Let R be a commutative ring with identity and M be unitary (left) R-module. The principal aim of this paper is to study the relationships between relatively cancellation module and multiplication modules, pure submodules and Noetherian (Artinian) modules.

The (Richard Wagner) of cultural figures rare collected between philosophy and literature and the arts to reach the concept of the artwork destruction (Gesamtkunstwerk), who called for by the movement romantic, he is a thinker, and composer renewed, and playwright, designer and architect of a special kind.Able ( Wagner ) that translates his thoughts technical and design in the field of opera and disclose those ideas models actual dealt joints essential this art heritage, which was developed and laid his modern rules approach by achieving his dream creates theater ideal, which was held in the city ( Bayreuth) in ( Bavaria ), one of the German Federal States .The study reviews the ideas of Wagner and their sources, which have had an import

In this paper, we introduce the concept of cubic bipolar-fuzzy ideals with thresholds (α,β),(ω,ϑ) of a semigroup in KU-algebra as a generalization of sets and in short (CBF). Firstly, a (CBF) sub-KU-semigroup with a threshold (α,β),(ω,ϑ) and some results in this notion are achieved. Also, (cubic bipolar fuzzy ideals and cubic bipolar fuzzy k-ideals) with thresholds (α,β),(ω ,ϑ) are defined and some properties of these ideals are given. Relations between a (CBF).sub algebra and-a (CBF) ideal are proved. A few characterizations of a (CBF) k-ideal with threshol

In this paper, we introduce the concept of cubic bipolar-fuzzy ideals with thresholds (α,β),(ω,ϑ) of a semigroup in KU-algebra as a generalization of sets and in short (CBF). Firstly, a (CBF) sub-KU-semigroup with a threshold (α,β),(ω,ϑ) and some results in this notion are achieved. Also, (cubic bipolar fuzzy ideals and cubic bipolar fuzzy k-ideals) with thresholds (α,β),(ω ,ϑ) are defined and some properties of these ideals are given. Relations between a (CBF).sub algebra and-a (CBF) ideal are proved. A few characterizations of a (CBF) k-ideal with thresholds (α, β), (ω,ϑ) are discussed. Finally, we proved that a (CBF) k-ideal and a (CBF) ideal with thresholds (α, β), (ω,ϑ) of a KU-semi group are equivalent relations.

True random number generators are essential components for communications to be conconfidentially secured. In this paper a new method is proposed to generate random sequences of numbers based on the difference of the arrival times of photons detected in a coincidence window between two single-photon counting modules

Let R be a ring with 1 and W is a left Module over R. A Submodule D of an R-Module W is small in W(D ≪ W) if whenever a Submodule V of W s.t W = D + V then V = W. A proper Submodule Y of an R-Module W is semismall in W(Y ≪_S W) if Y = 0 or Y/F ≪ W/F ∀ nonzero Submodules F of Y. A Submodule U of an R-Module E is essentially semismall(U ≪es E), if for every non zero semismall Submodule V of E, V∩U ≠ 0. An R-Module E is essentially semismall quasi-Dedekind(ESSQD) if Hom(E/W, E) = 0 ∀ W ≪es E. A ring R is ESSQD if R is an ESSQD R-Module. An R-Module E is a scalar R-Module if, ∀ , ∃ s.t V(e) = ze ∀ . In this paper, we study the relationship between ESSQD Modules with scalar and multiplication Modules. We show that

Vehicular ad hoc networks (VANETs) are considered an emerging technology in the industrial and educational fields. This technology is essential in the deployment of the intelligent transportation system, which is targeted to improve safety and efficiency of traffic. The implementation of VANETs can be effectively executed by transmitting data among vehicles with the use of multiple hops. However, the intrinsic characteristics of VANETs, such as its dynamic network topology and intermittent connectivity, limit data delivery. One particular challenge of this network is the possibility that the contributing node may only remain in the network for a limited time. Hence, to prevent data loss from that node, the information must reach the destina

This paper is devoted to introduce weak and strong forms of fibrewise fuzzy ω-topological spaces, namely the fibrewise fuzzy -ω-topological spaces, weakly fibrewise fuzzy -ω-topological spaces and strongly fibrewise fuzzy -ω- topological spaces. Also, Several characterizations and properties of this class are also given as well. Finally, we focused on studying the relationship between weakly fibrewise fuzzy -ω-topological spaces and strongly fibrewise fuzzy -ω-topological spaces.