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.

Fuzzy logic is used to solve the load flow and contingency analysis problems, so decreasing computing time and its the best selection instead of the traditional methods. The proposed  method is very accurate with outstanding computation time, which made the fuzzy load flow (FLF) suitable for real time application for small- as well as large-scale power systems. In addition that, the FLF efficiently able to solve load flow problem of ill-conditioned power systems and contingency analysis. The FLF method using Gaussian membership function requires less number of iterations and less computing time than that required in the FLF method using triangular membership function. Using sparsity technique for the input Ybus sparse matrix data gi

(DPA)) 5Cl3N3(NAM)) and compound (2) (P5Cl3N3The preparation of compound (1) ((P ) of the reaction hexachlorocyclotriphosphazene (A) and 2(Bc)4Cl3N3and compound (3) ((P Nicotinamide (B), di phenylamine (C) and Benzocaine (D) at different rates and by the frared inIR -presence of triethylamine. The synthe sized compounds were characterized by FT P NMR spectrum. 31H,1 and spectrum

Quantum channels enable the achievement of communication tasks inaccessible to their
classical counterparts. The most famous example is the distribution of secret keys. Unfortunately, the rate
of generation of the secret key by direct transmission is fundamentally limited by the distance. This limit
can be overcome by the implementation of a quantum repeater. In order to boost the performance of the
repeater, a quantum repeater based on cut-off with two different types of quantum memories is suggestd,
which reduces the effect of decoherence during the storage of a quantum state.

In this paper, the memorization capability of a multilayer interpolative neural network is exploited to estimate a mobile position based on three angles of arrival. The neural network is trained with ideal angles-position patterns distributed uniformly throughout the region. This approach is compared with two other analytical methods, the average-position method which relies on finding the average position of the vertices of the uncertainty triangular region and the optimal position method which relies on finding the nearest ideal angles-position pattern to the measured angles. Simulation results based on estimations of the mobile position of particles moving along a nonlinear path show that the interpolative neural network approach outperf

Background: Obesity tends to appear in modern societies and constitutes a significant public health problem with an increased risk of cardiovascular diseases.

Objective: This study aims to determine the agreement between actual and perceived body image in the general population.

Methods: A descriptive cross-sectional study design was conducted with a sample size of 300. The data were collected from eight major populated areas of Northern district of Karachi Sindh with a period of six months (10^th January 2020 to 21^st June 2020). The Figure rating questionnaire scale (FRS) was applied to collect the demographic data and perception about body weight. Body mass index (BMI) used for ass