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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

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

Approximation of weak sense stationary stochastic processes from local averages

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Science China Mathematics 2007年第4期50卷 457-463页

作者： Zhan-jie SONG wen-chang sun Shou-yuan YANG Guang-wen ZHU School of Science Tianjin UniversityTianjin 300072China Department of Mathematics and LPMC Nankai UniversityTianjin 300071China National Ocean Technology Center Tianjin 300111China

We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.

关键词： sampling theorem weak sense stationary stochastic processes local averages average sampling 42C15 60G10 94A20

Optimal Tracking Control for a Class of Unknown Discrete-time Systems with Actuator Saturation via Data-based ADP Algorithm

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自动化学报 2013年第9期39卷 1413-1420页

作者： SONG Rui-Zhuo XIAO wen-Dong sun chang-Yin School of Automation and Electrical Engineering University ofScience and Technology Beijing Beijing 100083 China

为有致动器浸透和未知动力学的分离时间的系统的一个班的一个新奇最佳的追踪控制方法在这份报纸被建议。计划基于反复的适应动态编程(自动数据处理) 算法。以便实现控制计划，一个 data-based 标识符首先为未知系统动力学被构造。由介绍... 详细信息

为有致动器浸透和未知动力学的分离时间的系统的一个班的一个新奇最佳的追踪控制方法在这份报纸被建议。计划基于反复的适应动态编程(自动数据处理) 算法。以便实现控制计划，一个 data-based 标识符首先为未知系统动力学被构造。由介绍 M 网络，稳定的控制的明确的公式被完成。以便消除致动器浸透的效果， nonquadratic 表演功能被介绍，然后一个反复的自动数据处理算法被建立与集中分析完成最佳的追踪控制解决方案。为实现最佳的控制方法，神经网络被用来建立 data-based 标识符，计算性能索引功能，近似最佳的控制政策并且分别地解决稳定的控制。模拟例子被提供验证介绍最佳的追踪的控制计划的有效性。

关键词：最优跟踪控制离散时间系统饱和执行器 DP算法控制方案神经网络性能指标系统动力学

SYNTHESIS AND CHARACTERIZATION OF BIS-[2-[[(2-ALKOXYPHENYL)IMINO]METHYL]-PHENOLATO-O,N,O]NICKEL(II)COMPLEXES AND THEIR NORBORNENE POLYMERIZATION

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Chinese Journal of Polymer Science 2005年第6期23卷 619-626页

作者： Dong-heng Zhang Su-yun Jie Hai-jian Yang Fei chang and wen-hua sun Key Laboratory of Engineering Plastics,Institute of Chemistry,Chinese Academy of Sciences,Beijing 100080,China Key Laboratory of Engineering Plastics Institute of Chemistry Chinese Academy of Sciences Beijing 100080 China

A series of salicylaldimines, synthesized in high yield via microwave-assisted condensation of salicylaldehyde and 2-alkoxyaniline were allowed to react with nickel chloride to form six-coordinated nickel complexes. These nickel complexes were carefully characterized, and the solid structure of la was elucidated by X-Ray diffraction. Activated with MAO, the nickel complexes showed good activity for homopolymerization of norbornene. Reaction parameters, such as the ratio of nickel precursor to MAO, monomer concentration, reaction time and the reaction temperature, as well as the nature of the ligands were found to have significant effects on the catalytic activity and some properties of the resulting polynorbornene.

关键词： Salicylaldirnine Nickel complex Norbornene Vinyl polymerization

Homogeneous Approximation Property for Wavelet Frames with Matrix Dilations,Ⅱ

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数学学报(中文版) 2013年第2期 292-292页

作者： Zhi Jing ZHAO wen chang sun

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 *** this paper,we show that every wavelet frame with nice wavelet function and arbitrary expansive dilation matrix possesses the *** results improve some known ones.

关键词：

Metal-organic frameworks with dinuclear metal centers for synergistically boosting CO2 photoreduction

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Science China Chemistry 2025年第1期68卷 201-208页

作者： Hui-Feng Wang wen-Jie Shi Yu-Xin Yang Bao-Xia Dong Tong-Bu Lu Di-chang Zhong School of Chemistry and Chemical Engineering Yangzhou University Institute for New Energy Materials and Low Carbon Technologies School of Materials Science and Engineering Tianjin University of Technology

Dinuclear metal synergistic catalysis （DMSC） has been proved powerful in boosting CO2reduction,while this has not been achieved in heterogeneous catalysts with long-range order *** this study,we,by introduction of metal catalytic centers into an indium-based metal-organic framework （MOF）,obtained a series of isostructural In-MOFs,including three MOFs with mononuclear metal catalytic center （M-In）,three MOFs with dinuclear homometallic catalytic centers （MM-In）,and three MOFs with dinuclear heterometallic catalytic centers (MM’-In,M/M’=Co（II）,Ni（II）,Zn（II）).It was found that all these MOFs can serve as catalysts for photochemical CO2reduction to *** with M-In,the catalytic activities of MM-In were obviously enhanced,and that of MM’-In was further significantly *** example,the CO yield of Co Zn-In reaches a record value of 12,700μmol g-1h-1,which is 4.0,8.1,9.4,and 18.6-fold higher than that of Co Co-In,Zn Zn-In,Co-In,and Zn-In,***,the catalytic activities of Co Ni-In and Ni Zn-In also show different fold increase than those of corresponding dinuclear homometallic and mononuclear metallic *** results of control experiments and theoretical calculation reveal that the higher catalytic activities of MM-In over M-In can be ascribed to the DMSC effect,and the higher catalytic activity of MM’-In over MM-In can be ascribed to the strengthened DMSC *** work reveals the relationship between DMSC effect and bimetal centers in CO2reduction,which provides new insights into the DMSC and paves a new way to design highly active catalysts for photochemical CO2reduction.

关键词： metal-organic frameworks dinuclear metal centers synergistic catalysis CO2 reduction photocatalysis

Visualization of the protective role of estrogen against female liver fibrosis via an ER viscosity NIR fluorescent probe

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Science China Chemistry 2025年第1期68卷 360-368页

作者： Zheng Liu changyu Zhang Zipeng Li Wanying Ma Jia Liu Xiang Xia Ning Xu wen sun Jianjun Du Jiangli Fan Xiaojun Peng State Key Laboratory of Fine Chemicals Dalian University of Technology Ningbo Institute of Dalian University of Technology

Endoplasmic reticulum(ER) viscosity has emerged as a new potential biomarker for hepatic fibrosis(HF). Herein, we report the first ER-targeting viscosity-responsive near-infrared(NIR) fluorescent probe HBT-PP for investigations of HF *** twisted intramolecular charge transfer(TICT) and the excited state intramolecular proton transfer(ESIPT) are combined to endow HBT-PP with the selective response towards viscosity(～62-fold) and a super large stokes shift(～320 nm). HBT-PP mainly targets organelle ER and is able to image the drug-or alcohol-induced viscosity elevation in living cells. Significantly,HBT-PP was successfully applied to visualize the gender difference in HF and the protective role of estrogen in restraining HF progression. Of note, after 10 min of stain with HBT-PP, HF lesions showed a stage-based response, indicating the potential of this probe in fast and early diagnosis of HF. These results clearly demonstrated the promising application of HBT-PP as a new tool for exploring ER viscosity-involved physiological and pathological processes.

关键词： NIR fluorescent probe ER viscosity hepatic fibrosis gender difference estrogen