On the Problem of Instability in the Dimensions of Spline Spaces over T-Meshes with T-Cycles

The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a basic problem for the theories and applications of splines. However, the problem of determining the dimension of a spline space is difficult since it heavily depends on the geometric properties of the partition. In many cases, the dimension is unstable. In this paper, we study the instability in the dimensions of spline spaces over T-meshes by using the smoothing cofactor-conformality method. The modified dimension formulas of spline spaces over T-meshes with T-cycles are also presented. Moreover, some examples are given to illustrate the instability in the dimensions of the spline spaces over some special meshes.     

高能电子辐射下聚四氟乙烯深层充电特性

介质深层充放电现象是诱发航天器异常故障的重要因素之一.分析了高能电子辐射下介质内部电荷沉积、能量沉积特性和电导特性,考虑了真空与介质界面电荷对电场分布的影响,建立了介质二维深层充电的物理模型,并基于有限元方法实现了数值计算.计算了高能电子辐射下聚四氟乙烯的深层充电特性.结果表明:真空环境下,介质的表面存在较弱的反向电场,随着介质深度增大,电场减小至零,随后逐渐增大,最大值出现在靠近接地附近,但在接地点,电场存在小幅降低.分析了不同辐射时间下(1 h,1 d,10 d和30 d),介质内部最大电位和最大电场的时空演变特性.随着辐射时间的增加,最大电位由-128V增加至-7.9×104V,最大电场由2.83×105V·m-1增加至1.76×108V·m-1.讨论了入射电子束流密度对最大电场的影响,典型空间电子环境(1×10-10A·m-2)下,电子辐照10 d时,介质内部最大电场为2.95×106V·m-1.而恶劣空间电子环境(2×10-8A·m-2)下,电子辐射42 h,介质内部最大电场即达到108V·m-1,超过材料击穿阈值(约为108V·m-1),极易发生放电现象.该物理模型和数值方法可以作为航天器复杂部件多维电场仿真的研究基础.     

Common complements of two subspaces of a Hilbert space

In this paper we find a necessary and sufficient condition for two closed subspaces, and , of a Hilbert space to have a common complement, i.e. a subspace having trivial intersection with and and such that .Unlike the finite-dimensional case the condition is significantly more subtle than simple equalities of dimensions and codimensions, and non-trivial examples of subspaces without a common complement are possible.     

Thin-walled Beams: A Derivation of Vlassov Theory via Γ-Convergence

This paper deals with the asymptotic analysis of the three-dimensional problem for a linearly elastic cantilever having an open cross-section which is the union of rectangles with sides of order ε and ε ², as ε goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the three-dimensional problem Γ-converges to the classical one-dimensional Vlassov model for thin-walled beams.      

冲击速度和轴向静载对红砂岩破碎及能耗的影响

地下岩体工程爆破开挖中,距爆源不同距离处岩体承受的地应力和动载荷大小不同,从动载荷的角度表征岩石动态破坏结果与工程实际更吻合。为研究动载荷和地应力大小对岩体破碎和能量耗散特性的影响,利用动静组合加载试验装置,分别设置7个冲击速度和轴向静应力等级,对红砂岩试件进行冲击试验。根据试件的破碎状况,分析不同静应力工况下冲击速度对岩石破坏模式和机理的影响。计算不同工况下的应力波能量值,研究冲击速度和轴向静应力对岩石能耗特性的影响。对破坏试件进行筛分试验,研究岩石破碎分形维数随冲击速度和轴向静应力的变化关系。结果表明,随着冲击速度的增大,试件的破坏程度逐渐加大。无轴压时岩石试件破坏后整体仍是一个圆柱体,属于张拉破坏;有轴压时岩石试件宏观破坏后呈沙漏状,属于拉剪破坏。岩石耗散能随冲击速度的升高呈二次函数关系递增;轴向静应力越高,递增幅度越小。随着冲击速度的升高,岩石分形维数由零逐渐增加;随着轴向静应力的升高,分形维数由零转为大于零的临界冲击速度先升高后降低。

     

A Note on the Dimension Theory of ℤ n -Graded Rings

In this note we want to generalize some of the results in [1 Brewer , J. , Montgomery , P. , Rutter E. , Heinzer , W. ( 1973 ). Krull dimension of polynomial rings in “Conference on Commutative Algebra, Lawrence 1972.” . Springer Lecture Notes in Mathematics 311 : 26 – 45 .[Crossref] , [Google Scholar]] from polynomial rings in several indeterminates to arbitrary ? ⁿ -graded commutative rings. We will prove an analogue of Jaffard's Special Chain Theorem and a similar result for the height of a prime ideal 𝔭 over its graded core 𝔭*.     

非退化扩散过程的极性与相交性

本文讨论非退化扩散过程的极性，得到了几个较好的充分条件，它可看作[1]的进一步深化，此外，我们将这些结果用来研究两个独立的非退化扩散过程的相交性，得到了一些有意思的结果。     

Testing for additivity with B-splines

Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.     

Finite dimensional semisimple Q-algebras

A Q-algebra can be represented as an operator algebra on an infinite dimensional Hilbert space. However we don’t know whether a finite n-dimensional Q-algebra can be represented on a Hilbert space of dimension n except n = 1, 2. It is known that a two dimensional Q-algebra is just a two dimensional commutative operator algebra on a two dimensional Hilbert space. In this paper we study a finite n-dimensional semisimple Q-algebra on a finite n-dimensional Hilbert space. In particular we describe a three dimensional Q-algebra of the disc algebra on a three dimensional Hilbert space. Our studies are related to the Pick interpolation problem for a uniform algebra.     

半导体超晶格属性的高分辨率X射线衍射研究

详细阐述了低维半导体材料的X射线衍射的动力学理论和运动学理论从高木陶平(T-T)方程出发,基于波动光学原理,推导出任意结构的多层膜的X射线衍射振幅的递推关系式并编写X射线衍射的程序,分别用动力学和运动学衍射理论模型模拟了20层GaAlAs/GaAs超晶格的X射线衍射结果,得到超晶格样品的结构参量.