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Wavelets and framelets from dual pseudo splines

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Science China Mathematics 2011年第6期54卷 1233-1242页

作者： SHEN Yi li song Department of Mathematics Zhejiang University Hangzhou 310027 China

Dual pseudo splines constitute a new class of refinable functions with B-splines as special *** this paper,we shall construct Riesz wavelet associated with dual pseudo ***,we use dual pseudo splines to construct tight... 详细信息

关键词： dual pseudo splines Riesz wavelet basis tight wavelet frame

Riesz multiwavelet bases generated by vector refinement equation

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Science China Mathematics 2009年第3期52卷 468-480页

作者： li song liU Zhisong Department of Mathematics Zhejiang UniversityHangzhou 310027China School of Mathematics Physics&Information ScienceZhejiang Ocean UniversityZhoushan 316004China

In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L 2(? s ). Suppose ψ = (ψ1,..., ψ r ) T and $ \tilde \psi = (\tilde \psi ^1 ,...,\tilde \psi ^r )^T $ are two compactly supported vectors of functions in the Sobolev space (H μ(? s )) r for some μ > 0. We provide a characterization for the sequences {ψ jk l : l = 1,...,r, j ε ?, k ε ? s } and $ \tilde \psi _{jk}^\ell :\ell = 1,...,r,j \in \mathbb{Z},k \in \mathbb{Z}^s $ to form two Riesz sequences for L 2(? s ), where ψ jk l = m j/2ψ l (M j ·?k) and $ \tilde \psi _{jk}^\ell = m^{{j \mathord{\left/ {\vphantom {j 2}} \right. \kern-0em} 2}} \tilde \psi ^\ell (M^j \cdot - k) $ , M is an s × s integer matrix such that lim n→∞ M ?n = 0 and m = |detM|. Furthermore, let ? = (?1,...,? r ) T and $ \tilde \phi = (\tilde \phi ^1 ,...,\tilde \phi ^r )^T $ be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, $ \tilde a $ and M, where a and $ \tilde a $ are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1,...,ψνr ) T and $ \tilde \psi ^\nu = (\tilde \psi ^{\nu 1} ,...,\tilde \psi ^{\nu r} )^T $ , ν = 1,..., m ? 1 such that two sequences {ψ jk νl : ν = 1,..., m ? 1, l = 1,...,r, j ε ?, k ε ? s } and { $ \tilde \psi _{jk}^\nu $ : ν=1,...,m?1,?=1,...,r, j ∈ ?, k ∈ ? s } form two Riesz multiwavelet bases for L 2(? s ). The bracket product [f, g] of two vectors of functions f, g in (L 2(? s )) r is an indispensable tool for our characterization.

关键词： vector refinement equations Riesz multiwavelet base biorthogonal wavelets 42C40 39B12 46B15 47A10 47B37

The bounds of restricted isometry constants for low rank matrices recovery

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Science China Mathematics 2013年第6期56卷 1117-1127页

作者： WANG HuiMin li song Department of Mathematics Shaoxing University Department of Mathematics Zhejiang University

This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is the restricted isometry constant （RIC）. Some papers provided the upper bounds of RIC to guarantee that the nuclear-norm minimization stably recovers a low-rank matrix. For example, Fazel improved the upper bounds to δ4Ar 〈 0.558 and δ3rA 〈 0.4721, respectively. Recently, the upper bounds of RIC can be improved to δ2rA 〈 0.307. In fact, by using some methods, the upper bounds of RIC can be improved to δ2tA 〈 0.4931 and δrA 〈 0.309. In this paper, we focus on the lower bounds of RIC, we show that there exists linear maps A with δ2rA 〉1√2 or δrA 〉 1/3 for which nuclear norm recovery fail on some matrix with rank at most r. These results indicate that there is only a little limited room for improving the upper bounds for δ2rA and δ***, we also discuss the upper bound of restricted isometry constant associated with linear maps A for Schatten p （0 〈 p 〈 1） quasi norm minimization problem.

