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.

Tensile strength is a critical property of Hot Mix Asphalt (HMA) pavements and is closely related to distresses such as fatigue cracking. This study aims to evaluate methods for assessing fatigue cracking in Asphalt Concrete (AC) mixes. In order to achieve optimum density at different binder contents, the mixes were compressed using a gyratory compactor. Tensile strength was assessed using the Indirect Tensile (IDT) and Semi-Circular Bend (SCB) tests. The results showed that the tensile strength measured by the SCB test was consistently higher than that measured by the IDT test at 25 °C. In addition, the SCB test showed a stronger correlation between increasing binder content and tensile strength. For binder contents ranging from 4

Thoudy sustainable development attention of researchers and scholars at various orientations intellectual economies were or Ssayasn, or others as gaining the process of paramount importance in the light of major developments and unprecedented in the modern world at the levels of all and which turned the world sprawling into something like a global village is small, being aimed at elimination of backwardness and development branches of the national economy and raise the level of economic performance, and what was the province of Kurdistan-Iraq from areas with privacy clear and meets the elements of economic development has seen the movement of economic development and social with special features de facto geographical, political a

Residential complexes have witnessed a great demand in most countries worldwide, as they are one of the main infrastructure elements, in addition to achieving a developed urban landscape. However, complex residential projects in developing countries face various factors that could be improved in their implementation, especially in Iraq. Sixty-two experts in residential complex projects were interviewed and surveyed to verify these projects' failure factors,. Fifty-one factors were the main failure factors, divided into four main components (leadership, management system, external forces, and project resources). The Relatively Important Index (RII) is used to determine the relative importance factors and obtain the top tw

Background. The motor response is a fundamental ability that is evident during any physical or motor activity. However, the need for this ability varies from one sport to another and depends on the specific skills required in each sport. Objectives. This study aims to compare the average motor reaction times of the arm and leg among handball, basketball, and volleyball players aged 14 to 16 years. Methods. The sample included 30 players aged 14-16 years from the sports talent care center, evenly distributed on handball, basketball, and volleyball. Standardized tests were used to measure the speed of motor response, including the Batak Micro test for hands, which records the number of responses to light stimuli in 30 seconds, and the Saqer t

New complexes were synthesized with Schiff base tetradentate ligand (L). The ligand was synthesized by the condensation reaction of the dimedone with 2-hydroxybenzohydrazide. The formula of complexes [M(L) (H2O)2].Cl2, where M represents Mn(II), Ni(II) Cu(II), [Co(L)Cl.H2O]Cl and [Zn(L)(H2O)2]Cl2.2H2O. The ligand was identified using m.p., UV-Vis, FT-IR, Mass, 1H-NMR, and C.H.N. These complexes were characterized using techniques including infrared, UV-Vis absorption, magnetic susceptibility, molar conductivity, elemental analyses, thermogravimetric analysis (TGA), chloride content determination using Mohr’s method, and atomic absorption spectroscopy. The measurements revealed that the complexes are electrolytic. FT-IR results dem

The research tagged (functional enhancement and its reflection on industrial product systems) focused on the possibility of enhancing industrial products in terms of form and functionality in a way that they are able to meet the needs of the user through the impact of technology and modern technologies on the functional enhancement of industrial products and their effectiveness in achieving formal and functional design variables, and producing products Industrial products are highly efficient and durable in order to improve them in order to meet the needs of the user, the transfer of technology between life forms and industrial products is desirable because the functional enhancement processes that occurred in general on industrial produ