The study of cohomology groups is one of the most intensive and exciting researches that arises from algebraic topology. Particularly, the dimension of cohomology groups is a highly useful invariant which plays a rigorous role in the geometric classification of associative algebras. This work focuses on the applications of low dimensional cohomology groups. In this regards, the cohomology groups of degree zero and degree one of nilpotent associative algebras in dimension four are described in matrix form.

      This paper investigates the concept (α, β) derivation on semiring and extend a few results of this map on prime semiring. We establish the commutativity of prime semiring and investigate when (α, β) derivation becomes zero.

Magnesium hydroxide was used as flame inhibitor to increased flame resistance for tires .Magnesium hydroxide was adding with (5%,10%) weight percents to rubber master batch of tire and then exposed the resulting material to a flame generated from gas torch with (10 mm) exposure distance . Method of measuring the surface temperature opposite to the flame was used to determine the heat transferred through tire material. The results were obtained shows enhanced flame resistance for tire by added magnesium hydroxide and this resistance increased by increasing hydroxide Percentage .

In this paper, author’s study sub diffusion bio heat transfer model and developed explicit finite difference scheme for time fractional sub diffusion bio heat transfer equation by using caputo fabrizio fractional derivative. Also discussed conditional stability and convergence of developed scheme. Furthermore numerical solution of time fractional sub diffusion bio heat transfer equation is obtained and it is represented graphically by Python.

The sole aim of the tribe of the Messenger of Allah (PBUH) and his basilica was to revoke the Umayyad heresy and to refute the suspicions through which they climbed to the top of the pyramid of power and legitimized the leadership of Muslims (heresy of hereditary rule) with the sword and blood. Therefore, Imam Hussein (peace be upon him) began his Ashura process with his short divine message in its words and great in its vocabulary and content and even the future of Mohammedan Islam over the times and spaces - what we will see in the folds of research, God willing.