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.
The physical, the thermal and the mechanical properties of Nano-composites, that consisted of Polyprime EP epoxy that reinforced by multi-walled carbon nanotubes (MWCNTs), have been studied. Various loading ratios, 0.1, 0.5, and 1 wt. %of MWCNT shave been infused into epoxy by a magnetic stirrer and then the hardener mixed with the mthat supplied with the epoxy. All sample shave been cutting using CNC machine. Tensile test, three-point bending, hardness tests, lee's disk, differential scanning calorimetry, water absorption and dielectric and electrical conductivity test were utilized on unfilled, MWCNT-filled epoxy to identify the loading effect on the properties of materials. Scanning electron microscopy (SEM) was used to determine the
... Show MoreThe importance of economic and technical feasibility studies include all of the investor, the society, the banks, the project and the government. As it will assist in achieving the optimal use of the available economic incomes on the national level and arranging the projects in priority which participates in achieving the government benefit without wasting the amounts .This is the research goal So, the research covered its theoretical aspect, of SAIs and the economic and technical feasibility studies then the role of the auditors in auditing those studies Then a mechanism was proposed includes a guidebook that provides guidelines for organizing the process of preparing and auditi
... Show MoreCadmium sulfide and Aluminum doped CdS thin films were prepared by thermal evaporation technique in vacuum on a heated glass substrates at 373K. A comparison between the optical properties of the pure and doped films was made through measuring and analyzing the transmittance curves, and the effect of the annealing temperature on these properties were estimated. All the films were found to exhibit high transmittance in the visible/ near infrared region from 500nm to 1100nm.The optical band gap energy was found to be in the range 2.68-2.60 eV and 2.65-2.44 eV for CdS and CdS:Al respectively , with changing the annealing temperature from room temperature to 423K.Optical constants such as refractive index, extinction coefficient, and complex di
... Show MoreMost of us are tired of the circumstances that surround us because of their deficiency, deprivation, and sullenness, even though troubles and pains are the soil in which the seeds of strong personality sprout.
The content of the research is summed up in the fact that there is no need to frown, so let our face be free, and our word good and tolerant, so that we can be the most loving people of those who give them, and the Messenger of God (may God’s prayers and peace be upon him and his family) was known to be the heaviest concerns of people, but he was most smiling of people, by smiling, we buy lives, so we should get used to it, because that gives us hope and finds the world in our hands, an
... Show MoreThe compounding of polyvinyl chloride (PVC) with two types of fillers and some additives were studied for the manufacturing of acid resistant tile. Various concentrations of two types of fillers namely; calcium carbonate and recycled glass powder were used along with different additives generally categorized as plasticizers, stabilizers, and lubricants were mixed in the standard concentration unit parts per hundred resins (phr) with the PVC as base polymer. The effects of filler materials on acid resistant towered different acids like sulphuric, nitric and hydrochloric at different concentration were studied. Samples which passed the test were further checked for dielectric strength and mechanical properties. It was found that the recycl
... Show MoreThe frog has a highly developed nervous system. It consists of a brain, a spinal cord and nerves. The brain is the only center for the control of all vital activities as it receives impulses from different parts of the body through sensory nerves and issues orders through motor fibers to different parts of the body for appropriate action. The Aims of studyis general morphological structural of the brain and spinal cord in the Iraqi frog Rana ridibunda ridibunda. The brains of twenty of frogs belonging to class Amphibia were studied using conventional techniques of dissecting microscopy. All samples were sacrificed and anesthetized and then they were removed completely from the neurocranium, cranial, sensory nerves and the meninges and trans
... Show MoreA numerical investigation has been performed to examine the effect of fluorine concentration on the chain reaction mechanisms and parameters of hydrogen fluoride (HF) chemical laser. The practical difficulties associated with this type of lasers impose that an alternative route might be quite useful. Thus, particular attention was paid to develop a computer program to investigate various processes. The results of this computer simulation program proved their credibility when compared with the little published data. This computer program is called Reaction Rate Simulation Model (RRSM). An entirely new approach to emulate the reaction mechanisms has been followed. The effectiveness of reaction rates in the processes of HF lase
... Show MoreThis article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters.
Background: Waterpipe and cigarette are two products of tobacco consumption, tobacco use has detrimental effects on the oral cavity, numerous studies around the world have reported a significant relationship between smoking and increase dental caries and viable count of cariogenic bacteria, Materials and Methods: unstimulated saliva was collected from 84 subjects and divided equally into three groups waterpipe smokers, cigarette smokers, and non-smokers all of the participants are adult male aged between 25-60 years, dental caries was measured by use DMFT index, while S.mutans and S.sobrinus were isolated by using a selective medium SB 20M (Sugar bacitracin-20 modified) agar Results: this present study showed a significant (p≤0.01)
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