基于液晶光调制器的夏克-哈特曼波前探测技术

微透镜阵列是夏克-哈特曼波前探测器的关键器件。利用液晶器件的空间相位调制特性,可实现微透镜阵列功能,且具有孔径和焦距可变的优点。论述了基于液晶光调制的夏克-哈特曼波前探测校正技术的特征、技术进展、及应用前景。     

A Schwarz-Pick inequality for harmonic quasiconformal mappings and its applications

The main result of this paper is the sharp generalized Schwarz-Pick inequality for euclidean harmonic quasiconformal mappings with convex ranges, which generalizes a result given by Mateljevi?. As its applications, we obtain the property of quasi-isometry with respect to the Poincaré distance and an analogue of the Koebe theorem for this class of mappings.     

Distortion theorems for convex mappings on homogeneous balls

Let B be the open unit ball of a complex Banach space X and let B be homogeneous. We prove distortion results for normalized convex mappings f:B→X which generalize various finite dimensional distortion theorems and improve some infinite dimensional ones. In particular, our results are valid for the open unit balls of complex Hilbert spaces and the Cartan domains.     

Solving variational inequalities by a modified projection method with an effective step-size

In this paper, we propose a new projection method for the solution of variational inequality problems. The method is simple, which uses only function evaluations and projections onto the feasible set. We adopt a new step-size rule and a new search direction in the new method. Under the mild conditions, we prove the proposed method is globally convergent. Preliminary numerical results are reported.     

Prym Representations of Mapping Class Groups

Let S be a closed orientable surface of genus at least 2 and let to S be a connected finite abelian covering with covering group $G$. The lifts of liftable mapping classes of S determine a central extension (by G) of a subgroup of finite index of the mapping class group of S. This extension acts on H₁( ). With a few exceptions for genus 2, we determine the Zariski closure of the image of this representation, and prove that the image is an arithmetic group.     

Miniaturized 3-D surface profilometer using a fiber optic coupler

A 3-D surface profilometer is described which uses a simple fiber optic coupler to form a Young's double pinhole interferometer. The Young's fringes are projected onto a surface, captured by a camera and analyzed using the Fourier transform method. The phase of the fringe pattern on the object is used to reconstruct the surface profile. System analysis, results from a simulation, and preliminary experimental results are provided which indicate a system resolution on the order of a tenth of a millimeter.     

Some new results on planar harmonic mappings

This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings.     

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.     

二维矢量边界推进非结构网格生成方法

提出二维矢量边界推进生成非结构三角形网格方法并证明其可行性.根据流场边界尺度布置边界节点并运用矢量边界推进方法生成背景网格,运用符号面积函数和概率筛选方法布置初始点阵,提出Spring-Laplace方法优化节点位置,同时利用边交换技术优化网格结构.该方法可包含任意点源、线源和内嵌边界,可自由进行局部自适应加密或稀疏,实现任意平面域内与尺度要求一致的高效光滑三角网格剖分.     

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.