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.

Our research sheds light on one of the most important aspects of David Grossman's play, "Ricky's Garden, גן ריקי " which is characterized by its realistic portrayal of characters. Grossman gradually moves towards the inner awareness of his characters, expressing their emotions and thoughts through conversations and emotional conflicts, referring to their past and rooted background. Grossman transformed the main subject of his play (psychological depth) into a presentation and arrangement of all the elements of the play in a way that expresses emotional nature more powerfully by each child in the garden. This is reflected in their actions and words, making Grossman's works suitable for study and always of interest to specialized resear

The term of heterocyclic chemistry focuses only on heterocyclic compounds, which consider as a percentage of organic chemistry, they equal to greater than sixty-five. These compounds are widely founded in nature and most of them are important to life. In the past few years, scientist fused on 1,2,4-triazoles and their condensed heterocyclic ring due to their medicinal significance, 1,2,4-triazole containing Sulphur atom is one of the important heterocyclic moieties due to its broad range of biological activities also their derivatives can accommodate one of the alternatives as electronic effect as exchanges of the electronic density (electron donating or withdrawing) groups ; for all what mentioned above they are consider as a core

Succinic acid is an essential base ingredient for manufacturing various industrial chemicals. Succinic acid has been acknowledged as one of the most significant bio based building block chemicals. Rapid demand for succinic acid has been noticed in the last 10 years. The production methods and mechanisms developed. Hence, these techniques and operations need to be revised. Recently, an omnibus rule for developing succinic acid is to find renewable carbohydrate Feedstocks. The sustainability of the resource is crucial to disintegrate the massive use of petroleum based-production. Accordingly, systematically reviewing the latest findings of bacterial production and related fermentation methods is critical. Therefore, this paper aims to stud

The human stomach is home to the Gram-negative bacterium Helicobacter pylori, which has been connected to several gastrointestinal disorders. There may be a link between H. pylori infection and the start of autoimmune disorders, according to recent research. This review examines the intricate connections between persistent H. pylori infection, immune system dysregulation, and their possible role in initiating autoimmune disorders. The study begins with a summary of H. pylori infection and its prevalence worldwide, emphasizing the mounting data that connects this bacterium to autoimmune disorders. Then, using experimental data from animal models and epidemiological research as support, it undertakes a thorough review of autoimmune di

Constitutional Review of 1992 and 1996 and the role of the Party of Progress and Socialism

The main objective of this study is to understand the work of the pile caps made of lightweight aerated foam concrete and study the many factors affecting the ability and the capacity of the shear. The study was done by analyzing previous practical and theoretical experiences on the reinforced concrete pile caps. The previous practical results indicated that all specimens failed by shear diagonal compression or tension modes except one specimen that failed flexural-shear mode. Based on test specimens' practical results and behavior, some theoretical methods for estimating the ultimate strength of reinforced concrete pile caps have been recommended, some of which evolved into the design documents available on the subject.

In this paper, a compact genetic algorithm (CGA) is enhanced by integrating its selection strategy with a steepest descent algorithm (SDA) as a local search method to give I-CGA-SDA. This system is an attempt to avoid the large CPU time and computational complexity of the standard genetic algorithm. Here, CGA dramatically reduces the number of bits required to store the population and has a faster convergence. Consequently, this integrated system is used to optimize the maximum likelihood function lnL(φ1, θ1) of the mixed model. Simulation results based on MSE were compared with those obtained from the SDA and showed that the hybrid genetic algorithm (HGA) and I-CGA-SDA can give a good estimator of (φ1, θ1) for the ARMA(1,1) model. Anot

The peculiarity of the theater does not lie in its dramatic content because many literary genres and other artistic styles share with it in this content. The peculiarity of the theater lies in contemplating the drama through what is architectural, and this architectural axis is what distinguishes its character. It is a spatial poetry which is composed by the laws of physics and chemistry, (Weight, height, distance, rhythm, gravity, impulses and chemical excretions). i.e., what cannot be expressed in words. This is a game of space to exchange and organize energy and communicate in space by the living body, which contains the possibilities of the living drawing in space: in the time and place. This research deals with the importance of the