关键词： restricted isometry constants low-rank matrix recovery Schatten-p norm nuclear norm com-pressed sensing convex optimization

Tau Accumulation and Defective Autophagy:A Common Pathological Mechanism Underlying Repeat-Expansion-Induced Neurodegenerative Diseases?

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Neuroscience Bulletin 2020年第12期36卷 1411-1413页

作者： li song Luoying Zhang Key Laboratory of Molecular Biophysics of the Ministry of Education College of Life Science and TechnologyHuazhong University of Science and TechnologyWuhan 430074China Institute of Brain Research Huazhong University of Science and TechnologyWuhan 430074China

Repetitive DNA tracts(microsatellites)occur thousands of times throughout the human genome,and their expansion is known to cause many *** of CAG repeats encoding poly glutamine(polyQ)tracts is a pathological cause of nine neurodegenerative diseases:spinal and bulbar muscular atrophy,Huntington’s disease,dentatorubropallidoluysian atrophy,and six autosomal dominant forms of spinocerebellar ataxia(SCA1,2,3,6,7,and 17)[1].

关键词： degenerative Huntington atrophy

Cooperative fault detection and recovery in the GNSS positioning of mobile agent swarms based on relative distance measurements

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Chinese Journal of Aeronautics 2022年第5期35卷 129-144页

作者： Qifeng CHEN Yunhe MENG song li Yuxin liAO School of Aeronautics and Astronautics Central South UniversityChangsha 410083China School of Physics and Astronomy Sun Yat-sen UniversityZhuhai 519082China

Relative measurements are exploited to cooperatively detect and recover faults in the positioning of Mobile Agent(MA)Swarms(MASs).First,a network vertex fault detection method based on edge testing is *** each edge,a property that has a functional relationship with the properties of its two vertices is measured and *** on the edge testing results of the network,the maximum likelihood principle is used to identify the vertex fault ***,an edge distance testing method based on the noncentral chi-square distribution is developed for detecting faults in the Global Navigation Satellite System(GNSS)positioning of ***,a recovery strategy for faults in the positioning of MASs based on distance measurement is *** effectiveness of the proposed methods is validated by a simulation case in which an MAS passes through a GNSS spoofing *** proposed methods are conducive to increasing the robustness of the positioning of MASs in complex *** main novelties include the following:(A)network vertex fault detection is based on concrete probability analysis rather than simple majority voting,and(B)the relation of detectability and recoverability of MAS positioning faults with the structure of the relative measurement network is first disclosed.

关键词： Fault detection and recovery Global Navigation Satellite System Mobile agents Network topology Positioning

Effects of electrode immersion depth and remelting rate on electroslag remelting process

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China Foundry 2014年第3期11卷 163-167页

作者： song Jinchun Wang Changzhou li song Northeastern University

In the electroslag remelting process, the electrode molten state is a critical factor determining the ingot quality, while the electrode immersion depth and melting rate are key factors for the stability of the electroslag re-melting process. Studies were carried out to investigate the microscopic and macroscopic effects of electrode immersion depth and melting rate on the potential distribution and heat density in the slag bath, and on the depth and shape of the molten bath. Based on the finite element method and the numerical solution method, the effect of the electrode immersion depth on the slag bath heat density was researched; the relationship between the electrode immersion depth and the slag resistance was obtained; and the unsteady-state model of the solidification process of the re-melting ingot was solved using the finite difference method. The mathematical model and physical model of the electrode melting process were established and solved; and the corresponding curves between the electrode molten-state and slag-bath physical parameters were obtained. The experimental results verified the simulated results studied in this paper.

