A stratification of a set, e.g. an analytic variety, is, roughly, a partition of it into manifolds so that these manifolds fit together “regularly”. Stratification theory was originated by Thom and Whitney for algebraic and analytic sets. It was one of the key ingredients in Mather’s proof of the topological stability theorem [Ma] (see [GM] and [PW] for the history and further applications of s...

A R T I C L E I N F O Strategy, Marketing, Loyalty, Customer, Bajapuik Savings & BPR Gunung Pangilun. Received 20 April 2011 Received in revised form 23 April 2011 Accepted 24 April 2011 Available online 26 April 2011 This study attempts to look and see if the marketing strategy of product, price, and location and upon promotion will affect customer loyalty bajapuik savings on PT.BPR Berok Gunu...

Let l ≥ 3 be a prime, and let p = 2 − 1 be the corresponding Mersenne number. The Lucas-Lehmer test for the primality of p goes as follows. Define the sequence of integers xk by the recursion x0 = 4, xk = x 2 k−1 − 2. Then p is a prime if and only if each xk is relatively prime to p, for 0 ≤ k ≤ l − 3, and gcd(xl−2, p) > 1. We show, in the first section, that this test is based on the successiv...

We consider Williams’ primality test for rational integers of the form 2h ·3n−1. We give an algebraic proof of the test, and we resolve a sign ambiguity. We also show that the conditions of the original test can be relaxed, especially if h is divisible by a power of 2.

We investigate the relationship between the facial structure of the unit ball of an operator algebra A and its algebraic structure, including the hereditary subalgebras and the socle of A. Many questions about the facial structure of A are studied with the aid of representation theory. For that purpose we establish the existence of reduced atomic type representations for certain nonselfadjoint ...

introduction: borago officinalis flower (borage) is a known sedative in herbal medicine the aim of the present study was to evaluate the antinociceptive effect of borage hydroalcoholic extract in formalin test male rats. methods: fifty-six adult male albino wistar rats were randomly divided into seven groups: control groups of a (intact), b (saline), and c (positive control) plus test groups of...