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 research has designed for studying the relationship between manufacturing strategy and its flexibility under the flexible manufacturing system with their reflection on the competitive environmental performance of the firm. To interpret and tackle the problem, a hypothesis has formulated stating that “ the competitive performance of a firm is interpreted by the manufacturing strategy and flexibility which are derived from the firm and its business  strategies under the flexible manufacturing system”. Related literatures with their theoretical dissertations, which enhanced the thoughtful content, have analyzed. An illustrative case study on the flexible manufacturing system at Toyota Motors Corporation working at the g

Background: Bacteriocin is a peptidic toxin has many advantages to bacteria in their ecological niche and has strong antibacterial activity. Objective: The aim of this study was to evaluation of bacteriocin using Streptococcus sanguinis isolated from human dental caries.

Subjects and Methods: Thirty five streptococcus isolates were diagnosed and tested for their production of bacteriocin, and then the optimal conditions for production of bacteriocin were determined.  After that, the purification of bacteriocin was made partially by ammonium sulfate at 95% saturation levels, followed by and gel filtration chromatography

abstract

the research discussed a stage of strategic management. The strategic of the evaluation of the proposed strategy through feedback is to ensure that it is implemented with the least possible variation. The research aims at evaluation  a proposed strategy for the Ministry of Planning for the years 2018-2022 in line with the orientations of the state, taking into account the surrounding environmental conditions. It relies on scientific bases and steps to formulate the strategy The extent of the strategy suitability was tested through a set of statistical means and its objectivity was verified through a survey of a number of specialized experts who were selected in accordance with the principle