Some Results on Fuzzy Zariski

Topology  on Spec(J.L)

This study has been conducted to know the level of microbial ( bacteria and fungi) contamination in 5 types of biscuits from local markets of Baghdad city. Fifty samples (ten sample for each kind of biscuit) were studed,Two are local,others are Iranian,Turkish,and Holandies. The following results have been achieved :1. The highest number of bacteria was 21.6×103 cell/g in Iranian biscuit while the lowest number was 14.3× 103 cell/g in local biscuit No.1 . The highest number of fungi was 16×103 colony/g and the lowest number was 5.3×103 colony/g in the Iranian and the local biscuit No.1,respectively.2. Staphylococcus aureus was the major bacteria appeared at highest level of 100% in Turkish biscuit. The lowest percentage was found in H

      Let  be a commutative ring with identity. The aim of this paper is introduce the notion of a pseudo primary-2-absorbing submodule as generalization of 2-absorbing submodule and a pseudo-2-absorbing submodules. A proper submodule  of an -module  is called pseudo primary-2-absorbing if whenever , for , , implies that either                  or  or . Many basic properties, examples and characterizations of these concepts are given. Furthermore, characterizations of pseudo primary-2-absorbing submodules in some classes of modules are introduced. Moreover, the behavior of a pseudo primary-2-absorbing submodul

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

The estimation of the regular regression model requires several assumptions to be satisfied such as "linearity". One problem occurs by partitioning the regression curve into two (or more) parts and then joining them by threshold point(s). This situation is regarded as a linearity violation of regression. Therefore, the multiphase regression model is received increasing attention as an alternative approach which describes the changing of the behavior of the phenomenon through threshold point estimation. Maximum likelihood estimator "MLE" has been used in both model and threshold point estimations. However, MLE is not resistant against violations such as outliers' existence or in case of the heavy-tailed error distribution. The main goal of t

In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

A chemical study was carried out to evaluate the efficiency of the liver enzyme concertation and uric acid level and its antagonists in the serum of the professors exposed to chemicals in the laboratories of the University of Samarra and their comparison with the healthy people. The research included 25 samples of the exposed professors and 20 samples as a group of officers.

              The results of the current study showed a significant increase in the level of   AST, ALT in the serum of professors exposed to chemicals compared to healthy people. The results showed no significant increase in

The study of cohomology groups is one of the most intensive and exciting researches that arises from algebraic topology. Particularly, the dimension of cohomology groups is a highly useful invariant which plays a rigorous role in the geometric classification of associative algebras. This work focuses on the applications of low dimensional cohomology groups. In this regards, the cohomology groups of degree zero and degree one of nilpotent associative algebras in dimension four are described in matrix form.