Modular arithmetic with prime moduli has been crucial in present day cryptography. The primes of Mersenne, Solinas, Crandall and the so called IKE-MODP primes have been widely used in efficient implementations. In this paper we study the density of primes with binary signed representation involving a small number of non-zero ±1-digits, and its repercussion in the generation of those primes.

We show that some pieces of cylinders bounded by two parallel straight lines bifurcate in a family of periodic nonrotational surfaces with constant mean curvature and with the same boundary conditions. These cylinders are initial interfaces in a problem of microscale range modeling the morphologies that adopt a liquid deposited in a chemically structured substrate with striped geometry or a liq...

1. Introduction In the past few years, computation of definite integrals to high precision has emerged as a very useful tool in experimental mathematics. In particular, it is often possible to recognize an otherwise unknown definite integral in analytic terms, provided its numerical value can be calculated to high accuracy. As a single example, recently the author, together with Jonathan Borwei...

the well-known tendency of particular maladies to show breed-specificity can be used to infer likely sharing of descent of the causative alleles. As made clear in the volume under review, this is as true of major-gene diseases such as copper toxicosis and various retinopathies, as it is of the more complex and more prevalent cardiomyopathies, cancers, and dermatitis. Conduction of clinical tria...

1. Lie groups and Lie algebras 2 1.1. Definition and examples of Lie groups 2 1.2. Left invariant vector fields and Lie algebras 3 1.3. The exponential map 6 2. Representations of Lie groups and Lie algebras 9 2.1. Definitions and examples 9 2.2. The adjoint representation 9 2.3. Semisimplicity and Schur’s lemma 9 2.4. Haar measure and Weyl’s trick 9 2.5. Characters 9 2.6. Examples 9 2.7. Peter...

Major histocompatibility complex (MHC) 1 genes, in particular those encoded in the I region of the murine H-2, have been shown to be of functional importance in several aspects of immune response regulation. Thus, I region-encoded immune response (It) genes determine responsiveness or unresponsiveness to a number of antigens (1); and T cell recognition of I region gene products is critical for ...

This book may be an important contribution to an argument developing in the scientific world about the origin of man. Darwin's theory of Evolution by Natural Selection was in its time a concept so heretical that it took Darwin, a Christian believer, many years before he could commit himself to expound it. It is now so universally accepted that to question it or to seek to modify it is almost eq...

Imitation is a powerful means of spreading culture teaching people to speak languages, children to play, and surgeons to operate. The basic unit of imitation is a replicator called meme which, like genes, carries and spreads information. The concepts of memes and the science of memetics were introduced by biologist Richard Dawkins in 1976. Since then, memes have been found everywhere, used to e...

Suppose that r and n are non-negative integers satisfying r + n > 0. Denote the moduli stack over SpecZ of smooth elliptic curves with n marked points and r non-zero tangent vectors by M1,n+r⃗. Here the n marked points and the anchor points of the r tangent vectors are distinct. Taking each tangent vector to its anchor point defines a morphism M1,n+r⃗ → M1,n+r that is a principal Gm-bundle. The D...