A Theorem on Rational Integral Symmetric Functions

On Sandwich Theorem for Certain Subclasses of Symmetric Analytic Functions Associated with Noor Integral Operator

In this paper, we obtain some interesting properties of differential subordination and superordination for the classes of symmetric analytic functions in the unit disk, by applying Noor integral operator. We investigate several sandwich theorems on basis of this theory.

A Fatou-type Theorem for Harmonic Functions on Symmetric Spaces

Integral Specialization of Families of Rational Functions

Suppose C is an algebraic curve, f is a rational function on C defined over Q, and A is a fractional ideal of Q. If f is not equivalent to a polynomial, then Siegel’s theorem gives a necessary condition for the set C(Q)∩f−1(A) to be infinite: C is of genus 0 and the fiber f−1(∞) consists of two conjugate quadratic real points. We consider a converse. Let P be a parameter space for a smooth fami...

Counting rotation symmetric functions using Polya's theorem

Homogeneous rotation symmetric (invariant under cyclic permutation of the variables) Boolean functions have been extensively studied in recent years due to their applications in cryptography. In this paper we give an explicit formula for the number of homogeneous rotation symmetric functions over the finite field GF(pm) using Polya’s enumeration theorem, which completely solves the open problem...

Noncommutative Vieta Theorem and Symmetric Functions

There are two ways to generalize basic constructions of commutative algebra for a noncommutative case. More traditional way is to define commutative functions like trace or determinant over noncommuting variables. Beginning with [6] this approach was widely used by different authors, see for example [5], [15], [14], [12], [11], [7]. However, there is another possibility to work with purely nonc...