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CONVERGENCE OF weighted averageS OF MARTINGALES IN NONCOMMUTATIVE BANACH FUNCTION SPACES

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Acta Mathematica Scientia 2012年第2期32卷 735-744页

作者：张超侯友良 School of Mathematics and Statistics Wuhan University Departamento de Matema'ticas Facultad de CienciasUniversidad Autónoma de MadridMadrid 28049Spain

Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.

关键词： weighted average noncommutative martingales noncommutative BanachfunCtion spaces uniform integrability

Convergence of weighted averages of noncommutative martingales

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Science China Mathematics 2013年第4期56卷 823-830页

作者： ZHANG Chao HOU YouLiang School of Mathematics and Statistics Wuhan University Departamento de Matema'ticas Universidad Auto'noma de Madrid

Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.

关键词： weighted average noncommutative martingales noncommutative Lp-space uniform integrability

weighted SOLUTION OF SMALL-DEFLECTION BUCKLING EQUATION OF THIN SHELL

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Applied Mathematics and Mechanics(English Edition) 2001年第12期22卷 1404-1409页

作者：王宗利王熙郝文华 Department of Engineering Mechanics Shanghai Jiaotong University Shanghai P R China

Based on small-deflection buckling equation, a weighted solution for critical load is presented. Usually, it is very difficult to solve the equation for general problems, especially those with complicated boundary conditions, Axisymmetric problem was studied as an example. Influencing factors were found from the equation and averaged as the buckling load by introducing weights. To determine those weights, some special known results were applied. This method solves general complicated problems by using the solutions of special simple problems, simplifies the solving procedure and expands the scope of solvable problem. Compared with numerical solution, it also has fine precision.

关键词： shell buckling critical load weighted average

DOUBLE Φ-INEQUALITIES FOR BANACH-SPACE-VALUED MARTINGALES

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Acta Mathematica Scientia 2012年第4期32卷 1627-1636页

作者：王迎占张超侯友良 School of Mathematics and Statistics Wuhan UniversityWuhan 430072China College of Mathematics and Information Sciences Guangzhou UniversityGuangzhou 510006China

Let B be a Banach space, φ1, φ2 be two generalized convex φ-functions and φ1, φ2 the Young complementary functions of ψ1, ψ2 respectively with∫t t0ψ2（s）/sds≤ds≤c0ψ1（c0t）（t〉t0）for some constants co 〉 0 and to 〉 0, where ψ1 and ψ2 are the left-continuous derivative functions of ψ1 and ψ2, respectively. We claim that：（i） If B is isomorphic to a p-uniformly smooth space （or q-uniformly convex space, respectively）, then there exists a constant c 〉 0 such that for any B-valued martingale f = （fn）n≥0,｜｜f^＊｜｜φ1≤｜｜S^（p）（f）｜｜φ2（of｜｜S^（q）（f）｜｜φ1≤c｜｜f^＊｜｜φ2,respectively）,where f^＊ and S^（p）（f） are the maximal function and the p-variation function of f respectively; （ii） If B is a UMD space, Tvf is the martingale transform of f with respect to v = （Vn）z≥0 （V^＊〈 1）, then ｜｜（Tvf）^＊｜｜Ф1≤f^＊｜｜Ф2.

关键词： martingale convex O-inequality martingale transform weighted average

A novel algorithm for ocean wave direction inversion from X-band radar images based on optical flow method

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Acta Oceanologica Sinica 2018年第3期37卷 88-93页

作者： WANG Li CHENG Yunfei HONG Lijuan LIU Xinyu Third Research Institute Ministry of Public Security

As one of the important sea state parameters for navigation safety and coastal resource management, the ocean wave direction represents the propagation direction of the wave. A novel algorithm based on an optical flow method is developed for the ocean wave direction inversion of the ocean wave fields imaged by the X-band radar continuously. The proposed algorithm utilizes the echo images received by the X-band wave monitoring radar to estimate the optical flow motion, and then the actual wave propagation direction can be obtained by taking a weighted average of the motion vector for each pixel. Compared with the traditional ocean wave direction inversion method based on frequency-domain, the novel algorithm is fully using a time-domain signal processing method without determination of a current velocity and a modulation transfer function（MTF）. In the meantime,the novel algorithm is simple, efficient and there is no need to do something more complicated here. Compared with traditional ocean wave direction inversion method, the ocean wave direction of derived by using this proposed method matches well with that measured by an in situ buoy nearby and the simulation data. These promising results demonstrate the efficiency and accuracy of the algorithm proposed in the paper.

