In modules there is a relation between supplemented and Ï€-projective semimodules. This relation was introduced, explained and investigated by many authors. This research will firstly introduce a concept of "supplement subsemimodule" analogues to the case in modules: a subsemimodule Y of a semimodule W is said to be supplement of  a subsemimodule X if it is minimal with the property X+Y=W. A subsemimodule Y is called a supplement subsemimodule if it is a supplement of some subsemimodule of W. Then, the concept of supplemented semimodule will be defined as follows: an S-semimodule W is said to be supplemented if every subsemimodule of W is a supplemen

The spread of novel coronavirus disease (COVID-19) has resulted in chaos around the globe. The infected cases are still increasing, with many countries still showing a trend of growing daily cases. To forecast the trend of active cases, a mathematical model, namely the SIR model was used, to visualize the spread of COVID-19. For this article, the forecast of the spread of the virus in Malaysia has been made, assuming that all Malaysian will eventually be susceptible. With no vaccine and antiviral drug currently developed, the visualization of how the peak of infection (namely flattening the curve) can be reduced to minimize the effect of COVID-19 disease. For Malaysians, let’s ensure to follow the rules and obey the SOP to lower the

     Let  be an R-module, and let  be a submodule of . A submodule  is called -Small submodule () if for every submodule  of  such that  implies that . In our work we give the definition of -coclosed submodule and -hollow-lifiting modules with many properties.

Let  be a commutative ring with an identity and be a unitary -module. We say that a non-zero submodule  of  is  primary if for each with en either or  and an -module  is a small primary if   =  for each proper submodule  small in. We provided and demonstrated some of the characterizations and features of these types of submodules (modules).  

In this paper, we introduce and study a new concept named couniform modules, which is a dual notion of uniform modules, where an R-module M is said to be couniform if every proper submodule N of M is either zero or there exists a proper submodule N1 of N such that is small submodule of Also many relationships are given between this class of modules and other related classes of modules. Finally, we consider the hereditary property between R-module M and R-module R in case M is couniform.

Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.

The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the stat

Let R be commutative ring with identity and let M be any unitary left R-module. In this paper we study the properties of ec-closed submodules, ECS- modules and the relation between ECS-modules and other kinds of modules. Also, we study the direct sum of ECS-modules.

المقدمة

تعد السياحة احد مستلزمات الحضارة الحديثة لما تفرزه من آثار ايجابية ودور متميز في دعم الاقتصاد الوطني وتقليل نسبة البطالة وتنشيط الحركة التجارية بين البلدان، اذ لا يمكن ان نتصور وجود بلد متحضر بلا فنادق ولا سياحة وتقديم مختلف السلع والخدمات سياحية التي يمكن ان تسبع الحاجات والرغبات واذواق السياح من خلال  وجود منشآت سياحية تعكس النمط السياحي القائم على اختلاف انواعه