Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices

Let be the set of entrywise nonnegative n×n matrices. Denote by r(A) the spectral radius (Perron root) of . Characterization is obtained for maps such that r(f(A)+f(B))=r(A+B) for all . In particular, it is shown that such a map has the form

     

Functional calculi for convolution operators on a discrete, periodic, solvable group

Suppose T is a bounded self-adjoint operator on the Hilbert space L²(X,μ) and let

     

Derivatives of the L-cosine transform

The L^p-cosine transform of an even, continuous function is defined by

     

Wave patterns, stability, and slow motions in inviscid and viscous hyperbolic equations with stiff reaction terms

We study the behavior of solutions to the inviscid (A=0) and the viscous (A>0) hyperbolic conservation laws with stiff source terms

     

Duality techniques for certain integral transforms to be starlike

For β<1, let denote the class of all normalized analytic functions f such that

     

Generation, propagation, and annihilation of metastable patterns

We study the full-time dynamics of the initial value problem, for u^ε=u^ε(x,t),

     

Some functional inverse Santaló inequalities

Let be a log-concave function and for z∈Rn, define

     

On the numerical radius of operators in Lebesgue spaces

We show that the absolute numerical index of the space Lp(μ) is (where ). In other words, we prove that

     

Complete decomposition of Dickson-type polynomials and related Diophantine equations

We characterize decomposition over C of polynomials defined by the generalized Dickson-type recursive relation (n?1)

     

Intersections of Leray complexes and regularity of monomial ideals

For a simplicial complex X and a field K, let .It is shown that if X,Y are complexes on the same vertex set, then for k?0

     

Bounded positive entire solutions of singular quasilinear elliptic equations

Suppose that β?0 is a constant and that is a continuous function with R₊:=(0,∞). This paper investigates N-dimensional singular, quasilinear elliptic equations of the form

     

Regularity for a fourth-order critical equation with gradient nonlinearity

Given Ω a smooth bounded domain of Rn, n?3, we consider functions that are weak solutions to the equation

     

The twelfth moment of central values of Hecke series

Let H_j(s) be the Hecke L-function attached to the Maass wave form for the jth eigenvalue of the hyperbolic Laplacian acting in the Hilbert space of automorphic functions for the full modular group. The following mean value estimate for the central values is proved: