Generalized Solution of a Kind of Nonparametric Curvature Evolution with Boundary Condition

The existence and uniqueness of the generalized solution for a kind of nonparametric curvature flow problem are obtained. This kind of curvature flow problem describes the evolution of graphs with speed depending on the reciprocal of the Gauss curvature.     

旋转锥镜相机研测动态曲率和斜率

采用旋转锥镜相机，进行激光散斑剪切照相，研测缓慢变形物体的动态曲率和斜率。拍摄一张散斑图即可获得曲率和斜率动态变化的全过程。     

电子碰撞诱导原子从低激态向高激态弛豫

本文根据空心阴极放电中电子能量分布的物理图象,分析了原子从低激态向高激态弛豫的可能途径。建立高低激态集居数密度增量的关系。讨论高激态集居数密度增量获得可观量的条件。根据此条件分别选取钠原子的基态3s~2S_(1/2)和铜原子的亚稳态4s~2D_(3/2)为与激光共振的下能级,并激发具有较大自发发射几率的3s~2S_(1/2)→3p~2P°_(1/2)(和3p~2P°_(3/2))和4s~2D_(3/2)→4p~2P°_(1/2)跃迁,在远离上能级的高激态上观测到敏化荧光,并精确测得这些态的自发发射系数比值,而在更高激态上没有观测到敏化荧光,表明讨论中提出的条件是合理的。     

MoO3、NiO、ZnO在小表面金红石上的分散行为

Dispersion of MoO3, NiO, ZnO on rutile TiO2 with low specific surface area was studied with Mercury Porosimeter, SEM, XPS and Ammonia Extraction method. The dispersion thresholds of MoO3, NiO, ZnO on three rutile TiO2 carriers were obtained with XPS, and com-pared with those on anatase TiO2 with high specific surf are area. Ammonia Extraction method was used to identify the surface oxide species interarting with support surface in different strength and it was found that the proportions of oxides that can not be extracted by ammonia extraction are different for MoO3, NiO and ZnO which are supported on rutile TiO2.     

Structural evolution of (Ca0.35Sr0.65)TiO3 perovskite at high pressures

Lattice parameters of a synthetic powder sample of Ca_0.35Sr_0.65TiO₃ perovskite have been determined by the method of Le Bail refinement, using synchrotron X-ray diffraction patterns collected at pressures up to 15.5 GPa with a membrane-driven diamond anvil cell. At ambient conditions, diffraction data were consistent with the I4/mcm structure reported previously in the literature for the same composition. Diffraction data collected at high pressures were consistent with tetragonal (or, at least, pseudo-tetragonal) lattice geometry, and no evidence was found for the development of any of the orthorhombic structures identified in other studies of (Ca, Sr)TiO₃ perovskites. Additional weak reflections, which could not be accounted for by the normal I4/mcm perovskite structure, were detected in diffraction patterns collected at pressures of 0.9-2.5 GPa, and above ∼13.5 GPa, however. Small anomalies in the evolution of unit cell volume and tetragonal strain were observed near 3 GPa, coinciding approximately with breaks in slope with increasing pressure of bulk and shear moduli for a sample with the same composition which had previously been reported. The anomalies could be due either to new tetragonal↔tetragonal/pseudo-tetragonal phase transitions or to subtle changes in compression mechanism of the tetragonal perovskite structure.     

Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature

The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in Rⁿ. They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces. In particular, they discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume, which can be seen as the higher-dimensional generalization of the pseudo-sphere.     

曲率流的参数化有限元逼近

许多物理现象可以在数学上描述为受曲率驱动的自由界面运动,例如薄膜和泡沫的演变、晶体生长,等等.这些薄膜和界面的运动常依赖于其表面曲率,从而可以用相应的曲率流来描述,其相关自由界面问题的数值计算和误差分析一直是计算数学领域中的难点.参数化有限元法是曲率流的一类有效计算方法,已经能够成功模拟一些曲面在几类基本的曲率流下的演化过程.本文重点讨论曲率流的参数化有限元逼近,它的产生、发展和当前的一些挑战.     

Curvature and finite domination

Upper bounds obtained by Gromov on the Betti numbers of certain closed Riemannian manifolds are shown to be upper bounds on the minimum number of cells in --spaces dominating such manifolds.

     

A global pinching theorem for compact surfaces inS 3 with constant mean curvature

LetM be a compact minimal surface inS ³. Y. J. Hsu^[5] proved that if S₂22, thenM is either the equatorial sphere or the Clifford torus, whereS is the square of the length of the second fundamental form ofM, ·₂ denotes theL ²-norm onM. In this paper, we generalize Hsu's result to any compact surfaces inS ³ with constant mean curvature.Supported by NSFH.     

Some remarks on R-contact flows

Let (M, ) be an R-contact manifold, then the set of periodic points of the characteristic vector field is a nonempty union of closed, totally geodesic odd-dimensional submanifolds. Moreover, the R-metric cannot have nonpositive sectional curvature. We also prove that no R-contact form can exist on any torus.