The main goal of this paper is to dualize the two concepts St-closed submodule and semi-extending module which were given by Ahmed and Abbas in 2015. These dualizations are called CSt-closed submodule and cosemi-extending mod- ule. Many important properties of these dualizations are investigated, as well as some others useful results which mentioned by those authors are dualized. Furthermore, the relationships of cosemi-extending and other related modules are considered.

يشكل السياق جانبا مهماً في فهم الخطاب والمقصود هنا العرض المسرحي، من خلال ما يمده السياق للمتلقي من مؤشرات، يتم الاعتماد عليها في استكمال المعنى الظاهر بالمعنى المستتر، فالسياق يعتمد في الاصل على المحيط المادي الاجتماعي الذي يتم فيه التواصل وفيه يتعرف المرسل والمتلقي أحدهما على الآخر وتتبلور الصورة التي يحملها الطرفان أحدهما عن الآخر، الى جانب كونه يمثل الاحداث التي سبق لهما أن عاشاها والتبادل القولي

Clarity and Visual Ratios of the Vibrant Place Making

There is no access to basic sanitation for half the world's population, leading to Socioeconomic issues, such as scarcity of drinking water and the spread of diseases. In this way, it is of vital importance to develop water management technologies relevant to the target population. In addition, in the separation form of water treatment, the compound often used as a coagulant in water treatment is aluminum sulfate, which provides good results for raw water turbidity and color removal. Studies show, however, that its deposition in the human body, even Alzheimer's disease, can cause serious harm to health and disease development. The study aims to improve the coagulation/flocculation stage related to the amount of flakes, i

The aim of this research is to compare traditional and modern methods to obtain the optimal solution using dynamic programming and intelligent algorithms to solve the problems of project management.

It shows the possible ways in which these problems can be addressed, drawing on a schedule of interrelated and sequential activities And clarifies the relationships between the activities to determine the beginning and end of each activity and determine the duration and cost of the total project and estimate the times used by each activity and determine the objectives sought by the project through planning, implementation and monitoring to maintain the budget assessed 

Consider the (p,q) simple connected graph . The sum absolute values of the spectrum of quotient matrix of a graph  make up the graph's quotient energy. The objective of this study is to examine the quotient energy of identity graphs and zero-divisor graphs  of commutative rings using group theory, graph theory, and applications. In this study, the identity graphs  derived from the group  and a few classes of zero-divisor graphs  of the commutative ring R are examined.