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

     

Some functional inverse Santaló inequalities

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

     

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)

     

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

     

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

     

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

     

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 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

     

Convergence of cascade algorithms by frequency approach

Starting with an initial function ?₀, the cascade algorithm generates a sequence by cascade operator Qa defined by

     

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 ,

     

The left-definite spectral theory for the Dunkl-Hermite differential-difference equation

In this paper, we develop the left-definite spectral theory associated with the self-adjoint operator A_μ in , generated from the Dunkl second-order Hermite differential equation

     

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