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Homogeneous Approximation Property for Wavelet Frames with Matrix Dilations,Ⅱ

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Acta Mathematica Sinica,English Series 2013年第1期29卷 183-192页

作者： Zhi Jing ZHAO Wen chang sun Department of Mathematics and LPMC Nankai University

The homogeneous approximation property （HAP） states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we show that every wavelet frame with nice wavelet function and arbitrary expansive dilation matrix possesses the HAP. Our results improve some known ones.

关键词： Wavelet frames homogeneous approximation property HAP matrix dilations

Weighted Estimates for Multilinear Pseudodifferential Operators

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Acta Mathematica Sinica,English Series 2014年第8期30卷 1281-1288页

作者： Kang Wei LI Wen chang sun School of Mathematical Sciences and LPMC Nankai University

In this paper,we study the weighted estimates for multilinear pseudodifferential *** show that a multilinear pseudodifferential operator is bounded with respect to multiple weights whenever its symbol satisfies some s... 详细信息

关键词： Multiple weights nmltilinear pseudodifferential operators

Reconstruction of Splines from Nonuniform Samples

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Acta Mathematica Sinica,English Series 2019年第2期35卷 245-256页

作者： Qing Yue ZHANG Wen chang sun College of Science Tianjin University of Technology School of Mathematical Sciences and LPMC Nankai University

In this paper, we study the reconstruction of spline functions from their nonuniform samples. We investigate the existence and uniqueness of the solution of the following problem: for given data {(x_n, y_n) : n ∈ Z}, find a cardinal spline f(x), of a given degree, satisfying yn = f(x_n), n ∈ *** necessary and/or sufficient conditions for the existence and uniqueness of the solution of the problem are derived. Finally, an example and some applications are presented to illustrate the main results.

关键词： Cardinal spline interpolation nonuniform sampling sampling set

Expansion of Frames to Tight Frames

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Acta Mathematica Sinica,English Series 2009年第2期25卷 287-298页

作者： Deng Feng LI Wen chang sun Institute of Applied Mathematics College of Mathematies and Information Science He'nan University Kaifeng 475001 P. R. China Department of Mathematics and LPMC Nankai University Tianjin 300071 P. R. China

We show that every Bessel sequence （and therefore every frame） in a separable Hilbert space can be expanded to a tight frame by adding some elements. The proof is based on a recent generalization of the frame concept, the g-frame, which illustrates that g-frames could be useful in the study of frame theory. As an application, we prove that any Gabor frame can be expanded to a tight frame by adding one window function.

关键词： frame tight frame g-frame Gabor frame frame expansion

Sufficient and Necessary Condition of Admissibility for Fractional-order Singular System

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自动化学报 2013年第12期39卷 2160-2164页

作者： YU Yao JIAO Zhuang sun chang-Yin School of Automation Electrical Engineering University of Science and Technology Beijing Beijing 100083 China Key Laboratory of Advanced Control of Iron and Steel Process Ministry of Education Beijing 100083 China Beijing Institute of Elec- tronic System Engineering Beijing 100854 China

这份报纸与顺序为部分顺序的单个系统集中于考虑条件吗？(0， 1 ) 。整齐的定义，没有推动并且考虑被给第一，然后，为部分顺序的单个系统的考虑的一个足够、必要的条件被建立。一个数字例子被包括说明建议条件。

关键词：奇异系统分数阶充要条件可容许充分必要条件

Projection on precipitation frequency of different intensities and precipitation amount in the Lancang-Mekong River basin in the 21st century

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Advances in Climate change Research 2021年第2期12卷 162-171页

作者： sun chang XIAO Zi-Niu Minh NGUYEN State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric PhysicsChinese Academy of SciencesBeijing100029China College of Earth and Planetary Sciences University of Chinese Academy of SciencesBeijing100049China Land and Water Australia's Commonwealth Scientific and Industrial Research OrganizationClaytonVic3168Australia

In the Lancang‒Mekong River basin(LMRB),agriculture,dominating the local economy,faces increasing challenges in water supply under climate *** projection of future precipitation in this basin is essential for understanding the *** this study,the Weather Research and Forecasting(WRF)model was applied to project the LMRB *** with the historical period(1986e2005),we analyzed the changes of both the projected precipitation amount and the frequency of rainless(100 mm d1)for three periods,namely the near-term(2016e2035),mid-term(2046e2065),and long-term(2080e2099).The results indicate that the precipitation amount during the wet season(AprileOctober)is expected to increase in most areas of the basin for the three *** for the precipitation during the dry season(NovembereMarch),an increase is projected in most areas for the near-term,while an increase in the lower reach of the basin and a decrease in the upper and middle reach for the mid-term and *** precipitation reduction is expected to be greatest in Myanmar,Laos,Thailand,and Yunnan province of China for the *** frequency of precipitation in different intensities has prominent regional and temporal *** the wet season,the days of rainless and light rain are expected to decrease in the middle reach,whereas the days of rainstorm and heavy rainstorm *** feature is especially strong in southern Thailand,southern Laos and Cambodia in the near-term and in Laos and Thailand for the mid-term and *** the dry season,there are projected increasing rainless days and decreasing days of precipitation for the other intensities in the middle reach,and opposite in the rest area of the *** projected precipitation changes have potential various impact in different parts of the *** middle re

关键词： Precipitation projection Lancang‒Mekong River basin Precipitation frequency Precipitation amount Precipitation intensity

Semi-analytic Solution of Steady Temperature Fields During Thin Plate Welding

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Chinese Journal of Aeronautics 2006年第B12期19卷 248-251页

作者： DAI Yao TAN Wei sun Qi sun chang-qing Department of Mechanical Engineering Armored Force Engineering College Beijing 100072 China Department of Materials Science and Engineering Armored Force Engineering College Beijing 100072 China

Usually, it is very difficult to find out an analytical solution to thermal conduction problems during high temperature welding. Therefore, as an important numerical approach, the method of lines （MOLs） is introduced to solve the temperature field characterized by high gradients. The basic idea of the method is to semi-discretize the governing equation of the problem into a system of ordinary differential equations （ODEs） defined on discrete lines by means of the finite difference method, by which the thermal boundary condition with high gradients are directly embodied in formulation. Thus the temperature field can be obtained by solving the ODEs. As a numerical example, the variation of an axisymmetrical temperature field along the plate thickness can be obtained.

关键词： steady temperature field method of lines thin plate welding semi-analytic solution high gradient

Fabrication of Chemically-Modified Electrode Containing 1:12 Phosphomolybdic Anions by Sol-Gel Technique and Its Electrocatalytic Reduction of BrO₃^-Anions

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Chinese Chemical Letters 1998年第12期9卷 0-0,0-0页

作者： Song, Wen Bo sun, chang Qing Department of Chemistry Jilin University Changchun 130023 China

A novel chemically-modified electrode containing 1:12 phosphomolybdic anions was achieved on the surface of platinum electrode by the sol-gel technique. The electrode exhibits a high catalytic activity towards the ele... 详细信息

关键词： Chemically-modified electrode Electrocatalysis Polyoxometallates Sol-gel technique

On a Class of Non-local Operators in Conformal Geometry

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Chinese Annals of Mathematics,Series B 2017年第1期38卷 215-234页

作者： sun Yung Alice chang Ray A.YANG Mathematics Department Princeton UniversityFine HallWashington RoadPrinceton New Jersey 08544-1000USA

In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.

关键词： High order fractional GJMS operator Generalized boundary Yamabe problem Sobolov trace extension