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:

     

On a class of analytic functions with missing coefficients

Let T_n(A,B,α) denote the class of functions of the form:

     

Layered solutions for a semilinear elliptic system in a ball

We consider the following system of Schrödinger-Poisson equations in the unit ball B₁ of R³:

     

Stable solutions of linear systems involving long chain of matrix multiplications

This paper is concerned with solving linear system (I_n+B_L?B₂B₁)x=b arising from the Green’s function calculation in the quantum Monte Carlo simulation of interacting electrons. The order of the system and integer L are adjustable. Also adjustable is the conditioning of the coefficient matrix to give rise an extreme ill-conditioned system. Two numerical methods based on the QR decomposition with column pivoting and the singular value decomposition, respectively, are studied in this paper. It is proved that the computed solution by each of the methods is weakly backward stable in the sense that the computed is close to the exact solution of a nearby linear system

     

Solitary charged waves interacting with the electrostatic field

In this paper we study the semiclassical limit for the following system of Schrödinger-Maxwell equations in the unit ball B₁ of R³:

     

Singular perturbations of abstract wave equations

Given, on the Hilbert space H₀, the self-adjoint operator B and the skew-adjoint operators C₁ and C₂, we consider, on the Hilbert space H?D(B)⊕H₀, the skew-adjoint operator

     

Generalized Bebiano-Lemos-Providência inequalities and their reverses

We improve Bebiano-Lemos-Providência inequality: For A,B?0

     

Multi-dimensional explosion due to a concentrated nonlinear source

Let D be a bounded n-dimensional domain, ∂D be its boundary, be its closure, T be a positive real number, B be an n-dimensional ball {x∈D:|x−b|<R} centered at b∈D with a radius R, be its closure, ∂B be its boundary, ν denote the unit inward normal at x∈∂B, and χ_B(x) be the characteristic function. This article studies the following multi-dimensional parabolic first initial-boundary value problem with a concentrated nonlinear source occupying :

     

Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls

For 0?σ<1/2 we characterize Carleson measures μ for the analytic Besov-Sobolev spaces on the unit ball Bn in Cn by the discrete tree condition

     

Browder spectra of upper-triangular operator matrices

Let be a 2×2 upper triangular operator matrix acting on the Hilbert space H⊕K. In this paper, for given operators A and B, we prove that

     

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

     

Browder spectra for upper triangular operator matrices

When A∈B(H) and B∈B(K) are given, we denote by MC the operator acting on the infinite dimensional separable Hilbert space H⊕K of the form . In this paper, we prove that

     

Cap pairings and spectral sequences

Let be a small category. For an -diagram X and -diagrams A and B of pointed spaces, each pairing X∧A→B satisfying the projection formula induces a pairing . In this note we show that there is an induced pairing of homotopy spectral sequences compatible with abutments in the sense that

     

Integral-type operators acting between weighted-type spaces on the unit ball

Let B denote the unit ball in Cⁿ and H(B) the space of all holomorphic functions on B. We study the boundedness and compactness of the following integral-type operators

     

On the structure of positive radial solutions to an equation containing a p-Laplacian with weight

Let A,B:(0,∞)?(0,∞) be two given weight functions and consider the equation