A Two-Cardinal Theorem and a Combinatorial Theorem

Cardinal p and a theorem of Pelczynski

Are two compactifications of ω homeomorphic if their remainders are homeomorphic? For metrizable compactifications the question was answered affirmatively by Pelzcynski. Can the same happen for some non-metrizable remainders? We consider the case when the remainder is D for some uncountable τ . We show that the answer is affirmative if τ < p and negative if τ = c. We prove that every isomorphis...

A Combinatorial Theorem for Trees

A GENERALIZATION OF A JACOBSON’S COMMUTATIVITY THEOREM

In this paper we study the structure and the commutativity of a ring R, in which for each x,y ? R, there exist two integers depending on x,y such that [x,y]k equals x n or y n.

Cardinal multiwavelets and the sampling theorem

This paper considers the classical Shannon sampling theorem in multiresolution spaceswith scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal. They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar function, which...

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.