In this article, we introduce and study two new families of analytic functions by using strong differential subordinations and superordinations associated with Wanas differential operator/. We also give and establish some important properties of these families.

Let R be an associative ring with identity, and let M be a unital left R-module, M is called totally generalized *cofinitely supplemented module for short ( T G*CS), if every submodule of M is a Generalized *cofinitely supplemented ( G*CS ). In this paper we prove among the results under certain condition the factor module of T G*CS is T G*CS and the finite sum of T G*CS is T G*CS.

Let M be ,-ring and X be ,M-module, Bresar and Vukman studied orthogonal
derivations on semiprime rings. Ashraf and Jamal defined the orthogonal derivations
on -rings M. This research defines and studies the concepts of orthogonal
derivation and orthogonal generalized derivations on ,M -Module X and introduces
the relation between the products of generalized derivations and orthogonality on
,M -module.

Background & Objective: Breast cancer (BC) is the most prevalent disease among women around the world, considered the world's leading cause of death (15% of the total cancer deaths) in women in 2018. β-catenin is a multifunctional protein located in the cytoplasm and/or nucleus of the cell. Several studies suggested that β-catenin expression plays a critical role in cancer invasion and metastasis. This research sought to examine β-catenin expression in breast cancer and its associations with clinico-pathological features (such as histopathological types, grade, and invasion depth of tumor as well as lymph node involvement) and breast cancer patient survival. Methods:

In this work the concept of semi-generalized regular topological space was introduced and studied via semi generalized open sets. Many properties and results was investigated and studied, also it was shown that the quotient space of semi-generalized regular topological space is not, in general semi-generalizedspace.

In this paper, we introduce weak and strong forms of ω-perfect mappings, namely the -ω-perfect, weakly -ω-perfect and strongly-ω-perfect mappings. Also, we investigate the fundamental properties of these mappings. Finally, we focused on studying the relationship between weakly -ω-perfect and strongly -ω-perfect mappings.

In the present paper, we will study the generalized ( p, q) -type and
generalized lower ( p, q) -type of an entire function in several complex
variables with respect to the proximate order with index pair ( p, q) are
defined and their coefficient characterizations are obtained.

This paper deal with the estimation of the shape parameter (a) of Generalized Exponential (GE) distribution when the scale parameter (l) is known via preliminary test single stage shrinkage estimator (SSSE) when a prior knowledge (a₀) a vailable about the shape parameter as initial value due past experiences as well as suitable region (R) for testing this prior knowledge.

The Expression for the Bias, Mean squared error [MSE] and Relative Efficiency [R.Eff(×)] for the proposed estimator are derived. Numerical results about beha

In this paper we introduce and study the concepts of semisimple gamma modules , regular gamma modules and fully idempotent gamma modules as a generalization of semisimple ring. An module is called fully idempotent (semisimple , regular) if for all submodule of (every submodule is a direct summand, for each , there exists and such that . We study some properties and relationships between them.