In the present paper, we investigate approximation to analytic function having property B by complex linear operators sequence in Parabolic domain. We apply Gergen, Dressel and Purcell's method to Chlodovsky type complex Szasz operators.

A new method of optimization on linear Parabolic solar collectors using exergy analysis is presented. A comprehensive mathematical modeling of thermal and optical performance is simulated and geometrical and thermodynamic parameters were assumed as optimization variables. By applying a derived expression for exergy efficiency, exergy losses were generated and the optimum design and operating conditions were investigated. The objective function (exergy efficiency) along with constraint equations constitutes a four-degree freedom optimization problem. Using Lagrange multipliers method, the optimization procedure was applied to a typical collector and the optimum design point was extracted. The optimum values of collector inlet temperature, oil mass flow rate, concentration ratio and glass envelope diameter are calculated simultaneously by numerical solution of a highly non-linear equations system. To study the effect of changes in optimization variables on the collected exergy, the sensitivity of optimization to changes in collector parameters and operating conditions is evaluated and variation of exergy fractions at this point are studied.

In this paper experimental study was carried out to investigate supercavitation around Parabolic cavitators. Various types of cavitators, such as disk, cone, and Parabolic, were designed and manufactured. Also, the shape of the cavities formed behind these bodies were considered and compared. Dimensionless parameters such as dimensionless length and the diameter of the cavity as well as the dimensionless required air flow on the cavitators were obtained. The results showed that Parabolic cavitators have an optimum design in comparison with the disk and cone cavitators due to their insignificant capability to reduce the drag force, yet the cavity’ s length has a moderate size. It was also observed that this type of cavitator is capable of forming a cavity with a dimensionless length up to L/d= 33 and a dimensionless width up to D/d= 3. 6. Moreover, Parabolic cavitators require the highest amount of air injected in comparison with the cone and disk types; therefore, they operate in lower cavitation numbers. Since no other experimental data has been reported so far, this work reports the experimental characteristic behavior of Parabolic cavitators.

In this study, a new unconditionally stable time integration is proposed for solving the differential equation of motion. Due to increase in order of variations of acceleration, proposed method has higher accuracy than classical methods. Two variable parameters are used to increase the stability and accuracy of the method. The proposed method is second order accurate and also it includes methods with numerical dissipation which can be used to filter the high undesirable frequencies. Moreover in the proposed method, equation of motion is exactly satisfied at the beginning and at the end of the time step.

Holder estimates of solutions of initial-boundary problem degenerate nonlinear Parabolic equations are obtained. Estimates for solutions and Parabolic Harnack inequality are proved. Also, one variant of weighted Poincare inequality is shown.

The boundary control of nonlinear Parabolic equation with an integral performance criterion and a fixed final state is considered. By means of a well-known process of embedding (used by Rubio and others) for finite-dimensional system, this problem is replaced by one in which a linear form is minimized over a set of pairs of positive radon measures satisfying linear constraints. The optimal pair measures are then approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution of this problem is used to construct a piecewise constant optimal control.The Advantages of this formulation are:(i) There is automatic existence theory.(ii) There exists the possibility of using linear functional analysis to developed the theory.(iii) The minimization is global.A numerical example is considered to illustrate the procedure.