Related papers: Relativistic formulation of abstract evolution equ…

This paper presents an alternative {\it relativistic nonlinear} approach to the vacuum case of classical electrodynamics. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature.…

We identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to…

We derive asymptotic formulae for the coefficients of bivariate generating functions with algebraic and logarithmic factors. Logarithms appear when encoding cycles of combinatorial objects, and also implicitly when objects can be broken…

In the framework of the Stueckelberg-Wheeler-Feynman concept of a ``one-electron Universe'' we consider a worldline implicitly defined by a system of algebraic (precisely, polynomial) equations. Collection of pointlike ``particles'' of two…

We consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used…

We consider infinite-dimensional parabolic rough evolution equations. Using regularizing properties of analytic semigroups we prove global-in-time existence of solutions and investigate random dynamical systems for such equations.

Time evolution is formulated and discussed in the framework of Schroeder's functional equation. The proposed method yields smooth, continuous dynamics without the prior need for local propagation equations.

There is an abundance of empirical evidence in the numerical relativity literature that the form in which the Einstein evolution equations are written plays a significant role in the lifetime of numerical simulations. This paper attempts to…

This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…

The coefficients of the nonlinear terms in a modified Altarelli-Parisi evolution equation with parton recombination are determined in the leading logarithmic ($Q^2$) approximation. The results are valid in the whole $x$ region and contain…

Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by…

We consider the problem of discretizing evolution operators of linear delay equations with the aim of approximating their spectra, which is useful in investigating the stability properties of (nonlinear) equations via the principle of…

The numerical solutions of the nonrelativistic and relativistic Boltzmann equations have been studied at various initial conditions. Particularly, the known analytical solution of the nonrelativistic Boltzmann equation at spherically…

Associated varieties are geometric objects appearing in infinite-dimensional representations of semisimple Lie algebras (groups). By applying Fourier transformations to the natural orthogonal oscillator representations of special linear Lie…

We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…

While evolution has inspired algorithmic methods of heuristic optimisation, little has been done in the way of using concepts of computation to advance our understanding of salient aspects of biological phenomena. We argue that under…

In the paper we investigate the evolution of the relativistic particle (massive and massless) with spin defined by Hamiltonian containing the terms with momentum-spin-orbit coupling. We integrate the corresponding Hamiltonian equations in…

We propose a binary representation of categorical values using a linear map. This linear representation preserves the neighborhood structure of categorical values. In the context of evolutionary algorithms, it means that every categorical…

We consider the recursion operators with nonlocal terms of special form for evolution systems in (1+1) dimensions, and extend them to well-defined operators on the space of nonlocal symmetries associated with the so-called universal Abelian…

We construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of countably infinite amenable groups and use these representations to find explicit generating partitions…