Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if

 the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are  introduced and given some  properties .

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, we prove that our proposed localization algorithm named Improved
Accuracy Distribution localization for wireless sensor networks (IADLoc) [1] is the
best when it is compared with the other localization algorithms by introducing many
cases of studies. The IADLoc is used to minimize the error rate of localization
without any additional cost and minimum energy consumption and also
decentralized implementation. The IADLoc is a range free and also range based
localization algorithm that uses both type of antenna (directional and omnidirectional)
it allows sensors to determine their location based on the region of
intersection (ROI) when the beacon nodes send the information to the sink node and
the la

In this paper we introduce a new type of functions called the generalized regular
continuous functions .These functions are weaker than regular continuous functions and
stronger than regular generalized continuous functions. Also, we study some
characterizations and basic properties of generalized regular continuous functions .Moreover
we study another types of generalized regular continuous functions and study the relation
among them

Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.

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.

The energy expectation values for Li and Li-like ions ( , and ) have been calculated and examined within the ground state and the excited state in position space. The partitioning technique of Hartree-Fock (H-F) has been used for existing wave functions.

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

In this paper, we prove that our proposed localization algorithm named Improved
Accuracy Distribution localization for wireless sensor networks (IADLoc) [1] is the
best when it is compared with the other localization algorithms by introducing many
cases of studies. The IADLoc is used to minimize the error rate of localization
without any additional cost and minimum energy consumption and also
decentralized implementation. The IADLoc is a range free and also range based
localization algorithm that uses both type of antenna (directional and omnidirectional)
it allows sensors to determine their location based on the region of
intersection (ROI) when the beacon nodes send the information to the sink node and
the la

In the United States, the pharmaceutical industry is actively devising strategies to improve the diversity of clinical trial participants. These efforts stem from a plethora of evidence indicating that various ethnic groups respond differently to a given treatment. Thus, increasing the diversity of trial participants would not only provide more robust and representative trial data but also lead to safer and more effective therapies. Further diversifying trial participants appear straightforward, but it is a complex process requiring feedback from multiple stakeholders such as pharmaceutical sponsors, regulators, community leaders, and research sites. Therefore, the objective of this paper is to describe three viable strategies that can p