三角B\''{e}zier曲面和四边B\''{e}zier曲面之间的相互转化

B\'{e}zier曲面有两种不同的形式:三角B\'{e}zier曲面和四边B\'{e}zier曲面,它们有着不同的基底和不同的几何拓扑结构, 但是它们也有很多共同的性质,因此三角B\'{e}zier曲面和四边B\'{e}zier曲面之间的相互转化就成为CAGD 里一个重要研究课题.在本文中, 我们用函数复合的方法实现两者之间的相互转化.被复合的两个函数, 一个用Polar形式表示,另一个用常见的Bernstein基形式表示.     

Sz\''asz-Kantorovich-B\''{e}zier算子在$L_p[0, \infty)$上的逼近定理

本文利用Ditzian-Totik模得到了Sz\'{a}sz-Kantorovich-B\'{e}zier算子在$L_{p}[0,\infty)$空间逼近的正逆定理及等价定理.     

由L\''{e}vy过程驱动的仿射方程关联的无限时区的最优二次控制

讨论线性二次最优控制问题, 其随机系统是由 L\'{e}vy 过程驱动的具有随机系数而且还具有仿射项的线性随机微分方程. 伴随方程具有无界系数, 其可解性不是显然的. 利用 $\mathscr{B}\mathscr{M}\mathscr{O}$ 鞅理论, 证明伴随方程在有限 时区解的存在唯一性. 在稳定性条件下, 无限时区的倒向随机 Riccati 微分方程和伴随倒向随机方程的解的存在性是通过对应有限 时区的方程的解来逼近的. 利用这些解能够合成最优控制.     

监测L\'{e}vy稳定过程均值变点的平均运行时间估计

平均运行长度(时间) (ARL)是判断一控制图监测变点效果好坏的一个重要工具\bd 本文主要研究L\'{e}vy 稳定过程的均值变点监测问题\bd 我们给出了三个控制图, 即EWMA, GEWMA和GLR的ARL 估计, 并通过数值模拟比较了4个控制图监测均值变点的效果和差异.     

带Neumann 边界条件的$p(x)$-Kirchhoff 型椭圆系统的研究

本文研究一类带Neumann 边界条件的~$p(x)$-Kirchhoff 型系统解的存在性. 借助于Ekeland变分原理和变指数Sobolev空间理论, 我们给出使得该问题存在解的合适条件.由于Poincar\'{e} 不等式在$W^{1,p(x)}(\Omega)$ 中不再成立, 我们将在$W^{1,p(x)}(\Omega)$ 的某个子空间中证明Poincar\'{e}-Wirtinger 不等式.     

厚尾相依序列的均值变点估计

本文研究了厚尾相依序列的均值变点估计. 证明了变点的CUSUM估计的一致性并得到了收敛速度.在方差无穷的情况下推广了H\'{a}jek--R\'{e}nyi不等式.     

单个多元正态总体均值向量联合置信区间的比较

单个多元正态总体均值向量的Bonferroni和Scheff\'{e}联合置信区间在实际中经常用到,本文主要采用解析的办法比较这两个置信区间的长短, 证明了当均值向量的维数$2\le p\le 12$时, Bonferroni联合置信区间比Scheff\'{e}联合置信区间短.     

关于局部凸空间中向量Ekeland变分原理的等价性

基于各种Ekeland变分原理的等价形式, 主要研究局部凸空间中给定有界凸子集乘以距离函数为扰动的单调半连续映射的向量Ekeand变分原理的等价性问题. 首先利用局部凸空间中的向量Ekeland变分原理证明了向量Caristi-Kirk不动点定理,向量 Takahashi非凸极小化定理和向量Oettli-Th\'{e}ra定理. 进一步研究了向量Ekeland变分原理与向量Caristi-Kirk不动点定理,向量Takahashi非凸极小化定理和向量Oettli-Th\'{e}ra定理的等价性.     

图的广义Randi\'{c} Estrada 指标的界

受图的Randi\'{c} Estrada 指标和广义 Randi\'{c} 能量的启发, 定义了图的广义 Randi\'{c} Estrada 指标. 利用代数方法和初等分析方法给出了n 阶简 单连通图和 r-正则图的广义Randi\'{c} Estrada指标的上下界, 推广了Bozkurt等人有关Randi\'{c} Estrada指标的结论.     

