In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.

We focus on studying the dynamics of bulk semiconductor optical amplifiers and their effects on the saturation region for short pulse that differ, however there is the same unsaturated gain for both dynamics. Parameters like current injection, fast dynamics present by carrier heating (CH), and spectra hole burning (SHB) are studied for regions that occur a response to certain dynamics. The behavior of the saturation region is found to be responsible for phenomena such as recovery time and chirp for the pulse under study.

The research aimed to study the role that the media play in shaping the public knowledge of human rights issues among the people of Kirkuk, which will be the focus of the study. The research was conducted by applying a survey panel to a random sample of the city's audience. The research dealt with the theoretical aspect of a theory that relied on the media, and the loans provided by the theory, on the basis of which the research was conducted and the research problem was determined based on a major question: What is the role that the mass media play in developing the knowledge of members of the public on human rights and the relationship between the intensity of view in that, as well as the identification of the effect of two variables G

As they are the smallest functional parts of the muscle, motor units (MUs) are considered as the basic building blocks of the neuromuscular system. Monitoring MU recruitment, de-recruitment, and firing rate (by either invasive or surface techniques) leads to the understanding of motor control strategies and of their pathological alterations. EMG signal decomposition is the process of identification and classification of individual motor unit action potentials (MUAPs) in the interference pattern detected with either intramuscular or surface electrodes. Signal processing techniques were used in EMG signal decomposition to understand fundamental and physiological issues. Many techniques have been developed to decompose intramuscularly detec

The paper studies the description of the colloquial and popular vocabulary  used by wholesales tradesmen in Varonech before the Bolshevik Revolution . The vocabulary were used in the personal letters written by the poet and sent to famous poets and critics like Belenisky, kryvesky and Malsheve. And some were sent to his father and his sister. Not only did these letter bear the personal taste, but they represented a literary product reflecting on the poet's impressions, views, ambitions, and opinion in arts, poetry, prose, and theatre. The researcher used about thirty instances of various levels of grammar, style and phonology, all representing colloquial vocabulary used commonly at the time of Alexi&nbsp

Taking into account the significance of food chains in the environment, it demonstrates the interdependence of all living things and has economic implications for people. Hunting cooperation, fear, and intraspecific competition are all included in a food chain model that has been developed and researched. The study tries to comprehend how these elements affect the behavior of species along the food chain. We first examined the suggested model's solution properties before calculating every potential equilibrium point and examining the stability and bifurcation nearby. We have identified the factors that guarantee the global stability of the positive equilibrium point using the geometric approach. Additionally, the circumstances that would gu

Loanwords are the words transferred from one language to another, which become essential part of the borrowing language. The loanwords have come from the source language to the recipient language because of many reasons. Detecting these loanwords is complicated task due to that there are no standard specifications for transferring words between languages and hence low accuracy. This work tries to enhance this accuracy of detecting loanwords between Turkish and Arabic language as a case study. In this paper, the proposed system contributes to find all possible loanwords using any set of characters either alphabetically or randomly arranged. Then, it processes the distortion in the pronunciation, and solves the problem of the missing lette

     In this paper, we introduce new definitions of the - spaces  namely the    - spaces  Here,  and  are natural numbers that are not necessarily equal, such that . The space  refers to the n-dimensional Euclidean space,  refers to the quaternions set and  refers to the N-dimensional quaternionic space. Furthermore, we establish and prove some properties of their elements. These elements are quaternion-valued N-vector functions defined on , and the  spaces  have never been introduced in this way before.

This paper presents the dynamic responses of generators in a multi-machine power system.  The fundamental swing equations for a multi-machine stability analysis are revisited. The swing equations are solved to investigate the influence of a three-phase fault on the network largest load bus. The Nigerian 330kV transmission network was used as a test case for the study. The time domain simulation approach was explored to determine if the system could withstand a 3-phase fault. The stability of the transmission network is estimated considering the dynamic behaviour of the system under various contingency conditions. This study identifies Egbin, Benin, Olorunsogo, Akangba, Sakete, Omotosho and Oshogbo as the key buses w

An eco-epidemiological system incorporating a vertically transmitted infectious disease is proposed and investigated. Micheal-Mentence type of harvesting is utilized to study the harvesting effort imposed on the predator. All the properties of the solution of the system are discussed. The dynamical behaviour of the system, involving local stability, global stability, and local bifurcation, is investigated. The work is finalized with the numerical simulation to observe the global behaviour of the solution.