This paper deals with the continuous classical optimal control problem for triple partial differential equations of parabolic type with initial and boundary conditions; the Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution for given continuous classical control vector. The proof of the existence theorem of a continuous classical optimal control vector associated with the triple linear partial differential equations of parabolic type is given. The derivation of the Fréchet derivative for the cost function is obtained. At the end, the theorem of the necessary conditions for optimality of this problem is stated and is proved.

Low-level microbial activity due to the production of organic acids is a recognized problem during the initial phase of food waste composting. Increasing such activity levels by adjusting the pH values during the initial composting phase is the primary objective to be investigated. In this study, sodium acetate (NaoAc) was introduced as an amendment to an in-vessel composting system. NaoAc was added when the pH of the compost mixture reached a low level (pH < 5), the addition increased pH to 5.8. This had a positive effect on the degradation of organic materials i.e. the formation of methane gas compared to the results without NaoAc addition.

The results also proved that anaerobic-aerobic in-vessel composting could reduce the

Artificial pancreas is simulated to handle Type I diabetic patients under intensive care by automatically controlling the insulin infusion rate. A Backstepping technique is used to apply the effect of PID controller to blood glucose level since there is no direct relation between insulin infusion (the manipulated variable) and glucose level in Bergman’s system model subjected to an oral glucose tolerance test by applying a meal translated into a disturbance. Backstepping technique is usually recommended to stabilize and control the states of Bergman's class of nonlinear systems. The results showed a very satisfactory behavior of glucose deviation to a sudden rise represented by the meal that increase the blood glucose

The reaction oisolated and characterized by elemental analysis (C,H,N) , 1H-NMR, mass spectra and Fourier transform (Ft-IR). The reaction of the (L-AZD) with: [VO(II), Cr(III), Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II)], has been investigated and was isolated as tri nuclear cluster and characterized by: Ft-IR, U. v- Visible, electrical conductivity, magnetic susceptibilities at 25 Co, atomic absorption and molar ratio. Spectroscopic evidence showed that the binding of metal ions were through azide and carbonyl moieties resulting in a six- coordinating metal ions in [Cr (III), Mn (II), Co (II) and Ni (II)]. The Vo (II), Cu (II), Zn (II), Cd (II) and Hg (II) were coordinated through azide group only forming square pyramidal

       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.    

       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.

The optimal combination of aluminum quality, sufficient strength, high stress to weight ratio and clean finish make it a good choice in driveshafts fabrication. This study has been devoted to experimentally investigate the effect of applying laser shock peening (LSP) on the fatigue performance for 6061-T6 aluminum alloy rotary shafts. Q-switched pulsed Nd:YAG laser was used with operating parameters of 500 mJ and 600 mJ pulse energies, 12 ns pulse duration and 10 Hz pulse repetition rate. The LSP is applied at the waist of the prepared samples for the cyclic fatigue test. The results show that applying 500 mJ pulse energy yields a noticeable effect on enhancing the fatigue strength by increasing the required number of cycles to fracture the

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Gas coning is one of the most serious problems in oil wells. Gas will reach the perforations and be produced with oil. Anyhow there is a certain production rate called critical production rate. The daily production rate should not exceed the critical production rate. In this research ten oil wells have been tested for problem of gas coning for a period of time of eighteen months. The production rates of these Ten oil wells are tabulated in a table exist in this research.
These production rates are considered as critical production rate because no gas coning has been observed in these wells. The critical production rates of these wells don't concide with those obtained from (Meyer, Gardiner, Pirson) method and also they don’t concide