The aim of this paper is to study the Zariski topology of a commutative KU-algebra. Firstly, we introduce new concepts of a KU-algebra, such as KU-lattice, involutory ideal and prime ideal and investigate some basic properties of these concepts. Secondly, the notion of the topology spectrum of a commutative KU-algebra is studied and several properties of this topology are provided. Also, we study the continuous map of this topological space.

A new definition of a graph called Pure graph of a ring denote Pur(R) was presented , where the vertices of the graph represent the elements of R such that there is an edge between the two vertices ???? and ???? if and only if ????=???????? ???????? ????=????????, denoted by pur(R) . In this work we studied some new properties of pur(R) finally we defined the complement of pur(R) and studied some of it is properties

This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

The concept of the order sum graph associated with a finite group based on the order of the group and order of group elements is introduced. Some of the properties and characteristics such as size, chromatic number, domination number, diameter, circumference, independence number, clique number, vertex connectivity, spectra, and Laplacian spectra of the order sum graph are determined. Characterizations of the order sum graph to be complete, perfect, etc. are also obtained.

We used to think of grammar as the bones of the language and vocabulary as the flesh to be added given that language consisted largely of life generated chunks of lexis. This “skeleton image” has been proverbially used to refer to that central feature of lexis named collocation- an idea that for the first 15 years of language study and analysis gave a moment‟s thought to English classroom material and methodology.
The work of John Sinclair, Dave Willis, Ron Carter, Michael McCarthy, Michael Lewis, and many others have all contributed to the way teachers today approach the area of lexis and what it means in the teaching/learning process of the language. This also seems to have incorporated lexical ideas into the teaching mechanis

In this paper, various aspects of smart grids are described. These aspects include the components of smart grids, the detailed functions of the smart energy meters within the smart grids and their effects on increasing the awareness, the advantages and disadvantages of smart grids, and the requirements of utilizing smart grids. To put some light on the difference between smart grids and traditional utility grids, some aspects of the traditional utility grids are covered in this paper as well.

An energy and exergy thermodynamic analysis using EES program was done for a domestic refrigerator working with R-134a using vapor compression refrigeration cycle. The analysis deals with the system component, i.e. compressor, condenser, evaporator and the expansion device. The analysis depends on the entropy generation minimization approach to improve the refrigerator performance by exploring the optimum design points. These design points were derived from three different theories governing the entropy generation minimization using exergy analyzing method. These theories were first applied to find the optimum balance between the hot inner condenser area and the cold inner evaporator area of the refrigerator and between

The subject of the provisions of prayer on the chairs of the important topics in the jurisprudence they fall under the door of the people of excuses, and this section of the important doors in Islamic jurisprudence because it permeates scourge, as prayer is one of the pillars of this religion, and the first thing to be held accountable on the Day of Resurrection prayer If the peace reconciled the rest of his work and spoil corrupted all his work, the street wise was interested in this matter and put him provisions overlooked by many people these days became insulted him and do not pardon him, and do not know the rules and provisions approved by Shara, and the omission of one of these provisions is possible To lead to the invalidity of hi

The research aims to develop a proposed mechanism for financial reporting on sustainable investment that takes the specificity of these investments.

To achieve this goal, the researcher used (what if scenario) where the future financial statements were prepared for the year 2026, after completion of the sustainable project and operation, as the project requires four years to be completed.

The researcher relied on the results of the researchers collected from various modern sources relevant to the research topic and published on the internet, and the financial data and information obtained to assess the reality of the company's activity and its environmental, social, and economic i