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

    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

Csaszar introduced the concept of generalized topological space and a new open set in a generalized topological space called -preopen in 2002 and 2005, respectively. Definitions of -preinterior and -preclosuer were given. Successively, several studies have appeared to give many generalizations for an open set. The object of our paper is to give a new type of generalization of an open set in a generalized topological space called -semi-p-open set. We present the definition of this set with its equivalent. We give definitions of -semi-p-interior and -semi-p-closure of a set and discuss their properties. Also the properties of -preinterior and -preclosuer are discussed. In addition, we give a new type of continuous function

In this paper, two of the local search algorithms are used (genetic algorithm and particle swarm optimization), in scheduling number of products (n jobs) on a single machine to minimize a multi-objective function which is denoted as  (total completion time, total tardiness, total earliness and the total late work). A branch and bound (BAB) method is used for comparing the results for (n) jobs starting from (5-18). The results show that the two algorithms have found the optimal and near optimal solutions in an appropriate times.

  Let M be an R-module, where R is commutative ring with unity. In this paper we study the behavior of strongly hollow and quasi hollow submodule in the class of strongly comultiplication modules. Beside this we give the relationships between strongly hollow and quasi hollow submodules with V-coprime, coprime, bi-hollow submodules.

      In this paper, we are mainly concerned with estimating cascade reliability model (2+1) based on inverted exponential distribution and comparing among the estimation methods that are used . The maximum likelihood estimator and uniformly minimum variance unbiased estimators are used to get  of the strengths  and the stress ;k=1,2,3 respectively then, by using the unbiased estimators, we propose Preliminary test single stage shrinkage (PTSSS) estimator when a prior knowledge is available for the scale parameter as initial value due past experiences . The Mean Squared Error [MSE] for the proposed estimator is derived to compare among the methods. Numerical results about conduct of the considered

     In this research, our aim is to study the optimal control problem (OCP) for triple nonlinear elliptic boundary value problem (TNLEBVP). The Mint-Browder theorem is used to prove the existence and uniqueness theorem of the solution of the state vector for fixed control vector. The existence theorem for the triple continuous classical optimal control vector (TCCOCV) related to the TNLEBVP is also proved. After studying the existence of a unique solution for the triple adjoint equations (TAEqs) related to the triple of the state equations, we derive The Fréchet derivative (FD) of the cost function using Hamiltonian function. Then the theorems of necessity conditions and the sufficient condition for optimality of

   In this paper, we introduce a new type of functions in bitopological spaces, namely, (1,2)*-proper functions. Also, we study the basic properties and characterizations of these functions . One of the most important of equivalent definitions to the (1,2)*-proper functions is given by using (1,2)*-cluster points of filters . Moreover we define and study (1,2)*-perfect functions and (1,2)*-compact functions in bitopological spaces and we study the relation between (1,2)*-proper functions and each of (1,2)*-closed functions , (1,2)*-perfect functions and (1,2)*-compact functions and we give an example when the converse may not be true .
 

The main idea of this research is to consider fibrewise pairwise versions of the more important separation axioms of ordinary bitopology named fibrewise pairwise - spaces, fibrewise pairwise - spaces, fibrewise pairwise - spaces, fibrewise pairwise -Hausdorff spaces, fibrewise pairwise functionally -Hausdorff spaces, fibrewise pairwise -regular spaces, fibrewise pairwise completely -regular spaces, fibrewise pairwise -normal spaces and fibrewise pairwise functionally -normal spaces. In addition we offer some results concerning it.