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.

In this paper two ranking functions are employed to treat the fuzzy multiple objective (FMO) programming model, then using two kinds of membership function, the first one is trapezoidal fuzzy (TF) ordinary membership function, the second one is trapezoidal fuzzy weighted membership function. When the objective function is fuzzy, then should transform and shrinkage the fuzzy model to traditional model, finally solving these models to know which one is better

This work is concerned with the vibration attenuation of a smart beam interacting with fluid using proportional-derivative PD control and adaptive approximation compensator AAC. The role of the AAC is to improve the PD performance by compensating for unmodelled dynamics using the concept of function approximation technique FAT. The key idea is to represent the unknown parameters using the weighting coefficient and basis function matrices/vectors. The weighting coefficient vector is updated using Lyapunov theory. This controller is applied to a flexible beam provided with surface bonded piezo-patches while the vibrating beam system is submerged in a fluid. Two main effects are considered: 1) axial stretching of the vibrating beam that leads

Survivin, a member of inhibitor of apoptosis family is increasingly used as a target for cancer therapy design because it has a key role in cell growth and inhibition of cell apoptosis. Also it can be used as a biomarker for targeting cancer because it is found in almost all cancer but not normal cells. Our strategy was to design (computationally) a molecule to be used as survivin inhibitor. This molecule was named lead10 and was used furthermore to find (virtually) existing drugs with a good survivin inhibition activity.

Objective: The incidence of infectious diseases among hospitalized children remains high. This study describes the environmental health indicator diseases and differences between gender and age of the affected children. Patients & Methods: A review of hospitalization and death causes among children admitted to the Child Teaching Hospital for Pediatrics in Baghdad, Iraq was performed. Medical records of children admitted throughout three years period were collected for demographics data and statistical analysis using Chi-square test. Results: A total of 4,272 admissions and 309 deaths were recorded. Infectious diseases remain the primary cause of hospitalization among children and frequently lead to death; which recorded (56%) followed by ac

 A mixture model is used to model data that come from more than one component. In recent years, it became an effective tool in drawing inferences about the complex data that we might come across in real life. Moreover, it can represent a tremendous confirmatory tool in classification observations based on similarities amongst them. In this paper, several mixture regression-based methods were conducted under the assumption that the data come from a finite number of components. A comparison of these methods has been made according to their results in estimating component parameters. Also, observation membership has been inferred and assessed for these methods. The results showed that the flexible mixture model outperformed the

 A mixture model is used to model data that come from more than one component. In recent years, it became an effective tool in drawing inferences about the complex data that we might come across in real life. Moreover, it can represent a tremendous confirmatory tool in classification observations based on similarities amongst them. In this paper, several mixture regression-based methods were conducted under the assumption that the data come from a finite number of components. A comparison of these methods has been made according to their results in estimating component parameters. Also, observation membership has been inferred and assessed for these methods. The results showed that the flexible mixture model outperformed the others

The differential protection of power transformers appears to be more difficult than any type of protection for any other part or element in a power system. Such difficulties arise from the existence of the magnetizing inrush phenomenon. Therefore, it is necessary to recognize between inrush current and the current arise from internal faults. In this paper, two approaches based on wavelet packet transform (WPT) and S-transform (ST) are applied to recognize different types of currents following in the transformer. In WPT approach, the selection of optimal mother wavelet and the optimal number of resolution is carried out using minimum description length (MDL) criteria before taking the decision for the extraction features from the WPT tree

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