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.

Background: The apical seal is the single most important factor in determining the success of surgical endodontics, the aim of this study was to compare the sealing ability of Mineral Trioxide Aggregate in three different cavity designs. Materials and Methods: Thirty extracted human single-rooted teeth were divided into three groups of ten teeth per group, a retrograde cavity preparation was carried out using a low speed handpiece and round bur with parallel walls in the first group, ultrasonic retrotip and unit in the second group and a low speed handpiece with a carbide inverted cone bur with undercuts in the third group, all the cavities were filled with MTA. microleakage was measured by dye penetration technique using methylene blue. Re

Background: During acrylic resin processing, the mold must be separated from the surface of the gypsum to prevent liquid resin from penetrating into the gypsum, and water from the gypsum seeping into the acrylic resin. For many years, tin foil was the most acceptable separating medium, and because it's difficult to apply, a tin-foil substitute is used. In this study, olive oil is used as an alternative to tin foil separating medium for first time, and evaluating its effect as a separating medium on some mechanical properties such as (indentation hardness and transverse strength) of acrylic resins denture base comparing it with those processed using tin-foil and tin foil substitute such as (cold mold seal) separating medium. Materials and M

This research was dealing with the aesthetic impact of encryption in form and content and aesthetic implications in the design of contemporary fabrics. That's where the design of the cloth is linked to the continuous development and continuous innovation and the pursuit of the all-new innovative designs and at the same time an unmarked Cryptographic with semantics and symbols reflect reality aesthetically pleasing and contains four chapters on the research :The first chapter discusses the research problem and its significance is the current quest ( encryption in form and content in contemporary designs fabrics and aesthetic implications ) in that it shows the importance of encryption in the design of fabrics and foundation design configu

The research included four topics: the definition of Imam al-Bazzazi, his scientific life, his sheikhs, his students, his writings, his death, and selected issues of his weight in the book of prayer. The Imam al-Bazazi is the son of Muhammad ibnShihabibn Yusuf. He is known as al-Khardizi al-Khawarizmi. The author did not adopt the definitions of language and terminology, and rarely mention the legal evidence adopted by the scholars in their opinions, and only to mention the views only, and the author, may God have mercy on him in his book on the sources of m The Prophet (peace and blessings of Allaah be upon him) said: "The Prophet (peace and blessings of Allaah be upon him) And fall down the order, the third issue, which is to leave the

           Biosynthesis of nanoparticles has received considerable attention due to the growing need to develop environmentally benign nanoparticle synthesis processes that do not use toxic chemicals. Therefore, biosynthetic methods employing both biological agents such as bacteria and fungus or plant extracts have emerged as a simple and a viable alternative to chemical synthetic and physical method .It is well known that many microbes produce an organic material either intracellular or extracellular which is playing important role in the remediation of toxic metals through reduction of metal ions and acting as interesting Nano factories. As a result, in the present study Ag NPs were syn

The measurements of major and trace elements in different brands of milk powder selected from the Iraqis market via the X-ray fluorescence (XRF) Technique have been studied in the present work. The result of the measurements reveals the high concentrations of sodium, phosphorus, sulfur, chlorine, potassium, calcium and magnesium. Furthermore, low concentrations of aluminum, silicon, iron, bromine, molybdenum, iodine, barium, titanium, manganese, cobalt, chrome, nickel, copper, zinc and lead were detected. Neutron activation analysis (NAA) and Kjeldahl technique were also employed to determine the concentrations of nitrogen. It was found that the nitrogen concentration was in the range of (1.96 - 3.23) % which is within the permissible li

0

The study explores the use of ergative verbs in constructing clauses and their impact on the backgrounding of the agent's role in two selected short stories. Contrary to hypothesis No. 1, the research indicates that changes in sentence patterns don't affect the meaning of the process. Additionally, hypothesis No. 2 is refuted as the middle structure is found to highlight the agent's role in the science fiction short story, Terra Infirmum, rather than concealing it as hypothesized for "The Invisible Man." The analysis uncovers that writers utilize ergative processes to narrate stories in various ways, including transitive/active voice, intransitive/active voice, and transitive/passive voice. Furthermore, the findings suggest that writers emp

Background: The ideal maxillofacial prosthesis should have fine and thin boundaries that bindwith the surrounding facial structures and possess high tear strength.This study aims to determinethe best percentages of nanofiller (TiO2) and intrinsic pigment (silicone functional intrinsic) thatcould be mixed in as additives to improve the tear strength of Cosmesil M511 andVST50F siliconeelastomers with the least effect on their hardness.Materials and Methods: In this in vitro experimental study, a total of 80 samples, 40 for eachelastomer, were fabricated. Each elastomer sample was split into two equal groups to test for tearstrength and Shore A hardness. Each group consisted of 20 samples, including 10 control sampleswithout additives and 10 e