In this paper mildly-regular topological space was introduced via the concept of mildly g-open sets. Many properties of mildly - regular space are investigated and the interactions between mildly-regular space and certain types of topological spaces are considered. Also the concept of strong mildly-regular space was introduced and a main theorem on this space was proved.

This paper is concerned with introducing and studying the first new approximation operators using mixed degree system and second new approximation operators using mixed degree system which are the core concept in this paper. In addition, the approximations of graphs using the operators first lower and first upper are accurate then the approximations obtained by using the operators second lower and second upper sincefirst accuracy less then second accuracy. For this reason, we study in detail the properties of second lower and second upper in this paper. Furthermore, we summarize the results for the properties of approximation operators second lower and second upper when the graph G is arbitrary, serial 1, serial 2, reflexive, symmetric, tra

In this paper, we present the almost approximately nearly quasi compactly packed (submodules) modules as an application of the almost approximately nearly quasiprime submodule. We give some examples, remarks, and properties of this concept. Also, as the strong form of this concept, we introduce the strongly, almost approximately nearly quasi compactly packed (submodules) modules. Moreover, we present the definitions of almost approximately nearly quasiprime radical submodules and almost approximately nearly quasiprime radical submodules and give some basic properties of these concepts that will be needed in section four of this research. We study these two concepts extensively.

       It is a common Knowledge that adverbs in Turkish languages can modify verbs, adjectives, nouns or other adverbs. Moreover, adverbs can determine the meanings of nouns and verbs in a sentence as far as time, place, manner, quantity and interrogative are concerned. The present study debates adverbs’ functions in Namiq Kamal’s play Vatan yahut Silistre.

 The study sheds light on the author’s use of the adverbs to describe the required theatrical actions of the play  and to convey his reflections and thoughts easily to the auidence. One of the main hindrances encountered in conducting the study is the shortage of the  upto date academic resources necessary for

There are many methods of searching large amount of data to find one particular piece of information. Such as find name of person in record of mobile. Certain methods of organizing data make the search process more efficient the objective of these methods is to find the element with least cost (least time). Binary search algorithm is faster than sequential and other commonly used search algorithms. This research develops binary search algorithm by using new structure called Triple, structure in this structure data are represented as triple. It consists of three locations (1-Top, 2-Left, and 3-Right) Binary search algorithm divide the search interval in half, this process makes the maximum number of comparisons (Average case com

The main purpose of this work is to introduce some types of fuzzy convergence sequences of operators defined on a standard fuzzy normed space (SFN-spaces) and investigate some properties and relationships between these concepts. Firstly, the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators  are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit  where linear operator from complete standard fuzzy normed space  into a standard fuzzy normed space  then  belongs to the set of all fuzzy bounded linear operators

     We introduce and discuss the modern type of fibrewise topological spaces, namely fibrewise fuzzy topological spaces. Also, we introduce the concepts of fibrewise closed fuzzy topological spaces, fibrewise open fuzzy topological spaces, fibrewise locally sliceable fuzzy topological spaces and fibrewise locally sectionable fuzzy topological spaces. Furthermore, we state and prove several theorems concerning these concepts.

We introduce and discus recent type of fibrewise topological spaces, namely fibrewise bitopological spaces, Also, we introduce the concepts of fibrewise closed bitopological spaces, fibrewise open bitopological spaces, fibrewise locally sliceable bitopological spaces and fibrewise locally sectionable bitopological spaces. Furthermore, we state and prove several propositions concerning with these concepts.

The essential objective of this paper is to introduce new notions of fibrewise topological spaces on D that are named to be upper perfect topological spaces, lower perfect topological spaces, multi-perfect topological spaces, fibrewise upper perfect topological spaces, and fibrewise lower perfect topological spaces. fibrewise multi-perfect topological spaces, filter base, contact point, rigid, multi-rigid, multi-rigid, fibrewise upper weakly closed, fibrewise lower weakly closed, fibrewise multi-weakly closed, set, almost upper perfect, almost lower perfect, almost multi-perfect, fibrewise almost upper perfect, fibrewise almost lower perfect, fibrewise almost multi-perfect, upper^* continuous fibrewise upper^∗ topol

    We introduce in this paper the concept of approximaitly semi-prime submodules of unitary left -module  over a commutative ring  with identity as a generalization of a prime submodules and semi-prime submodules, also generalization of quasi-prime submodules and approximaitly prime submodules. Various basic properties of an approximaitly semi-prime submodules are discussed, where a proper submodule  of an -module  is called an approximaitly semi-prime submodule of  , if whenever , where ,  and , implies that . Furthermore the behaviors of approximaitly semi-prime submodule in some classes of modules are studied. On the other hand several characterizations of this concept are