Some functional inverse Santaló inequalities

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

     

Duality techniques for certain integral transforms to be starlike

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

     

Derivatives of the L-cosine transform

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

     

Simultaneous Diophantine approximation on manifolds and Hausdorff dimension

Let M be an m-dimensional, C^k manifold in , for any , and for any τ>0 let

     

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:

     

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)

     

A min-max theorem for complex symmetric matrices

We optimize the form Re x^tTx to obtain the singular values of a complex symmetric matrix T. We prove that for ,

     

Bounded perturbations of homogeneous quasilinear operators using bifurcations from infinity

This paper deals with existence results for the following nonlinear problem with the Dirichlet p-Laplacian Δ_p in a bounded domain :

     

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

     

Norm estimates of almost Mathieu operators

We estimate the norm of the almost Mathieu operator , regarded as an element in the rotation C^*-algebra . In the process, we prove for every λ∈R and the inequality

     

On a factorization of homeomorphisms of the circle possessing periodic points

We prove that for every orientation-preserving homeomorphism possessing periodic points of order n there exist a homeomorphism such that Tn=id and a homeomorphism without periodic points except fixed points such that

F=Tq○G     

Global branch from the second eigenvalue for a semilinear Neumann problem in a ball

Let (n?3) be a ball, and let f∈C³. We are concerned with the Neumann problem

     

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

     

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