关键词： X-band radar optical flow weighted average ocean wave direction radar image

Extraction of failure characteristic of rolling element bearing based on wavelet transform under strong noise

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Journal of Harbin Institute of Technology(New Series) 2005年第2期12卷 169-172页

作者：张辉王淑娟 Dept. of Electrical Engineering Harbin Institute of Technology Harbin 150001 China

There has been a lot of research has been performed regarding diagnosing rolling element bearing faults using wavelet analysis, but almost all methods are not ideal for picking up fault signal characteristics under strong noise. Therefore, this paper proposes auto-correlation, cross-correlation and weighted average fault diagnosis methods based on wavelet transform (WT) de-noising which combine correlation analysis with WT for the first time. These three methods compute the auto-correlation, the cross-correlation and the weighted average of the measured vibration signals, then de-noise by thresholding and computing the auto-correlation of de-noised coefficients of WT and FFT of energy sequence. The simulation results indicate that all methods enhance the capabilities of fault diagnosis of rolling bearings and pick up the fault characteristics effectively.

关键词： rolling bearing wavelet transform auto-correlation cross-correlation weighted average

Interval weighted Multi-template Matching for Accurate Measurement

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Interval Weighted Multi-template Matching for Accurate Measu...

Fusion of infrared and visible images based on discrete wavelet transform

2012 IEEE 11th International Conference on Signal Processing(ICSP 2012)

作者： Xiaoli Li Qiuqi Ruan Gaoyun An Chengxiong Ruan Institution of Information Science Beijing Jiaotong University Beijing Key Laboratory of Advanced Information Science and Network Technology

This paper employs the interval weighted multi- template matching approach for accurate measurement. Generally, a vernier caliper is used as the subject to capture the analyzing image. However, the vernier caliper has many similar regions which all effect the measure accuracy. The traditional template matching with only one template is not suitable, as the matching region may only stands for one local region. To reduce this effect, the multi-template matching is employed to get different matching regions with different templates. Then the interval which the matching result belongs to is weighted, and the final measure accuracy is obtained based on the weighted average approach. Compared with the true value, the final result is just sub-pixel error which shows that the interval weighted multi-template matching method is efficient for accurate measurement and it’s simple to implement.

关键词： accurate measurement multi-template match weighted average histogram

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Fusion of infrared and visible images based on discrete wave...

Research on acoustic velocity correction algorithm in underwater acoustic positioning

国防光电子论坛第二届新型探测技术及其应用研讨会

作者： Xiao Han Li li Zhang Li yao Du Ke wei Huan Xiao guang Shi Changchun University of Science and Technology Institute of Science Jilin Jianzhu University

In the view of the situation that single-sensor image cannot fully reflect the scene information efficiently. A fusion method of infrared and visible images based on discrete wavelet transform is presented and comparatively analyzed with traditional methods. Firstly, the wavelet multi-scale decomposition technique is applied to the source images that will be fused to give a series of sub-band coefficient. Feature extraction and weighted average with adaptive weighting factors are used to process the high-frequency coefficients. A strategy of the absolute value comparing is adopted to the low-frequency coefficients. Finally, the fusion image is reconstructed by multi-scale wavelet inversing transformation for low frequency and high frequency coefficients. Experimental results demonstrate that infrared and visible images can be more effectively fused by the algorithm presented than traditional methods.

关键词： Image fusion Infrared &visible image Wavelet transform Feature extraction weighted average

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Research on acoustic velocity correction algorithm in underw...