关键词： electroslag remelting electrode molten state immersion depth melting rate

Boosting electrocatalytic hydrazine oxidation at single-crystalline Ni nanosheets with embedded NiZn

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Progress in Natural Science:Materials International 2023年第5期33卷 710-717页

作者： Xia Wei Hongbin Dai Chuangwei liu song li School of Material Science and Engineering Northeastern University

Hydrazine oxidation reaction(Hz OR) plays a crucial role in direct hydrazine fuel cells and holds promise for replacing the kinetics-sluggish oxygen evolution reaction in splitting water. While Ni–Zn alloys exhibit exceptional activity for Hz OR, their synthesis under mild conditions remains a challenge. Herein, a Ni–Zn nanosheet catalyst with Ni Zn inclusion was prepared on Ni foam by controllable chemical etching together with ethylene glycol reduction. X-ray diffraction and transmission electron microscopy confirmed the single-crystalline nature and the presence of intermetallic Ni Zn. The strong interaction between Ni and Zn O, along with defects, facilitated the formation of this intermetallic compound. The Ni–Zn/Ni foam exhibits remarkable catalytic activity(214.3m A cm-2at 0.1 V) and durability(87.8 % retention after 24 h) towards hydrazine electrooxidation, thanks to the combined benefits of intermetallic Ni Zn, mesoporous nanosheets, microscopic defects, single-crystalline characteristics, and a coherent Ni–Ni Zn interface. This study provides a new method for designing highly active Ni–Zn electrocatalysts for Hz OR.

关键词： Hydrazine electrooxidation Intermetallic NiZn Single-crystalline Coherent interface Microscopic defects

Automatic microseismic events detection using morphological multiscale top-hat transformation

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Petroleum Science 2022年第5期19卷 2027-2045页

作者： Guo-Jun Shang Wei-lin Huang li-Kun Yuan Jin-song Shen Fei Gao li-song Zhao State Key Laboratory of Petroleum Resources and Prospecting China University of Petroleum-BeijingBeijing102249China Department of Automation China University of Petroleum-BeijingBeijing102249China Hebei Coal Research Institute Company Ltd. Jizhong Energy GroupXingtaiHebei 054000China

The occurrence of microseismic is not random but is related to the physical properties of the underground *** to the low intensity and the influence of noise,microseismic eventually lead to poor signal-to-noise *** proposed a method for automatic detection of microseismic events by adoption of multiscale top-hat *** method is based on the difference between the signal and noise in the multiscale top-hat transform section and achieves the detection on a specific *** microseismic data are decomposed into different scales by multiscale morphology top-hat transformation *** the potential microseismic events could be detected by picking up the peak value in the multiscale top-hat section,and the characteristic profile obtains the start point with a specific threshold ***,the synthetic data experiences demonstrate the advantages of this method under strong and weak noisy conditions,and the filed data example also shows its reliability and adaptability.

关键词： Microseismic events detection Multiscale morphology Top-hat transformation

Sensitivity optimization of a monolithic high-shock three-axis piezoresistive accelerometer with single sensing element

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Chinese Science Bulletin 2009年第19期54卷 3600-3607页

作者： song Ping li QingZhou li KeJie School of Aerospace Science and Engineering Beijing Institute of Technology Beijing 100081 China

There exist several difficulties in the design of monolithic high-shock three-axis accelerometer, such as high g overload, transverse overload and the cross coupling in three dimensions, etc. It is necessary to optimize the sensitivity to improve the performance of the accelerometer. For the monolithic high-shock three-axis accelerometer, the complexity of the sensitivity optimization is that it should consider not only the sensitivity difference between different axes but also the elimination of cross-coupling outputs, together with the natural frequency, structural integrity and high g overload. In this paper, the optimization process for decreasing the difference of the sensitivities between different axes of a monolithic high-shock three-axis piezoresistive accelerometer with single sensing element is established. The optimization is conducted in the condition of 100000 g acceleration by two methods-the method based on the optimization module of ANSYS and the ACO (ant colony optimization) method. The comparison between un-optimized and optimized models proves the efficiency of the optimization methods. In addition, the optimization results show that the ACO method combined with the FEA (finite element analysis) is much more efficient than the method based on the optimization module of ANSYS for the structural optimization problem. And the ACO method can be widely used in the optimization problem of the sensing elements with complicated structure.

关键词：单片电路最佳化设计研究 ACO