In this paper, we established a mathematical model of an SI1I2R epidemic disease with saturated incidence and general recovery functions of the first disease I1. Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stability is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we carried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct numerical simulations that supported our theoretical findings
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Abstract
This research studies Abu Baker Al-Siddiq’s commandments to the leaders of his armies. The research is organized into an Introduction, three sections, and a Conclusion.
The Introduction presents a definition of Style and Commandment terminologies. It also presents a brief biography of Abu Baker Al-Siddiq may Allah be pleased with him.
The first section explains the characteristics of the Composition and its rhetorical significance. In this Section, I study the types of predicate and the methods of construction in Abu Baker’s commandments and the rhetoric in using the connection and disconnection modifiers in his expressions.
The second section e
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Copper oxide (CuO) nanoparticles were synthesized through the thermal decomposition of a copper(II) Schiff-base complex. The complex was formed by reacting cupric acetate with a Schiff base in a 2:1 metal-to-ligand ratio. The Schiff base itself was synthesized via the condensation of benzidine and 2-hydroxybenzaldehyde in the presence of glacial acetic acid. This newly synthesized symmetric Schiff base served as the ligand for the Cu(II) metal ion complex. The ligand and its complex were characterized using several spectroscopic methods, including FTIR, UV-vis, 1H-NMR, 13C-NMR, CHNS, and AAS, along with TGA, molar conductivity and magnetic susceptibility measurements. The CuO nanoparticles were produced by thermally decomposing the
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Transient three-dimensional natural convection heat transfer due to the influences of heating from one side of an enclosure filled with a saturated porous media, whereas the opposite side is maintained at a constant cold temperature, and the other four sides are adiabatic, were investigated in the present work experimentally. Silica sand was used as a porous media saturated with distilled water filled in a cubic enclosure heated from the side,using six electrical controlled heaters, at constant temperatures of (60, 70, 80, 90, and 100oC). The inverse side cooled at a constant temperature of (24oC) using an aluminum heat exchanger, consisted of 15 channels feeded with constant temperature water. Eighty thermocouples were used to control t
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