In this work we shall introduce the concept of weakly quasi-prime modules and give some properties of this type of modules.

Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.

Abstract  

  In this work, two algorithms of Metaheuristic algorithms were hybridized. The first is Invasive Weed Optimization algorithm (IWO) it is a numerical stochastic optimization algorithm and the second is Whale Optimization Algorithm (WOA) it is an algorithm based on the intelligence of swarms and community intelligence. Invasive Weed Optimization Algorithm (IWO) is an algorithm inspired by nature and specifically from the colonizing weeds behavior of weeds, first proposed in 2006 by Mehrabian and Lucas. Due to their strength and adaptability, weeds pose a serious threat to cultivated plants, making them a threat to the cultivation process. The behavior of these weeds has been simulated and used in Invas

The Vulnerable Indian Roofed Turtle Pangshura tecta (Gray, 1831) (Testudines: Geoemydidae) occurs in the Sub-Himalayan lowlands of India, Nepal, Bangladesh, and Pakistan. Little is known about its natural history, no studies have been conducted revealing its natural predators. In this study, a group of Large-billed Crow Corvus macrorhynchos Wagler, 1827 (Passeriformes: Corvidae) was observed hunting and predating on an Indian Roofed Turtle carcass in the bank of river Kuakhai, Bhubaneswar, India. The first record of this predation behaviour is reported and substantiated by photographic evidence.

The present research is descriptive and analytical by nature; it practically presents the method of implementing the standard pattern in an unconventional way using the bias-cut line. The study aims at investigating the variables of bias-cut and their suitability for fitting large-shaped Iraqi ladies. It also aims at exploring the artistic and innovative features of the bias-cut. Therefore, one needs to understand the rules and basics of clothing and the nature of the body to reach the maximum degree of control.Consequently, the study is to answer the following questions: What is the effectiveness of tailoring on the bias-cut in fitting a standard template of a large-shaped Iraqi ladies? Is it possible to obtain from the offered possibil

Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.