A német Pz. IV-es Jagdpanzer vadászpáncélosok

Pe Ct Iv Es . . Interest Rate Modeling : a Conscientious Choice

Growth in SL3(Z/pZ)

Let G = SL3(Z/pZ), p a prime. Let A be a set of generators of G. Then A grows under the group operation. To be precise: denote by |S| the number of elements of a finite set S. Assume |A| < |G| for some ǫ > 0. Then |A ·A ·A| > |A| , where δ > 0 depends only on ǫ. We will also study subsets A ⊂ G that do not generate G. Other results on growth and generation follow.

PZ: A Z-based Formalism for Modeling Probabilistic Behavior

Probabilistic techniques in computer programs are becoming more and more widely used. Therefore, there is a big interest in the formal specification, verification, and development of probabilistic programs. In our work-in-progress project, we are attempting to make a constructive framework for developing probabilistic programs formally. The main contribution of this paper is to introduce an int...

Growth and generation in SL2(Z/pZ

We show that every subset of SL2(Z/pZ) grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators A of SL2(Z/pZ), every element of SL2(Z/pZ) can be expressed as a product of at most O((log p)) elements of A ∪ A, where c and the implied constant are absolute.

The Lotka–Volterra equation over a finite ring Z/pZ

The discrete Lotka–Volterra equation over p-adic space was constructed since p-adic space is a prototype of spaces with non-Archimedean valuations and the space given by taking the ultra-discrete limit studied in soliton theory should be regarded as a space with the non-Archimedean valuations given in my previous paper (Matsutani S 2001 Int. J. Math. Math. Sci.). In this paper, using the natura...