We enumerate and describe the Sylow p-groups of the group of polynomial permutations of the integers mod p . MSC 2000: primary 20D20, secondary 11T06, 13M10, 11C08, 13F20, 20E18.

The problem of a multiplier ω(n) of the Nörlund means and convex maps of the unit disc is being considered again, but with a multiplier ω(n) of different form then that appeared by Ziad S. Ali in [1]. With this we would have brought up again in a rather unified approach the results of G. Pólya, and I.J. Schonberg in [7], T. Basgoze, J.L. Frank and F.R. Keogh in [3], and Ziad S. Ali in [2]. The ...

We argue that the study of the statistics of the landscape of string vacua provides the first potentially predictive – and also falsifiable – framework for string theory. The question of whether the theory does or does not predict low energy supersym-metry breaking may well be the most accessible to analysis. We argue that low energy – possibly very low energy – supersymmetry breaking is likely...

We introduce a variation of chip-firing games on connected graphs. These ‘burn-off’ games incorporate the loss of energy that may occur in the physical processes that classical chipfiring games have been used to model. For a graph G = (V,E), a configuration of ‘chips’ on its nodes is a mapping C : V → N. We study the configurations that can arise in the course of iterating a burn-off game. Afte...

Cyber defenses based on dynamic platform techniques have been proposed as a way to make systems more resilient to attacks. These defenses change the properties of the platforms in order to make attacks more complicated. Unfortunately, little work has been done on measuring the effectiveness of these defenses. In this work, we first measure the protection provided by a dynamic platform technique...

Following the classical approach of Pólya-Schur theory [14] we initiate in this paper the study of linear operators acting on R[x] and preserving either the set of positive univariate polynomials or similar sets of non-negative and elliptic polynomials.

Let G be any abelian group and {asGs}ks=1 be a finite system of cosets of subgroups G1, . . . , Gk. We show that if {asGs} k s=1 covers all the elements of G at least m times with the coset atGt irredundant then [G : Gt] 6 2 and furthermore k > m + f([G : Gt]), where f( ∏ r i=1 p αi i ) = ∑ r i=1 αi(pi − 1) if p1, . . . , pr are distinct primes and α1, . . . , αr are nonnegative integers. This ...

Let g = g0 ⊕ g1 be a simple Z2-graded Lie algebra and let b0 be a fixed Borel subalgebra of g0. We describe and enumerate the abelian b0-stable subalgebras of g1.

A famous “curious identity” of Wallis gives a representation of the constant π in terms of a simply structured infinite product of fractions. Sondow and Yi [Amer. Math. Monthly 117 (2010), 912-917] identified a general scheme for evaluating Wallis-type infinite products. The main purpose of this paper is to discuss an interpretation of the scheme by means of Pólya urn models.

For many years, people have considered various problems in the enumeration of graphs, beginning with the enumeration of trees. Extensive work on the enumeration of maps did not begin until Tutte's work in the 1960's; however, one map enumeration problem| the determination of the number of combinatorially inequivalent 3-dimensional convex polytopes|is over a century old. Traditionally an map has...