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Estimations of directional Hlder regularity by shearlets

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Science China Mathematics 2015年第4期58卷 791-812页

作者： HU Lin liu youming Department of Applied Mathematics Beijing University of Technology Department of Basic Courses Beijing Union University

This paper studies directional Hlder regularity of two-variable functions by their shearlet coefficients, where the shearlets are defined by Guo and Labate(2013). We provide necessary conditions for a function possessing some directional H¨older regularity and the corresponding sufficient conditions, motivated by the work of Sampo and Sumetkijakan(2009) and Lakhonchai et al.(2010).

关键词： Holder space shearlet directional regularity

Adaptive Wavelet Solution to the Stokes Problem

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Acta Mathematicae Applicatae Sinica 2008年第4期24卷 613-626页

作者： Ying-chun Jiang youming liu College of Mathematics and Computer Sciences Guilin University of Electronic Technology Cuilin 541004 China Department of Applied Mathematics Beijing University of Technology Beijing 100022 China

This paper deals with the design and analysis of adaptive wavelet method for the Stokes problem. First, the limitation of Richardson iteration is explained and the multiplied matrix M0 in the paper of Bramble and Pasciak is proved to be the simplest possible in an appropiate sense. Similar to the divergence operator, an exact application of its dual is shown; Second, based on these above observations, an adaptive wavelet algorithm for the Stokes problem is designed. Error analysis and computational complexity are given; Finally, since our algorithm is mainly to deal with an elliptic and positive definite operator equation, the last section is devoted to the Galerkin solution of an elliptic and positive definite equation. It turns out that the upper bound for error estimation may be improved.

关键词： Richardson iteration adaptive algorithm wavelets Stokes problem Galerkin solution

Wavelets with Differential Relation

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Acta Mathematica Sinica,English Series 2011年第5期27卷 1011-1022页

作者： Zhi-Tao CHUANG youming liu Department of Applied Mathematics Beijing University of Technology Beijing 100124 P. R. China

Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli＇s work.

关键词： Differential relation interpolation wavelets scaling functions symmetry

Wavelet estimations for density derivatives

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Science China Mathematics 2013年第3期56卷 483-495页

作者： liu youming WANG HuiYing Department of Applied Mathematics Beijing University of Technology School of Applied Mathematics Central University of Finance and Economics

Donoho et al. in 1996 have made almost perfect achievements in wavelet estimation for a density function f in Besov spaces Bsr,q(R). Motivated by their work, we define new linear and nonlinear wavelet estimators flin,nm, fnonn,m for density derivatives f(m). It turns out that the linear estimation E(‖flinn,m-f(m)‖p) for f(m) ∈ Bsr,q(R) attains the optimal when r≥ p, and the nonlinear one E(‖fnonn,m-f(m)‖p) does the same if r≤p/2(s+m)+1 . In addition, our method is applied to Sobolev spaces with non-negative integer exponents as well.

关键词： wavelet estimators optimality Besov spaces Sobolev spaces density derivative

On Cardinal Wavelets with Compact Support and Their Duals

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Acta Mathematica Sinica,English Series 1997年第1期13卷 127-132页

作者： liu youming (Department of Applied Mathematics,Beijing Polytechnic University,Beijing 100022,China) Department of Applied Mathematics Beijing Polytechnic University

Some people try to construct an orthonormal wavelet such that the corresponding scaling function（t）has the cardinal property,i.e.（n）=δn0,since such wavelets have many good ***]y it is impossible to do so,except for a trivial *** this work,a family of non-orthogonal cardinal wavelets with compact support is constructed and their duals are investigated.

关键词： wavelet cardinal scaling function dual

Convergence of Hermite interpolatory operators

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Science China Mathematics 2010年第8期53卷 2115-2126页

作者： liu youming & ZHAO JunJian Department of Applied Mathematics,Beijing University of Technology,Beijing 100124,China 1. Department of Applied Mathematics Beijing University of Technology Beijing 100124 China

Divergence-free wavelets play important roles in both partial differential equations and fluid *** constructions of those wavelets depend usually on Hermite *** study several types of convergence of the related Hermite interpolatory operators in this *** precisely,the uniform convergence is firstly discussed in the second part;then,the third section provides the convergence in the Donoho's *** on these results,the last two parts are devoted to show the convergence in some Besov spaces,which concludes the completeness of Bittner and Urban's expansions.

关键词： Besov spaces Hermite splines convergence completeness

Sub-30 fs Yb-fiber laser source based on a hybrid cascaded nonlinear compression approach

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Chinese Optics Letters 2022年第10期20卷 25-29页

作者： youming liu Bowen liu Youjian Song Minglie Hu Ultrafast Laser Laboratory Key Laboratory of Opto-electronic Information Science and Technology of Ministry of EducationSchool of Precision Instruments and Opto-electronics EngineeringTianjin UniversityTianjin 300072China

Ultrafast lasers with high repetition rate,high energy,and ultrashort pulse duration have enabled numerous applications in science and *** efficient route to generate such pulses is postcompression of high-power Yb-doped ***,we report on the generation of 24.5 fs pulses with an output energy of 1.6μJ and a repetition rate of 500 *** pulses are obtained by using a hybrid cascaded nonlinear compression of the pulses delivered by a Yb-based fiber chirped pulse amplification(CPA)*** the first stage,the initial 390 fs laser pulses are compressed to 100.7 fs based on spectral broadening in three fused silica *** the second stage,the pulses have been shortened to sub-30 fs by means of nonlinear compression in a hollow-core ***,we could achieve∼16 times temporal shortening with the proposed *** results show that our system can effectively generate few-cycle pulses at a relatively high repetition rate and high energy,which can benefit future possible applications.

关键词： multiple-plate medium hollow-core photonic crystal fiber pulse compression

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D_4类小波的时频局部性质

数学年刊（A辑） 2008年第1期29卷 1-14页

作者：刘有明北京工业大学应用数学系北京100022

尽管小波分析已取得了许多重要成就,但主要集中在函数空间内.例如,不确定性原理的研究就是这样.然而,从应用的角度看(从图像压缩到数值计算),研究离散空间中的小波更加自然,更为重要.因此将研究离散空间l^2(Z_N)中的不确定性原理,D_4类... 详细信息

尽管小波分析已取得了许多重要成就,但主要集中在函数空间内.例如,不确定性原理的研究就是这样.然而,从应用的角度看(从图像压缩到数值计算),研究离散空间中的小波更加自然,更为重要.因此将研究离散空间l^2(Z_N)中的不确定性原理,D_4类小波以及其它一些小波的时频局部性质.

关键词：小波分析不确定性原理局部化离散Fourier变换

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流域经济区产业发展模式比较研究

学术研究 2011年第3期 83-88页

作者：刘有明武汉大学经济与管理学院

世界各国都把流域经济区发展作为国家经济建设的重心和主轴。流域经济区成为许多国家的产业密集带和城市密集带。对美国密西西比河、德国莱茵河流域产业发展模式以及国内重要的湖北长江经济带、西江经济带产业发展模式进行比较分析,找... 详细信息

世界各国都把流域经济区发展作为国家经济建设的重心和主轴。流域经济区成为许多国家的产业密集带和城市密集带。对美国密西西比河、德国莱茵河流域产业发展模式以及国内重要的湖北长江经济带、西江经济带产业发展模式进行比较分析,找出流域经济区产业发展模式的主要内在规律,对加快我国流域经济区产业发展具有现实的指导意义。

关键词：流域经济区长江经济带西江经济带