Related papers: Relativistic formulation of abstract evolution equ…
A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be…
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields.…
Extending the work of Freese and Cook, which develop the basic theory of calculus and power series over real associative algebras, we examine what can be said about the logarithmic functions over an algebra. In particular, we find that for…
The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler-Lagrange equation,…
Many real-world systems exhibit ``noisy'' evolution in time; interpreting their finitely-sampled behavior as arising from continuous-time processes (in the It\^o or Stratonovich sense) has led to significant success in modeling and analysis…
A formula for the apparent rotation of a relativistically moving object has been known for some time, but it seems not to have been realized that this formula has a very pretty interpretation in terms of formal group laws. Version 2…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
The causal structure of Einstein's evolution equations is considered. We show that in general they can be written as a first order system of balance laws for any choice of slicing or shift. We also show how certain terms in the evolution…
A version of the nonlinear Hodge equations is introduced in which the irrotationality condition is weakened. An elliptic estimate for solutions is derived.
The short-time and global behaviour are studied for an autonomous linear evolution equation, which is defined by a generator inducing a uniformly bounded holomorphic semigroup in a Hilbert space. A general necessary and sufficient condition…
The group classification problem for the class of (1+1)-dimensional linear $r$th order evolution equations is solved for arbitrary values of $r>2$. It is shown that a related maximally gauged class of homogeneous linear evolution equations…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
A critical analysis of the relativistic formulation of matter reveals some surprising inconsistencies and paradoxes. Corrections are discovered which lead to the long-sought-after equality of the gravitational and inertial masses, which are…
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
This short note provides positive answers to two conjectures of Camacho, Khudoyberdiyev, and Omirov on the classification of complete evolution algebras. Our approach is based on analysing the solution set of a generic non-linear polynomial…
We analyze the relationship of generalized conditional symmetries of evolution equations to the formal compatibility and passivity of systems of differential equations as well as to systems of vector fields in involution. Earlier results on…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. The so-called numerical relativity (computational simulations in general relativity) is a promising research field matching with…
The starting point of this work is that the class of evolution algebras over a fixed field is closed under tensor product. This arises questions about the inheritance of properties from the tensor product to the factors and conversely. For…
The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the…