We give a complete and self-contained proof of folklore theorem which says that in an Alexandrov space the distance between point γ(t) on geodesic γ compact set K is right-differentiable function t. Moreover, value this right-derivative given by negative cosine minimal angle any shortest path to (Theorem 4.3). Our treatment serves as general introduction metric geometry relies only basic elemen...

This is the first part of a paper that classifies 2-compact groups. In this first part we formulate a general classification scheme for 2-compact groups in terms of their maximal torus normalizer pairs. We apply this general classification procedure to the simple 2-compact groups of the A-family and show that any simple 2-compact group that is locally isomorphic to PGL(n+ 1,C) is uniquely N -de...

For n 1, let fxjngnj=1 be n distinct points and let Ln[ ] denote the corresponding Lagrange Interpolation operator. Let W : R ! [0;1). What conditions on the array fxjng1 j n; n 1 ensure the existence of p > 0 such that lim n!1 k (f Ln[f ])W b kLp(R)= 0 for every continuous f : R ! Rwith suitably restricted growth, and some “weighting factor” ? We obtain a necessary and su¢ cient condition for ...

Let C be a convex body in Euclidean d-space IE , i.e., a compact convex set with non-empty interior, and denote by P i n and P (n) the set of polytopes with at most n vertices inscribed to C and the set of polytopes with at most n facets circumscribed to C, respectively. Denote by δ(., .) the symmetric difference metric. Beginning with the work of L. Fejes Tóth [2], there are many investigation...

Residue Number System is a kind of numerical systems that uses the remainder of division in several different moduli. Conversion of a number to smaller ones and carrying out parallel calculations on these numbers will increase the speed of the arithmetic operations in this system. However, the main factor that affects performance of system is hardware complexity of reverse converter. Reverse co...

with respect to the property of being the product of continua of type P, where a continuum C is said to be of type P provided the closure of the complement of C consists of a finite number of components Di, each Di intersecting C in a single point pi, and where T(p,) e (D, pi). It is then shown that N is a subset of an F-set, and finally that N contains a continuum 7r such that T(7r) Dir. As re...