To understand the rule of prime numbers on the scenario of natural numbers is one of the most interesting tasks in mathematics today.In this work we present a model that shows how prime numbers appear in the natural sequence 1, 2, 3, ..., where they are hidden, and how to find then with 100%...

Soient : un fibré principal de groupe structural , et 1 1 une extension de à noyau commutatif . Le problème d'étendre le groupe structural de , en , est formulé par la théorie des gerbes. Nous étudions la situation plus générale suivante: considérons une famille d'extensions à noyaux...

The class of all complementary pairs B, ∼B of propositions of CLFO [ = Classical Logic of Finite Order] is partitioned as {{U}, {K}, {N}}, where both {U} and {K} are recursively-enumerable. This leaves {N} as non r.e. and hence necessarily the “home” of the class of all...

We introduce a metric on probability distributions by extending a metric on the sample space to a metric on the space of sample sets. The extension is based on an idea of conversion of sets that minimizes the total cost of the conversions of samples in the sets. In principle this offers a model...

Birkhoff's reduction problem is to find an analytic or meromorphic transformation that reduces a linear system of meromorphic ordinary differential equations to a form in which the coefficients are polynomials. In this article, existing results for this problem are reviewed, and several new ones...

Numerical-analytical study of the three-dimensional nonlinear stochastic partial differential equation, analogous to that proposed by V. N. Nikolaevskii [Recent Advances in Engineering Science (Springer – Verlag, Berlin. 1989)] to describe longitudinal seismic waves, is presented. The equation...

A solution is developed for a convection-diffusion equation describing chemical transport with sorption, decay, and production. The problem is formulated in a finite domain where the appropriate conservation law yields Robin conditions at the ends. When the input concentration is arbitrary, the...

Sei G ein endlicher, ebener, zusammenhängender, schlichter Graph. Die Vielecke von G seien alle bis auf höchstens eins - etwa - Dreiecke, k bezeichne die Anzahl der Ecken von . Dann gibt gibt es mindestens 2 vierfarbige Färbungen der Ecken von G, derart, daß Ecken, die durch eine Kante...

Ist G ein endlicher, schlichter Graph mit chromatischer Zahl n und der vollständige Graph mit n Ecken dann gibt es einen Homomorphismus G > .Is G a finite simple graph with chromatic number n and the complete graph with n vertices then exists a homomorphisme G >