在几何和参数上表示同一条曲线的两条有理NURBS曲线的权与控制顶点之间的关系

The paper discusses the relationship between weights and control vertices of two rational NURBS curves of degree two or three with all weights larger than zero when they represent the same curve parametrically and geometrically, and gives sufficient and necessary conditions for coincidence of two rational NURBS curves in non-degeneracy case.     

固载化聚乙二醇三相催化下香豆素的合成

研究了固载化聚乙二醇三相催化下香豆素的合成，探讨了影响反应的主要因素。结果表明，该反应的最佳反应条件为：水杨醛与碳酸钾的摩尔比为 １： ０．７５，反应温度为１７５℃，反应时间为３．５ ｈ，该条件下香豆素的收率为 ６５．７％。     

Dynamic and Quantitative Control of the DNA‐Mediated Growth of Gold Plasmonic Nanostructures

Reproducible and controllable growth of nanostructures with well‐defined physical and chemical properties is a longstanding problem in nanoscience. A key step to address this issue is to understand their underlying growth mechanism, which is often entangled in the complexity of growth environments and obscured by rapid reaction speeds. Herein, we demonstrate that the evolution of size, surface morphology, and the optical properties of gold plasmonic nanostructures could be quantitatively intercepted by dynamic and stoichiometric control of the DNA‐mediated growth. By combining synchrotron‐based small‐angle X‐ray scattering (SAXS) with transmission electron microscopy (TEM), we reliably obtained quantitative structural parameters for these fine nanostructures that correlate well with their optical properties as identified by UV/Vis absorption and dark‐field scattering spectroscopy. Through this comprehensive study, we report a growth mechanism for gold plasmonic nanostructures, and the first semiquantitative revelation of the remarkable interplay between their morphology and unique plasmonic properties.     

Effects of mechanical loadings on the performance of a piezoelectric hetero-junction

A fully-coupled model for a piezoelectric hetero-junction subjected to a pair of stresses is proposed by discarding the depletion layer approximation. The effect of mechanical loadings on PN junction performance is discussed in detail. Numerical examples are carried out for a p-Si/ZnO-n hetero-junction under a pair of stresses acting on the ntype ZnO portion near the PN interface, where ZnO has the piezoelectric property while Si is not. It is found that the bottom of conduction band is lowered/raised near the two loading points due to the decrease/increase in the electron potential energy there induced by a tensile-stress mode via sucking in majority-carriers from two outside regions, which implies appearance of a potential barrier and a potential well near two loading points. Furthermore, the barrier height and well depth gradually become large with increasing tensile stress such that more and more electrons/holes are inhaled in loading region from the n-/p-zone, respectively. Conversely, rising/dropping of conduction band bottom is brought out near the two loading points by a compressive-stress mode due to the increase/decrease in the potential energy of electrons by pumping out the majority-carriers from the loading region to the two outside regions. Therefore, a potential well and a potential barrier are induced near the two loading points, such that more and more electrons/holes are driven away from the loading region to the n-zone/p-zone, respectively, with the increasing compressive stress. These effects are important to tune the carrier recombination rate near the PN interface. Thus, the present study possesses great referential significance to piezotronic devices.     

Reconstruction of Sparse Polynomials via Quasi-Orthogonal Matching Pursuit Method

In this paper, we propose a Quasi-Orthogonal Matching Pursuit (QOMP) algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal polynomials. For the two kinds of sampled data, data with noises and without noises, we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct $s$-sparse Legendre polynomials, Chebyshev polynomials and trigonometric polynomials in $s$ step iterations. The results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal polynomials. Finally, numerical experiments will be presented to verify the effectiveness of the QOMP method.     

Exact evaluation of the multidimensional Franck–Condon integrals based on the contour integral method

Adopting a different method from the Sharp–Rosenstock generating function method and the Doktorov coherent state method, a closed form expression for the Franck–Condon integrals between arbitrary multidimensional harmonic oscillators is derived exactly under the Duschinsky mixing effects on the base of the contour integral form expression of Hermite polynomials. In addition, an analytical expression for the calculation of the four-mode Franck–Condon factors is presented.     

经有限口径均匀加宽放大介质后基模高斯光束的M_Q~2因子变化

数值计算了基模高斯光束经有限口径的均匀加宽放大介质后，其Ｍ２Ｑ因于随输入光与放大器各参数的变化的规律。计算表明：激光放大均使光束质量变坏，且集中在放大器口径ａ与高斯光束的ω的比值处在１～４之间时；低的输入光强，小的放大器总增益，和大的饱和光强有利于保持放大器输出光的光束质量。     

GdBa_2Cu_(3-x)Fe_xO_(7-δ)超导体系结构相变及拉曼谱特征

采用固态反应法制备了GdBa2Cu3-xFexO7-δ(x=0.00-0.30)系列样品,利用X射线衍射、拉曼光谱以及电测量技术对体系的晶体结构、拉曼散射谱特征以及电输运特性进行了系统研究。结果表明,当Fe掺杂量在x=0.05-0.10区间时,体系的晶体结构发生了从正交相到四方相的转变。通过对拉曼光谱中典型振动模的指认及振动模随Fe掺杂量的变化规律,得到了拉曼谱随体系正交-四方结构相变的变化特征:对于具有正交相的x=0.00-0.05样品,拉曼谱具有五个与正交相结构相对应的特征峰;而对于具有四方相的x=0.10-0.30样品,随Fe掺杂量增加,振动模强度变弱,且典型振动模发生了不同程度的展宽或频移。电输运测量表明,随Fe掺杂量的增加,超导临界温度Tc降低,正常态电阻率增加且发生了金属-半导体相变。