It is shown that if a subset of a topological space (χ, τ) is δ-semi.closed, then it is semi.closed. By use this fact, we introduce the concept regularity of a topological space (χ, τ) via δ-semi.open sets. Many properties and results were investigated and studied. In addition we study some maps that preserve the δ-semi.regularity of spaces.

   In this paper, a new class of sets, namely - semi-regular closed sets is introduced and studied for topological spaces. This class properly contains the class of semi--closed sets and is property contained in the class of pre-semi-closed sets. Also, we introduce and study srcontinuity and sr-irresoleteness. We showed that sr-continuity falls strictly in between semi-- continuity and pre-semi-continuity.

      Let  be a ring with identity and let  be a left R-module. If is  a proper submodule of  and  ,  is called --semi regular element in  , If there exists a decoposition  such that  is projective submodule of  and  . The aim of this paper is to introduce properties of F-J-semi regular module. In particular, its characterizations are given. Furthermore, we introduce the concepts of Jacobson hollow semi regular module and --semiregular module. Finally, many results of Jacobson hollow semi regular module and --semiregular module are presented.

Let  be a commutative ring with identity, and  be a unitary left -module. In this paper we introduce the concept pseudo weakly closed submodule as a generalization of -closed submodules, where a submodule  of an -module  is called a pseudo weakly closed submodule, if for all , there exists a -closed submodule  of  with  is a submodule of  such that . Several basic properties, examples and results of pseudo weakly closed submodules are given. Furthermore the behavior of pseudo weakly closed submodules in class of multiplication modules are studied. On the other hand modules with chain conditions on pseudo weakly closed submodules are established. Also, the relationships of  pseudo weakly closed

Many of the key stream generators which are used in practice are LFSR-based in the sense that they produce the key stream according to a rule y = C(L(x)), where L(x) denotes an internal linear bit stream, produced by small number of parallel linear feedback shift registers (LFSRs), and C denotes some nonlinear compression function. In this paper we combine between the output sequences from the linear feedback shift registers with the sequences out from non linear key generator to get the final very strong key sequence

In this paper, a new idea to configure a special graph from the discrete topological space is given. Several properties and bounds of this topological graph are introduced. Such that if the order of the non-empty set equals two, then the topological graph is isomorphic to the complete graph. If the order equals three, then the topological graph is isomorphic to the complement of the cycle graph. Our topological graph has  complete induced subgraphs with order  or more. It also has a cycle subgraph. In addition, the clique number is obtained. The topological graph is proved simple, undirected, connected graph. It has no pendant vertex, no isolated vertex and no cut vertex. The minimum and maximum degrees are evaluated. So , the radius 

Let G be a finite group and X be a conjugacy class of order 3 in G. In this paper, we introduce a new type of graphs, namely A₄-graph of  G, as a simple graph denoted by A₄(G,X) which has X as a vertex set. Two vertices,  x and y, are adjacent if and only if  x≠y and  x y^-1=y x^-1. General properties  of the A₄-graph as well as the structure of A₄(G,X) when G@ ³D₄(2) will be studied.

Vorwort :
Bernd Heinrich von Kleist wurde am 18. Oktober 1777 in Frankfurt an der Oder geboren . 1 1794 schrieb Kleist seinen ersten Aufsatz , der Aufsatz , den sichern Weg des Glücks zu finden heißt . Diese frühe Schrift bestimmet die Ideen der Aufklärung , besonders die von Vernunft und Tugend . 2
Obwohl Kleist der Sohn eines Offizier war , fand er im Militär keine Erfüllung , und im Jahre 1799 verliess er das Militär . Im Jahre 1800 verlobte er sich mit Wilhelmine von Zonge . 3
Nachdem er im Jahre 1801 die Philosophie von Kant gelesen hatte , erlebte Kleist seine erste Gemütskries . Kleist hatte immer der Vernunft den höchsten Wert gegeben , aber er fühlte , dass es etwas Anders gab .
Seine Verlobte wollte keine

     The Syriac language is one of the ancient Semitic languages that appeared in the first century AD. It is currently used in a number of cities in Iraq, Turkey, and others. In this research paper, we tried to apply the work of  Ali and Mahmood 2020  on the letters and words in the Syriac language to find a new encoding for them and increase the possibility of reading the message by other people.

Advances in digital technology and the World Wide Web has led to the increase of digital documents that are used for various purposes such as publishing and digital library. This phenomenon raises awareness for the requirement of effective techniques that can help during the search and retrieval of text. One of the most needed tasks is clustering, which categorizes documents automatically into meaningful groups. Clustering is an important task in data mining and machine learning. The accuracy of clustering depends tightly on the selection of the text representation method. Traditional methods of text representation model documents as bags of words using term-frequency index document frequency (TFIDF). This method ignores the relationship an