In this work, some properties of amply weak essential supplemented modules are investigated. Let M be a projective and weakly module. Then every finitely M-generated module is supplemented. R any ring. if only generated R-module an e-supplement submodule in

We prove the weak positivity of the kernels of Kodaira-Spencertype maps for pure Hodge module extensions of generically defined variations of Hodge structure.

The objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel matrix multiplication can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel matr...

Let p ≥ 3 be a prime. We consider the cyclotomic extension Z(p)[ζp2] of Z(p), with Galois group G := (Z/p2)∗. Since this extension is wildly ramified, Z(p)[ζp2] is not projective as a module over the group ring Z(p)G (Speiser). Extending this module structure, we can regard Z(p)[ζp2 ] as a module over the twisted group ring Z(p)[ζp2] ≀G; as such, it remains faithful and non projective. We calcu...

This short paper describes a surprising connection between two previously unrelated topics: the probability of winning certain gambling games, and the invariance of certain measures under pointwise multiplication on the circle. The former has been well-studied by probabilists, notably in the book of Dubins and Savage (1965). The latter is the subject of an important and well-studied conjecture ...

On purpose to elevate the efficiency of elliptic curve scalar multiplication in the device with weak computation power and to improve computational security, in this paper we pioneer a novel algorithm named Improvedm-ary, which is based on the depth first addition chain scheme and the improved m-ary mechanism compatible with a flexible width window. At first, we research and analyze the advanta...

(c) μ(rs,m) = μ(r, μ(s,m)) (d) if 1 ∈ R, then μ(1,m) = m. We shall usually omit the notation of μ and simply write r ·m for μ(r,m). Thus axiom (c) would be written (rs) ·m = r · (s ·m), etc. Exercise 1. We denote by EndGrp(M) the set of group endomorphisms of M : An element φ ∈ EndGrp(M) is a group homomorphism φ : M → M . EndGrp(M) is naturally a ring, with addition and multiplication defined ...

In constrast to group actions, however, one cannot always convert left module structures to right structures and vice versa. To clarify the situation, it is convenient to introduce the opposite ring R, which has the same underlying abelian group R but with multiplication a · b = ba. Then a left module over R is the same thing as a right module over R, and vice versa. Consequently, if R happens ...

In 1999, Smart has shown how to solve in linear time ECDLP for elliptic curves of trace 1 defined over a prime finite field Fp, the so-called anomalous elliptic curves. In this article, we show how to construct such cryptographically weak curves for primes p of industrial length, using complex multiplication theory.

In the current signal measuring equipment in measurable characteristics under the condition of weak signal, the signal measurement accuracy is not high. Therefore, this study designs and realizes a kind of equipment based on TD SCDMA dual polarized antenna for weak signal measurement system. System uses the 2.4 GHz ISM A7105 RF transmitter sent via baud generator clock for electromagnetic wave ...