Numerical realization of the conditions of Max Nther's residual intersection theorem

The aim of this paper is to study numerical realization of the conditions of Max Nther's residual intersection theorem. The numerical realization relies on obtaining the intersection of two algebraic curves by homotopy continuation method, computing the approximate places of an algebraic curve, getting the exact orders of a polynomial at the places, and determining the multiplicity and character of a point of an algebraic curve. The numerical experiments show that our method is accurate, effective and robust without using multiprecision arithmetic,even if the coefficients of algebraic curves are inexact. We also conclude that the computational complexity of the numerical realization is polynomial time.     

沸石基纳米材料的水热分散法制备及其发光

用水热分散法,通过进行分步化学反应,在沸石分子筛的孔道中简便有效地制备了沸石基纳米发光材料．样品的发光表现出纳米粒子的量子尺寸效应     

Dispersion Theory for Two-phase Layered-Geometry Nanocomposites

A dispersion theory for linear optical properties of two-phase layered-geometry nanocomposites is presented. Generalized dispersion relations and sum rules are stated using the results from complex analysis. The concept of Lorentzian linear susceptibility is exploited in theoretical treatment of the effective linear susceptibility of the nanocomposite. The meromorphism of total reflectance in the case of effective meromorphic nonlinear susceptibility was observed.     

Mössbauer study of the vibrational anisotropy and of the light-induced population of metastable states in single-crystalline guanidinium nitroprusside

M?ssbauer studies were performed on single crystals of guanidinium nitroprusside with different orientations of their principal crystallographic axes (a, b, c) with respect to the incident radiation. The markedly anisotropic Lamb-M?ssbauer factor f _LM , i.e. f _LM ^(a) = 0.118(8), f _LM ^(b) = 0.174(8), f _LM ^(c) = 0.202(8) is in contrast to that of nitroprussides with inorganic anions. The observed anisotropy is ascribed to the anisotropic vibrational mean-square displacement of the nitroprusside anions as a whole which is due to the specific packing of both, anions and cations, as well as the very weak chemical bonding between the ions, typical only for guanidinium nitroprusside. The vibrational anisotropy of iron atoms in barium nitroprusside that has been observed by X-ray structural investigations has a different origin and therefore does not result in an anisotropic Lamb-M?ssbauer factor. We have also investigated metastable states in guanidinium nitroprusside that have been populated by means of incoherent irradiation from light-emitting diodes. With a specific orientation of the guanidinium nitroprusside single crystal a population of the metastable states up to 26% could be achieved. Populations of comparable size on lithium, sodium and potassium nitroprussides have only been reached using coherent laser irradiation. Received 15 December 1998 and Received in final form 3 March 1999     

卡托普利在汞电极表面的电化学行为

用循环伏安法、阴极溶出伏安法和电毛细管曲线测量等方法研究了卡托普利在汞电极表面的电氧化机理。实验结果表明,酸性溶液中卡托普利比较稳定,而在中、碱性溶液中卡托普利不稳定。在酸性溶液中有质子参与电极过程,卡托普利在电极表面发生单电子转移,生成汞（Ｉ）－硫化合物,该化合物在电极表面有强吸附,并进一步转化成汞（Ⅱ）－硫化合物。按照实验结果,计算了卡托普利的扩散系数和电极反应速率常数,提出了卡托普利电化学氧     

Influence of metal ions on the alkali-swelling behavior of carboxylated acrylic polymer latexes

The alkalization of carboxylated acrylic polymer latexes by sodium hydroxide gives rise to swelling of the particles. For a poly(n-butyl acrylate) latex copolymerized with 15 wt % methacrylic acid (MAA) and 7 wt % acrylonitrile the particle volume increases by a factor of 30. The alkali-swelling does not depend on the type of monovalent cation used in the base (LiOH, NaOH, KOH, NH₄OH). In contrast, when bivalent cation bases such as Ca(OH)₂ are employed no latex swelling is observed during neutralization because of ionic crosslinking of the copolymer chains. Crosslinking also takes place when the bivalent cations (Ca²⁺, Zn²⁺, Mg²⁺) are added as chlorides to dispersions with latexes previously swollen by sodium hydroxide. In these experiments the original size of the latexes is reached again at a molar ratio MAA: bivalent metal ion of 2:1, i.e. at charge compensation of the carboxyl groups. The shrinking behavior is almost independent of the type of bivalent metal ion used. On the other hand, it is more pronounced when trivalent cations such as Fe³⁺ are added. In general, the experiments demonstrate that the alkali swelling of acrylic latexes is dominated by electrostatic forces. Received: 18 August 1998 Accepted in revised form: 26 October 1998     

Verifying the Implicitization Formulae for Degree N Rational Bézier Curves

This is a continuation of short communication$^{[1]}$. In [1] a verification of the implicitization equation for degree two rational Bézier curves is presented which does not require the use of resultants. This paper presents these verifications in the general cases, i.e., for degree $n$ rational Bézier curves. Thus some interesting interplay between the structure of the $n×n$ implicitization matrix and the de Casteljau algorithm is revealed.     

ON THE MODULI NUMBER OF PLANE CURVE SINGULARITIES WITH ONE CHARACTERISTIC PAIR

61.IntroductionSincethepoineeringworkofZariskil1o]therehavebeenmanypaperspublishedonthemodulinumberofplanecurvesingUlaritiesl5-9].TheproblemhowtocomputethemodulinumberattractsmWattentions[3'6-1o1.Asfarastheauthors'knowledgethemostgener-aJizedalgorithmistheworkof[3]whichdependsonthedivisiontheoremin[1,2].HerewegivealinearalgebraicproofoftheBriancon-Granger-Maisonobe,stheoremlwhichavoidstheDivisiontheorem.Sincethedivisiontheoremonlyholdsindimension2,itseemsquitehopefUlthattheproofherewil1beg…     

拟合隐函数曲线的GNL法

１参数可线性化的曲线拟合问题假设我们已经获得ｎ组独立观测值（ｘｉ,ｙｉ）,其中是精确观测值,ｉ＝１,２,…,ｎ,下同．现欲在最小二乘意义下,拟合非线性模型并假设观测点都分布在模型函数曲线附近．其中为连续可导函数ｇ（ｙ）的反函数,且在我们所研究的ｙ变化范围内恒有ｇ’（ｙ）≠０,（ｊ＝１,２.....下同）为ｐ（＜ｎ）个待定参数．（ｘ）为区间Ｘ内ｐ个线性无关的已知连续函数．随机变量,即为也就是要求求解残差平方和Ｑ（）的无条件极值问题其中参数向量,残差向量,而残差都是微量．对这类常见问题,有以下几种算法．…     

PVDF压电计在低阻抗介质动态力学性能测试中的应用

介绍了ＰＶＤＦ的压电特性,讨论了用ＰＶＤＦ测试材料动态应力应变曲线的实验方法和数据处理方法,并以聚氨酯泡沫塑料为例,说明了它在对低阻抗介质的动态测试中避开了常规Ｈｏｐ ｋｉｎｓｏｎ压杆方法的难处且实验结果具有更高的精确度。