Related papers: On hereditary models of polymers
A family of systems related to a linear and bilinear evolution of roots of polynomials in the complex plane is considered. Restricted to the line, the evolution induces dynamics of the Coulomb charges in external potentials, while its fixed…
Conditions for linear integral operators on $L_p$ over measure spaces to satisfy the polynomial covariance type commutation relations are described in terms of defining kernels of the corresponding integral operators. Representation by…
This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of…
The breeder's equation is a cornerstone of quantitative genetics and is widely used in evolutionary modeling. The equation which reads R=h^{2}S relates response to selection R (the mean phenotype of the progeny) to the selection…
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…
We start with a Riemann-Hilbert Problems (RHP) with canonical normalization whose sewing functions depends on two or more additional variables. Using Zakharov-Shabat theorem we are able to construct a family of ordinary differential…
We compare exact and SU(2)-cluster approximate calculation schemes to determine dynamics of the second-harmonic generation model using its reformulation in terms of a polynomial Lie algebra $su_{pd}(2)$ and related spectral representations…
The structural constants of an evolution algebra is given by a quadratic matrix $A$. In this work we establish equivalence between nil, right nilpotent evolution algebras and evolution algebras, which are defined by upper triangular matrix…
We construct a set $M_d$ whose points parametrize families of Meixner polynomials in $d$ variables. There is a natural bispectral involution $b$ on $M_d$ which corresponds to a symmetry between the variables and the degree indices of the…
Let a sequence $(P_n)$ of polynomials in one complex variable satisfy a recurre ce relation with length growing slowlier than linearly. It is shown that $(P_n) $ is an orthonormal basis in $L^2_{\mu}$ for some measure $\mu$ on $\C$, if and…
We consider a family of nonlinear recurrences with the Laurent property. Although these recurrences are not generated by mutations in a cluster algebra, they fit within the broader framework of Laurent phenomenon algebras, as introduced…
The replicator equations are a family of ordinary differential equations that arise in evolutionary game theory, and are closely related to Lotka-Volterra. We produce an infinite family of replicator equations which are Liouville-Arnold…
The Hultman numbers enumerate permutations whose cycle graph has a given number of alternating cycles (they are relevant to the Bafna-Pevzner approach to genome comparison and genome rearrangements). We give two new interpretations of the…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
The aim of this paper is to present a generalization of Lunn-Senior's mathematical model of isomerism in organic chemistry. The main idea of Lunn and Senior is that if the type of isomerism is fixed, a molecule with a fixed skeleton and d…
We use the method of similar operators to study a mixed problem for a differential equation with an involution and an operator-valued potential function. The differential operator defined by the equation is transformed into a similar…
We study linear integro-differential equations in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations are covered by the class of…
We study modular and integral flow polynomials of graphs by means of subgroup arrangements and lattice polytopes. We introduce an Eulerian equivalence relation on orientations, flow arrangements, and flow polytopes; and we apply the theory…
Integral operators play an important role modeling various physical and biological processes. In this article we consider such a nonlinear integro-differential equation. We study several properties of equilibrium solutions of the operator…