In this paper the queuing system (M/Er/1/N) has been considered in equilibrium. The method of stages introduced by Erlang has been used. The system of equations which governs the equilibrium probabilities of various stages has been given. For general N the probability of j stages of service are left in the system, has been introduced. And the probability for the empty system has been calculated in the explicit form.

Let R be a commutative ring with non-zero identity element. For two fixed positive integers m and n. A right R-module M is called fully (m,n) -stable relative to ideal A of , if for each n-generated submodule of Mm and R-homomorphism . In this paper we give some characterization theorems and properties of fully (m,n) -stable modules relative to an ideal A of . which generalize the results of fully stable modules relative to an ideal A of R.

ABSTRACT

This research included the preparation and characterization of new demulsifies from natural and synthetic polymers of chitosan and polyvinyl alcohol that are environmentally friendly and at the same time have high efficacy comparable to emulsifiers. imported foreign. The prepared compounds were examined using infrared spectroscopy and nuclear magnetic resonance spectroscopy, and all the spectral signals of the polymers were in good agreement with the chemical composition of the polymers. And the melting and decomposition that occur on polymers at high temperatures. The effect of the length and type of side chain in the compositions of polymers on the process of water separation of oil emulsions w

Abstract 

Locally natural occurring Iraqi rocks of Bauxite and Porcelanite (after pre calcinations at 1000^oC for 1hr) were used, with the addition of different proportions of MgO and Al₂O₃, to prepare refractory materials. The effects of these additives on the physical and thermal properties of the prepared refractories were investigated.

Many batches of Bauxite/MgO, Bauxite/Al₂O₃, Bauxite/MgO/Al₂O₃, and   Porcelanite/ MgO/Al₂O₃ were prepared. The mixture is milled and classified into different size fractions; fine (less than 45μm) 40%, middle (45-75μm) 40%, and coarse (75-106μm) 20% .

Azo derivative ligand[H3L] have been synthesized by the reaction of diazonium salt of p-amino benzoic acid with orcinol in(1:1)mole ratio. The bidente ligand was reacted with the metal ions MnII,FeIIandCrIIIin(2:1)mole ratio via reflux in ethanol using Et3N as a base to give complexes of the general formula: [ M(H2L)2(H2O)x]Cly The synthesized compounds were characterized by spectroscopic methods[ I.R , UV-Vis, A.A and H1 NMR]along with melting point, chloride content and conductivity measurements. The complexes were screend for their in vitro antibacterial activity against one strain of staphylococcus as Gram(+) positive and one strain of pseudomonas as Gram(-) Negative, using the agar diffusion technique.