有限个渐近伪压缩映射近迫点序列的收敛性

研究了Banach空间中有限个渐近伪压缩映射近迫点序列的收敛性问题,此结果推广了以前的结论.     

有限级拟亚纯映射在Borel方向上的充满圆

对于开平面上有限正级的K-拟亚纯映射在Borel方向上的性质进行了研究,用比较简单的方法证明了有限正级K-拟亚纯映射在其Borel方向上一定存在充满圆序列.把A.Rauch关于亚纯函数的结果推广到K-拟亚纯映射上.     

导体栅的静电屏蔽作用

采用保角变换的方法 ,计算了导体栅作屏蔽罩时的场强分布 ,所得结果表明导体栅具有很好的静电屏蔽作用     

Development of a “Built-in” Scanning Near Field Microscope Head for an Atomic Force Microscope System and Stress Mapping of an Al2O3/ZrO2 Eutectic Composite

We constructed a scanning near-field optical microscope (SNOM) on a commercially available atomic force microscopy (AFM) apparatus (SPM-9500J2; Shimadzu Corp.) to measure the stress distribution in ceramic composite materials. Features of our SNOM system are: (1) a compact SNOM head substituted for the original AFM head; (2) a wide scanning range (125 × 125 μm²) inherited from the original scanner; (3) use of conventional shear-force regulation; (4) an optical system for the illumination-collection (I-C) mode; (5) excitation by a 488 nm line of an Ar-ion laser, and (6) light detection by photon counting or a polychromator equipped with an electronically cooled charge coupled device (CCD). This SNOM system was used to measure the surface structure and stress distribution of an Al₂O₃/ZrO₂ eutectic composite. We simultaneously measured topographic images and fluorescence spectra of an Al₂O₃/ZrO₂ eutectic composite. We estimated its peak intensity, peak position, and peak width from the fluorescence spectrum during scanning, which respectively correspond to the abundance of Al₂O₃, stress in the grain, and the anisotropy of that stress. Mapping images showed that the stress and its anisotropy were weaker in the center of the Al₂O₃ grain than its boundary between Al₂O₃ and ZrO₂. That observation suggests that Al₂O₃ underwent intense anisotropic stress induced by volume expansion in the phase transition of ZrO₂ from the cubic phase to the monoclinic phase during preparation.     

A novel multi‐detection technique for three‐dimensional reciprocal‐space mapping in grazing‐incidence X‐ray diffraction

A new scattering technique in grazing‐incidence X‐ray diffraction geometry is described which enables three‐dimensional mapping of reciprocal space by a single rocking scan of the sample. This is achieved by using a two‐dimensional detector. The new set‐up is discussed in terms of angular resolution and dynamic range of scattered intensity. As an example the diffuse scattering from a strained multilayer of self‐assembled (In,Ga)As quantum dots grown on GaAs substrate is presented.     

(2+1)维广义Nizhnik-Novikov-Veselov系统的新严格解和复合波激发

利用拓展的Riccati方程映射法与变量分离法，得到了(2+1)维广义Nizhnik-Novikov-Veselov(GNNV)系统新的含有两个任意函数的相当广义的变量分离严格解.根据其中的周期波解，找到了该系统的复合波，即在周期波背景下的孤立波，并简要讨论了其演化行为. 关键词： GNNV系统 拓展Riccati映射 周期波解 孤立波     

A general mapping approach and new travelling wave solutions to the general variable coefficient KdV equation

A general mapping deformation method is applied to a generalized variable coefficient KdV equation. Many new types of exact solutions, including solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions and other exact excitations are obtained by the use of a simple algebraic transformation relation between the generalized variable coefficient KdV equation and a generalized cubic nonlinear Klein－Gordon equation.     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

思维导图促进分析化学课堂思政教学的探索——以“酸碱滴定法基本原理”为例

在分析化学课程的教学中,通过充分发掘其中的思政元素,将其与教学内容进行有机结合,达到育人的目的。通过引入思维导图教学法,搭建思政元素与教学内容的桥梁,学生可以快速把握所学知识。通过学生的表现,分析教学效果,存在的问题等,为课堂思政与本科化学教学有机结合提供一定的借鉴。     

The class of mappings with bounded specific oscillation,and integrability of mappings with bounded distortion on Carnot groups

This paper is the first of the author’s three articles on stability in the Liouville theorem on the Heisenberg group. The aim is to prove that each mapping with bounded distortion of a John domain on the Heisenberg group is close to a conformal mapping with order of closeness \(\sqrt {K - 1} \) in the uniform norm and order of closeness K ? 1 in the Sobolev norm L _p ¹ for all \(p < \tfrac{C}{{K - 1}}\).In the present article we study integrability of mappings with bounded specific oscillation on spaces of homogeneous type. As an example, we consider mappings with bounded distortion on the Heisenberg group. We prove that a mapping with bounded distortion belongs to the Sobolev class W _p,loc ¹ , where p → ∞ as the distortion coefficient tends to 1.