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.
According to the extraction procedure , Eucalyptus incrassata leave sample yielded 5% and 2% w/w(Based on dry leaves ) of the aqueous extract and essential oils respectively. Disk diffusion method was used to determine the antimicrobial activity of aqueous extract and essential oils of E . incrassata leaves against eight isolates of multidrug- resistant of Staphylococcus aureus ( S. aureus) . It was found that aqueous extract and essential oils have variable antimicrobial activity(the inhibition zone diameter ranged from 7 to 14 mm respectively ) , while essential oils showed more effect than aqueous extract . It was noticed that values of Minimal Inhibitory Concentration ( MIC ) for
... Show MoreThis study was conducted to describe a protocol for the callus establishing culture of Lavandula angustifolia plant and estimating their content of volatile oil. The quantity of volatile oil callus tissues was compared with that of leaves production. Callus was induced from leaf explants on Murashige and Skoog medium (MS) supplemented with Naphthalene acetic acid (NAA) and Benzyl adenine (BA) in different concentrations. Maximum callus fresh weight was obtained in the combination of 10 mg/L BA and 3 mg/L NAA which reached 18 g after four weeks. The results of this work showed that the quantity of volatile oil from the highest fresh weight callus was 6 ml compared with quantity of 18g of leaves which gave 0.5 ml. Volatile o
... Show MoreIn this work, we introduce a new generalization of both Rationally extending and Goldie extending which is Goldie Rationally extending module which is known as follows: if for any submodule K of an R-module M there is a direct summand U of M (denoted by U⊆_⊕ M) such that K β_r U. A β_r is a relation of K⊆M and U⊆M, which defined as K β_r U if and only if K ⋂U⊆_r K and K⋂U⊆_r U.
In this research, we introduce a small essentially quasi−Dedekind R-module to generalize the term of an essentially quasi.−Dedekind R-module. We also give some of the basic properties and a number of examples that illustrate these properties.
Form the series of generalization of the topic of supra topology is the generalization of separation axioms . In this paper we have been introduced (S * - SS *) regular spaces . Most of the properties of both spaces have been investigated and reinforced with examples . In the last part we presented the notations of supra *- -space ( =0,1) and we studied their relationship with (S * - SS *) regular spaces.
In this paper, we introduce a type of modules, namely S-K-nonsingular modules, which is a generalization of K-nonsingular modules. A comprehensive study of these classes of modules is given.
In this paper we present a new method for solving fully fuzzy multi-objective linear programming problems and find the fuzzy optimal solution of it. Numerical examples are provided to illustrate the method.
Some researchers are interested in using the flexible and applicable properties of quadratic functions as activation functions for FNNs. We study the essential approximation rate of any Lebesgue-integrable monotone function by a neural network of quadratic activation functions. The simultaneous degree of essential approximation is also studied. Both estimates are proved to be within the second order of modulus of smoothness.
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
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