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

Let  be a commutative ring with 1 and  be left unitary  . In this papers we introduced and studied concept P-small compressible  (An     is said to be P-small compressible if  can be embedded in every of it is nonzero P-small submodule of . Equivalently,  is P-small compressible if there exists a monomorphism  , ,     is said to be P-small retractable if  , for every non-zero P-small submodule of . Equivalently,  is P-small retractable if there exists a homomorphism  whenever  as a generalization of compressible  and retractable  respectively and give some of their advantages characterizations and examples.

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

In this paper the reinforced materials manufactured from steel continues fibers are used in Aluminum matrix to build a composite material. Most of researches concentrated on reinforced materials and its position in the matrix according to its size and distribution, and their effects on the magnitude of different kinds of the stresses, so this paper presents and concentrate on the geometrical shape of reinforced material and its effects on the internal stresses and strains on the composite strength using FEM as a method for analysis after loaded by certain force showing the deference magnitudes of stresses according to the different geometrical shapes of reinforced materials.

Natural fibers and particles reinforced composites are being broadly used due to their bio and specific properties such as low density and easy to machine and production with low cost. In this work, water absorption and mechanical properties such as tensile strength, flexural strength and impact strength of recycled jute fibers reinforced epoxy resin were enhanced by treating these fibers with alkaline solution. The recycled jute fibers were treated with different concentration of (NaOH) solution at (25 ⁰C) for a period of (24) hours. From the obtained results, it was found that all these properties are improved when fibers treated with (7.5wt% NaOH) related to untreated fibers. Conversely, the mentioned properties of composit

    In this work, we use the explicit and the implicit finite-difference methods to solve the nonlocal problem that consists of the diffusion equations together with nonlocal conditions. The nonlocal conditions for these partial differential equations are approximated by using the composite trapezoidal rule, the composite Simpson's 1/3 and 3/8 rules. Also, some numerical examples are presented to show the efficiency of these methods.

In this paper, we study the growth of solutions of the second order linear complex differential equations  insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .

The aim of this paper is to approximate multidimensional functions f∈C(R^s) by developing a new type of Feedforward neural networks (FFNS) which we called it Greedy ridge function neural networks (GRGFNNS). Also, we introduce a modification to the greedy algorithm which is used to train the greedy ridge function neural networks. An error bound are introduced in Sobolov space. Finally, a comparison was made between the three algorithms (modified greedy algorithm, Backpropagation algorithm and the result in [1]).

Copper electrodeposition by electrorefining process in acidic sulfate media contains 40 g/l of cupric ions and 160 g/l of sulfuric acid was achieved to study the influence of the operating parameters on cathode purity, surface morphology, deposition rate, current efficiency and power consumption. These operating parameters and there ranges are: current density 200, 300 and 400 A/m², electrolyte temperature 35, 50 and 65 ^oC, electrodes spacing 15, 30 and 45 mm and electrolyte residence time 6, 4 and 2 h were utilized. XRF, SEM and EDX analyses were attained to clarify the properties of the produced cathode.

Widespread use of antihypertensive agents in clinical practice necessitates the knowledge of their pleiotropic effects. At the present time there are no sufficient evidences of positive effect of these medications on bone coming from randomized controlled trials; knowledge of additional effects of those drugs on the bone metabolism will allow doctors to choose optimal treatment of hypertension, taking into account the state of bone tissue. At the same time it will also allow to prevent osteoporosis in patients having osteoporosis risk factors or initial signs of bone loss.

Ten elderly hypertensive women age > 60 years old (64.2±3.6) treated with captopril for a 5-6 years ago while they attending Al Yarmouk Teaching Hospital i