The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

In most manufacturing processes, and in spite of statistical control, several process capability indices refer to non conformance of the true mean (µc ) from the target mean ( µT ), and the variation is also high. In this paper, data have been analyzed and studied for a blow molded plastic product (Zahi Bottle) (ZB). WinQSB software was used to facilitate the statistical process control, and process capability analysis and some of capability indices. The relationship between different process capability indices and the true mean of the process were represented, and then with the standard deviation (σ ), of achievement of process capability value that can reduce the standard deviation value and improve production out of theoretical con

The effects of shot peening treatment (SPT) were studied at (10,20, and 30) minutes on the rotating bending fatigue behavior and the behavior of the alloy steel DIN 41Cr4 vibrations. The hardness test, tensile test, constant amplitude fatigue tests, and the vibration measurements were performed on samples with and without cracks at room temperature (RT), also, the fracture surface was examined and analyzed by a Scanning Electron Microscope (SEM). The results of the investigations, for example, Stress to Number of cycles to failure (S-N) curves, fatigue strength improvement factor of 5% to 10%, the decreasing percentage of maximum Fast Fourier Transform (FFT) acceleration of the shot-peened condition were compared to untr

In this study water quality was indicated in terms of Water Quality Index that was determined through summarizing multiple parameters of water test results. This index offers a useful representation of the overall quality of water for public or any intended use as well as indicating pollution, which are useful in water quality management and decision making. The application of Water Quality Index (WQI) with ten physicochemical water quality parameters was performed to evaluate the quality of Euphrates River water for drinking usage. This was done by subjecting the water samples collected from seven stations within Al-Anbar province during the period 2004-2010 to comprehensive physicochemical analysis. The ten physicochemical parame

In this study water quality was indicated in terms of Water Quality Index that was determined through summarizing multiple parameters of water test results. This index offers a useful representation of the overall quality of water for public or any intended
use as well as indicating pollution, which are useful in water quality management and decision making. The application of Water Quality Index (WQI) with ten physicochemical water quality parameters was performed to evaluate the quality of Euphrates River water for drinking usage. This was done by subjecting the water samples collected from seven stations within Al-Anbar province during the period 2004-2010 to comprehensive physicochemical analysis. The ten physicochemical paramete

In this work, the relationship between the ionospheric parameters (Maximum Usable Frequency (MUF), Lowest Usable Frequency (LUF) and Optimum working Frequency (OWF)) has been studied for the ionosphere layer over the Iraqi zone. The capital Baghdad (44.42^oE, 33.32^oN) has been selected to represent the transmitter station and many other cities that spread over Iraqi region have represented as receiver stations. The REC533 communication model considered as one of the modern radio broadcasting version of ITU has been used to calculate the LUF parameter, while the MUF and OWF ionospheric parameters have been generated using ASAPS international communication model which represents one of the most advanced  and

Passive optical network (PON) is a point to multipoint, bidirectional, high rate optical network for data communication. Different standards of PONs are being implemented, first of all PON was ATM PON (APON) which evolved in Broadband PON (BPON). The two major types are Ethernet PON (EPON) and Gigabit passive optical network (GPON). PON with these different standards is called xPON. To have an efficient performance for the last two standards of PON, some important issues will considered. In our work we will integrate a network with different queuing models such M/M/1 and M/M/m model. After analyzing IPACT as a DBA scheme for this integrated network, we modulate cycle time, traffic load, throughput, utilization and overall delay

       In this paper, the classical continuous triple optimal control problem (CCTOCP) for the triple nonlinear parabolic boundary value problem (TNLPBVP) with state vector constraints (SVCs) is studied.  The solvability theorem for the classical continuous triple optimal control vector CCTOCV with the SVCs is stated and proved. This is done under suitable conditions. The mathematical formulation of the adjoint triple boundary value problem (ATHBVP) associated with TNLPBVP is discovered. The Fréchet derivative of the Hamiltonian" is derived.  Under suitable conditions, theorems of necessary  and sufficient conditions for the optimality of the TNLPBVP with the SVCs are stated and proved.    

Direct field-orientation Control (DFOC) of induction motor drives without mechanical speed sensors at the motor shaft has the attractions of low cost and high reliability. To replace the sensor, information on the rotor speed and position are extracted from measured stator currents and from voltages at motor terminals. In this paper presents direct field-orientation control (DFOC) with two type of kalman filter (complete order and reduced order extended kalman filter) to estimate flux, speed, torque and position. Simulated results show how good performance for reduced order extended kalman filter over that of complete  order extended kalman filter in tracking performance and reduced time of state estimation.

       In this work, we prove that the triple linear partial differential equations (PDEs) of elliptic type (TLEPDEs) with a given classical continuous boundary control vector (CCBCVr) has a unique "state" solution vector (SSV)  by utilizing the Galerkin's method (GME). Also, we prove the existence of a classical continuous boundary optimal control vector (CCBOCVr) ruled by the TLEPDEs. We study the existence solution for the triple adjoint equations (TAJEs) related with the triple state equations (TSEs). The Fréchet derivative (FDe) for the objective function is derived. At the end we prove the necessary "conditions" theorem (NCTh) for optimality for the problem.