This paper is concerned with the quaternary nonlinear hyperbolic boundary value problem (QNLHBVP) studding constraints quaternary optimal classical continuous control vector (CQOCCCV), the cost function (CF), and the equality and inequality quaternary state and control constraints vector (EIQSCCV). The existence of a CQOCCCV dominating by the QNLHBVP is stated and demonstrated using the Aubin compactness theorem (ACTH) under appropriate hypotheses (HYPs). Furthermore, mathematical formulation of the quaternary adjoint equations (QAEs) related to the quaternary state equations (QSE) are discovere so as its weak form (WF) . The directional derivative (DD) of the Hamiltonian (Ham) is calculated. The necessary and sufficient conditions for optimality (NCSO) theorems for the proposed problem are stated and proved.
One of the most significant environmental issues facing the planet today is air pollution. Due to development in industry and population density, air pollution has lately gotten worse. Like many developing nations, Iraq suffers from air pollution, particularly in its urban areas with heavy industry. Our research was carried out in Baghdad's Al-Nahrawan neighbourhood. Recently, ground surveys and remote sensing were used to study the monitoring of air pollution. In order to extract different gaseous and particle data, Earth Data source, Google Earth Engine (GEE), and Geographic Information Systems (GIS) software were all employed. The findings demonstrated that there is a significant positive connection between data collected by ground-ba
... Show MoreThe research aims to highlight the significance and composition and the diversity of meanings and the Quranic context in the necessary and transgressive verbs in Surat (Abs).
This research consists of : a preamble , and two studies . The researcher addressed in the preliminary the importance of the phenomenon of necessity and infringement, the signs of the necessary action , the structure and controls of the act , the methods of infringement , its sections and signs.
As for the first topic : The researcher addressed the necessary verbs in Surat Abs , an applied study in terms of grammati
... Show More