Abstract Throughout this paper R represents commutative ring with identity and M is a unitary left R-module, the purpose of this paper is to study a new concept, (up to our knowledge), named St-closed submodules. It is stronger than the concept of closed submodules, where a submodule N of an R-module M is called St-closed (briefly N ≤Stc M) in M, if it has no proper semi-essential extensions in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K then N = K. An ideal I of R is called St-closed if I is an St-closed R-submodule. Various properties of St-closed submodules are considered.

  In this paper, the concept of contraction mapping on a -metric space is extended with a consideration on local contraction.  As a result, two fixed point theorems were proved for contraction on a closed ball in a complete -metric space.

The goal of this discussion is to study the twigged of pure-small (pr-small) sub- moduleof a module W as recirculation of a small sub-module, and we give some basic idiosyncrasy and instances of this kind of sub-module. Also, we give the acquaint of pure radical of a module W (pr-radical) with peculiarities.

The main objective of this thesis is to study new concepts (up to our knowledge) which are P-rational submodules, P-polyform and fully polyform modules. We studied a special type of rational submodule, called the P-rational submodule. A submodule N of an R-module M is called P-rational (Simply, N≤_prM), if N is pure and Hom_R (M/N,E(M))=0 where E(M) is the injective hull of M. Many properties of the P-rational submodules were investigated, and various characteristics were given and discussed that are analogous to the results which are known in the concept of the rational submodule. We used a P-rational submodule to define a P-polyform module which is contained properly in the polyform module. An R-module M is called P-polyform if every es

In this paper, an eco-epidemiological prey-predator system when the predator is subjected to the weak Allee effect, and harvesting was proposed and studied. The set of ordinary differential equations that simulate the system’s dynamic is constructed. The impact of fear and Allee’s effect on the system's dynamic behavior is one of our main objectives. The properties of the solution of the system were studied. All possible equilibrium points were determined, and their local, as well as global stabilities, were investigated. The possibility of the occurrence of local bifurcation was studied. Numerical simulation was used to further evaluate the global dynamics and understood the effects of varying parameters on the asymptotic behavior of t

The aim of this study is to evaluate the anti fungal activity of a combination of essential oils against water molds. HPLC analysis was done to evaluate the quantity and quality of the active compounds in this combination which extracted from three herbs( Peppermint Menthapiperita ,Thyme Thymusvulgaris, Common sage Salvia officinalis L.) and the active compounds are Camphor,Menthol,,Thujone and Thymol with different concentrations. In this study (MIC) , (MFC) were measured and (LD50) determined after 48,96 h from fingerlings treatment of common carp in aquariums .The results of (MIC) were 0.025µl/ml for Aphanomyces sp. and 0.015µl/ml for both Achlya sp. and Fusariumsolani which showed significant differences(p<0.05) from Malachite gre

This experiment presented essential oils by GC/MS, pigment content, and their antioxidant activities as well as sensory evaluation of delight samples. Limonene (66.88%) was the most prevalent yield. The peels of clementine had DPPH and ABT Scavenging activity. All levels of pigment extract had better scores for all sensory values and recorded acceptable scores in terms of appearance, color, aroma, and overall acceptability compared to control delight. Besides, delight samples containing 15 mg astaxanthin pigment extract showed maximum sensory scores compared to other samples and control delight. On the other hand, the product was less acceptable to the panelists compared to control in the case of the addition of 3.75 mg astaxanthin pigme

    The weak and strong forms are so called because it is not their lexical content that primary matter, but the role they have in the sentence. The problematic confusion, our students encounter, in recognizing and producing the correct pronunciation of weak and strong forms of the English function words is the main incentive behind conducting  this study. In order to gather the data, this paper used two types of tests: a recognition test and a production test. The general results reached  through the analysis of the students' answers seem to conform to the researcher's assumption: students face a critical problem in recognizing and producing correct pronunciation of the weak and strong forms of the English funct

Background: Herbal medicine can be called one of the branches of medicine in various forms. Turmericcurcumin has proved its efficiencies a coloring, flavoring agent and has been traditionally used in medicine, exhibiting remarkable anti-inflammatory and antioxidant properties. The varied biological properties of curcumin and lack of toxicity even when administered at higher doses makes it attractive to explore its use in various disorders like diseases of skin. It is good potential agent for wound healing. Materials and methods: Sixty four new Zealand rabbits were used in this study ,they were divided into four groups,each group was subdivided as follows:Experimental groups(8 rabbits) right facial side of animals for essential oil applicati