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.

Braces in straight bridge systems improve the lateral-torsional buckling resistance of the girders by reducing the unbraced length, while in horizontally curved and skew bridges, the braces are primary structural elements for controlling deformations by engaging adjacent girders to act as a system to resist the potentially large forces and torques caused by the curved or skewed geometry of the bridge. The cross-frames are usually designed as torsional braces, which increase the overall strength and stiffness of the individual girders by creating a girder system that translates and rotates as a unit along the bracing lines. However, when they transmit the truck’s live load forces, they can produce fatigue cracks at their connection

Low-Density-Parity-Check (LDPC) codes are a cornerstone for achieving robust error correction capabilities in 5G New Radio applications, significantly improving the reliability of data transmission across noisy and unpredictable wireless channels. Since an evaluation and discussion of the performance with channel coding is significantly absent in two-dimensional Index Modulation (IM)-Differential Chaos Shift Keying (DCSK) schemes. Therefore, in this study, the 5G new radio LDPC codes based generalized joint subcarrier-time index modulation DCSK system (5G NR-LDPC-GJSTIM-DCSK) is proposed, where 5G NR-LDPC codes are used as channel coding. The aim is to improve the system’s performance specifically across AWGN (additive white gauss

Background: Secretory Immunoglobulin A (SIgA) is a subclass of Immunoglobulin A (IgA), It is an antibody that plays an important role in mucosal immunity. It is the main immunoglobulin found in mucous secretions from mammary glands, tear glands and salivary glands, every pathologic process in the body involves the immune system, and periodontal inflammation is one of them and is not an exception. Material and methods: this study was consisted of 60 healthy male participants of an age ranged between (35-50) years old ; 25 of them with generalized moderate chronic periodontists(Clinical Attachment Loss equal to 3-4mm at ≥ 30% of the sites; 20 participants with plaque induced gingivitis and 15 participants had clinically healthy pe

There is substantial data supporting the importance of both endogenous and exogenous estrogen in maintaining reproductive health and preventing chronic disease, androgens in women's health are rarely discussed. This is one of the first researches to investigate correlates of blood testosterone concentrations in women with osteopenia, in anticipation of the growing interest in the role of androgens in women's health. A 65 volunteer women were enrolled in the current study, they were divided into two groups, 35 postmenopausal women with osteopenia were in the first group, and the second group contained 30 postmenopausal women without osteopenia as a control. Blood samples were collected from all participants and analyzed for testosterone l