An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum’s arithmetic autocorrelations. Large families of sequences are constructed with ideal (vanishing) arithmetic cross-correlations. These sequences are decimations of the 2-adic expansions of rational numbers p/q such that 2 is a primitive root modulo q.

To achieve high resource utilization for multi-issue Digital Signal Processors (DSPs), production compilers commonly include variants of the iterative modulo scheduling algorithm. However, excessive cyclic data dependences, which exist in communication and media processing loops, often prevent the modulo scheduler from achieving ideal loop initiation intervals. As a result, replicated functiona...

motivated by an arens regularity problem, we introduce the concepts of matrix banach space and matrix banach algebra. the notion of matrix normed space in the sense of ruan is a special case of our matrix normed system. a matrix banach algebra is a matrix banach space with a completely contractive multiplication. we study the structure of matrix banach spaces and matrix banach algebras. then we...

We prove the existence of a subset, with positive natural density, squarefree integers n>0 such that 4–rank ideal class group ℚ(-n,n) is ω 3 (n)-1, where (n) number prime divisors n are modulo 4. Recall for groups associated to ℚ(n) or ℚ(-n) an analogous subset does not exist.

An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum’s arithmetic autocorrelations. Large families of sequences are constructed with ideal (vanishing) arithmetic crosscorrelations. These sequences are decimations of the 2adic expansions of rational numbers p=q such that 2 is a primitive root modulo q.

We show that a ring $R$ has stable range one if and only every left unit lifts modulo principal ideal. also quasi-morphic it is uniquely generated. Thus we answer in the affirmative two questions raised by W. K. Nicholson.

Let k be an algebraic number eld with maximal order o k and let m 0 be an ideal of o k. We develop an algorithm for the computation of the multiplicative group (o k =m 0) of the residue class ring o k =m 0. It is applied to the computation of the ray class group Cl m k modulo m = m 0 m 1 , where m 1 denotes a formal product of real innnite places, and also to the computation of the conductor of...

In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.

In 2005, A. Abdollahi and A. Rejali, studied the relations betweenparadoxical decomposition and configuration for semigroups. In thepresent paper, we introduce one other concept of amenability typeon semigroups and groups which includes amenability of semigroupsand inner-amenability of groups. We have extend the previous knownresults to semigroups and groups satisfying this concept.