Our aim in this paper is to study the relationships between min-cs modules and some other known generalizations of cs-modules such as ECS-modules, P-extending modules and n-extending modules. Also we introduce and study the relationships between direct sum of mic-cs modules and mc-injectivity.

    We introduce in this paper the concept of approximaitly semi-prime submodules of unitary left -module  over a commutative ring  with identity as a generalization of a prime submodules and semi-prime submodules, also generalization of quasi-prime submodules and approximaitly prime submodules. Various basic properties of an approximaitly semi-prime submodules are discussed, where a proper submodule  of an -module  is called an approximaitly semi-prime submodule of  , if whenever , where ,  and , implies that . Furthermore the behaviors of approximaitly semi-prime submodule in some classes of modules are studied. On the other hand several characterizations of this concept are

           Let R be  commutative Ring , and let T be  unitary left .In this paper ,WAPP-quasi prime submodules are introduced as  new generalization of Weakly quasi prime submodules , where  proper submodule C of an R-module T is called WAPP –quasi prime submodule of T, if whenever 0≠rstϵC, for r, s ϵR , t ϵT, implies that either  r tϵ C +soc   or  s tϵC +soc  .Many examples of characterizations and basic properties are given . Furthermore several characterizations of WAPP-quasi prime submodules in the class of multiplication modules are established.

How I was eager to research the ruling on three of the most dangerous types to Islam and Muslims (the heretic, the sorcerer, the innovator, and related terms).
Because it is the most dangerous deadly disease that destroys the hearts of Muslims, and may even expel a Muslim from the circle of Islam, and how many Muslims have done or committed such a thing without knowing it. Indeed, how many Muslims have left Islam and whose wife has abandoned him without realizing it, and among them are those who have committed it without knowing it. As well as related words associated with heresy.( )
Because people debated such matters between extremists and lenient ones, most of whom were extremists, and they did not reach a conclusion. So I decid

Generalized Additive Model has been considered as a multivariate smoother that appeared recently in Nonparametric Regression Analysis. Thus, this research is devoted to study the mixed situation, i.e. for the phenomena that changes its behaviour from linear (with known functional form) represented in parametric part, to nonlinear (with unknown functional form: here, smoothing spline) represented in nonparametric part of the model. Furthermore, we propose robust semiparametric GAM estimator, which compared with two other existed techniques.

This paper demonstrates the construction of a modern generalized Exponential Rayleigh distribution by merging two distributions with a single parameter. The "New generalized Exponential-Rayleigh distribution" specifies joining the Reliability function of exponential pdf with the Reliability function of Rayleigh pdf, and then adding a shape parameter for this distribution. Finally, the mathematical and statistical characteristics of such a distribution are accomplished

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