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.

Abstract Globalization dominated in the last decade of the twentieth century and the eve of the third millennium over economic,politics,psychology,culture,communications and information sciences,it's a historical phenomenon refer to many important transitions in humanitarian life.It foxes on that state has illusion its historical role in the psychologist,economic and political buldings. Globalization issue and its influence in North Korea put a spotlight on political,economic and cultural situations,the political system resists any change with many limitations on political freedoms,human rights and political multiplicity.Libralism trends and free market are so weaken when it comparing within the bad economic situation of the coun

Cohesive soils present difficulties in construction projects because it usually contains expansive clay minerals. However, the engineering properties of cohesive soils can be stabilized by using various techniques. The research aims to elaborate on the influences of using hydrated lime on the consistency, compaction, and shear strength properties of clayey soil samples from Sulaimnai city, northern Iraq. The proportions of added hydrated lime are 0%, 2.5%, 5%, 7.5% and 10% to the natural soil sample. The results yielded considerable effects of hydrated lime on the engineering properties of the treated soil sample and enhancement its strength. The soil's liquid limit, plasticity index, and optimum moisture content were de

The world is currently challenging the serious effects of the pandemic of the Coronavirus disease (COVID-19) caused by severe acute respiratory syndrome Coronavirus 2 (SARS-CoV-2). Data on pediatric COVID are rare and scattered in the literature. In this article, we presented the updated knowledge on the pediatric COVID-19 from different aspects. We hope it will increase the awareness of the pediatricians and health care professionals on this pandemic.

High frequency (HF) communications have an important role in long distances wireless communications. This frequency band is more important than VHF and UHF, as HF frequencies can cut longer distance with a single hopping. It has a low operation cost because it offers over-the-horizon communications without repeaters, therefore it can be used as a backup for satellite communications in emergency conditions. One of the main problems in HF communications is the prediction of the propagation direction and the frequency of optimum transmission (FOT) that must be used at a certain time. This paper introduces a new technique based on Oblique Ionosonde Station (OIS) to overcome this problem with a low cost and an easier way. This technique uses the

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.