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.

n this study, Cr−Mo−N thin films with different Mo contents were synthesised via closed field unbalanced magnetron sputtering ion plating. The effects of Mo content on the microstructure, chemical bonding state, and optical properties of the prepared films were investigated by X-ray diffraction spectroscopy (XRD), X-ray photoelectron spectroscopy (XPS), field emission scanning electron microscopy, and ultraviolet-visible spectrophotometry. XRD results determined the face centered cubic (fcc) structure of pure CrN film. The incorporation of molybdenum (Mo) in the CrN matrix was confirmed by both XRD and XPS analyses. The CrMoN coatings demonstrate various polycrystalline phases including CrN, γ-Mo2N, Cr with oxides layers of MoO3, CrO3,

In this study, Cr−Mo−N thin films with different Mo contents were synthesised via closed field unbalanced magnetron sputtering ion plating. The effects of Mo content on the microstructure, chemical bonding state, and optical properties of the prepared films were investigated by X-ray diffraction spectroscopy (XRD), X-ray photoelectron spectroscopy (XPS), field emission scanning electron microscopy, and ultraviolet-visible spectrophotometry. XRD results determined the face centered cubic (fcc) structure of pure CrN film. The incorporation of molybdenum (Mo) in the CrN matrix was confirmed by both XRD and XPS analyses. The CrMoN coatings demonstrate various polycrystalline phases including CrN, γ-Mo2N, Cr with oxides layers of MoO3, CrO3

Praise be to God, Lord of the worlds, and may blessings and peace be upon the most honorable of all creation, Abi Al-Qasim Muhammad, who is the messenger of mercy to the worlds and upon the God of the pure and good companions all

Praise be to God, Lord of the worlds, and may blessings and peace be upon the most honorable of all creation, Abi Al-Qasim Muhammad, who is the messenger of mercy to the worlds and upon the God of the pure and good companions all

   Due to their recalcitrant characteristics, Azo dyes such as methyl orange (MO) are extremely poisonous substances, making their removal from textile industry wastewater a major problem. By employing various EC-Adsorption combined system configurations and reusing alum sludge as an adsorbent, the current study seeks to investigate the efficiency of these various systems in removing MO dye. To estimate their benefits and limitations, experiments were carried out utilizing nickel foam (NiF) and aluminum plate (Al plate) as anodes, and stainless-steel mesh (SS mesh) as cathode in the presence of alum sludge as an adsorbent in all systems. The EC-Adsorption combined system with NiF as anode and two SS meshes as cathodes with 10 g/L

The recent escalation in Southeast Asia showed that the region is on the verge of political and economic crises through the United States and its allies imposing economic sanctions against China, and a military escalation that may begin with China’s invasion of Taiwan, especially since two-thirds of the American forces in the world are located in the Taiwan Strait and the South China Sea.

The United States claims that it is ready to defend the island of Taiwan in the event of the start of Chinese military operations, but the reality shows that the United States supports Taiwan militarily by equipping it with modern weapons to defend itself. Supporting Taiwan economically by engaging it in trade agreements with US allies in the r

The researcher of human history finds that the first social relations on earth were represented by the violence of Adam, peace be upon him, Cain and Abel. Violence has been a phenomenon of life and society. The history of history is full of all forms of violence and its forms. It speaks of cruelty, oppression and states. History began, in some of its chapters, written with the blood of the victims. It is a testimony to the cruelty of human beings. His human nature and his sin have played a major role that can not be overlooked in the development of important and fundamental developments in some historical turning points where violence was a necessity for life, and its launching change, renewal and reform, and major revolutions in human h

Ultraviolet spectrophotometric studies for antibiotic (amino glycoside) derivatives including, Neomycin, Streptomycin, Gentamycin and Kanamycin with special reagents, which are benzoyl chloride; benzene sulfonyl chloride, toluenesulfonyl chloride and phthalic anhydride were made. Amino glycosides derivatives were followed through measurements of the ultraviolet absorbance (A) from which the absorptivity (ε) of the complexes was deduced and molar absorbances using Ultraviolet for products and calculate the number of reagents molecule that combine to amino glycosides.

Objective: Synthesized a series of new thiourea (TU) derivatives, tested their antioxidant activity, and investigated their expected biological activity by theoretical study (computational methods). Methods: The derivatives were made using a one-pot reaction with two steps. Initially, succinyl chloride was mixed with KSCN to make succinyl isothiocyanate. Then, primary and secondary amines were used to make TU derivatives. The theoretical studies were done by Swiss ADME and molecular docking via Genetic Optimization of Linkage Docking (GOLD). Then evaluate antioxidant activity using the DPPH scavenging method. Results: FT-IR, 1H NMR, and 13C NMR spectroscopy show the verification of all the prepared derivatives. Compounds (II), (VIII),