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.

    Годы, принадлежащие концу XIX – началу XX столетия, вошли в русскую литературу под красивым названием Серебряный век. В это время в стране появился целый ряд выдающихся поэтов, имена которых навсегда останутся в русской и мировой литературе. Это Ахматова, Гумилев, Блок, Маяковский и многие другие. Все эти люди творили в нелегкое для России время. Началом Серебряного века условно считают 189

Background: Asthma is a disease of the airways characterized by chronic inflammation associated with airway hyper-responsiveness and airway wall remodeling. Aims of the study: The aims of this study was to determine the prevalence of oral manifestations , identify different microorganism from oral micro flora and determination of salivary IgA and salivary flow rate in asthmatic patients taking different dose of Prednisolone in comparison with control group. Subjects, materials and methods: The study included 17 patients under treatment with Prednisolone (10-20 mg),15 patients take (20-30 mg) of Prednisolone and other 18 patients take (30 – 40mg) of Prednisolone, and 25 healthy control group (10 male and 15 female). Results : The mo

ABSTRACT

The study evaluated the effect of adding quercetin to some characteristics of the sperm of the ram. This study was conducted in the animal field, Department of Animal Production, College of Agricultural Engineering Science, University of Baghdad for the period 5/12/2021 to 20/2/2022. In this experiment, 3 rams were used at the age of 2-2.5 years and weighed 50-55 kg. The semen was collected early in the morning and once a week and the semen was pooled to remove the individual differences. The treatments were divided: quercetin-free control group, treatment T1 (3 µL/mL quercetin), T2 treatment (6 µL/mL quercetin), T3 treatment (9 µL/mL quercetin). The result of the study showed

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

The importance of the research comes from dealing with the problem of lack of traffic awareness, which causes accidents and the occurrence of human and material losses, and the research aims to study the role of satellite channels in forming traffic awareness among the public, and a sample was chosen from Baghdad consisting of (280) individuals, male and female, and used the questionnaire tool. To obtain the data, which included several questions, the results were analyzed statistically and several results were reached, the most important of which is that there is an interest among the public in following traffic programs at a rate of one to two hours to receive information through traffic programs and to identify and apply gener

This study presents a mathematical model describing the interaction of gut bacteria in the participation of probiotics and antibiotics, assuming that some good bacteria become harmful through mutations due to antibiotic exposure. The qualitative analysis exposes twelve equilibrium points, such as a good-bacteria equilibrium, a bad-bacteria equilibrium, and a coexisting endemic equilibrium in which both bacteria exist while being exposed to antibiotics. The theory of the Sotomayor theorem is applied to study the local bifurcation around all possible equilibrium points. It’s noticed that the transcritical and saddle-node bifurcation could occur near some of the system’s equilibrium points, while pitchfork bifurcation cannot be accrued at

Witch stories are part of American popular culture, and this culture is extremely influenced by a continuing reliance on its past. The modern obsession of Americans with witches, whether real or metaphorical, is related to politics especially when it came to issues of gender politics. This article exposes a modern image of the female character seen from a male author point of view. John Updike, influenced by the changes that happened to women within second wave of feminism, attempted to write The Witches of Eastwick (1984). Actually, he presented women who did have a sort of careers. His witches are professional active and dynamic. What do witches stand for in American Culture? Why did Updike choose to write

This article deals with the study of theories about verbal periphrasis as a grammatical construction; the aim of this point it offers good and valid guidelines to improve the linguistic description. The interest in the subject comes from its importance in the process of language teaching for the students of Spanish and to clarify this type of curriculum of this research we analyzed a literary text. From "Zurita"

A great abbey in the Shari'a, and is therefore destined to be preserved in many texts and by methods
There are many prayers in the Qur'an and Sunnah to encourage them
They have a clear relationship with the preservation of the purposes of the Sharia in general, and with a purpose
Save the mind in particular, but the scholars - the mercy of God - when they declare that the costs of Sharia
Due to the preservation of my intentions in the creature, they limit their words to orders and intentions, and are not exposed
In particular,
If they were included in the texts of the Shariah and Tawjiyatiya,
To be related to the preservation of the purposes of the law, which confirms the words of the former leaders, and light the li