Set maps, umbral calculus, and the chromatic polynomial

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

     

Oscillation of linear difference equations in Banach spaces

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

     

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

The equation

     

Population dynamical behavior of Lotka-Volterra system under regime switching

In this paper, we investigate a Lotka-Volterra system under regime switching

     

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

     

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:

     

Deduction of L. Hörmander's extension of Ásgeirsson's mean value theorem

L. Hörmander's extension of Ásgeirsson's mean value theorem states that if u is a solution of the inhomogeneous ultrahyperbolic equation (Δ_x−Δ_y)u=f, , , then

     

On the support of solutions to the Zakharov-Kuznetsov equation

In this article we prove that sufficiently smooth solutions of the Zakharov-Kuznetsov equation: