In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.

The main aim of conducting this research is to identify the applications of Smart libraries in the Arab world. The Researcher relied on the documentary and Survey approach to collect information and data through the Internet, and to get to know these libraries. Then the Research came in three sections dealing with the first topic: The general framework of the study. The second topic deals with: introducing Smart libraries and indicating their types and characteristics. The Third topic dealt with the requirements of Smart libraries'application by identifying the basic components of it (Smart building, Smart Librarian , Smart devices, systems and software, Smart information sources,and Smart beneficiaries), and dealt with Smart libraries appl

The current research deals with the subject of spatial transformations and visual construction in contemporary theater. How the visual system works to create spatial diversity in the contemporary Iraqi theater performance and how visual construction contributes to a spatial development process capable of building a tourism system that creates an architectural architecture that leaves the topography of the scriptural architecture. And the production of various indications and patterns in the scene of theatrical presentation in order to produce the new foundational meaning by creating a new structure that leads to diversity and diversity in the visual system and the beginning of visual constructions and their applications. Knowledge and te

This paper focuses on the concept of cognition and its clarification in the light of Islamic epistemology. Knowledge passes through two essential parts: conception and assent. Conception explains simple knowledge, while assent explains knowledge involving a judgment. The paper proceeded with the identification of the problem of relationship blurring between cognition and knowledge. The external and inner senses have explained the relationship between the stages of knowledge and cognition. The external senses receive stimuli and form primary conceptions. These conceptions transfer to the first part of the inner senses, which is common sense; it collects the sensations and transmits them to pictorial power. Secondary conceptions are f

The group for the multiplication of closets is the set G|N of all closets of N in G, if G is a group and N is a normal subgroup of G. The term “G by N factor group” describes this set. In the quotient group G|N, N is the identity element. In this paper, we procure K(SL(2,125)) and K(SL(2,3125)) from the character table of rational representations for each group.

The research studies the sculptural formation in the third millennium: styles and trends, by taking the most important results of sculpture in the third millennium. The problem of the research is to search for the new sculptural formation in what it constitutes of social and human importance, and what are the important factors in forming the   contemporary sculptural structure, and what is the mechanism of showing and producing the new formation. The research requires the study of the most important thing that the (sculptural formation in the third millennium styles and trends) represents. The importance of research depends on the importance of the sculptural formation after the twentieth century and the importance that the for

The Internet makes the world like a small village. It has the ability to make groups of the same ideas, thoughts, and identity close to each other by gathering them in one place. It is a way to communicate and share information and opinion; shaping and sharing of comprising individuals with common interests and the participation of individuals in a fruitful dialogue results in achieving a set of goals promote ideas and mobilizing people about issues and events of common interests.

To address the relationship of the internet via interactive communication and its ability to achieve social capital and discuss issues and various social events, the study sees that the problem of the study could be formulated as follows:

Consid

A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.