Number theorists believe that primes play a central role in Number theory and that solving problems related to primes could lead to the resolution of many other unsolved conjectures, including the prime k-tuples conjecture. This paper aims to demonstrate the existence of this conjecture for admissible k-tuples in a positive proportion. The authors achieved this by refining the methods of “Goldston, Pintz and Yildirim” and “James Maynard” for studying bounded gaps between primes and prime k-tuples. These refinements enabled to overcome the previous limitations and restrictions and to show that for a positive proportion of admissible k-tuples, there is the existence of the prime k-tuples conjecture holding for each “k”. The sig

   The aim of this paper is to introduce and study new class of fuzzy function called fuzzy semi pre homeomorphism in a fuzzy topological space by utilizing fuzzy semi pre-open sets. Therefore, some of their characterization has been proved; In addition to that we define, study and develop corresponding to new class of fuzzy semi pre homeomorphism in fuzzy topological spaces using this new class of functions.

Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .

    In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of

In this paper the full stable Banach gamma-algebra modules, fully stable Banach gamma-algebra modules relative to ideal are introduced. Some properties and characterizations of these classes of full stability are studied.

Purpose – The main purpose of this research is to highlight the main role of strategic leadership skills for top managements in accessing to effective management in accordance with the (VUCA Prime) methodology in (VUCA) environment as Miniature virtual environment, which refers to (Volatility), (Uncertainty), (Complexity), and (Ambiguity).

methodology – To achieve the research objective, this study selected the quantitative approach in research design, Questionnaire was used as the main instrument for data collection, the sample comprised the opinion poll (106) individual who functions as a head department. (Structural equation modelling by (Smart Pls3)

The main purpose of this work is to introduce the concept of higher N-derivation and study this concept into 2-torsion free prime ring we proved that:Let R be a prime ring of char. 2, U be a Jordan ideal of R and be a higher N-derivation of R, then , for all u U , r R , n N .

   The purpose of this paper is to study   new  types of open sets in bitopological spaces.    We shall introduce the concepts of  L- pre-open and L-semi-p-open sets

The purpose of this paper is to study a new types of compactness in the dual bitopological spaces. We shall introduce the concepts of L-pre- compactness and L-semi-P- compactness .

The significance of the work is to introduce the new class of open sets, which is said Ǥ- -open set with some of properties. Then clarify how to calculate the boundary area for these sets using the upper and lower approximation and obtain the best accuracy.

 The purpose of this research is to investigate the effects of rotation on heat transfer using
inclination magnetohydrodynamics for a couple-stress fluid in a non-uniform canal. When the
Reynolds number is low and the wavelength is long, math formulas are used to describe the stream
function, as well as the gradient of pressure, temperature, pressure rise and axial velocity per
wavelength, which have been calculated analytically. The many parameters in the current model
are assigned a definite set of values. It has been noticed that both the pressure rise and the pressure
gradient decrease with the rise of the rotation and couple stress, while they increase with an
increase in viscosity and Hartmann nu