A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number  is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.

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.

The current study was conductedas a pot experiment to determine the effect of soil texture on biological nitrogen fixation (BNF) of six most efficient local isolates, specified, of Bradyrhizobium. Cowpea (Vignaunguiculata L.), as a legume host crop, was used as a host crop and 15N dilution analysis was used for accurate determination of the amount of N biologically fixed under experimental parameters specified. Soils used are clay loam, sandy clay loam and sandy loam. Biological Nitrogen Fixation (BNF), in different soil textural classes, was as in the following order: medium texture soil > heavy texture soil > light textured soil. Statistical analysis showed that there is a significant variation in BNF % among six Iraqi isolates in the th

The flexible joint robot manipulators provide various benefits, but also present many control challenges such as nonlinearities, strong coupling, vibration, etc. This paper proposes optimal second order integral sliding mode control (OSOISMC) for a single link flexible joint manipulator to achieve robust and smooth performance. Firstly, the integral sliding mode control is designed, which consists of a linear quadratic regulator (LQR) as a nominal control, and switching control. This control guarantees the system robustness for the entire process. Then, a nonsingularterminal sliding surface is added to give a second order integral sliding mode control (SOISMC), which reduces chartering effect and gives the finite time convergence as well. S

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect

A series of new coumarin and N-amino-2-quinolone derivatives have been synthesized. The reaction of coumarin (1) with excess of  Hydrazine hydrate 98% yielded 1-amino-2-quinolone (2), Compound (2) was reacted with different Sulfonyl chloride to yield Sulfonamides [ N-(2-oxoquinolin-1(2H)-yl) methane sulfonamide (3), N-(2-oxoquinolin-1(2H)-yl) Benzene sulfonamide (4) and 4-methyl-N-(2-oxoquinolin-1(2H)-yl) benzene sulfonamide (5) ], while  reaction of  2-(4-methyl-2-oxo-2H-chromen-7-yloxy) acetic acid (8) with different amines yielded compounds [  2-(4-methyl-2-oxo-2H-chromen-7-yloxy)-N-(2-oxoquinolin-1(2H)-yl) acetamide (9) and N-(5-methyl-1,3,4-thiadiazol-2-yl)-2-(4-methyl-2-oxo-2H-chromen-7-yloxy)acetamide (10) ] th

ABSTRACT. 4-Sulfosalicylic acid (SSA) was used as a ligand to prepare new triphenyltin and dimethyl-tin complexes by condensation with the corresponding organotin chloride salts. The complexes were identified by different techniques, such as infrared spectra (tin and proton), magnetic resonance, and elemental analyses. The 119Sn-NMR was studied to determine the prepared complexes' geometrical shape. Two methods examined the antioxidant activity of (SSA) and prepared complexes; Free radical scavenging activity (DPPH) and CUPRRAC methods. Tri and di-tin complexes gave high percentage inhibition than ligands with both methods due to tin moiety; the triphenyltin carboxylate complex was the best compared with the others. Also, antibacter