A non-zero submodule N of M is called essential if N L for each non-zero submodule L of M. And a non-zero submodule K of M is called semi-essential if K P for each non-zero prime submodule P of M. In this paper we investigate a class of submodules that lies between essential submodules and semi-essential submodules, we call these class of submodules weak essential submodules.

In this paper, as generalization of second modules we introduce type of modules namely (essentially second modules). A comprehensive study of this class of modules is given, also many results concerned with this type and other related modules presented.

The aim of current study is estimate the ability of low cost adsorbents, which consist of extracted silica from rice husk ash in treatment of Industrial waste water that contains heavy metals (Cd, Co and Pb) with other pollutants by fixed filters technique with determine the best method for that, and study the effect of a number of variables and parameters. This study involved one waste water samples were collected from. State battery manufacturing company (SBMC) (before treatment unit) at 5th and 22th, of the January 2015. Adsorption tests showed that all tested adsorbent materials had a significant heavy metal removal efficiency. pH values showed a significant impact on adsorption process, but best removal efficiency occurred at pH 4.5

Let R be a ring and let A be a unitary left R-module. A proper submodule H of an R-module A is called 2-absorbing , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H or rs∈[H:A], and a proper submodule H of an R-module A is called quasi-prime , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H. This led us to introduce the concept pseudo quasi-2-absorbing submodule, as a generalization of both concepts above, where a proper submodule H of an R-module A is called a pseudo quasi-2-absorbing submodule of A, if whenever rsta∈H,where r,s,t∈R,a∈A, implies that either rsa∈H+soc(A) or sta∈H+soc(A) or rta∈H+soc(A), where soc(A) is socal of an

Background: Extensive reports denote the biological role of trace elements (Cu Zn ", Se ') in many various physiological and pathological conditions, one of the list is shown to be Behcet's disease (BD).The aim of this study was directed towards the distribution of trace elements (Cu 2,Zn, 2,Se 2) in sera of BD patients, and control groups.
Methods: Fifty Arab Iraqi patients who fulfdled the ISO criteria for diagnosis BD.compared with 21 patients control with recurrent oral ulcer (ROU), healthy control groups (2Ihealthy relative and 21healthy volunteer). Typing HLA Class I was carried out at Alkarama hospital, by using microlympho-cytotoxicity test. The concentrations of serum Cu ', Zn ", and Se" were determined by atomic absorption s

Based on a finite element analysis using Matlab coding, eigenvalue problem has been formulated and solved for the buckling analysis of non-prismatic columns. Different numbers of elements per column length have been used to assess the rate of convergence for the model. Then the proposed model has been used to determine the critical buckling load factor () for the idealized supported columns based on the comparison of their buckling loads with the corresponding hinge supported columns . Finally in this study the critical buckling factor () under end force (P) increases by about 3.71% with the tapered ratio increment of 10% for different end supported columns and the relationship between normalized critical load and slenderness ratio was g

The effect of number of pulses of pulsed laser on materials is studied analytically, different pulses has been used with the same delay time.  The depth of possible damage to the surface of copper and titanium as well as depth of the crater to both materials were considered in this study.  The study revealed that linear model is only possible when estimating depth of possible damage for copper material, this means that the depth of possible damage increases with the increment of number of laser pulses .As for titanium material, it is found  the relationship is nonlinear.  The depth of possible damage of titanium and copper is not the same, and copper seems to be more predictable than titanium.  
 

      As a new technology, blockchain provides the necessary capabilities to assure data integrity and data security through encryption. Mostly, all existing algorithms that provide security rely on the process of discovering a suitable key. Hence, key generation is considered the core of powerful encryption. This paper uses Zernike moment and Mersenne prime numbers to generate strong prime numbers by extracting the features from biometrics (speech). This proposed system sends these unique and strong prime numbers to the RSA algorithm to generate the keys. These keys represent a public address and a private key in a cryptocurrency wallet that is used to encrypt transactions. The benefit of this work is that it provides a high degree

  In this paper we introduce the notion of semiprime fuzzy module as a generalization of semiprime module. We investigate several characterizations and properties of this concept.

Let  be a commutative ring with identity, and  be a unitary left -module. In this paper we introduce the concept pseudo weakly closed submodule as a generalization of -closed submodules, where a submodule  of an -module  is called a pseudo weakly closed submodule, if for all , there exists a -closed submodule  of  with  is a submodule of  such that . Several basic properties, examples and results of pseudo weakly closed submodules are given. Furthermore the behavior of pseudo weakly closed submodules in class of multiplication modules are studied. On the other hand modules with chain conditions on pseudo weakly closed submodules are established. Also, the relationships of  pseudo weakly closed