Spider Covers and Their Applications

Covers of the Integers with Odd Moduli and Their Applications

In this paper we construct a cover {as(mod ns)}s=1 of Z with odd moduli such that there are distinct primes p1, . . . , pk dividing 2 n1 − 1, . . . , 2k − 1 respectively. Using this cover we show that for any positive integer m divisible by none of 3, 5, 7, 11, 13 there exists an infinite arithmetic progression of positive odd integers the mth powers of whose terms are never of the form 2 ± p w...

Magentotactic bacteria and their applications

Magentotactic bacteria are the types of bacteria capable of orientation in an external magnetic field because of the ability to produce structures called magnetosomes. Magnetosomes, nanometer-scale structures, are present in most of the magnetotactice bacteria. They are intracellular organelles composed of magnetic iron mineral crystals individually surrounded by a phospholipid layer. Because o...

Sequential Methods and Their Applications

Spider Silk Composites and Applications

In the past few years a number of reviews, books and journal articles featuring silks have been published. Silks are produced by over 41,000 species of spiders (class Arachnida) and by many insects (terrestrial and aquatic), particularly in the order Lepidoptera (Foelix, 1996); they are defined as externally spun fibrous material generated from protein secretions. The cocoon silk from the domes...

Economical covers with geometric applications

A cover of a hypergraph is a collection of edges whose union contains all vertices. Let H = (V, E) be a k-uniform, D-regular hypergraph on n vertices, in which no two vertices are contained in more than o(D/e log D) edges as D tends to infinity. Our results include that if k = o(log D), then there is a cover of (1 + o(1))n/k edges, extending the known result that this holds for fixed k. On the ...