The prime-factor decomposition is a fast computational technique for many important digital signal processing operations, such as the convolution, the discrete Fourier transform, the discrete Hartley transform, and the discrete cosine transform (DCT). In this paper, we present a new prime-factor algorithm for the DCT. We also design a prime-factor algorithm for the discrete sine transform which...

Let N be a positive integer and let A and B be dense subsets of {1, . . . , N}. The purpose of this paper is to establish a good lower bound for the greatest prime factor of ab+ 1 as a and b run over the elements of A and B respectively. 1991 AMS Mathematics Subject Classification. Primary 11N30, Secondary 11L05, keywords: greatest prime factor, Selberg’s sieve, Kloosterman sums.

This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived. Moreover, since most graphs are prime although they can have a product-like structure, also known as approximate graph products, the practical application of the...

It has long been known that the class of connected nonbipartite graphs (with loops allowed) obeys unique prime factorization over the direct product of graphs. Moreover, it is known that prime factorization is not necessarily unique in the class of connected bipartite graphs. But any prime factorization of a connected bipartite graph has exactly one bipartite factor. It has become folklore in s...

let r be a g-graded ring and m be a g-graded r-module. in this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.