Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of  Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope

2-hydrazinylbenzo[d]thiazole compound [1] is produced from reaction of 2-mercapto-benzothiazole with hydrazine hydride in ethanol. Compound [1] reacted with maleic anhydride in DMF to produce (Z)-4-(2-(benzo[d] thiazol-2yl) hydrazinyl)-4-oxobut-2-enoic acid [compound (2)]. While the treatment of compound [2] with the ammonium persulfate (NH4)2S2O8 (as the initiator) in order to produce compound [3], then compound [3] reacted with thionyl chloride in benzene to produce compound [4], finally compound [4] reaction with various drugs: cephalexin, amoxicillin, sulfamethizole, elecoxib obtained polymers [5–8]. The structure of synthesized compounds identified by spectral data: fourier transform infrared (FTIR) and proton nuclear magneti

Conventional hardening, sometimes, is not economically viable due to consuming additional costs and energy. This makes applying selective hardening on specific regions an attractive alternative for members subjected to local friction and wear. This work is devoted for applying cold working hardening on discrete values on regions of aluminum 6061-O alloy using nanosecond fiber laser of 100 W average power and pulse duration of 81 ns. An exaggerated plasma pressure resulted from ablation a thin coat layer on the metal surface was built in order to cause cold plastic deformation and increase the surface hardness of the alloy. The power density (Pd) and pulse overlap percentage (OV) were employed as working parameters. Due to the sensit

The reinforced concrete column is designed to have a nominal axial resistance. Under different conditions like errors in design, and changing the use of the building from residential to public or storage (extra live loads), the reinforced concrete column will not be able to sustain the desired applied load, and the strengthening is required. This paper presents a finite element model to simulate and investigate the behavior of adding steel jacket to a preloaded and non-damaged reinforced concrete column. Depending on the loading state of the non-strengthened reinforced concrete column and the purpose of adding the steel jacket, two possible cases have been studied. In the first case, which is suitable to investigate the reinforced c