A non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.

Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called special selfgenerator or weak multiplication module if for each cyclic submodule Ra of M (equivalently, for each submodule N of M) there exists a family {fi} of endomorphism of M such that Ra = ∑_i▒f_i (M) (equivalently N = ∑_i▒f_i (M)). In this paper we introduce a class of modules properly contained in selfgenerator modules called special selfgenerator modules, and we study some of properties of these modules.

There are two (non-equivalent) generalizations of Von Neuman regular rings to modules; one in the sense of Zelmanowize which is elementwise generalization, and the other in the sense of Fieldhowse. In this work, we introduced and studied the approximately regular modules, as well as many properties and characterizations are considered, also we study the relation between them by using approximately pointwise-projective modules.

Static Synchronous Series Compensator (SSSC) is a well known device for effectively regulating the active power flow in a power system. In this paper, the SSSC linearized power flow equations are incorporated into Newton-Raphson algorithm in a MATLAB written program to investigate the control of active poweer flow and the transient stability of a five bus and a thirty bus IEEE test systems, during abnormal conduction (three phase fault near buses). A comparison of the results obtained for the base case without SSSC and with it to investigate the effectiveness of the device on both of the active power flow and the transient stability.

The effect of approaching nozzle jet from the deposition surface
on structural, optical and morphology properties of copper oxide thin
films was studied. The film was prepared by homemade fully
computerized CNC spray pyrolysis deposition technique at
preparations speed (3, 4, 5, and 6 mm/sec). The repeated line mode
was used at deposition temperature equal 450 °C whereas the
spraying time was in the range of (15-30 min) according to the
deposition speed. The film exhibit polycrystalline structure with
preferred orientation along (-111), (022) and (011), (002) at a 2θ
value of (35.63o) and (38.8o) respectively. Optical band gaps were
recorded at these speed shows variance in value from (1.53-2.08 eV).
Fi

In this paper, Nordhaus-Gaddum type relations on open support independence number of some derived graphs of path related graphs under addition and multiplication are studied.

Number theorists believe that primes play a central role in Number theory and that solving problems related to primes could lead to the resolution of many other unsolved conjectures, including the prime k-tuples conjecture. This paper aims to demonstrate the existence of this conjecture for admissible k-tuples in a positive proportion. The authors achieved this by refining the methods of “Goldston, Pintz and Yildirim” and “James Maynard” for studying bounded gaps between primes and prime k-tuples. These refinements enabled to overcome the previous limitations and restrictions and to show that for a positive proportion of admissible k-tuples, there is the existence of the prime k-tuples conjecture holding for each “k”. The sig

The current Iraqi standard specifications for roads and bridges allowed the prepared Job-Mix Formula for asphalt mixtures to witness some tolerances with regard to the following: coarse aggregate gradation by ± 6.0 %, fine aggregate gradation by ± 4.0 %, filler gradation by ± 2.0 %, asphalt cement content by ± 0.3 % and mixing temperature by ± 15 ^oC. The objective of this work is to evaluate the behavior of asphalt mixtures prepared by different aggregates gradations (12.5 mm nominal maximum size) that fabricated by several asphalt contents (40-50 grade) and various mixing temperature. All the tolerances specified in the specifications are taken into account, furthermore, the zones beyond these tolerances