We assume that numbers are represented in base B with B = 264. A digit in base B is called a limb. M(n) is the time needed to multiply n limb numbers. We assume thatM(Cn) is approximately CM(n), which meansM(n) is mostly linear, which is the case when handling very large numbers with the Schönhage-Strassen multiplication [5]. log(n) means the natural logarithm of n. log2(n) is log(n)/ log(2). S...

Residue Number System (RNS) is a method for representing an integer as an n-tuple of its residues with respect to a given base. Since RNS has inherent parallelism, it is actively researched to implement fast public-key cryptography using RNS. This paper derives the exact error bound of approximation on the Cox-Rower architecture which was proposed for RNS modular multiplication. This is the tig...

 Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

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...

There is a body of literature concerning or related to the detection of source code texts that have the same origin. This paper presents a survey of such literature, and provides an overview of the topic.

The concept of index and co-index a paracompact Hausdorff space X equipped with free involutions relative to the antipodal action on spheres were introduced by Conner Floyd [2] . In this paper, we extend notion for G -spaces , where is finitistic = S 1 (with complex multiplication) 3 quaternionic multiplication). We prove that less than or equal mod 2 cohomology also compute ring orbit / whose ...

In a series of papers we classify the possible torsion structures rational elliptic curves base-extended to number fields fixed degree. this paper turn our attention question how an curve with complex multiplication defined over rationals grows quadratic fields. We go further and give explicit characterization where in terms some invariants attached curve.

Silica-bonded n-propyltriethylene-tetramine (SBNPTT) was found as an efficient solid base for the synthesis of 2-amino-5-oxo-5,6,7,8-tetrahydro-4H-chromenes. Chromene derivatives were obtained via the three-component condensation reaction of aromatic aldehydes, malononitrile, and dimedone at 80 oC under solvent-free conditions. The heterogeneous solid base showed much the same efficiency when u...