On limit points of Laplacian spectral radii of graphs

The study of limit points of eigenvalues of adjacency matrices of graphs was initiated by Hoffman [A.J. Hoffman, On limit points of spectral radii of non-negative symmetric integral matrices, in: Y. Alavi et al. (Eds.), Lecture Notes Math., vol. 303, Springer-Verlag, Berlin, Heidelberg, New York, 1972, pp. 165-172]. There he described all of the limit points of the largest eigenvalue of adjacency matrices of graphs that are no more than . In this paper, we investigate limit points of Laplacian spectral radii of graphs. The result is obtained: Let , β₀=1 and be the largest positive root of

     

Population dynamical behavior of Lotka-Volterra system under regime switching

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

     

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

     

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:

     

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

     

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

     

Relaxation and regularity in the calculus of variations

In this work we prove that, if L(t,u,ξ) is a continuous function in t and u, Borel measurable in ξ, with bounded non-convex pieces in ξ, then any absolutely continuous solution to the variational problem