Note on Euler's $\varphi$-function

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

A note on the Hopf-Stiefel function

We give a short elementary proof for a formula for the Hopf–Stiefel function that was found recently by Plagne via additive number theory. c © 2006 Elsevier Ltd. All rights reserved. The Hopf–Stiefel function ◦, introduced by Hopf [3] and Stiefel [8], plays an important role in additive number theory and bilinear algebra; see e.g. Plagne [6] for an overview and many references, for example [5] ...

A Note on Formal Iterated Function Systems

A note on radial basis function computing

This note carries three purposes involving our latest advances on the radial basis function (RBF) approach. First, we will introduce a new scheme employing the boundary knot method (BKM) [1] to nonlinear convection-diffusion problem. It is stressed that the new scheme directly results in a linear BKM formulation of nonlinear problems by using response point-dependent RBFs, which can be solved b...

A Note on the Kasami Power Function

This work is motivated by the observation that the function F2m to F2m defined by x + (x + 1) + a for some a ∈ F2m can be used to construct difference sets. A desired condition is, that the functionφd(x) := x+(x+1) is a 2-to-1 mapping. If s = 1, then the function x has to be APN. If s > 1, then there is up to equivalence only one function known: The function φd is a 2-to-1 mapping if d is the G...