Related papers: Considerations on the genetic equilibrium law
Our goal is to present the basic results on one-dimensional Gibbs and equilibrium states viewed as special invariant measures on symbolic dynamical systems, and then to describe without technicalities a sample of results they allowed to…
The aim of this work is to use the notions of Riemann's geometry introduced in Part I, to analyze the foundations of Einstein's theory of general relativity.
The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic…
The aim of this paper is to present a self contained introduction to the Hubbard model and some of its applications.The paper consists of two parts: the first will introduce the basic notions of the Hubbard model starting from the…
The lattice regularization of the Higgs sector of the standard model is summarized. The triviality bound and vacuum instability bound are described. The question of chiral gauge theories is discussed. Some aspects of the numerical…
In a very general quasilinear setting, we show that the regularizing effect of a first order term causes the existence of energy solutions for problems involving the Hardy potential and $L^1$ data. In the same setting we study sharp (local…
We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a…
This paper is devoted to general balance laws (with a possibly non local source term) with a non-characteristic boundary. Basic well posedness results are obtained, trying to provide sharp estimates. In particular, bounds tend to blow up as…
This short survey paper is concerned with a new method to prove global well-posedness results for dispersive equations below energy spaces, namely $H^{1}$ for the Schr\"odinger equation and $L^{2}$ for the KdV equation. The main ingredient…
This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular homogeneous space of non-reductive type, the so…
We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple…
This work is devoted to the structure of the time-discrete Green-Naghdi equations including bathymetry. We use the projection structure of the equations to characterize homogeneous and inhomogeneous boundary conditions for which the…
The goal of this paper is to describe an elementary combinatorial heuristic that predicts Hardy and Littlewood's extended Goldbach's conjecture. We examine common features of other heuristics in additive prime number theory, such as…
In a certain way, this paper presents the continuation of the previous one which discussed the harmonic structure of the genetic code (Rakocevic, 2004). Several new harmonic structures presented in this paper, through specific unity and…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
In my previous paper I have contrived a Ginzburg-Landau heat flow with a time-dependent parameter and by using it, I constructed a harmonic heat flow into spheres with a monotonical inequality and a reverse Poincar\'{e} inequality. This…
This paper deals with the famous isoperimetric inequality. In a first part, we give some new functional form of the isoperimetric inequality, and in a second part, we give a quantitative form with a remainder term involving Wasserstein…
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
A conceptual framework for variational formulations of physical theories is proposed. Such a framework is displayed here just for statics, but it is designed to be subsequently adapted to variational formulations of static field theories…
Conditional Equi-concentration of Types on I-projections is presented. It provides an extension of Conditional Weak Law of Large Numbers to the case of several I-projections. Also a multiple I-projections extension of Gibbs Conditioning…