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.
We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.
This work, introduces some concepts in bitopological spaces, which are nm-j-ω-converges to a subset, nm-j-ω-directed toward a set, nm-j-ω-closed mappings, nm-j-ω-rigid set, and nm-j-ω-continuous mappings. The mainline idea in this paper is nm-j-ω-perfect mappings in bitopological spaces such that n = 1,2 and m =1,2 n ≠ m. Characterizations concerning these concepts and several theorems are studied, where j = q , δ, a , pre, b, b.
Let R be an associative ring with identity and M a non – zero unitary R-module.In this paper we introduce the definition of purely co-Hopfian module, where an R-module M is said to be purely co-Hopfian if for any monomorphism f ˛ End (M), Imf is pure in M and we give some properties of this kind of modules.
In the present work the performance of semifluidized bed adsorber was evaluated for removal of phenolic compound from wastewater using commercial activated carbon as adsorbent. P-chlorophenol (4-Chlorophenol) and o-cresol (2-methylphenol) was selected as a phenolic compound for that purpose. The phenols percent removal, in term of breakthrough curves were studied as affected by hydrodynamics limitations which include minimum and maximum semifluidization velocities and packed bed formation in the column by varying various parameters such as inlet liquid superficial velocity (from Uminsf to 8Uminsf m/s), and retaining grid (sometimes referred to as adsorbent loading) to initial static bed height ratio (from 3-4.5). In
... Show MoreA new novel series of metalcomplexes are prepared from reactions between 2-benzoylthio- benzimidazole (L) with metal salts of Co (II) , Fe(III) and Rh (III) , while Pd(II) complex was obtained by mixing ligandsof 2-benzoylthiobenzimidazole (L) as primary ligand and bipyridine (L/)as secondary ligand as well as palladium chloride as metal salt in an ethanoic medium. The geometry of these compounds were identified using C.H.N.microanalysis, Ultraviolet–visible, Fourier transforms infrared, magnetic susceptibility, molar conductivity and flame atomic absorption (A.A). From the dataobtained by these spectral analyses, the molecular structures for Rh and Fe complexes were proposed to be octahedral geometry. A square planar const
... Show MoreIn this work semi–empirical method (PM3) calculations are carried out by (MOPAC) computational packages have been employed to calculate the molecular orbital's energies for some organic pollutants. The long– chain quaternary ammonium cations called Iraqi Clays (Bentonite – modified) are used to remove these organic pollutants from water, by adding a small cationic surfactant so as to result in floes which are agglomerates of organobentonite to remove organic pollutants. This calculation which suggests the best surface active material, can be used to modify the adsorption efficiency of aniline , phenol, phenol deriviatives, Tri methyl glycine, ester and pecticides , on Iraqi Clay (bentonite) by comparing the theoretical results w
... Show MoreThis study aims to find out the effectiveness of instructional scaffolding strategy in the development of academic achievement and critical thinking of female second grade secondary mathematics students. Semi-experimental and relational descriptive method was used. The sample of the study consisted of (50) students divided into an experimental group and a control group. The experimental group was taught using scaffolding strategy whereas the control group was taught using traditional method. Pre- and Post-tests were used to achieve the objective of the study. The results of the study revealed that there are statistically significant differences in the mean scores of the experimental and control groups in the posttest for both the academi
... Show MoreIn this paper, some basic notions and facts in the b-modular space similar to those in the modular spaces as a type of generalization are given. For example, concepts of convergence, best approximate, uniformly convexity etc. And then, two results about relation between semi compactness and approximation are proved which are used to prove a theorem on the existence of best approximation for a semi-compact subset of b-modular space.
An accurate assessment of the pipes’ conditions is required for effective management of the trunk sewers. In this paper the semi-Markov model was developed and tested using the sewer dataset from the Zublin trunk sewer in Baghdad, Iraq, in order to evaluate the future performance of the sewer. For the development of this model the cumulative waiting time distribution of sewers was used in each condition that was derived directly from the sewer condition class and age data. Results showed that the semi-Markov model was inconsistent with the data by adopting ( 2 test) and also, showed that the error in prediction is due to lack of data on the sewer waiting times at each condition state which can be solved by using successive conditi
... Show MoreThe main aim of this paper is to use the notion which was introduced in [1], to offered new classes of separation axioms in ideal spaces. So, we offered new type of notions of convergence in ideal spaces via the set. Relations among several types of separation axioms that offered were explained.