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.

        Nowadays, datacenters become more complicated and handle many more users’ requests. Custom protocols are becoming more demanded, and an advanced load balancer to distribute the  requests among servers is essential to serve the users quickly and efficiently. P4 introduced a new way to manipulate all packet headers. Therefore, by making use of the P4 ability to decapsulate the transport layer header, a new algorithm of load balancing is proposed. The algorithm has three main parts. First, a TCP/UDP separation  is used to separate the flows based on the network layer information about the used protocol in the transport layer. Second, a flow size prediction technique is adopted, which re

The study aimed to determine of some Optimum conditions for bioremediation and removing of seven mineral elements included hexavalent chromium, nickel, cobalt, cadmium, lead, iron and copper as either alone or in group by living and heat treated cells of baker’s yeast Saccharomyces cerevisiae. The dried baker's yeast from Aldnaamaya China Company was used in this study. Biochemical tests was used to ensure yeast belonging to S. cerevisiae and then used to remove the mentioned mineral elementes under different conditions which included incubation period, pH, and temperature. It was found that the best of these conditions was 60 minutes for duration of incubation, 6 for pH, 25 ᵒC for temperature. During the study the behavior of living

 The adsorption of Ru and Ce were carried out using manganese dioxide as adsorbent. The Optimization of the adsorption conditions were studied as a function of shaking time, nitric acid, metal ions, concentrations and temperature effects.      A rapid initial adsorption on MnO2 is followed by a steady and slow increase of metal uptake. The equilibration time is reached after four hours shaking for Ru and Ce and    the adsorption is much better from one molar acidic solution and 90°C.

Design of experiments (DOE) was made by Minitab software for the study of three factors used in the precipitation process of the Sodium Aluminate solution prepared from digestion of α-Al₂O₃  to determine the optimum conditions to a produce Boehmite which is used in production of ɤ-Al₂O₃ during drying and calcination processes, the factors are; the temperature of the sodium aluminate solution, concentration of HCl acid added for the precipitation and the pH of the solution at which the precipitation was ended. The design of the experiments leads to 18 experiments.

   The results show that the optimum conditions for the precipitation of the sodium aluminate solution which

     The aim of this paper is to study the quaternary classical continuous optimal control for a quaternary linear parabolic boundary value problems(QLPBVPs). The existence and uniqueness theorem of the continuous quaternary state vector solution  for the weak form of the QLPBVPs with given quaternary classical continuous control vector (QCCCV)  is stated and proved via the Galerkin Method. In addition, the existence theorem of a quaternary classical continuous optimal control vector governinig by the QLPBVPs is stated and demonstrated. The Fréchet derivative for the cost function is derived. Finally, the necessary conditions for the optimality theorem  of the proposed problem is stated and  demonstrated.

This paper is concerned with finding the approximation solution (APPS) of a certain type of nonlinear hyperbolic boundary value problem (NOLHYBVP).  The given BVP is written in its discrete (DI) weak form (WEF), and is proved that  it has a unique APPS, which is obtained via the mixed Galerkin finite element method (GFE) with implicit method (MGFEIM) that reduces the problem to solve the Galerkin nonlinear algebraic system  (GNAS).  In this part, the predictor and the corrector technique (PT and CT) are proved convergent and are used to transform the obtained GNAS to  linear (GLAS ), then the GLAS is solved using the Cholesky method (ChMe). The stability and the convergence of the method are studied. The results

A new simple sensitive and selective spectrophotometric method has been developed for the analysis of vanadium(V) in three randomly chosen samples from river water at different locations by continuous flow injection analysis. The method based on the oxidation of pyrogallol by vanadium(V) in acidic solution to form color species and the same species was determined using homemade Ayah 6SX1-T-2D solar cell analyser . Chemical and physical parameters were investigated using the high intensity of snow white light emitted diode as a source. The linear dynamic range for the instrument response versus vanadium(V) concentration was 1-200 mg.L-1 with correlation coefficient r = 0.9920. The limit of detection (S/N=3) was 70 ng/ sample from the step

A new simple sensitive and selective spectrophotometric method has been
developed for the analysis of vanadium(V) in three randomly chosen samples from
river water at different locations by continuous flow injection analysis. The method
based on the oxidation of pyrogallol by vanadium(V) in acidic solution to form color
species and the same species was determined using homemade Ayah 6SX1-T-2D
solar cell analyser . Chemical and physical parameters were investigated using the
high intensity of snow white light emitted diode as a source. The linear dynamic
range for the instrument response versus vanadium(V) concentration was 1-200
mg.L-1 with correlation coefficient r = 0.9920. The limit of detection (S/N=3) was 70<