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.
This histological study was carried out to compare between the thyroid gland of mice (as a model of the mammals) and the thyroid tissue of fish. Unlike mice, the thyroid gland of fish can't be recognized by naked eye. The present study revealed that the thyroid of mice varied from that of fish by the location and the histological structure. The study classified the physiological state of the thyroid of mice into three states and that of the fish into only two states. Accordingly, the study concluded that the metabolism of thyroid fish was of moderate type.
Background: Community pharmacists endure significantly elevated levels of work-related stress and depression, posing a threat to their overall well-being and possibly affecting the quality of patient care. Objectives: To explore workplace-associated stress and depression in Iraqi community pharmacists. Methods: This observational study was conducted using a cross-sectional design. Information was gathered through the utilization of an internet-based survey. The study involved a community pharmacist with a minimum of one year of experience working at community pharmacies. The survey utilized pre-validated questionnaires. The level of stress experienced was assessed using the Perceived Stress Scale (PSS)-10, while the level of depression was
... Show MoreIn this paper, the effect of wear in the fluid film journal bearings on the dynamic stability of rotor bearing system has been studied depending on the development of new analytical equations for motion, instability threshold speed and steady state harmonic response for rotor with offset disc supported by worn journal bearings. Finite element method had been used for modeling the rotor bearing system. The analytical model is verified by comparing its results with that obtained numerically for a rotor supported on the short bearings. The analytical and numerical results showed good agreement with about 8.5% percentage error in the value of critical speed and about 3.5% percentage error in the value of harmonic response. T
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