Topic
Product (mathematics)
About: Product (mathematics) is a research topic. Over the lifetime, 44382 publications have been published within this topic receiving 377809 citations.
Papers published on a yearly basis
Papers
More filters
[...]
TL;DR: The notion of strongly G-graded rings was introduced by Dade as discussed by the authors, who showed that R × R → 1 is a group graded ring if and only if R1 is a crossed product R1 * G.
Abstract: Let R be a group graded ring . The map ( , ): R × R →1 defined by: (x,y) = (xy)1 , is an inner product on R. In this paper we investigate aspects of nondegeneracy of the product, which is a generalization of the notion of strongly G —graded rings,introduced by Dade. We show that various chain conditions are satisfied by R if and only if they are satisfied by R1 , and that when R1 is simple artinian, then R is a crossed product R1 * G. We give conditions for simple R-modules to be completely reducible R1 -modules . Finally, we prove an incomparability theorem,when G is finite abelian.
151 citations
151 citations
TL;DR: In this article, the authors dealt with the reaction between two solids A and B to form one or more product phases (A m B n ), during which the reaction has to be attributed to a transport of the reactants across phase boundaries and through reaction product.
Abstract: This chapter deals essentially with the reaction between two solids A and B to form one or more product phases (A m B n ). During the course of this heterogeneous solid-solid reaction A m B n separates the reactants spatially. Therefore the progress of the reaction has to be attributed to a transport of the reactants across phase boundaries and through the reaction product.
150 citations
TL;DR: The first algorithm solves the problem of computingitnesses for the Boolean product of two matrices, and the second algorithm is a nearly linear time deterministic procedure for constructing a perfect hash function for a givenn-subset of {1,...,m}.
Abstract: Small sample spaces with almost independent random variables are applied to design efficient sequential deterministic algorithms for two problems. The first algorithm, motivated by the attempt to design efficient algorithms for the All Pairs Shortest Path problem using fast matrix multiplication, solves the problem of computing witnesses for the Boolean product of two matrices. That is, if A and B are two n by n matrices, and C = AB is their Boolean product, the algorithm finds for every entry C>sub /sub sub /sub sub /sub< = 1. Its running time exceeds that of computing the product of two n by n matrices with small integer entries by a polylogarithmic factor. The second algorithm is a nearly linear time deterministic procedure for constructing a perfect hash function for a given n-subset of {1,?,m}.
150 citations
TL;DR: In this article, the binding energy of an excitonic molecule is calculated as a function of electron-to-hole mass ratio and of anisotropy in the hole bands, which is a product of a Hylleraas and Ore correlated excition function and an overlap function of the hole-hole separation.
Abstract: The binding energy of the excitonic molecule is calculated as a function of electron-to-hole mass ratio and of anisotropy in the hole bands. A variational wave function is used which is a product of a Hylleraas and Ore correlated excition function and an overlap function of the hole-hole separation. The results are tabulated for CuCl, CuBr, ${\mathrm{Cu}}_{2}$O, and for a number of II-VI compounds.
150 citations