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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In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler an

Abstract

The  common types of movement disorders are ; dystonia which is a syndrome  of  repetitive muscle contractions. While , Huntington disease is autosomal dominant progressive neurodegenerative disorder, which is characterized by involuntary movements (“chorea”).

Tetrabenazine therapy has been shown to effectively control this movements compared with placebo.

Design the proper dosing approach for patients treated with tetrabenazine with genotype polymorphisms and their hepatic effect on patients.

A prospective case controlled study was carried on 50 patients whom    divided into 2 groups :first group involved 25 patients who had cho

Fuzzy Based Clustering for Grayscale Image Steganalysis

In this paper, two of the local search algorithms are used (genetic algorithm and particle swarm optimization), in scheduling number of products (n jobs) on a single machine to minimize a multi-objective function which is denoted as  (total completion time, total tardiness, total earliness and the total late work). A branch and bound (BAB) method is used for comparing the results for (n) jobs starting from (5-18). The results show that the two algorithms have found the optimal and near optimal solutions in an appropriate times.

In this paper, we generalized the principle of Banach contractive to the relative formula and then used this formula to prove that the set valued mapping has a fixed point in a complete partial metric space. We also showed that the set-valued mapping can have a fixed point in a complete partial metric space without satisfying the contraction condition. Additionally, we justified an example for our proof.

        In our research, we introduced new concepts, namely ^*and **-light mappings, after we knew ^*and **-totally disconnected mappings through the use of -open sets.

Many examples, facts, relationships and results have been given to support our work.

The research aims to evaluate the suppliers at Diyala general electric industries company conducted in an environment of uncertainty and fuzzy where there is no particular system followed by the company, and also aims to use the problem of traveling salesman problem in the process of transporting raw materials from suppliers to the company in a fuzzy environment. Therefore, a system based on mathematical methods and quantity was developed to evaluate the suppliers. Fuzzy inference system (FIS) and fuzzy set theory were used to solve this problem through (Matlab) and the problem of the traveling salesman in two stages was also solved by the first stage of eliminating the fuzzing of the environment using the rank function method, w

   This study includes Estimating scale parameter, location parameter  and reliability function  for Extreme Value (EXV) distribution by two methods, namely: -
- Maximum Likelihood Method (MLE).
- Probability Weighted Moments Method (PWM).

 Used simulations to generate the required samples to estimate the parameters and reliability function of different sizes(n=10,25,50,100) , and give real values for the parameters are and , replicate the simulation experiments (R_P=1000)

Design sampling plan was and still one of most importance subjects because it give lowest cost  comparing with others, time live statistical distribution should be known to give best estimators for  parameters of sampling plan and get best sampling plan.

Research dell with design sampling plan when live time distribution follow Logistic distribution with () as location and shape parameters, using these information can help us getting (number of groups, sample size) associated with reject or accept the Lot

Experimental results for simulated data shows the least number of groups and sample size needs to reject or accept the Lot with certain probability of