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 a semi-extending modules, as generalization of extending modules, where an Rmodule M is called semi-extending if every sub module of M is a semi-essential in a direct summand of M. Various properties of semi-extending module are considered. Moreover, we investigate the relationships between semi-extending modules and other related concepts, such as CLS-modules and FI- extending modules.

Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .     In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of their adv

The esterification of oleic acid with 2-ethylhexanol in presence of sulfuric acid  as homogeneous catalyst was investigated in this work to produce 2-ethylhexyl oleate (biodiesel) by using semi batch reactive distillation. The effect of reaction temperature (100 to 130°C), 2-ethylhexanol:oleic acid molar ratio (1:1 to 1:3) and catalysts concentration (0.2 to 1wt%) were studied. Higher conversion of 97% was achieved with operating conditions of reaction temperature of 130°C, molar ratio of free fatty acid to alcohol of 1:2 and catalyst concentration of 1wt%. A simulation was adopted from basic principles of the reactive distillation using MATLAB to describe the process. Good agreement was achieved.

Background: Implant stability is a mandatory factor for dental implant (DI) osseointegration and long-term success. The aim of this study was to evaluate the effect of implant length, diameter, and recipient jaw on the pre- and post-functional loading stability. Materials and methods: This study included 17 healthy patients with an age range of 24-61 years. Twenty-two DI were inserted into healed extraction sockets to replace missing tooth/ teeth in premolar and molar regions in upper and lower jaws. Implant stability was measured for each implant and was recorded as implant stability quotient (ISQ) immediately (ISQ0), and at 8 (ISQ8) and 12 (ISQ12) weeks postoperatively, as well as post-functional loading (ISQPFL). The pattern of implant

As the bit rate of fiber optic transmission systems is increased to more than , the system will suffer from an important random phenomena, which is called polarization mode dispersion. This phenomenon contributes effectively to: increasing pulse width, power decreasing, time jittering, and shape distortion. The time jittering means that the pulse center will shift to left or right. So that, time jittering leads to interference between neighboring pulses. On the other hand, increasing bit period will prevent the possibility of sending high rates. In this paper, an accurate mathematical analysis to increase the rates of transmission, which contain all physical random variables that contribute to determine the transmission rates, is presen

This research is concerned to investigate the behavior of reinforced concrete (RC) deep beams strengthened with carbon fiber reinforced polymer (CFRP) strips. The experimental part of this research is carried out by testing seven RC deep beams having the same dimensions and steel reinforcement which have been divided into two groups according to the strengthening schemes. Group one was consisted of three deep beams strengthened with vertical U-wrapped CFRP strips. While, Group two was consisted of three deep beams strengthened with inclined CFRP strips oriented by 45^o with the longitudinal axis of the beam. The remaining beam is kept unstrengthening as a reference beam. For each group, the variable considered