In this paper, selection principles are defined and studied in the realm of irresolute topological groups. Especially, s-Menger-bounded s-Rothberger-bounded type covering properties introduced studied.

Let $A_\Phi$ be a matrix valued truncated Toeplitz operator -- the compression of multiplication to vector model space $H^2(E)\ominus \Theta H^2(E)$, where $\Theta$ is non constant inner function. Under supplementary assumptions, we find necessary and sufficient condition that product $A_\Phi A_\Psi$ itself operator.

Let E be a real reflexive and strictly convex Banach space which has a uniformly Gâteaux differentiable norm and let C be a closed convex nonempty subset of E. Strong convergence theorems for approximation of a common zero of a countably infinite family of m-accretive mappings from C to E are proved. Consequently, we obtained strong convergence theorems for a countably infinite family of pseudo...

The combined effect of mean and thermal particle motion on Doppler line shape is evaluated. Optical radiation transverse to the axis of a source flow with semi-angle theta(e) is considered in the limit theta(2)(e) <<1. Expressions for gain and anomalous index of refraction are deduced in terms of radiation frequency and a parameter X(e) which characterizes the ratio of mean to thermal motion in...

in this paper the concepts of fuzzifying β − irresolute functions and fuzzifying β − compactspaces are characterized in terms of fuzzifying β − open sets and some of their properties are discussed.

Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classical functional equations involving shifts by the multiplicative periods. This paper shows that for a certain subclass of period lattices (compatible with the quantization form), quantum thetas satisfy an analog of ano...

T h e homotopic invariance of fixed points of set-valued contractions and nonexpansive mappings is studied. As application, nonlinear alternative principles are given. A LeraySchauder alternative and an antipodal theorem for set-valued nonexpansive mappings are also included.

Motivated by the discovery that the eighth root of the theta series of the E 8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we investigate the question of when an arbitrary element f ∈ Z[[x]]

Tke theta function of a sphere packing gives the number of centers at each distance from the origin. The theta functions of a number of important packings (An, D, , E,, the Leech lattice, and others) and tables of the first fifty or so of their coefficients are given in this paper.