Let n be a positive integer and  denotes the number of overpartition triples. In this note, we prove two identities modulo 16 and 32 for . We provide a new method to reprove a result of Lin Wang for completely determining and  modulo 16. Also, we find and prove an infinite family of congruences modulo 32 for . The new method relies on expanding the fourth power of the overpartition infinite product together with the help of Gauss' identity.

In this work we present the concepts of topological Γ-ring, norm of topological Γ-ring, homomorphism, kernel of topological Γ-ring and compact topological Γ-ring

Background: Inflammation of the brain parenchyma brought on by a virus is known as viral encephalitis. It coexists frequently with viral meningitis and is the most prevalent kind of encephalitis.

Objectives: To throw light on viral encephalitis, its types, epidemiology, symptoms and complications.

Results: Although it can affect people of all ages, viral infections are the most prevalent cause of viral encephalitis, which is typically seen in young children and old people. Arboviruses, rhabdoviruses, enteroviruses, herpesviruses, retroviruses, orthomyxoviruses, orthopneumoviruses, and coronaviruses are just a few of the viruses that have been known to cause encephalitis.

Background: Ruptured posterior communicating artery (PCoA) aneurysms are common; they usually present with subarachnoid haemorrhage (SAH) and oculomotor nerve palsy. The aneurysmal dome projection may influence the safety access and aneurysmal neck clipping. Here, we discuss additional intraoperative steps that may be required to widen the surgical field to ensure safe surgical clipping of a rupture pure posteriorly directed PCoA aneurysm. Case description: A previously healthy 38-year-old male reported sudden severe headache and disturbed level of consciousness with a Glasgow coma scale (GCS) of 13. His initial computed tomography (CT) scan of the head showed SAH in the basal cistern. 3D-constructed CT angiography (CTA) revealed a

The study included the collection of samples of raw cow milk to isolate Leuconostoc bacteria, samples were sub cultured on De-Man Rogosa Sharpe-Vancomycin medium, the pure colonies were selected and subjected to the cultural and microscopically tests, according to that 25 cocci bacterial isolates were obtained, then isolates were subjected to biochemical tests. Result of tests showed that 12 isolates belong to the genus Leuconostoc out of 25 cocci bacterial isolates, Vitek2 system was used as a supplementary step. Results of final identification showed that 3 sub species were obtained included Leuconostoc mesenteroides ssp. cremoris 9 out of 12 isolates, while it was 2 isolates of Leuconostoc mesenteroides ssp. mesenteroides and one isol

Abstract

      The research aims to identify the mediator role of  workplace spirituality in the  relationship between psychological capital and entrepreneurial  behavior: field research to a sample opinions from employees at the center of the Iraqi ministry of Oil . The importance of the current research emerged from paucity of studies that have attempted to identify and know the nature of the relationship between the variables as well as trying to find the current address and realistic problem directly affects the performance of employees in the Iraqi oil sector.

 In order to achieve the goal of research the use of the analytical method (quantitative)

The study was enriched by examining (Islamic Sharia’s position on the phenomenon of bullying) becausee bullying is a recurring aggressive behavior that Is one of the types of violence directed by a person or group of prsons; With the intent of deliberately harming and offending anotherr person or group of persons, It has several verbal, physical, electronIc or other formsforms Bullies may follow a policy of Ientimidation or intimidation, as well as ridicule; In order to belittle the victim .The study aims to know the Islamic Sharia ruling on bullying as a modern term for a content that Is as old as man, and the study reached several results, Including: Islam’s affirmation of the prohibition of this phenomenon In word, deed and gesture,

    In this paper, we introduce the bi-normality set, denoted by , which is an extension of the normality set, denoted by  for any operators  in the Banach algebra . Furthermore, we show some interesting properties and remarkable results. Finally, we prove that it is not invariant via some transpose linear operators.