Y. Meyer小波的一般形式

首先我们证明了，如果尺度函数有紧支集，来自多尺度分析的小波函数的支集形式，然后我们证明了Y．Meyer小波的尺度函的一般形式。最后给出了它的另外两种形式和对应的Y．Meyer小波。     

多-尺度加细函数及其性质的研究

引入伸缩因子为α的多-尺度加细函数和平移不变子空间的概念．研究了多-尺度加细方程解存在的条件．特别地，给出这种方程的解是正交的充分必要条件．建立了多-尺度加细函数与两尺度加细函数之间的关系．并讨论了它们的一些性质．最后给出相应的构造算例．     

具有矩阵伸缩的尺度函数双正交特征

考虑了高维具有矩阵伸缩的尺度函数双正交性问题．给出了这种情形下尺度函数双正交性的三个特征刻划及尺度函数属于Ｌ～２（Ｒ～ｄ）的几个充分条件．     

小波的传递函数构造法

本文从小波与尺度函数的传递函数出发 ,给出了构造小波母函数及尺度函数的构造方法 .根据此方法 ,首先以小波与其尺度函数的传递函数为起点 ,构造了一个非正交小波 ,随后以此小波和一个已有的非正交小波为基准 ,进一步推广得到了一类非正交小波及尺度函数类 .在非正交小波的基础上 ,利用将尺度函数正交化的方法 ,构造出了相应正交小波的函数族 .     

小波的传递函数构造法

本从小波与尺度函数的传递函数出发,给出了构造小波母函数及尺度函数的构造方法,根据此方法,首先以小波与其尺度函数的传递函数为起点,构造了一个非正交小波,随后以此小波和一个已有的非正交步波为基准,进一步推广得到了一类非正交小波及尺度函数类,在非正交小波的基础上,利用将尺度函数正交化的方法,构造出了相应正交小波的函数值。     

a尺度正交多尺度函数和正交多小波

基于a 尺度正交单尺度函数，分别给出重数为2和3的a 尺度正交多尺度函数的构造算法。并给出对应正交多小波的显式构造。最后给出伸缩因子为3的正交多小波的构造算例。     

Meyer型正交小波基的构造与性质

本文基于多分辨分析理论与A．W．W方法将Meyer正交小波的构造规范化,给出其设计方法,并证明此类Meyer型小波母函数ψ（x)及相应的尺度函数ψ(x)具有优良的性质,如速降性O（│x│^-N-1(│x│→∞）、N阶消失矩、线性相位、对称性、频谱有限性、并且双尺度序列（滤波器）hn=ψ（n/2）等,并给出N＝2时构造小波函的具体实例。     

具有矩阵伸缩的尺度函数双正交特征

考虑了高维具有矩阵伸缩的尺度函数双正交性问题.给出了这种情形下尺度函数双正交性的三个特征刻划及尺度函数属于L2(Rd)的几个充分条件.     

二维周期基数插值小波尺度函数

设f（x）是一个Fourier系数为正的周期函数，我们构造了关f（x）的二维周期基数插值小波的尺度函数，并得到了一些对构造小波函数有重要意义的性质．     

小波尺度函数计算的广义高斯积分法及其应用

对于小波尺度函数变换的分解系数的积分运算建立了以尺度函数为权的广义高斯积分方法的运算格式．借助于样条函数,证明了其广义高斯积分随小波分解水平（resolutionlevel）指标的上升而收敛．在此基础上给出了以小波尺度函数变换重构或逼近任一函数的显式解析式,并对具有函数算子、微分或积分算子的运算给出了变换规则．这对于求解复杂非线性方程（组）是一种强有力的工具．最后给出了用该文方法求解非线性二点边值问题的算例．     

Characterization of periodic multiresolution analysis and an application

In this paper, we study the properties of periodic multiresolution analysis, and present a complete characterization of the scaling function sequence, which enables us to construct a new scaling function sequence from a given one. An application of the main results is given at the end.     

Geometry of the vacant set left by random walk on random graphs,Wright's constants,and critical random graphs with prescribed degrees

We provide an explicit algorithm for sampling a uniform simple connected random graph with a given degree sequence. By products of this central result include: (1) continuum scaling limits of uniform simple connected graphs with given degree sequence and asymptotics for the number of simple connected graphs with given degree sequence under some regularity conditions, and (2) scaling limits for the metric space structure of the maximal components in the critical regime of both the configuration model and the uniform simple random graph model with prescribed degree sequence under finite third moment assumption on the degree sequence. As a substantive application we answer a question raised by ?erný and Teixeira study by obtaining the metric space scaling limit of maximal components in the vacant set left by random walks on random regular graphs.     

