错误的根源在于混淆了质心与重心吗?

1一道习题引起的思考 有这样一道习题：一个半径为尺，质量为M的均匀实心球体，球心为O，在该球内挖出一个半径为R/2的空腔，距球心O为L=2R的位置处有一质量为m的质点，如图1所示．求阴影部分球体与质点m之间的万有引力大小．     

Facile Fabrication of Large Area Polystyrene Colloidal Crystal Monolayer via Surfactant-free Langmuir-Blodgett Technique

A facile and novel method for the production of a large area of well-ordered polystyrene(PS)colloidal crystal monolayer was established using the surfactant-free Langmuir-Blodgett(LB)technique.The hydrophobic property(film-forming ability)of PS spheres was improved by a thermo-rheology treatment before LB assembly,and a large film was obtained.In contrast to the traditional LB technique,no surfactant was needed in this method,which could eliminate the additional contamination of surfactants in the preparation process and provided the products with versatile applications in nanosphere lithography(NSL)for biosensor,surface plasmon resonance,and surface enhanced Raman spectroscopy.     

Noncommutativity in Haldane＇s Model

We treat Haldane‘s model by the standard Dirac procedure. After canonical quantization, the coordinates of the particle become noncommutative, and the commutation relations for the coordinates coincide exactly with those defining a fuzzy two-dimensional sphere.     

HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE

A theory of a class of higher order singular integral under the operator(Lf)(u)=1/(ū [ū1 f u 1(u) 1 f ū1(u)+f(u)] is given.We transform the higher order singular integral to a usual Cauchy integral,extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case,and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.     

聚N-异丙基丙烯酰胺在十二烷基硫酸钠水溶液中的线团球体转变

高分子链在溶液中,当溶剂由良变劣时,将发生线团-球体转变,而同时由于链间聚集造成的相分离,使得很难真正观察到热力学意义上稳定的高分子单链紧缩球体。表面活性剂的加入有助于阻止高分子链间发生聚集,在不同的外部条件下,表面活性剂同高分子链将形成形态迥异且又复杂有趣的复合结构。本文主要讨论了聚N-异丙基丙烯酰胺在十二烷基硫酸钠水溶液体系中的线团-球体转变行为,以及聚N-异丙基丙烯酰胺与十二烷基硫酸钠分子间的相互作用及结构模型。     

Preparation of PDMS-coated microspheres by sol-gel method for sorptive extraction of PAHs

In this paper, a novel SPME mode, PDMS-coated solid glass microspheres （SGMs）, were prepared by sol-gel method. Using homemade thermal desorption unit coupled with CGC-FID, six PAHs as model analytes, the performance of the new mode was characterized. The new extractive phase exhibited high thermal stability and satisfactory extraction capability. The detection limits were 0.01-0.045 ng/mL, and the linearity was from 0.5 ng/mL to 96 ng/mL. The R.S.D.s of repeatability for retention time and peak area were all within 0.074% and 6.7%, respectively. The recoveries of the PAHs were 78-127% from the samples taken from river water.     

Preparation,Characterization,and in vitro Release of Biodegradable Erythromycin-gelatin Microspheres

Blank and erythromycin-loaded gelatin microspheres were successfully fabricated via emulsion chemical- crosslinking technique. The surface morphology of the microspheres was characterized by scanning electron microscope（SEM） and optical microscope. The results show that the microspheres were spherical and smooth. The particle average size of erythromycin-loaded microspheres was found to be 20.6 μm, with a high purity of more than 90% and with a good dispersibility. The microspheres could be obtained in a high yield. Erythromycin released from the microspheres was monitored in buffer and artificial body fluid at 37 ℃. Average drug content was 27.2%, and erythromycin-loaded gelatin microspheres showed good release profiles with a nearly constant release during 4-8 h in artificial body fluid in vitro degradation studies. These gelatin microspheres are useful for studying and developing various drug-delivery systems.     

HITTING TIME AND PLACE TO A SPHERE OR SPHERICAL SHELL FOR BROWNIAN MOTION

61.IntroductionLetX~{X,(w),t20}beastandardd-dimensionalBrownianmotioninR'(d22).ThefirsthittingtimeofXforaBorelsetBinRdisdefinedtobeThefirsthittingplaceisX(TB).InthispapergwemainlyconsiderthesphereZ'--,(0,r)~{x:xERd,lxl~r}andthesphericalshellZ'--,(0,a)UZ'--,(0,b)~{x.xER',lxl=aorlxl~b},wherer>0,a>0,b>0anda相似文献   

幂强化材料和超弹性材料组合球体中孔穴的动态生成

在简单加载条件下,研究幂强化材料和超弹性材料组合球体中的动态孔穴生成和增长问题,首先在有限变形动力学的框架下建立了相应的非线性数学模型,得到了应力的表达式,利用变量变换的方法求得了外加载荷和孔穴半径之间的一个精确的微分关系式,证明了当突加载荷超过其临界值时,球体内部有孔穴的突然生成,并随时间呈现非线性的周期振动．通过数值计算,分析了材料参数和球体的半径比对孔穴生成和增长的影响,并与相应的静态结果进行了比较．结果发现,惯性力的影响降低孔穴生成的临界载荷,而且材料的塑性对孔穴生成和增长有明显的影响．     

简化超球体SRUKF的GPS/MIMU组合姿态估计

针对加速度计、磁强计易受机动加速度和周围环境影响的问题,提出了一种单基线GPS/MIMU组合姿态估计方法。该方法利用单基线GPS天线代替磁强计提供航向信息,并利用GPS的速度信息对加速度计输出的机动加速度分量进行补偿,构成单基线GPS/MIMU组合姿态确定单元。同时考虑实时性要求,在SRUKF的基础上,引入加性非扩展形式和超球体单形采样,提出了简化超球体平方根UKF算法,通过减少状态维数和采样点的数量,降低算法计算量。建立加性噪声下的单基线GPS/MIMU姿态模型,并采用简化超球体平方根UKF算法进行姿态估计。实验结果表明,单基线GPS的速度信息可以有效提高加速度计对水平倾角的确定精度,姿态估计算法收敛后的最大误差小于0.8°,估计精度与UKF相当,且执行时间仅是UKF的42%。