基于龙基光栅塔尔博特效应的长焦距测量

提出通过对龙基光栅的塔尔博特效应所产生的莫尔条纹角度的计量来测量长焦距的方法。并在此基础上推导了长焦距的计算公式，分析了这种方法的测量误差。这种长焦距测量方法具有实时测量、精度高的特点。     

钠改型天然斜发沸石对铵离子的交换性能

对分别来自国内三个产地和澳大利亚的沸石样品进行了铵离子交换性能的研究。在25℃下了样品的交换速率曲线。利用Verrmeulen's模型处理动力学数据，计算得到扩散系数，与文献报道的结果相一致，并发现不同样品的扩散系数与其致密程度相关。将粒度200mesh的沸石分别用三种不同方法聚集为颗粒，并测定了表观的扩散系数，均高于原颗粒的扩散系数，其中凝胶颗粒提高了一个数量级。     

Corrections to scaling for diffusion exponents on three-dimensional percolation systems at criticality

Recent results of Monte Carlo simulations of the ant-in-the-labyrinth method in three-dimensional percolation lattices are reanalyzed in the light of more accurate corrections to scaling ansatz, motivated by inconsistent results that have appeared in the literature. The results are observed to be sensitive to the form of the scaling correction terms. Using a single correction term, we estimate the valuek=0.197±0.004 for the anomalous diffusion exponent at criticality. When two correction terms are included,k=0.200±0.002 is obtained. These new estimates are consistent with known theoretical bounds, with recent series expansion results, and with numerical calculations of the conductance of random resistor networks above criticality.     

GENERALIZED SOLUTION OF SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS

The singularly perturbed initial boundary value problem for reaction diffusion equation is considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of the generalized solution for the problems are studied.     

First production of ultracold neutrons with a solid deuterium source at the pulsed reactor TRIGA Mainz⋆

The production rates of ultracold neutrons (UCN) with a solid deuterium converter have been measured at the pulsed reactor TRIGA Mainz. Exposed to a thermal neutron fluence of n·cm^-2·pulse^-1, the number of detected very cold and ultracold neutrons ranges up to 200 000 at 7mol of solid deuterium (sD₂) in combination with a pre-moderator (mesitylene). About 50% of the measured neutrons can be assigned to UCN with energies E of where V _F(sD ₂) = 105 neV and V _F(guide) = 190 neV are the Fermi potentials of the sD₂ converter and our stainless steel neutron guides, respectively. Thermal cycling of solid deuterium, which was frozen out from the gas phase, considerably improved the UCN yield, in particular at higher amounts of sD₂.     

Chernoff approximations of Feller semigroups in Riemannian manifolds

Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks.     

带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

本文针对带非线性源项的Riesz回火分数阶扩散方程,利用预估校正方法离散时间偏导数,并用修正的二阶Lubich回火差分算子逼近Riesz空间回火的分数阶偏导数,构造出一类新的数值格式.给出了数值格式在一定条件下的稳定性与收敛性分析,且该格式的时间与空间收敛阶均为二阶.数值试验表明数值方法是有效的.     

A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters

We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points lines, where three interfaces meet, and at the boundary points lines, where an interface meets a fixed planar boundary. We propose a parametric finite element method based on a suitable variational formulation. The constructed method is semi-implicit and can be shown to satisfy the volume conservation of each enclosed bubble and the unconditional energy-stability, thus preserving the two fundamental geometric structures of the flow. Besides, the method has very good properties with respect to the distribution of mesh points, thus no mesh smoothing or regularization technique is required. A generalization of the introduced scheme to the case of anisotropic surface energies and non-neutral external boundaries is also considered. Numerical results are presented for the evolution of two-dimensional curve networks and three-dimensional surface clusters in the cases of both isotropic and anisotropic surface energies.     

Secondary-school teachers’ noticing of aspects of mathematics teaching talk in the context of one-day workshops

In a research project with one-day teacher education workshops for secondary-school mathematics teachers, our study explores the potential of tool-supported discussions in helping them to notice important and critical aspects of mathematics teaching talk. Mathematical practices of naming and explaining in teaching talk, students’ content learning challenges, and noticing processes of identifying, interpreting and deciding are the components of our framework and the tools that guided the design and implementation of three workshops on linear equations, fractions and plane isometries. The data was collected during the discussions with the seven teachers and the teacher educator throughout these workshops. The coding of the discussions allowed us to see discourse moves that reveal the teachers’ noticing of: (i) challenges in the identification of mathematical naming, (ii) mathematical explaining that voices the students’ learning, (iii) classroom practice in relation to mathematical naming and explaining.     

A numerical technique based on B-spline for a class of time-fractional diffusion equation

This paper presents an efficient numerical technique for solving a class of time-fractional diffusion equation. The time-fractional derivative is described in the Caputo form. The L1 scheme is used for discretization of Caputo fractional derivative and a collocation approach based on sextic B-spline basis function is employed for discretization of space variable. The unconditional stability of the fully-discrete scheme is analyzed. Two numerical examples are considered to demonstrate the accuracy and applicability of our scheme. The proposed scheme is shown to be sixth order accuracy with respect to space variable and (2 − α)-th order accuracy with respect to time variable, where α is the order of temporal fractional derivative. The numerical results obtained are compared with other existing numerical methods to justify the advantage of present method. The CPU time for the proposed scheme is provided.