http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Two-point <sup> G 1 </sup> Hermite interpolation in biangular coordinates
Ziatdinov, Rushan,Kim, Tae-wan,Nabiyev, Rifkat I. Koninklijke Vlaamse Ingenieursvereniging 2015 Journal of computational and applied mathematics Vol.287 No.-
<P><B>Abstract</B></P> <P>We construct <SUP> G 1 </SUP> Hermite interpolating curves in biangular coordinates, and provide sufficient conditions for their convexity. In a biangular coordinate system, the problem reduces to that of choosing suitable functions interpolating the biangular coordinates of the curve at its end points. The simplest linear equations, γ = ( ( 1 − t ) α , t β ) , in biangular coordinates correspond to a sectrix of Maclaurin, which we extend by introducing two shape parameters that pull the curve towards the sides of its triangular envelope. In addition, we consider a class of curves whose biangular coordinates have a constant sum, and we analyze their shape and curvature.</P> <P><B>Highlights</B></P> <P> <UL> <LI> The equations of most curves in biangular coordinate system are not yet known. </LI> <LI> We construct <SUP> G 1 </SUP> Hermite interpolating curves in biangular coordinates. </LI> <LI> Interpolation problem reduces to choosing suitable functions in biangular coordinates. </LI> <LI> The simplest linear equations correspond to the sectrix of Maclaurin. </LI> <LI> Proposed interpolation method may reduce the computational cost in some cases. </LI> </UL> </P> <P><B>Graphical abstract</B></P> <P>[DISPLAY OMISSION]</P>
Pei Chen,Haipei Bie,Rushan Bie 한국화학공학회 2018 Korean Journal of Chemical Engineering Vol.35 No.9
Fundamental studies on the removal of metal impurities are essential for the production of nanosilica by combustion. This study reports the leaching characteristics, leaching kinetics and occurrence form of the metal impurities present in rice husk based on acid pretreatment. Acid pretreatment removes most of the metal impurities present in rice husk. In particular, 98wt% removal of potassium can be reached. The acid concentration, leaching time and reagent type have significant effects on the leaching of metal impurities, and optimal conditions exist for the acid pretreatment process. Furthermore, the leaching of metal impurities occurs through two stages, and parts of the metal impurities exist in organic-bound form, which can be leached through ion exchange. The results show that the pseudosecond- order model is suitable for describing the leaching kinetics of the metal impurities present in rice husk, and empirical formulas for predicting the metal contents leached from rice husk during acid pretreatment at ambient temperature are also obtained. Additionally, the different occurrence form and quantities of metal impurities in rice husk lead to different leaching effects, which strongly influences the chemical properties and quality of the obtained silica particles.