In the present investigation we solve Fekete–Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions.

Fekete’s lemma is a well known combinatorial result on number sequences: we extend it to functions defined on d-tuples of integers. As an application of the new variant, we show that nonsurjective d-dimensional cellular automata are characterized by loss of arbitrarily much information on finite supports, at a growth rate greater than that of the support’s boundary determined by the automaton’s...

Given a set of rectangular items of different sizes and a rectangular container, the aim of the bi-dimensional Orthogonal Packing Problem (OPP-2 for short) is to decide whether there exists a non-overlapping packing of the items in this container. The rotation of items is not allowed. In this paper we present a new exact algorithm for solving OPP-2, based upon the characterization of solutions ...

We prove sieve-type lower bounds for the Mahler measure of polynomials on subarcs of the unit circle of the complex plane. This is then applied to give an essentially sharp lower bound for the Mahler measure of the Fekete polynomials on subarcs.

Abstract. In this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order b, using a linear multiplier differential operator D λ,μf(z). In this paper, for these classes the Fekete–Szegö problem is completely solved. Various new special cases of our results are also pointed out.

We consider a compact CR manifold with transversal locally free circle action endowed an S1-equivariant positive line bundle. prove that certain weighted Fourier–Szeg? kernel of the sections in high tensor powers admits full asymptotic expansion. As consequence, we establish equivariant Kodaira embedding theorem.

Many Bayesian clinical trial methods are based on random inequalities. For some distribution families, these inequalities can be computed in closed form. For example, [1] gives closed-form solutions to computing P(X > Y) when X and Y are either independent normal or independent gamma random variables. However the case of beta random variables is very important and no closed form solution for th...

The minimizers of the anisotropic fractional isoperimetric inequality with respect to a convex body $ K in \mathbb{R}^n are shown be equivalent star bodies whenever is strictly and unconditional. From this Pólya-Szeg? principle for seminorms derived by using symmetrization bodies.