A par t i t ion of n is a mul t i se t of positive integers whose sum is n. The summands , i.e., the e lements of the mult iset , are called parts. Let 9 , be the set of all par t i t ions of n, and let P ( n ) = [ 9 , [ . Put the un i fo rm probabi l i ty measure on ~ , ; mn({A}) = 1 / P ( n ) for all h ~ , . T h e n any real va lued func t ion X~ on ~ , can be regarded as a r a n d o m variab...

One of the main problems in all-optical packet-switched networks is the lack of optical buffers, and one feasible technology for the constructions of optical buffers is to use optical crossbar Switches and fiber Delay Lines (SDL). In this two-part paper, we consider SDL constructions of optical queues with a limited number of recirculations through the optical switches and the fiber delay lines...

1382 NOTICES OF THE AMS VOLUME 47, NUMBER 11 I n Part I of this article we introduced “lattices” L ⊂ Rn and described some of their relations with other branches of mathematics, focusing on “theta functions”. Those ideas have a natural combinatorial analogue in the theory of “linear codes”. This theory, though much more recent than the study of lattices, is more accessible, and its numerous app...

Let α = −2+ √ −1 be a root of the polynomial p(x) = x +4x+5. It is well-known that the pair (α, {0, 1, 2, 3, 4}) forms a canonical number system, i.e., that each γ ∈ Z[α] admits a finite representation of the shape γ = a0 + a1α+ · · ·+ alα with ai ∈ {0, 1, 2, 3, 4}. The set T of points with integer part 0 in this number system

The use of dental implants in replacing missing teeth is an integral part of restorative dental treatment. Use of conventional complete dentures is associated with several problems such as lack of denture stability, support and retention. However, when mandibular complete dentures were used with two or more implants, an improvement in the patients' psychological and social well-being could be s...

For the past few years, Philadelphia has been experiencing a restaurant “boom’ ‘— a renaissance of creative dining establishments. 1.2In addition to exotic foods prepared in unusual or extravagant ways, a significant part of this gastronomic revolution has been the prominence of wine as a part of the meal and an accompanying increase in interest in types of wines and how they are served. One of...

The series constitute ‘ideas in progress,’ after the notion described by I.J. Good in ‘The Scientist Speculates.’ Good also describes ideas about ideas as ‘partly baked ideas’ believing that “ ... it is often better to be stimulating and wrong than boring and right.” While the papers do not take this tenet as an excuse for licence at the expense of rigour, they are exploratory and the ideas may...

This paper is the second part of our comprehensive study on the structure of the solutions for the following Chern-Simons-Higgs equation: { ∆u+ 1 ε2 e (1− e) = 4π ∑N j=1 δpj , in Ω, u is doubly periodic on ∂Ω, (0.1) where Ω is a parallelogram in R and ε > 0 is a small parameter. In part 1 [28], we proved the non-coexistence of different bubbles in the bubbling solutions and obtained an existenc...

the chromatic number of a graph g, denoted by χ(g), is the minimum number of colors such that g can be colored with these colors in such a way that no two adjacent vertices have the same color. a clique in a graph is a set of mutually adjacent vertices. the maximum size of a clique in a graph g is called the clique number of g. the turán graph tn(k) is a complete k-partite graph whose partition...