Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes

In this paper, the series solution is applied to solve third order fuzzy differential equations with a fuzzy initial value. The proposed method applies Taylor expansion in solving the system and the approximate solution of the problem which is calculated in the form of a rapid convergent series; some definitions and theorems are reviewed as a basis in solving fuzzy differential equations. An example is applied to illustrate the proposed technical accuracy. Also, a comparison between the obtained results is made, in addition to the application of the crisp solution, when the-level equals one.

الملخص ان حق الملكية هو الحق الاوسع نطاقا يمنح صاحبه صلاحية ممارسة السلطات كافة ويكون محل هذه السلطات كل ما يملك الشخص سواء كان شقه او طبقة اسوة بالعقارات الاخرى كدار للسكن او ارض ، ومن اهم هذه السلطات واوسعها نطاقا ( هو سلطة التصرف ). تعد هذه السلطة جوهر حق الملكية وأخطر السلطات الممنوحة للمالك كونه بواسطتها يمكنه الاستغناء عن ملكه بأي تصرف ناقل له كالبيع أو الهبة او الوصية مثلا ، ولأهمية هذه السلط

Let R be a ring with identity and M be a right unitary R-module. In this paper we
introduce the notion of strongly coretractable modules. Some basic properties of this
class of modules are investigated and some relationships between these modules and
other related concepts are introduced. 

An R-module M is called ET-H-supplemented module if for each submodule X of M, there exists a direct summand D of M, such that T⊆X+K if and only if T⊆D+K, for every essential submodule K of M and T M. Also, let T, X and Y be submodules of a module M , then we say that Y is ET-weak supplemented of X in M if T⊆X+Y and (X⋂Y M. Also, we say that M is ET-weak supplemented module if each submodule of M has an ET-weak supplement in M. We give many characterizations of the ET-H-supplemented module and the ET-weak supplement. Also, we give the relation between the ET-H-supplemented and ET-lifting modules, along with the relationship between the ET weak -supplemented and ET-lifting modules.

Two well-known fluorescent molecules: fluorescein sodium salt (FSS) and 2,7-dichloro fluorescein (DCF) were tried to prove the efficiency, trustability and repeatability of ISNAG fluorimeter by using discrete and continuous flow injection analysis modes.A linear range of 0.002-1 mmol/L for FSS and 0.003-0.7 mmol/L was for DCF, with LOD 0.0018 mmol/L and 0.002 mmol/L for FSS and DCF respectively, were obtained for discrete mode of analysis. While the continuous mode gave a linear range of 0.002-0.7 mmol/L and 0.003-0.5 mmol/L for FSS and DCF respectively, the LOD were 0.0016mmol/L and 0.0018 mmol/L for FSS and DCF respectively. The results were compared with classical method at variable λ_ex for both fluorescent molecules at 95

The effect of thickness variation on some physical properties of hematite α-Fe2O3 thin films was investigated. An Fe2O3 bulk in the form of pellet was prepared by cold pressing of Fe2O3 powder with subsequent sintering at 800 . Thin films with various thicknesses were obtained on glass substrates by pulsed laser deposition technique. The films properties were characterized by XRD, and FT-IR. The deposited iron oxide thin films showed a single hematite phase with polycrystalline rhombohedral crystal structure .The thickness of films were estimated by using spectrometer to be (185-232) nm. Using Debye Scherrerś formula, the average grain size for the samples was found to be (18-32) nm. Atomic force microscopy indicated that the films had

In this article, an efficient reliable method, which is the residual power series method (RPSM), is used in order to investigate the approximate solutions of conformable time fractional nonlinear evolution equations with conformable derivatives under initial conditions. In particular, two types of equations are considered, which are time coupled diffusion-reaction equations (CD-REs) and MKdv equations coupled with conformable fractional time derivative of order α. The attitude of RPSM and the influence of different values of α are shown graphically.