Set maps, umbral calculus, and the chromatic polynomial

Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying

     

Homoclinic orbits for a nonperiodic Hamiltonian system

In this paper we prove the existence and multiplicity of homoclinic orbits for first order Hamiltonian systems of the form

     

Stability properties of solutions of linear second order differential equations with random coefficients

The equation

     

Oscillation of linear difference equations in Banach spaces

One can easily show that almost all solutions of the difference equation

     

Cyclic bandwidth with an edge added

B_c(G) denotes the cyclic bandwidth of graph G. In this paper, we obtain the maximum cyclic bandwidth of graphs of order p with adding an edge as follows:

     

Graph colourings and solutions of systems of equations over finite fields

A congruence (p is a prime) is said to be strong homogeneous if it has the form

     

On the uniqueness of discontinuous solutions to the Degasperis-Procesi equation

We prove uniqueness within a class of discontinuous solutions to the nonlinear and third order dispersive Degasperis-Procesi equation

     

Nonoscillation and positivity of solutions to first order state-dependent differential equations with impulses in variable moments

The state-dependent delay differential equation

     

Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

We consider the Sobolev inner product

     

Global bifurcation for equations involving nonhomogeneous operators in an unbounded domain

We study the structure of the set of solutions of a nonlinear equation involving nonhomogeneous operators:

     

On the support of solutions to the Ostrovsky equation with negative dispersion

In this article we prove that sufficiently smooth solutions of the Ostrovsky equation with negative dispersion:

     

A basic class of symmetric orthogonal functions with six free parameters

In a previous paper, we introduced a basic class of symmetric orthogonal functions (BCSOF) by an extended theorem for Sturm-Liouville problems with symmetric solutions. We showed that the foresaid class satisfies the differential equation