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.

This paper is concerned with introducing and studying the M-space by using the mixed degree systems which are the core concept in this paper. The necessary and sufficient condition for the equivalence of two reflexive M-spaces is super imposed. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are introduced. From an M-space, a unique supratopological space is introduced. Furthermore, the m-continuous (m-open and m-closed) functions are defined and the fundamental theorem of the m-continuity is provided. Finally, the m-homeomorphism is defined and some of its properties are investigated.

Weil das Wort als Kern der Sprache ist und es als das wichtigste Element betrachtet wird, beschäftigten sich die Sprachwissenschaftler nicht nur zur Zeit sondern seit hunderten Jahren mit dem Wort und seiner Bedeutung. Deswegen wurden viele Forschungen darüber geschafft.

Aus der Wichtigkeit des Wortes wird in dieser Forschung  besonders vom Wort gesprochen, das mehrere Bedeutungen hat und das problematisch bei der  Übersetzungsprozess sein kann.    

 Aus den vielschichtigen Themen habe ich dieses Thema ausgewählt,                       da durch die Übersetzung

A (k,n)-arc is a set of k points of PG(2,q) for some n, but not n + 1 of them, are collinear. A (k,n)-arc is complete if it is not contained in a (k + 1,n)-arc. In this paper we construct complete (kn,n)-arcs in PG(2,5), n = 2,3,4,5, by geometric method, with the related blocking sets and projective codes.

Most real-life situations need some sort of approximation to fit mathematical models. The beauty of using topology in approximation is achieved via obtaining approximation for qualitative subgraphs without coding or using assumption. The aim of this paper is to apply near concepts in the -closure approximation spaces. The basic notions of near approximations are introduced and sufficiently illustrated. Near approximations are considered as mathematical tools to modify the approximations of graphs. Moreover, proved results, examples, and counterexamples are provided.

Bekanntlich hat jede Sprache ihre eigenen charakteristischen Besonderheiten. Davon ausgehend gibt es auch gewisse Unterschiede zwischen dem Arabischen und dem Deutschen. Zu den wichtigsten Gebieten der deutschen Grammatik gehören die zusammengesetzten Sätze, vor allem Satzgefüge mit den über- und untergeordneten Sätzen. Dazu gehören auch die Äquivalente der Nebensätze, besonders die Infinitiv- und Partizipialkonstruktionen.

Die vorliegende Recherche hat eine der grammatischen Strukturen des Arabischen und des Deutschen nämlich die dass-Sätze und Infintivsätze mit zu und deren Wiedergabemöglichkeiten in den beiden Sprachen zum Inhalt, weil die Infinitivsätze mit zu den Deutschlernenden beson

Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation  on a set  can always be represented by a digraph. Topology on a set  can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

The basic concepts of some near open subgraphs, near rough, near exact and near fuzzy graphs are introduced and sufficiently illustrated. The Gm-closure space induced by closure operators is used to generalize the basic rough graph concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of graphs. We give a new definition for a membership function to find near interior, near boundary and near exterior vertices. Moreover, proved results, examples and counter examples are provided. The Gm-closure structure which suggested in this paper opens up the way for applying rich amount of topological facts and methods in the process of granular computing.