where dA is the normalized area measure in D. The case where α = 0 is known as the (unweighted) Bergman space, often simply denoted by A2. Let φ be an analytic map from the open unit disk D into itself. The operator that takes the analytic map f to f ◦ φ is a composition operator and is denoted by Cφ . A natural generalization of a composition operator is an operator that takes f to ψ · f ◦ φ, ...

We introduce the sequence spaces [ ˆ w(M)] and [ ˆ w(M)] θ of strong almost convergence and lacunary strong almost convergence respectively defined by the Orlicz function M. We establish certain inclusion relations and show that the above spaces are same for any bounded sequences. 1. Definitions and notations A sequence x ∈ l ∞ , the space of bounded sequences x = (x k), is said to be almost co...

In this chapter we discuss basic terminology and notation for graphs, some fundamental algorithms, and a few other mathematical preliminaries. We denote the set of integers by , the set of real numbers by , the set of complex numbers by , and the set of rationals by . For a set X of numbers, X denotes the subset of positive numbers in X , and X 0 the subset of nonnegative numbers. The set of po...

The purpose of this first set of lecture notes is to summarize background material on linear algebra and analysis that is used throughout the course. Proofs of most of the stated facts may be found in the references listed at the end of the notes. It is my intention that this first set of notes will mostly serve as a useful reference later in the course. The theory of quantum information is bas...

(IAS/Princeton). Any electrically charged gauge boson outside of the Standard Model is generically denoted W 0. A W 0 always couples to two diierent avors of fermions, similar to the W boson. In particular, if a W 0 couples quarks to leptons it is a leptoquark gauge boson. The most attractive candidate for W 0 is the W R gauge boson associated with the left-right symmetric models 1]. These mode...

(IAS/Princeton). Any electrically charged gauge boson outside of the Standard Model is generically denoted W 0. A W 0 always couples to two diierent avors of fermions, similar to the W boson. In particular, if a W 0 couples quarks to leptons it is a leptoquark gauge boson. The most attractive candidate for W 0 is the W R gauge boson associated with the left-right symmetric models 1]. These mode...

The main purpose of this paper is to describe two examples. The first is that of an almost continuous, Baire class two, non-extendable function f : [0, 1] → [0, 1] with a Gδ graph. This answers a question of Gibson [15]. The second example is that of a connectivity function F : R → R with dense graph such that F−1(0) is contained in a countable union of straight lines. This easily implies the e...

A proper edge t-coloring of a graph is a coloring of its edges with colors 1, 2, ..., t such that all colors are used, and no two adjacent edges receive the same color. For any integer n ≥ 3, all possible values of t are found, for which there exists such a proper edge t-coloring of the simple cycle C(n), which uses for each pair of adjacent edges either consecutive colors or the first and the ...