This paper adapted the neural network for the estimating of the direction of arrival (DOA). It uses an unsupervised adaptive neural network with GHA algorithm to extract the principal components that in turn, are used by Capon method to estimate the DOA, where by the PCA neural network we take signal subspace only and use it in Capon (i.e. we will ignore the noise subspace, and take the signal subspace only).

In this article, the inverse source problem is determined by the partition hyperbolic equation under the left end flux tension of the string, where the extra measurement is considered. The approximate solution is obtained in the form of splitting and applying the finite difference method (FDM). Moreover, this problem is ill-posed, dealing with instability of force after adding noise to the additional condition. To stabilize the solution, the regularization matrix is considered. Consequently, it is proved by error estimates between the regularized solution and the exact solution. The numerical results show that the method is efficient and stable.

          In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

The study presents the test results of Completely Decomposed Granite (CDG) soil tested under drained triaxial compression, direct shear and simple shear tests. Special attention was focused on the modification of the upper halve of conventional Direct Shear Test (DST) to behave as free
head in movement along with vertical strain control during shear stage by using Geotechnical Digital System (GDS). The results show that Free Direct Shear Test (FDST) has clear effect on the measured shear stress and vertical strain during the test. It has been found that shear strength
parameters measured from FDST were closer to those measured from simple shear and drained triaxial compression test. This study also provides an independent check on

        In this article, unless otherwise established, all rings are commutative with identity and all modules are unitary left R-module. We offer this concept of WN-prime as new generalization of weakly prime submodules. Some basic properties of weakly nearly prime submodules are given. Many characterizations, examples of this concept are stablished.

Gangyong Lee, S.Tariq Rizvi, and Cosmin S.Roman studied Rickart modules.

The main purpose of this paper is to develop the properties of Rickart modules .

We prove that each injective and prime module is a Rickart module. And we give characterizations of some kind of rings in term of Rickart modules.

In this article we derive two reliability mathematical expressions of two kinds of s-out of -k stress-strength model systems; and . Both stress and strength are assumed to have an Inverse Lomax distribution with unknown shape parameters and a common known scale parameter. The increase and decrease in the real values of the two reliabilities are studied according to the increase and decrease in the distribution parameters. Two estimation methods are used to estimate the distribution parameters and the reliabilities, which are Maximum Likelihood and Regression. A comparison is made between the estimators based on a simulation study by the mean squared error criteria, which revealed that the maximum likelihood estimator works the best.

     In this research, an unknown space-dependent force function in the wave equation is studied. This is a natural continuation of [1] and chapter 2 of [2] and [3], where the finite difference method (FDM)/boundary element method (BEM), with the separation of variables method, were considered. Additional data are given by the one end displacement measurement. Moreover, it is a continuation of [3], with exchanging the boundary condition, where  are extra data, by the initial condition. This is an ill-posed inverse force problem for linear hyperbolic equation. Therefore, in order to stabilize the solution, a zeroth-order Tikhonov regularization method is provided. To assess the accuracy, the minimum error between

In this paper, we develop the work of Ghawi on close dual Rickart modules and discuss y-closed dual Rickart modules with some properties. Then, we prove that, if are y-closed simple -modues and if -y-closed is a dual Rickart module, then either Hom ( ) =0 or . Also, we study the direct sum of y-closed dual Rickart modules.