伪多元函数的Padé型逼近

给出伪多元函数的Pad\'{e}型逼近,其优点在于:简化了多元函数有理逼近的计算,加速了函数在奇点处的收敛.并讨论其性质以及误差分析.     

The equivariant family index theorem in odd dimensions

In this paper, we prove a local odd dimensional equivariant family index theorem which generalizes Freed's odd dimensional index formula. Then we extend this theorem to the noncommutative geometry framework. As a corollary, we get the odd family Lichnerowicz vanishing theorem and the odd family Atiyah-Hirzebruch vanishing theorem.     

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??A class of backward doubly stochastic differential equations driven by white noises and Poisson random measures are studied in this paper. The definitions of solutions and Yamada-Watanabe type theorem to this equation are established.     

概率区间空间中的新型KKM定理及应用

本文建立了概率区间空间的概念，并在此框架下建立了一个新型的ＫＫＭ定理．作为应用我们得到了概率区间空间中的一个新的极大极小定理和截口定理，匹配定理及一些重合点定理．所得结果均是全新的，它们不仅包含了ＶｏｍＮｅｕｍａｎｎ［７］中的主要结果，而且将［１］［３～４］［６］，［８］中的相应结果推广到概率区间空间。     

Asymptotic analysis of a kernel estimator for parabolic stochastic partial differential equations driven by fractional noises

We study a strongly elliptic partial differential operator with time-varying coeffcient in a parabolic diagonalizable stochastic equation driven by fractional noises. Based on the existence and uniqueness of the solution, we then obtain a kernel estimator of time-varying coeffcient and the convergence rates. An example is given to illustrate the theorem.     

Nonsmooth version of Fountain theorem and its application to a Dirichlet-type differential inclusion problem

In this paper we establish a nonsmooth version of Fountain theorem by adopting the framework of nonsmooth analysis theory, which is a generalization of Theorem 3.6 of Willem (1996) [2]. Then we present an application of this theorem to a Dirichlet-type differential inclusion problem.     

UPPER SEMI-CONTINUITY OF RANDOM ATTRACTORS FOR A NON-AUTONOMOUS DYNAMICAL SYSTEM WITH A WEAK CONVERGENCE CONDITION

In this paper, we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit. As an application,we obtain the convergence of random attractors for non-autonomous stochastic reactiondiffusion equations on unbounded domains, when the density of stochastic noises approaches zero. The weak convergence of solutions is proved by means of Alaoglu weak compactness theorem. A differentiability condition on nonlinearity is omitted, which implies that the existence conditions for random attractors are sufficient to ensure their upper semi-continuity.These results greatly strengthen the upper semi-continuity notion that has been developed in the literature.     

Moderate deviation and central limit theorem for stochastic differential delay equations with polynomial growth

Employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderate deviation for a class of stochastic differential delay equations with small noises, where the coefficients are allowed to be highly nonlinear growth with respect to the variables. Moreover, we obtain the central limit theorem for stochastic differential delay equations which the coefficients are polynomial growth with respect to the delay variables.     

Local completeness, drop theorem and Ekeland's variational principle

By using a very general drop theorem in locally convex spaces we obtain some extended versions of Ekeland's variational principle, which only need assume local completeness of some related sets and improve Hamel's recent results. From this, we derive some new versions of Caristi's fixed points theorems. In the framework of locally convex spaces, we prove that Daneš' drop theorem, Ekeland's variational principle, Caristi's fixed points theorem and Phelps lemma are equivalent to each other.     

Involutive moving frames II; The Lie-Tresse theorem

This paper continues the project, begun in [1], of harmonizing Cartan's classical equivalence method and the modern equivariant moving frame in a framework dubbed involutive moving frames. As an attestation of the fruitfulness of our framework, we obtain a new, constructive and intuitive proof of the Lie-Tresse theorem (Fundamental basis theorem) and a first general upper bound on the minimal number of generating differential invariants for Lie pseudo-groups. Further, we demonstrate the computational advantages of this framework by studying the equivalence problem for first order PDE in two independent variables and one dependent variable under point transformations.     

Counterexamples to a triality theorem in “Canonical dual least square method”

In this short note we give two counterexamples to the Triality Theorem concerning the optimization problem presented in Ruan et al., Comput. Optim. Appl. (2008). In order to understand the problem first we introduce the framework of this paper and quote the theorem we have in view. Then, while trying to verify this theorem we encounter several difficulties and note their nature. We end by revealing our counterexamples.