In this paper, the nonclassical approach to dynamic programming for the optimal control problem via strongly continuous semigroup has been presented. The dual value function VD ( .,. ) of the problem is defined and characterized. We find that it satisfied the dual dynamic programming principle and dual Hamilton Jacobi –Bellman equation. Also, some properties of VD (. , .) have been studied, such as, various kinds of continuities and boundedness, these properties used to give a sufficient condition for optimality. A suitable verification theorem to find a dual optimal feedback control has been proved. Finally gives an example which illustrates the value of the theorem which deals with the sufficient condition for optimality.

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ABSTRACT

         The effect of adding raw bacteriocin produced by Lactobacillus bulgaricus to cheese curd at an amount of (5 and 10 and 15) mL/kg cheese as a biological preservative to prolong the shelf life of soft cheese, in addition to the control treatment, knowing that each 1 mL of bacteriocin filter contains 15 units/ mL of bacteriocin. The results of the physicochemical, microbial and sensory tests for cheese stored at refrigerator temperature for a period (zero) to (21) d of adding bacteriocin showed the superiority of the treatment of cheese added to 15 mL/kg cheese of bacteriocin over the rest of the other treatments during the storage period, wh

The research focuses,in the first place, on six fields.The most important one is
curriculum field which includes the revision of the current academic curriculums and
substitute them with recent ones, beside the rehabilitation of academic labs and factories by
providing them with modern scientific technologies employed in the world. Regarding the
economical field, it seeks to provide high-level training staffs to serve different social and
economical sectors through modern effective technological and scientific
curriculums.Whereas the social field assures the concern of different social classes who
deprived from the grace of higher education such as retirees and elderly people and to set-up
some educational and ent

High   Alumina   Glasses   "Alumina   Silicate   Glasses"   was prepared by utilizing powder technology technique. The starting materials are wasted soda-lime glass from an industrial site, Iraqi­ Duekhla raw kaolin and small amounts of potassium carbonates.

X-ray Diffraction and FTIR analysis show complete vitreous glasses are obtained. Increasing Alumina content plays an obvious role in improving physical and mechanical properties of the prepared high  alumina  glass.   In  addition,  the   increased  alumina  content enhanced the dielectric constant and reduced dielectric loss. These results may be interpreted as du

      The service system has become a necessity of life in modern cities to be the most basic necessities of modern humans, they constitute a major base, which is based on the sustainability of life in the city and a standard measured through the degree of well-being and progress of civilized peoples and their interaction with the surrounding environment, making the services sector as a need not be an option, whenever the cities widened in population and space whenever provision of services and upgrading the quality and quantity more pressing, which made the subject of the services takes the biggest area of the trends and thinking of urban planners and those who in charge of drawing the cities policies. Consideri

Buckling analysis of composite laminates for critical thermal (uniform and linear) and mechanical loads is reported here. The objective of this work is to carry out theoretical investigation of buckling analysis of composite plates under thermomechanical loads, and experimental investigation under mechanical loads. The analytical investigation involved certain mathematical preliminaries, a study of equations of orthotropic elasticity for classical laminated plate theory (CLPT), higher order shear deformation plate theory (HSDT) , and numerical analysis (Finite element method), then the equation of motion are derived and solved using Navier method and Levy method for symmetric and anti-symmetric cross-ply and angle-ply laminated plates t

In this work, 332 Al alloy was prepared and reinforced with (0.5% and 1%) nano-Al₂O₃ particles. The prepared unreinforced and reinforced 332 Al alloy with nano-Al₂O₃ were solution heat treated (T6) at 510 ̊C and aged at 225 ̊C with different times (1, 3, and 5 h). Hardness test was performed on all the prepared alloys. All prepared alloys were dry slided under different applied loads (5, 10, 15, and 20 N) against steel counterface surface using pin on disk apparatus. The results showed that refinement effect was observed after addition of nano-Al₂O₃ particles and a change in silicon morphology after performing the solution heat treatment. The results also showed that har

Reciprocal Teaching is an interactive method that is used to improve reading comprehension. Using this teaching strategy, teachers and students take turns leading discussions regarding sections of text using the four strategies: predicting, questioning, clarifying and summarizing. This study is an attempt to investigate the effect of using reciprocal teaching on improving female college students' achievement in reading comprehension. To fulfill the aim of the study, the researcher has adopted two null hypotheses: first, there is no significant difference between the achievement of students' who practice the reciprocal teaching technique and that of students who do not practice it. Second, there is no statistically significant difference

The present research has investigated the effect of microwave energy on improving the flow properties of heavy crude oil. The fragmentation of crude oil molecules was carried out with and without using 1 and 10 wt. % concentration of various types of H-donors like tetralin, cyclohexane, and naphtha.  Microwave power of 320, 385, and 540 W and radiation time 1-9 min, and temperature were studied. The kinematic viscosity and asphaltene content were measured for evaluation the improving of heavy crude oil.

   Results show that viscosity of crude oil decreased with increase H-donor concentration, a maximum percentage of viscosity reduction was10.63 % for tetralin at 6 min radiation time, while 8.67%, and 7.34% for cycl