This paper  concerns with the state and proof the existence and uniqueness theorem of triple state vector solution (TSVS) for the triple nonlinear parabolic partial differential equations (TNPPDEs) ,and triple state vector equations (TSVEs), under suitable assumptions. when the continuous classical triple control vector (CCTCV) is given by using the method of Galerkin (MGA). The existence theorem of a continuous classical optimal triple control vector (CCTOCV) for the continuous classical optimal control governing by the TNPPDEs under suitable conditions is proved.  

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

The goal of the research is to introduce new types of maps called semi totally Bc-continuous map and totally Bc-continuous map furthermore, study its properties. Additionally, we study the relationship of these functions and other known mappings are discussed.

The studies on unbonded post-tensioned concrete members strengthened with Carbon Fiber Reinforced Polymers (CFRPs) are limited and the effect of strengthening on the strain of unbonded pre-stressed steel is not well characterized. Estimating the flexural capacity of unbound post-tensioned members using the design methodology specified in the design guidelines for FRP strengthening techniques of bonded post-tensioned members does not provide a reliable evaluation. This study investigates the behavior of unbonded post-tensioned concrete members with partial strand damage (14.3% and 28.6% damage) and strengthened with CFRP laminates using a near-surface mounted technique with and without U-wrap anchorages. The experimental results show

      In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules as a generalization to the type of R- maximal submodule, where a proper submodule  of an R-module  is called Pr- maximal if  ,for any submodule  of W is a pure submodule of W, We offer some properties of a Pr-maximal submodules, and we give Definition of the concept, near-maximal, a proper submodule  

 of an R-module  is named near (N-maximal) whensoever  is pure submodule of  such that  then K=.Al so we offer the concept Pr-module, An R-module W is named Pr-module, if every proper submodule of  is Pr-maximal. A ring  is named Pr-ring if whole proper ideal of  is a Pr-maximal ideal, we offer the concept pure local (Pr-loc

In this paper, the path of the extracted and focused ions by the electrostatic lense having three electrodes of the same size and shape have been studied. However, the first and third electrodes had a different potential from the second electrode and the distance between any three electrodes was (d).The beams of the charged particles were controlled by using electrostatic fields which are used for accelerating and focusing. This paper focuses also on the effect of electrodes potentials on ion beam focusing. It is found that the best focusing was achieved when the values of the potential of the first and third electrode are equal to half of the value of the second electrode. Concerning transmiting and acumulating the ions beams, the study sh

 In this paper, we propose a method using continuous wavelets to study the multivariate fractional Brownian motion through the deviations of the transformed random process to find an efficient estimate of Hurst exponent using eigenvalue regression of the covariance matrix. The results of simulations experiments shown that the performance of the proposed estimator was efficient in bias but the variance get increase as signal change from short to long memory the MASE increase relatively. The estimation process was made by calculating the eigenvalues for the variance-covariance matrix of Meyer’s continuous wavelet details coefficients.

 In this paper, we propose a method using continuous wavelets to study the multivariate fractional Brownian motion through the deviations of the transformed random process to find an efficient estimate of Hurst exponent using eigenvalue regression of the covariance matrix. The results of simulations experiments shown that the performance of the proposed estimator was efficient in bias but the variance get increase as signal change from short to long memory the MASE increase relatively. The estimation process was made by calculating the eigenvalues for the variance-covariance matrix of Meyer’s continuous wavelet details coefficients.