In this article, we study the notion of closed Rickart modules. A right R-module M is said to be closed Rickart if, for each , is a closed submodule of M. Closed Rickart modules is a proper generalization of Rickart modules. Many properties of closed Rickart modules are investigated. Also, we provide some characterizations of closed Rickart modules. A necessary and sufficient condition is provided to ensure that this property is preserved under direct sums. Several connections between closed Rickart modules and other classes of modules are given. It is shown that every closed Rickart module is -nonsingular module. Examples which delineate this concept and some results are provided.

     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, the Normality set  will be investigated. Then, the study highlights some concepts properties and important results. In addition, it will prove that every operator with normality set has non trivial invariant subspace of  .

Establishing coverage of the target sensing field and extending the network’s lifetime, together known as Coverage-lifetime is the key issue in wireless sensor networks (WSNs). Recent studies realize the important role of nature-inspired algorithms in handling coverage-lifetime problem with different optimization aspects. One of the main formulations is to define coverage-lifetime problem as a disjoint set covers problem. In this paper, we propose an evolutionary algorithm for solving coverage-lifetime problem as a disjoint set covers function. The main interest in this paper is to reflect both models of sensing: Boolean and probabilistic. Moreover, a heuristic operator is proposed as a local refinement operator to improve the quality

    The attribute quality control charts are one of the main useful tools to use in control of quality product in companies. In this paper utilizing the statistical procedures to find the attribute quality control charts for through fuzzified the real data which we got it from Baghdad Soft Drink Company in Iraq, by using triangular membership function to obtain the fuzzy numbers then employing the proposed ranking function to transform to traditional sample. Then, compare between crisp and fuzzy attribute quality control.

In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.

This paper is concerned with the quaternary nonlinear hyperbolic boundary value problem (QNLHBVP) studding constraints quaternary optimal classical continuous control vector (CQOCCCV), the cost function (CF), and the equality and inequality quaternary state and control constraints vector (EIQSCCV). The existence of a CQOCCCV dominating by the QNLHBVP is stated and demonstrated using the Aubin compactness theorem (ACTH) under appropriate hypotheses (HYPs). Furthermore, mathematical formulation of the quaternary adjoint equations (QAEs) related to the quaternary state equations (QSE) are discovere  so as its weak form (WF) . The directional derivative (DD) of the Hamiltonian (Ham) is calculated. The necessary and sufficient conditions for

     Group action on the projective space PG(3,q)  is a method which can be used to construct some geometric objects for example cap. We constructed new caps in PG(3,13)  of degrees 2, 3, 4, 7,14 and sizes 2, 4, 5, 7, 10, 14, 17, 20, 28, 34, 35, 68, 70, 85, 119, 140, 170, 238, 340, 476, 595, 1190. Then the incomplete caps are extended to complete caps. 

Identifying people by their ear has recently received import attention in the literature. The accurate segmentation of the ear region is vital in order to make successful person identification decisions. This paper presents an effective approach for ear region segmentation from color ear images. Firstly, the RGB color model was converted to the HSV color model. Secondly, thresholding was utilized to segment the ear region. Finally, the morphological operations were applied to remove small islands and fill the gaps. The proposed method was tested on a database which consisted of 105 ear images taken from the right sides of 105 subjects. The experimental results of the proposed approach on a variety of ear images revealed that this approac

      The purpose of this article is to partition PG(3,11) into orbits. These orbits are studied from the view of caps using the subgroups of PGL(4,11) which are determined by nontrivial positive divisors of the order of PG(3,11). The τ_i-distribution and c_i-distribution are also founded for each cap.