Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof. Lu Jianke

In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.     

In risposta al richiamo di priorità del Prof. R. Occhipinti

Rendiconti del Circolo Matematico di Palermo Series 1 -     

Dedication on the occasion of Professor Xiaqi Ding’s 80th birthday

This volume is dedicated to Professor Xiaqi Ding, an academician of the Chinese Academy of Sciences, on the occasion of his eightieth birthday.     

Julia sets of permutable Holomorphic maps Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Let f and g be two permutable transcendental holomorphic maps in the plane. We shall discuss the dynamical properties of f, g and f o g and prove, among other things, that if either f has no wandering domains or f is of bounded type, then the Julia sets of f and f(g) coincide.     

New series of odd non-congruent numbers Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

We determine all square-free odd positive integers n such that the 2-Selmer groups Sn and Sn of the elliptic curve En: y2 = x(x -n)(x - 2n) and its dual curve En: y2 = x3 6nx2 n2x have the smallest size: Sn = {1}, Sn = {1,2,n,2n}. It is well known that for such integer n, the rank of group En(Q) of the rational points on En is zero so that n is a non-congruent number. In this way we obtain many new series of elliptic curves En with rank zero and such series of integers n are non-congruent numbers.