Existence of a complete holomorphic vector field via the Kähler–Einstein metric

In this paper, we study the existence of a complete holomorphic vector field on a strongly pseudoconvex complex manifold admitting a negatively curved complete Kähler–Einstein metric and a discrete sequence of automorphisms. Using the method of potential scaling, we will show that there is a potential function of the Kähler–Einstein metric whose differential has a constant length. Then, we will construct a complete holomorphic vector field from the gradient vector field of the potential function.

     

A finitization of the bead process

The bead process is the particle system defined on parallel lines, with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace, and zero weight otherwise. Motivated by the statistical mechanical model of the tiling of an abc-hexagon by three species of rhombi, a finitized version of the bead process is defined. The corresponding joint distribution can be realized as an eigenvalue probability density function for a sequence of random matrices. The finitized bead process is determinantal, and we give the correlation kernel in terms of Jacobi polynomials. Two scaling limits are considered: a global limit in which the spacing between lines goes to zero, and a certain bulk scaling limit. In the global limit the shape of the support of the particles is determined, while in the bulk scaling limit the bead process kernel of Boutillier is reclaimed, after appropriate identification of the anisotropy parameter therein.     

Smooth classification of geometrically finite one-dimensional maps

The scaling function of a one-dimensional Markov map is defined and studied. We prove that the scaling function of a non-critical geometrically finite one-dimensional map is Hölder continuous, while the scaling function of a critical geometrically finite one-dimensional map is discontinuous. We prove that scaling functions determine Lipschitz conjugacy classes, and moreover, that the scaling function and the exponents and asymmetries of a geometrically finite one-dimensional map are complete -invariants within a mixing topological conjugacy class.

     

Linear scaling and the DIRECT algorithm

In this paper, we discuss the performance of the DIRECT global optimization algorithm on problems with linear scaling. We show with computations that the performance of DIRECT can be affected by linear scaling of the objective function. We also provide a theoretical result which shows that DIRECT does not perform well when the absolute value of the objective function is large enough. Then we present DIRECT-a, a modification of DIRECT, to eliminate the sensitivity to linear scaling of the objective function. We prove theoretically that linear scaling of the objective function does not affect the performance of DIRECT-a. Similarly, we prove that some modifications of DIRECT are also unaffected by linear scaling of the objective function, while the original DIRECT algorithm is sensitive to linear scaling. Numerical results in this paper show that DIRECT-a is more robust than the original DIRECT algorithm, which support the theoretical results. Numerical results also show that careful choices of the parameter ε can help DIRECT perform well when the objective function is poorly linearly scaled.     

三进制双正交对称小波的设计

本文给出了一种三进制双正交对称小波的设计方法.在给定插值紧支撑对称尺度函数的情况下,指出了如果对偶尺度函数同为紧支撑插值的,则它们同为1-型对称.并且给出了对偶尺度函数为紧支撑插值和非插值情况下的通解计算公式.还提出了频率优化方法设计对偶尺度函数和小波函数,把双正交条件归结为线性约束的二次规划问题,最后通过线性方程组来求解.对于小波函数本文也给出了一组特解公式.     

二维3带插值型的尺度函数

1引言众所周知,在实际应用中用小波处理信号时,小波的对称性能使信号避免失真,小波的紧支撑性使得快速小波变换的和是有限和,小波的正交性能够保持能量等等,因而构造     

Convergence analysis of the projective scaling algorithm based on a long-step homogeneous affine scaling algorithm

In this paper we give a new convergence analysis of a projective scaling algorithm. We consider a long-step affine scaling algorithm applied to a homogeneous linear programming problem obtained from the original linear programming problem. This algorithm takes a fixed fraction λ≤2/3 of the way towards the boundary of the nonnegative orthant at each iteration. The iteration sequence for the original problem is obtained by pulling back the homogeneous iterates onto the original feasible region with a conical projection, which generates the same search direction as the original projective scaling algorithm at each iterate. The recent convergence results for the long-step affine scaling algorithm by the authors are applied to this algorithm to obtain some convergence results on the projective scaling algorithm. Specifically, we will show (i) polynomiality of the algorithm with complexities of O(nL) and O(n ² L) iterations for λ<2/3 and λ=2/3, respectively; (ii) global covnergence of the algorithm when the optimal face is unbounded; (iii) convergence of the primal iterates to a relative interior point of the optimal face; (iv) convergence of the dual estimates to the analytic center of the dual optimal face; and (v) convergence of the reduction rate of the objective function value to 1−λ.     

Frame scaling function sets and frame wavelet sets in

In this paper, we classify frame wavelet sets and frame scaling function sets in higher dimensions. Firstly, we obtain a necessary condition for a set to be the frame wavelet sets. Then, we present a necessary and sufficient condition for a set to be a frame scaling function set. We give a property of frame scaling function sets, too. Some corresponding examples are given to prove our theory in each section.