This paper presents works on reducible polynomials in Galois theory. It gives a fundamental theorem about the Galois ideals associated with a product of groups. These results are used for the practical determination of Galois groups of polynomials of degrees up to 7. : : :). The following tools are used: resolvents (relative or absolute), p-adic methods, Grr obner bases or block systems. In gen...

Player i's payoff in a noncooperative game is generally expressed as a function of the vector of strategies of all players. However, in some games 'simply reducible games' the payoff of player i is a function of two arguments the strategy chosen by i, and the sum of the strategies of all players in the game. Cournot oligopoly, public good provision, costand surplus-sharing, and open access reso...

Reducible matrices are closely associated with the connection of directed graph and can be used in stochastic processes, biology others. In this paper, we investigate reducible solution to a system matrix equations over Hamilton quaternion algebra. We establish necessary sufficient conditions for have derive formula general when it is solvable. Finally, present numerical example illustrate main...

The braid group Bn is the mapping class group of an n-punctured disk. An n-braid is reducible if it has an invariant essential curve system in the punctured disk. We show that for some class of reducible braids (including split braids), finding a reduction system is as easy as finding one element in the ultra summit set.

In this paper, we discuss hamiltonian problems for reducible Powgraphs. The main result is finding, in linear time, the unique hamiltonian cycle, if it exists. In order to obtain this result, two other related problems are solved: finding the hamiltonian path starting at the source vertex and finding the hamiltonian cycle given the hamiltonian path.

In 2007 West Coast Number Theory conference Walsh asked to determine all irreducible polynomials of the form P (x) = x + x + x + 4 with integer exponents i > j > k > 0, such that for some positive integer l the polynomial P (x) is reducible in Z[x]. In this paper we prove that such polynomials are quadrinomials x4m + x3m + x2m + 4, where m is an odd positive integer. In addition, Walsh asked fo...

We propose a new synthesis approach based on the SPP three-level logic minimization of D-reducible Boolean functions. This approach supplies a new tool for efficient minimization, based on the idea of exploiting a Boolean function regularity to get more compact expressions. D-reducible functions can be efficiently synthesized giving rise to new four-level logic forms called DRedSPP. These forms...

Proof. Now suppose that ρp is absolutely reducible and we want to show that for any other λ ∈ Spec(E), ρλ is also absolutely reducible. Note that there exists a finite extension K over Ep such that ρp is reducible. Then there is a vector e1 in the underline space V ′ = V ⊗Ep K such that G is stable over e1. Let χ1 be the character of G acts on e1, χ2 the character G acts on V ′/K · e1. Since χi...

It is proved here that each finite completely reducible linear group of dimension d (over an arbitrary field) can be generated by L 3 d] elements. If a finite linear group G of dimension d is not completely reducible, then its characteristic is a prime, p say, and the factor group of G modulo the largest normal p-subgroup O.p(G) may be viewed as a completely reducible linear group acting on the...

A system for the isolation of anaerobes based upon the use of reducible solid media is described. Plates of reducible media prepared and stored aerobically were reduced before use by incubation in a GasPak jar for 24 h. Clinical specimens for culture were carefully selected. The value of Amies transport medium was confirmed. Selective and nonselective formulations of reducible media were used f...