In this paper, an intelligent tracking control system of both single- and double-axis Piezoelectric Micropositioner stage is designed using Genetic Algorithms (GAs) method for the optimal Proportional-Integral-Derivative (PID) controller tuning parameters. The (GA)-based PID control design approach is a methodology to tune a (PID) controller in an optimal control sense with respect to specified objective function. By using the (GA)-based PID control approach, the high-performance trajectory tracking responses of the Piezoelectric Micropositioner stage can be obtained. The (GA) code was built and the simulation results were obtained using MATLAB environment. The Piezoelectric Micropositioner simulation model with th

 Summary

    I wanted to address this topic because of creedal purposes importance,and its r le in regulating lives of individuals and society, and to talk about purposes of Almighty's saying:{It is easy for me},to simplify its meanings for general educated person to obtain the believe of the Creator’s power and his oneness.

Therefore,this research came,whichincludes:an introduction and topics, first :concept of creedal objectives and their divisions,second: creedal purposes in Almighty’s saying:{It is easy for me},and conclusion:in where most important results were included:

Background: To assess the alveolar bone crest level (ABCL) by Cone Beam Computed To-mography (CBCT) and to investigate several variables as predictors for the height of the alveolar bone in adolescents. Materials and methods: Age, sex, and ethnic groups were rec-orded for each patient. CBCT images were used to obtain measurements of the interproximal alveolar bone level from the cementoenamel junction (CEJ) to the alveolar crest. The highest measurement in each sextant was recorded along with any presence of a vertical bone defect or calculus. Results: Total of 720 measurements were recorded for 120 subjects. No vertical bony defects or calculus were observed radiographically. Statistically significant (P< 0.05) differences were observed be

    Our aim in this work is to study the classical continuous boundary control vector  problem for triple nonlinear partial differential equations of elliptic type involving a Neumann boundary control. At first, we prove that the triple nonlinear partial differential equations of elliptic type with a given classical continuous boundary control vector have a unique "state" solution vector,  by using the Minty-Browder Theorem. In addition, we prove the existence of a classical continuous boundary optimal control vector ruled by the triple nonlinear partial differential equations of elliptic type with equality and inequality constraints. We study the existence of the unique solution for the triple adjoint equations

In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).

The Voluntary Obedience has great importance for the modern taxes systems and its management and this is meant the taxpayer whom in charge to pay of his taxes obligations voluntarily , he is very known of himself whereas he prepared his finishing accountings and present them as samples prepared by taxes management and settle the tax sum directly according to specified income , which has an impact to find end to tax evasion as result lead to increase the tax income and achieve the justice for the taxpayer and the state treasury

This research aims to determine the extent of the contribution of organizational downsizing strategies to enhance the health of the researched organization represented by the Directorate of Education in Nineveh, and to achieve this goal, the study provided a simplified intellectual framework for the most important topics covered by writers and researchers for search variables, reinforced by an applied analytical framework for the opinions of (79) individuals responsible for the researched organization. The research adopted organizational downsizing as an independent variable that includes three dimensions represented by (reduction of human resources, job redesign, systemic strategy), while the organizational health represented th