Search

A new procedure for linearizing dynamic error, without using state transformation, and linearizing nonlinear terms has been presented. The nonlinear term in the error differential equation has been analyzed in terms of the dynamic error and then has been replaced in the matrix of error factors. With stabilizing this matrix, the differential equation can be linearized and the gains of the observer have been obtained in nonlinear terms of the estimated state and the actual output. In other words, utilizing nonlinear gain factors, the nonlinearity in the final form of differential equation can be removed, and thus, differential equation of dynamic error can be linearized. The required conditions for observer construction and the procedure for linearizing of dynamic error have thoroughly been presented in detail. The robustness of designed observer to Lipschitz constant has been studied, and the absolute robustness of observer has been proved. Additionally, robustness to uncertainty has been investigated, and finally, the results for a sample nonlinear Lipschitz system, in the absence and the presence of uncertainty, are elicited and presented. The extracted results have shown good ability of observer in state estimation of studied system in the presence and absence of uncertainty. Furthermore, the presented results proved absolute robustness of designed observer to Lipschitz nonlinearity.

In the current study, elemental analysis and microscopic investigations were conducted to characterize the minerals present in an iron ore sample. The iron content was below 24%, with the dominant iron-bearing minerals being hematite and magnetite. Consequently, gravity and magnetic separation methods were employed to enhance the iron content. However, the processing results less than what was expecting due to incomplete sample characterization. The sample was further analyzed using quantitative X-ray diffraction analysis. This more comprehensive examination revealed additional iron-bearing minerals as goethite, ankerite, and limonite. The behavior of these minerals likely contributed to the unsuccessful separation process which was thoroughly explored in this article. Understanding the mineralogical composition of iron ores is paramount for optimizing processing operations and achieving successful outcomes.

Nowadays, one of the methods to prevent the progress of Alzheimer's disease (AD) is to prescribe compounds that inhibit the acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) enzymes. Researchers are actively pursuing compounds, particularly of natural origin, that exhibit enhanced efficacy and reduced side effects. The inhibition of AChE and BChE using natural flavonoids represents a promising avenue for regulating AD. This study aims to identify alternative flavonoids capable of modulating AD by down-regulating AChE and BChE activity through a molecular docking approach. Molecular docking analysis identified Ginkgetin and Kolaflavanone as potent inhibitors of AChE and BChE, respectively, among the selected flavonoids. Asn87 and Ala127 involved in the interactions of AChE-Ginkgetin complex through conventional hydrogen bonds. While in the BChE-Kolaflavanone complex, Asn83, Ser79, Gln 47, and Ser287 are involved. In vitroanalysis further corroborated the inhibitory potential, with Ginkgetin exhibiting an IC50of 3.2 mM against AChE, and Kolaflavanone displaying an IC50of 3.6 mM against BChE. These findings underscore the potential of Ginkgetin and Kolaflavanone as candidate inhibitors for the treatment of AD through the inhibition of AChE and BChE enzymes. Nevertheless, additional in vitroand in vivostudies are imperative to validate the efficacy of these compounds.