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 the case where a shallow foundation does not satisfy with design requirements alone, the addition of a pile may be suitable to improve the performance of the foundation design. The lack of in-situ data and the complexity of the issues caused by lagging in the research area of pile foundations are notable. In this study, different types of piles were used under the same geometric conditions to determine the load-settlement relationships with various sandy soil relative densities. The ultimate pile capacity for each selected pile is obtained from a modified California Bearing Ratio (CBR) machine to be suitable for axial pile loading. Based on the results, the values of Qu for close-ended square pile were increased by 15

This study focuses on the modeling of manufactured damper when used in steel buildings. The main aim of the manufactured dampers is to protect the steel buildings from the damaging effects that may result due to earthquakes by introducing an extra damping in addition to the traditional damping.
Only Pure Manufactured Dampers, has been considered in this study. Viscous modeling of damping is generally preferred in structural engineering as it leads to a linear model then it has been used during this study to simulate the behavior of the Pure Manufactured Damper.
After definition of structural parameters of a manufactured damper (its stiffness and its damping) it can be used as a structural element that can be added to a mathematica

The corrosion behavior of bare and chemical conversion coated (through anodizing) aluminum ASA 606 I in stagnant chromic acid solutions . Solutions of 2, 6 & J O wt. % Cr03 at 45°C, have been investigated using polarization technique. The anodizing experiments were conducted under fixed conditions of 35 minute exposure time and 30 volt supplied voltage. The most important feature achieved was the great difference in behavior between the anodic polarization curves for bare and anodized aluminum in different concentrations of chromic acid solutions.

Phenoxathiin was prepared by the reaction of diphenyl ether with sulfur in the presence of anhydrous aluminum chloride. This work comprised the synthesis of new phenoxathiin derivatives containing heterocyclic moieties. These heterocyclic compounds were synthesized in three groups. The first group was made up of 2-(oxoalken-1-yl) phenoxathiin derivatives (3a-3j) obtained from the reaction of 2-acetylphenoxathiin with different aromatic aldehyde in the presence of sodium hydroxide. The other two groups involved compounds produced from the reaction of (3a-3j) with hydrazine hydrate in acetic acid to get 2-(1-acetyl pyrazolin-3-yl) phenoxathiin derivatives (4a-4j), and phenyl hydrazine in the presence of piperidine to afford 2-(1-phenyl pyrazo

The importance of the present work falls on the pitting corrosion behavior investigation of 304 SS and 316 SS alloys in 3.5 wt%  of aqueous solution bearing with chloride and bromide anion  at different solutions temperature range starting from (20-50)^oC due to the pitting corrosion tremendous effect on the economic, safety and materials loss due to leakage. The impact of solution temperatures on the pitting corrosion resistance at 3.5wt% (NaCl and  NaBr) solutions for the 304 SS and 316 SS has been investigated utilizing the cyclic polarization techniques at the potential range -400 to1000 mV vs. SCE at 40 mV/sec scan rate followed by the surface characterization employing Scanning Electron&nbs