weights over manifolds with a large number of dimensions, e.g., in some field theoretical settings, poses a problem for the use of Monte Carlo techniques. Here it is shown that very general…
The study explores the conformable electromagnetic field theory. The concept of the conformable delta function is introduced. Subsequently, the conformable Maxwell's equations are derived.
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…
We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…
The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann…
In these notes we consider power series representations of functions on the unit disk in the complex plane which define harmonic and holomorphic functions and related matters concerning boundary values, Poisson kernels, and so on.