Related papers: Evolution equations for eigenvalues and coefficien…
We provide certain compatibility conditions for m-accretive operators such that the adjoint of the sum is given by the closure of the sum of the respective adjoint. We revisit the proof of well-posedness of the abstract class of partial…
The main purpose of this paper is to present the generalization of the inequalities between the modulus of the polar derivative and the polynomial itself, depending on consideration of the zeros inside and outside of a closed disk and the…
A recently presented method for the study of evolving self-gravitating relativistic spheres is applied to the description of the evolution of relativistic polytropes. Two different definitions of relativistic polytrope, yielding the same…
We consider the class of two-lag linear delay differential equations and develop a series expansion to solve for the roots of the nonlinear characteristic equation. Supporting numerical results are presented along with application of our…
We are concerned with polynomial involutions in characteristic two. In this note, we look for involutions among triangular automorphisms of the four-dimensional polynomial ring in characteristic two and obtain three types of such…
We study the problem of generalization of Oresme numbers with a new sequence of numbers called Oresme polynomials. Moreover, by using the matrix methods for Oresme polynomials, we obtain the identities including the general bilinear…
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…
The evolution equations for the generalized microscopic phase densities are introduced. The evolution equations of average values of microscopic phase densities are derived and a solution of the initial-value problem of the obtained…
The theory of evolutionary computation for discrete search spaces has made significant progress in the last ten years. This survey summarizes some of the most important recent results in this research area. It discusses fine-grained models…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
Starting with some determinants of binomial coefficients which are related to Fibonacci and Lucas polynomials we study similar determinants for some generalizations of these polynomials and their q-analogues.
In this note, we extend an evolutionary stochastic portfolio optimization framework to include probabilistic constraints. Both the stochastic programming-based modeling environment as well as the evolutionary optimization environment are…
We show that the sequence of moduli of the eigenvalues of a matrix polynomial is log-majorized, up to universal constants, by a sequence of "tropical roots" depending only on the norms of the matrix coefficients. These tropical roots are…
An approach to stochastic evolution equations based on a simple generalization of known embedding theorems is presented. It allows for the inclusion of problems which have nonlinear non monotone operators. This is used to discuss the…
A mathematical development of the Walsh transform, Walsh basis, and Walsh coefficients is given. The author was prompted to write this by a wish to give a unified treatment of epistatic coordinates as they are used in evolutionary biology.…
We study continuity of the roots of nonmonic polynomials as a function of their coefficients using only the most elementary results from an introductory course in real analysis and the theory of single variable polynomials. Our approach…
We study the secular dynamics of extrasolar planetary systems by extending the Lagrange-Laplace theory to high order and by including the relativistic effects. We investigate the long-term evolution of the planetary eccentricities via…
We present various identities in the form of convolutions involving Stirling numbers of both kinds, Lah numbers, and binomial coefficients. Certain convolution polynomials are discussed also. The proofs are based on several series…
We consider double parton distributions in the general case in which the virtualities of the interacting partons are different. We elaborate the corresponding evolution equations and their extension to next-to-leading logarithmic accuracy.
Graph polynomials are polynomials assigned to graphs. Interestingly, they also arise in many areas outside graph theory as well. Many properties of graph polynomials have been widely studied. In this paper, we survey some results on the…