Strong immersion is a well-quasi-ordering for semicomplete digraphs

We prove that the strong immersion order is a well-quasi-ordering on the class of semicomplete digraphs, thereby strengthening a result of Chudnovsky and Seymour (2011, J. Comb. Theory, Series B, 101, 47–53) that this holds for the class of tournaments.     

Complex affine distributions

Geometry of affine immersions is the study of hypersurfaces that are invariant under affine transformations. As with the hypersurface theory on the Euclidean space, an affine immersion can induce a torsion-free affine connection and a (pseudo)-Riemannian metric on the hypersurface. Moreover, an affine immersion can induce a statistical manifold, which plays a central role in information geometry. Recently, a statistical manifold with a complex structure is actively studied since it connects information geometry and Kähler geometry. However, a holomorphic complex affine immersion cannot induce such a statistical manifold with a Kähler structure. In this paper, we introduce complex affine distributions, which are non-integrable generalizations of complex affine immersions. We then present the fundamental theorem for a complex affine distribution, and show that a complex affine distribution can induce a statistical manifold with a Kähler structure.     

基于多元高斯声束模型的圆柱体超声检测声场仿真

为了提高圆柱体缺陷检测的准确性,需了解其超声声场分布。针对圆柱体实际检测的要求,本文采用超声水浸检测法。通过多元高斯声束模型分别模拟了实心圆柱体及空心圆柱体中的辐射声场,计算仿真了垂直入射与倾斜入射至圆柱体时的声场,实现了检测声场的可视化。通过计算得出仿真结构与实际理论相符,表明本论文的方法能够应用在圆柱体结构超声声场仿真中。     

阴极透镜层流电子枪调制特性

通过求解第一类边界条件的拉普拉斯方程,获得了典型的三电极阴极透镜中轴上电位的解析表达式。以此为基础,分析了阴极透镜各几何参数及电位参数对其聚焦性能的影响,得知通过增大调制极电位或其孔径、增加调制极与加速极的间距或缩小调制极与阴极的间距的方法,可以保证在改善初始粒子时间、空间弥散特性的基础上,相对减小轴向电场的非均匀性以减弱其会聚电场强度,从而使带电粒子束在阴极透镜区域中不能形成交叠点,达到构成其中电子运动具有层流性质的阴极透镜层流电子枪的工程应用目的。另外也获得了采用厚度较小的调制极有助于整个电子光学系统性能优化的结论。     

Asymmetric membrane formation via immersion precipitation method. I. Kinetic effect

The kinetic effect of the phase inversion process on the membrane morphology is explored, with emphasis on the diffusion coefficient of the nonsolvent as a measure of the solvent/nonsolvent exchange rate. The diffusion coefficient is closely related to the nonsolvent tolerance of the polymer solution, which was estimated from a pseudo-ternary phase diagram of the following system: polymer: polysulfone; solvent system: a mixture of the solvent 1-methyl-2-pyrrolidinone and a solvent additive (formic acid, water or ethanol); and nonsolvent: ethanol. Regardless of the kind of solvent additive employed, when the diffusion coefficient of the nonsolvent is high for a given gelation medium, then the membrane consists of a smooth, defect-free surface and macrovoid-free cross section, and is highly permeable to oxygen. However, using a polymer solution with a low diffusion coefficient results in a membrane of a rather defective morphology. Therefore, it is concluded that the diffusion coefficient of the nonsolvent is a crucial parameter in controlling membrane morphology.     

Complex Polynomial Vector Fields Having a Finitely Curved Orbit

The author proves that a non-singular polynomial vector field without invariant lines and having an entire finitely curved transcendent orbit on C^2 must be equivalent to a trivial vector field by a holomorphic change of coordinates. Other classification results are obtained for polynomial vector fields having a finitely curved orbit on C^2.     

The isometric extension problem in the unit spheres of l<Superscript>p</Superscript>(Г) (<Emphasis Type="Italic">p</Emphasis> >1) type spaces

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of l ^p (Г) (@#@(p >) 1,p ≠ 2 type spaces, and then we conclude that such mappings can be extended to the whole space as real linear isometries by using the previous result of the author.     

Twisted Semigroup Crossed Products and Twisted Toeplitz Algebras of Ordered Groups

Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the theorem of Ji.     

Topological,affine and isometric actions on flat riemannian manifolds II

Explicit examples of finite subgroups of the group of homotopy classes of self-homotopy equivalences of some flat Riemannian manifolds which cannot be lifted to effective actions are given. It is also shown that no finite subgroups of the kernel of π₀(Homeo(M))→Out π₁(M) can be lifted back to Homeo(M), for a large class of flat manifolds M. Some results of an earlier paper by the authors are refined and related to recent work of R. Schoen and S.T. Yau.     

构造正交小波基的基本方法之一

本文不仅给出一种构造局部性好的正交小波基的方法,并且给出了构造各种优良性质的正交小波基的一般思想方法。其特点:使构造的小波母函数有具体的表达式,既有较好的光滑性,又有很好的局部性,并且其收敛速度与│t│~（-（3k 1））同阶,其中k为任意自然数。这种方法不需要每次重新构造函数,只要改变k的值,就能满足不同实际问题的需要。