Bivariate quartic spline spaces and quasi-interpolation operators

In this paper, we study two bivariate quartic spline spaces and , and present two classes of quasi-interpolation operators in the two spaces, respectively. Some results on the operators are given.     

Finite-part integrals over polygons by an 8-node quadrilateral spline finite element

In this paper we consider the numerical integration on a polygonal domain Ω in ?² of a function F(x,y) which is integrable except at a point \(P_{0}=(x_{0},y_{0})\in{\stackrel{\circ}{\Omega}}\), where F becomes infinite of order two. We approximate either the finite-part or the two-dimensional Cauchy principal value of the integral by using a spline finite element method combined with a subdivision technique also of adaptive type. We prove the convergence of the obtained sequence of cubatures. Finally, to illustrate the behaviour of the proposed method, we present some numerical examples.     

Numerical integration over polygons using an eight-node quadrilateral spline finite element

In this paper, a cubature formula over polygons is proposed and analysed. It is based on an eight-node quadrilateral spline finite element [C.-J. Li, R.-H. Wang, A new 8-node quadrilateral spline finite element, J. Comp. Appl. Math. 195 (2006) 54–65] and is exact for quadratic polynomials on arbitrary convex quadrangulations and for cubic polynomials on rectangular partitions. The convergence of sequences of the above cubatures is proved for continuous integrand functions and error bounds are derived. Some numerical examples are given, by comparisons with other known cubatures.     

Orientation effects on the bandgap and dispersion behavior of 0.91Pb（Zn_（1/3）Nb_（2/3））O_3-0.09PbTiO_3 single crystals

0.91Pb(Zn_1/3Nb_2/3)O₃--0.09PbTiO₃ (PZN--9%PT) single crystals with different orientations are investigated by using a spectroscopic ellipsometer, and the refractive indices and the extinction coefficients are obtained. The Sellmeier dispersion equations for the refractive indices are obtained by the least square fitting, which can be used to calculate the refractive indices in a low absorption wavelength range. Average Sellmeier oscillator parameters E_o, $\lambda$_o, S_o, and E_d are calculated by fitting with the single-term oscillator equation, which are related directly to the electronic energy band structure. The optical energy bandgaps are obtained from the absorption coefficient spectra. Our results show that the optical properties of [001] and [111] poled crystals are very similar, but quite different from those of the [011] poled crystal.     

Minimal quasi-Bézier surface

The quasi-Bézier surface is a kind of commonly used surfaces in CAGD/CAD systems. In this paper, we study how to find the quasi-Bézier surface of minimal area among all the quasi-Bézier surfaces with prescribed borders, i.e., the Plateau-quasi-Bézier problem. The prescribed borders can not only be polynomial curves, but also catenaries and circular arcs. Moreover, the harmonic and biharmonic quasi-Bézier surfaces are investigated.     

The Electrochemical Behavior of Polypyrrole under Ultrasound

Polypyrrole (PPy) is one of the most important conducting polymers. It has been widely studied for the uses of chemical sensors, electrocatalysis, rechargeable batteries and protective layers on semiconductor electrodes^[1].     

聚吡咯纳米阵列电极的光电化学

以多孔的铝阳极氧化膜(AAO)为模板制备了直径约为80 nm聚吡咯(PPy)纳米线的阵列电极, 并研究了它的光电化学响应. 结果表明, 在电极电位低于－0.1 V(vs Ag/AgCl)时出现的阴极光电流是由聚吡咯纳米线的p型半导体性质引起的, 其平带电位为－0.217 V. 聚吡咯纳米线的长度对光电流的影响较大, 最佳长度为42 nm. 这是因为在很短的聚吡咯纳米线阵列中PPy太少, 产生的光电流弱, 而在过长的聚吡咯纳米线阵列中光生电子在到达电极基底前易于与光生空穴复合而消失. 聚吡咯纳米线有可能作为纳米光电器件用于未来微器件系统.     

L-丙氨酰Betti碱催化环己酮对硝基烯不对称Michael加成反应

合成了3个手性Betti碱的L-丙氨酰衍生物, 并用它们来催化环己酮与硝基烯的Michael加成反应. 发现1a是其中最有效的催化剂, ee值最高大于99%, dr值最高大于99∶1. 考察了催化剂结构与用量、添加剂用量、底物结构等因素对反应的化学产率和光学收率的影响.     

高电位胶体颗粒强相互作用的近似表达式

When surface potential of the particles, ,is high,sinh y can be approximated by ≈ey/2 in the nonlinear Poisson Boltzmann equation.Thus,we present a simple method of calculating the interaction force and energy per unit area between two dissimilar plates with high potentials at constant surface potential.These formulae could be applicable to the case of repulsive case,in which the derivative of y must vanish at an interior point,and a minimum ymin=u always exists.A turning point at ～kh≈2(1)e－y1/2 for the repulsion or attraction between dissimilar planar surfaces.These formulae are divergent at 阧∞,and zero point at kh≈2 .This means that they can only be used at 阧 < 2 and accurate location is at kh ≤ 4. 　　Agreement of the approximation for force,Eq.（13）,is good with the exact numerical values of the interaction of dissimilar plates given by Devereux [6] for high surface potentials.For y1 ≥5 kh ≤ 3.0 the relative errors of Eq.(13) are less than 5％,and for kh ≤ 3.5 relative errors are less than 10％.For the interaction energy,Eq.(15),the applicable range extends to kh =4.0.Beyond this range the error increases rapidly.The higher surface potential is the better the precision of Eq.（13）and Eq.( 15).The condition of the strong interaction has been satisfied.     

Electrochromic Properties of Rhodium Oxide Films Prepared by Sol-gel Method

Electrochromic materials have been extensively investigated for their significant potential in information display, automotive, sensor and smart windows^[1]. Many studies have been carried out on the inorganic electrochromic materials, such as WO₃, MoO₃, NiO_x and so on^[2]. In this paper, We first report the electrochromic behavior of rhodium oxide film prepared by sol-gel method on transparent conductor substrate. The film exhibited reversible two color (from bright yellow to dark green) electrochromic behavior with satisfactory contrast at anodic and cathodic forms when the applied potential was reversed successively.