对2012年全国高考理综21题的讨论

2012年全国高考理综全国卷有两道题背景相同,一道是新课标卷21题,试题如下.【题目1】假设地球是一半径为R,质量分布均匀的球体.一矿井深度为d.已知质量分布均匀的球壳对壳内物体的引力为零.矿井底部和地面处的重力加速度大小之比为     

无穷维欧氏空间中球体及球面的Lebesgue测度

本分别给出了使在无穷维欧氏空间中球体和球面具有有限的,但又不是无穷小的测度的半径集合。     

滚动小球的线速度

目的让水平运动的实心小球和气轨滑块做非弹性碰撞来测量小球水平运动的速度,并由测量出的小球速度来确定当小球从斜面滚下时,百分之几的势能用来旋转小球,百分之几的势能转变成小球的线速度。     

Preparation of Nanocrystalline MoS2 Hollow Spheres

NanocrystaUine MoS2 with hollow spherical morphology has been prepared by the hydrothermal method. The products are characterized by means of X-ray powder diffraction,transmission electron microscopy and high-resolution transmission electron microscopy. The experimental results give the evidence that the sample is consists of hollow spheres 400～600nm in diameter, and there is much whisker on the surface of MoS2 hollow sphere.     

PREPARATION AND ADSORBABILITY OF DEXTRAN MICROSPHERES WITH UNIFORM DIAMETER

The method of preparing uniform dextran microspheres with a narrow diameter distribution was introduced and the adsorbability of these microspheres was evaluated. The microspheres were prepared in W/O microemulsion using 0.5% dextran solution as the aqueous phase and n-hexane as the oil phase. Characteristics of the prepared dextran microspheres were examined with laser light blocking technique, optical microscope and ultraviolet spectrometer. The results show that the prepared dextran microspheres have uniform morphology and narrow diameter distribution, nearly 92% of them having a diameter of 56.6μm. In vitro evaluation of adsorbability, wet dextran microspheres have good adsorption of 98.32mg/g of model drug methylene blue in 20.86mg/L methylene blue solution at 25℃, The adsorption of dried dextran microspheres under the same condition is 132.15mg/g, which is even higher. And the adsorbability of dextran microspheres has significant relationship with the concentration of methylene blue and temperature. The adsorbability is better at lower temperature and higher concentration of methylene blue.     

Synthesis and Characterization of Copolymercore-Silvershell Composite Microspheres

Composite microspheres composed of monodispersed poly（St-co-MAA） latices with diameter about 260 nm as core and Ag nanocrystals as shell were prepared by an in situ reduction method. The shell thickness could be controlled in the range of 15--45 nm by this coating process. The structure and the composition of the core-shell microspheres were characterized by transmission electron microscopy （TEM）, X-ray diffractometry （XRD）, X-ray photoelectron spectroscopy （XPS）, and thermogravimetric analysis （TG）. The formation of the composite microspheres is explained by the nucleation of silver on the surface of the latices followed by growth of the silver shell.     

在Rd上凸体的双弦幂积分

本文给出在Rd上凸体的双弦幂积分概念,并得到双弦幂积分不等式、双弦幂积分与弦幂积分的关系和球体的双弦幂积分值.     

变限积分求导公式在高维典型立体上的推广

将变限积分求导公式推广到高维空间中变边界的超长方体和超球体上,得到简洁优美的结果,并给出其应用.     

利用高斯定理求空心球体引力场

针对现阶段 A P物理教学中引力有关定律推导问题, 采取与以往建立微分式不同的方法, 即利用高斯 定律来求解空心引力场值: 地球谐振子模型和空心球壳, 为广大教师提供一个新的授课思路     

Monoenergetic electron parameters in a spheroid bubble model

A reliable analytical expression for the potential of plasma waves with phase velocities near the speed of light is derived.The presented spheroid cavity model is more consistent than the previous spherical and ellipsoidal models and it explains the mono-energetic electron trajectory more accurately,especially at the relativistic region.The maximum energy of electrons is calculated and it is shown that the maximum energy of the spheroid model is less than that of the spherical model.The electron energy spectrum is also calculated and it is found that the energy distribution ratio of electrons △E/E for the spheroid model under the conditions reported here is half that of the spherical model and it is in good agreement with the experimental value in the same conditions.As a result,the quasi-mono-energetic electron output beam interacting with the laser plasma can be more appropriately described with this model.