Let Ḿ be a unitary R-module and R is a commutative ring with identity. Our aim in this paper  to study the concepts T-ABSO fuzzy ideals, T-ABSO fuzzy submodules and T-ABSO quasi primary fuzzy submodules, also we discuss these concepts in the class of multiplication fuzzy modules and relationships between these concepts. Many new basic properties and characterizations on these concepts are given.

  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.

     A novel, safe and efficient method was developed to encapsulate a blend of essential oils (EOs) into biodegradable nanoparticles (NPs). The biodegradable and biocompatible nanoparticles were made from chitosan (CH) and lecithin (LE) . The quality of the essential oils was verified using gas chromatography/mass spectrometry (GC/MS). The synthesis of nanoparticles included emulsification, followed by sonication, homogenization, and extrusion. Transmission electron microscopy (TEM) indicated that the nanoparticles were spherical in shape with sizes ranging from 25 to 70 nm, while dynamic light scattering (DLS) showed high negative zeta potentials. The stability of the final formula was evaluated in gastric and intes

Let  be a module over a commutative ring  with identity. Before studying the concept of the Strongly Pseudo Nearly Semi-2-Absorbing submodule, we need to mention the ideal  and the basics that you need to study the  concept of the Strongly Pseudo Nearly Semi-2-Absorbing submodule. Also, we introduce several characteristics of the Strongly Pseudo Nearly Semi-2-Absorbing submodule in classes of multiplication modules and other types of modules. We also had no luck because the ideal  is not a Strongly Pseudo Nearly Semi-2-Absorbing ideal. Also, it is noted that  is the Strongly Pseudo Nearly Semi-2-Absorbing ideal under several conditions, which is this faithful module, projective module, Z-regular module and content module and non-si

     This study was designed to evaluate the antimicrobial effect of Cymbopogon citratus and Mentha spicata essential oils, separately and mixed, against the microorganisms in yogurt, as well as study the possibility of these essential oils (EO) as natural preservatives and flavors additives/enhancers in yogurt product. Yogurt samples were treated with lemongrass and spearmint EOin different concentrations (250, 500, 1000 ppm: 6250µg/50 ml yogurt, 12500 µg/50 ml yogurt and 25000 µg/50 ml yogurt respectively). The control and treated samples were preserved both at room (25°C) and refrigerator (5°C)  temperatures. In control, the contamination was observed through 2 weeks at 25°C and for about one month at 5°C

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.

    Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as  we discuss the relation between this concept and some other related concepts.

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