Let R be a commutative ring with  identity . In this paper  we study  the concepts of  essentially quasi-invertible submodules and essentially  quasi-Dedekind modules  as  a generalization of  quasi-invertible submodules and quasi-Dedekind  modules  . Among the results that we obtain is the following : M  is an essentially  quasi-Dedekind  module if and only if M is aK-nonsingular module,where a module M is K-nonsingular if, for each  , Kerf ≤_e M   implies   f = 0 .

The goal of this discussion is to study the twigged of pure-small (pr-small) sub- moduleof a module W as recirculation of a small sub-module, and we give some basic idiosyncrasy and instances of this kind of sub-module. Also, we give the acquaint of pure radical of a module W (pr-radical) with peculiarities.

The   study   of  torsion  {torsion   free)  fuzzy  modules   over   fuzzy

integtal  domain  as a generalization oftorsion (torsion free) modules.

The main goal of this paper is to dualize the two concepts St-closed submodule and semi-extending module which were given by Ahmed and Abbas in 2015. These dualizations are called CSt-closed submodule and cosemi-extending mod- ule. Many important properties of these dualizations are investigated, as well as some others useful results which mentioned by those authors are dualized. Furthermore, the relationships of cosemi-extending and other related modules are considered.

The goal of this paper is to design a robust controller for controlling a pendulum
system. The control of nonlinear systems is a common problem that is facing the researchers in control systems design. The Sliding Mode Controller (SMC) is the best solution for controlling a nonlinear system. The classical SMC consists from two phases. The first phase is the reaching phase and the second is the sliding phase. The SMC suffers from the chattering phenomenon which is considered as a severe problem and undesirable property. It is a zigzag motion along the switching surface. In this paper, the chattering is reduced by using a saturation function instead of sign function. In spite of SMC is a good method for controlling a nonlinear system b

Abstract Ternary Silver Indium selenide Sulfur AgInSe1.8S0.2 in pure form and with a 0.2 ratio of Sulfur were fabricated via thermal evaporation under vacuum 3*10-6 torr on glasses substrates with a thickness of (550) nm. These films were investigated to understand their structural, optical, and Hall Characteristics. X-ray diffraction analysis was employed to examine the impact of varying Sulfur ratios on the structural properties. The results revealed that the AgInSe1.8S0.2 thin films in their pure form and with a 0.2 Sulfur ratio, both at room temperature and after annealing at 500 K, exhibited a polycrystalline nature with a tetragonal structure and a predominant orientation along the (112) plane, indicating an enhanced de

The Immanence in S. Abdu; Saboor Poetry

After this stage in the Bible is problematic and the profane in the poetry of the AL-Sayeghs,
and found that the poems path heading towards obey religious authority because of their wills
and powers, and the insurgency in other areas, as it did not employ shady methods and puns
and intriguing, and I find the reason for this is due to the fear poet focused toward the
influence of political Sergeant, more than effusion direction ascendancy religious sergeant,
was a AL-Sayeghs stop at this border; but went to the formulations problematic diversity in
the cognitive system, he tries it all to critique, as submitted by the history of the conflicts
produced generations of oppression and conflict and tension (what my fault I

Objective: To evaluate male patients complaining of
urethritis clinically according to the isolated organisms.
Method: A total of 100 male patients attending to of
Dermatological and Venereal private clinics for the period
April 2003 to November 2003 were included in the study.
Urethral swab was obtained from each male for culture and
direct immunofluorescence examination was done.
Demographic data was obtained, also.
Results: N. gonorrhoea was the predominate cause of
infection in 22%. A peak of infection was reported in the
second decade of age. Highest rate reported among single
males. A significant association was noticed between
profuse discharge and infection with gonorrhoea.
Conclusion: This