Related papers: Evolution equations for eigenvalues and coefficien…
To an algebraic variety equipped with an involution, we associate a cycle class in the modulo two Chow group of its fixed locus. This association is functorial with respect to proper morphisms having a degree and preserving the involutions.…
We give an outline of a formalism for the solution of the evolution equations for off-forward parton distributions in leading and next-to-leading orders based on partial conformal wave expansion and orthogonal polynomials reconstruction.
We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution…
Let $K$ be an algebraically closed field with an absolute value. This note gives an elementary proof of the classical result that the roots of a polynomial with coefficients in $K$ are continuous functions of the coefficients of the…
A modification of the symmetry approach for the classification of integrable differential-difference equations of the form $$ u_{n,t} = f_n(u_{n-1}, u_n, u_{n+1}), $$ where $n$ is a discrete integer variable, is presented (the well-known…
Discrete dynamical systems defined by the iteration of a polynomial map of the unit simplex to itself appear in the context of population genetic systems evolving under mutation, recombination and weak selection. Although exceptional…
Evolutionary processes proved very useful for solving optimization problems. In this work, we build a formalization of the notion of cooperation and competition of multiple systems working toward a common optimization goal of the population…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
Stochastic evolution equations with compensated Poisson noise are considered in the variational approach with monotone and coercive coefficients. Here the Poisson noise is assumed to be time-homogeneous with $\sigma$-finite intensity…
In this paper we classify a family of three-dimensional real evolution algebras. We also consider an evolution operator for an evolution algebra and find fixed points of this operator for two and three-dimensional cases. Then we construct…
We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. We study basic properties of the algebra. This algebra is…
We address a connection between the energy evolution of the polygonal light-like Wilson exponentials and the geometry of the loop space with the gauge invariant Wilson loops of a variety of shapes being the fundamental degrees of freedom.…
In this paper we use key elements of the Olver's approach to Hamiltonian evolution equations in partial derivatives and propose an algebraic construction appropriate for Hamiltonian evolution systems with constraints.
In this paper we focus on two new families of polynomials which are connected with exponential polynomials and geometric polynomials. We discuss their generalizations and show that these new families of polynomials and their generalizations…
We present a general formalism which allows us to derive the evolution equations describing one-dimensional (1D) and isotropic 2D interfacelike systems, that is based on symmetries, conservation laws, multiple scale arguments, and exploits…
The evolution of sub-spaces in the framework of gravity with higher derivatives is studied. Numerical solutions to exact differential equations are found. It is shown that the initial conditions play crucial role in the space dynamic.…
We prove some separation results for the roots of the generalized Fibonacci polynomials and their absolute values
We classify the four dimensional perfect non-simple evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.
We obtain slow dynamics for self-adjoint semigroups and unitary evolution groups. For semigroups, the slow dynamics is for orbits, and for the average return probability in the case of unitary evolution groups. We present an application to…
This manuscript contains nothing new, but synthesizes known results: For the theoretical population geneticist with a probabilistic background, we provide a summary of some key results on stochastic differential equations. For the…