Selected Title s i n Thi s Serie s

25 Dongga o Deng , Dare n Huang , Rong-Qin g Jia , We i Lin , an d Jianzhon g Wang , Editors, Wavele t Analysi s an d Applications , 200 2

24 Jan e Gilman , Wil l ia m W . Menasco , an d Xiao-Son g Lin , Editors , Knots , Braids ,

and Mappin g Clas s Groups—Paper s Dedicate d t o Joa n S . Birman , 200 1

23 Cumru n Vaf a an d S.-T . Yau , Editors , Winte r Schoo l o n Mirro r Symmetry , Vecto r

Bundles an d Lagrangia n Submanifolds , 200 1

22 Carlo s Berenstein , Der-Che n Chang , an d Jingzh i Tie , Laguerr e Calculu s an d It s

Applications o n th e Heisenber g Group , 200 1

21 Jiirge n Jost , Bosoni c Strings : A Mathematica l Treatment , 200 1

20 L o Yan g an d S.-T . Yau , Editors , Firs t Internationa l Congres s o f Chines e

Mathematicians, 200 1

19 So-Chi n Che n an d Mei-Ch i Shaw , Partia l Differentia l Equation s i n Severa l Comple x

Variables, 200 1

18 Fangyan g Zheng , Comple x Differentia l Geometry , 200 0

17 Le i Gu o an d Stephe n S.-T . Yau , Editors , Lecture s o n Systems , Control , an d

Information, 200 0

16 Rud i Weikar d an d Gilber t Weinstein , Editors , Differentia l Equation s an d

Mathematical Physics , 200 0

15 Lin g Hsia o an d Zhoupin g Xin , Editors , Som e Curren t Topic s o n Nonlinea r

Conservation Laws , 200 0

14 Jun-ich i Igusa , A n Introductio n t o th e Theor y o f Loca l Zet a Functions , 200 0

13 Vasilio s Alexiade s an d Georg e Siopsis , Editors , Trend s i n Mathematica l Physics ,

1999

12 Shen g Gong , Th e Bieberbac h Conjecture , 199 9

11 Shinich i Mochizuki , Foundation s o f p-adi c Teichmiille r Theory , 199 9

10 Duon g H . Phong , Lu c Vinet , an d Shing-Tun g Yau , Editors , Mirro r Symmetr y III ,

1999

9 Shing-Tun g Yau , Editor , Mirro r Symmetr y I , 199 8

8 Jiirge n Jost , Wilfri d Kendall , U m b e r t o Mosco , Michae l Rockner ,

and Karl-Theodo r Sturm , Ne w Direction s i n Dirichle t Forms , 199 8

7 D . A . Buel l an d J . T . Teitelbaum , Editors , Computationa l Perspective s o n Numbe r

Theory, 199 8

6 Harol d Levine , Partia l Differentia l Equations , 199 7

5 Qi-ken g Lu , Stephe n S.-T . Yau , an d Anato l y Libgober , Editors , Singularitie s an d

Complex Geometry , 199 7

4 Vyjayanth i Char i an d Iva n B . Penkov , Editors , Modula r Interfaces : Modula r Li e

Algebras, Quantu m Groups , an d Li e Superalgebras , 199 7

3 Xia-X i Din g an d Tai-Pin g Liu , Editors , Nonlinea r Evolutionar y Partia l Differentia l

Equations, 199 7

2.2 Wil l ia m H . Kazez , Editor , Geometri c Topology , 199 7

2.1 Wil l ia m H . Kazez , Editor , Geometri c Topology , 199 7

1 B . Green e an d S.-T . Yau , Editors , Mirro r Symmetr y II , 199 7

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Wavelet Analysis and Applications

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AMS/IP Studies in Advanced Mathematics Volume 25

Wavelet Analysi s and Application s Proceedings of an International Conferenc e on Wavelet Analysis and Its Applications November 15-20 , 1999 Zhongshan Universit y Guangzhou, China

Donggao Deng, Daren Huang, Rong-Qing Jia, Wei Lin, and Jianzhong Wang, Editors

American Mathematical Society • International Press

https://doi.org/10.1090/amsip/025

Shing-Tung Yau , Genera l Edito r

2000 Mathematics Subject Classification. Primar y 42C40 .

Library o f Congres s Cataloging-in-Publicatio n Dat a

Wavelet analysi s an d application s : proceeding s o f an internationa l conferenc e o n wavele t analysi s and it s applications , Novembe r 15-20 , 1999 , Zhongsha n University , Guangzhou , Chin a / Dongga o Deng .. . [ed al.] , editors .

p. cm . — (AMS/I P studie s i n advance d mathematics , ISS N 1089-328 8 ; v. 25 ) Includes bibliographica l references . ISBN 0-8218-2991- 2 (alk . paper ) 1. Wavelet s (Mathematics)—Congresses . I . Deng , Dong-Gao , 1935 — II . Series .

QA403.3 .W336 200 2 515'.2433—dc21 200105656 8

Copying an d reprinting . Materia l i n thi s boo k ma y b e reproduce d b y an y mean s fo r edu -cational an d scientifi c purpose s withou t fe e o r permissio n wit h th e exceptio n o f reproductio n b y services tha t collec t fee s fo r deliver y o f document s an d provide d tha t th e customar y acknowledg -ment o f th e sourc e i s given . Thi s consen t doe s no t exten d t o othe r kind s o f copyin g fo r genera l distribution, fo r advertisin g o r promotiona l purposes , o r fo r resale . Request s fo r permissio n fo r commercial us e o f materia l shoul d b e addresse d t o th e Acquisition s Department , America n Math -ematical Society , P . O. Bo x 6248 , Providence , Rhod e Islan d 02940-6248 . Request s ca n als o b e made b y e-mai l t o reprint-permission@ams.org .

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10 9 8 7 6 5 4 3 2 1 0 7 0 6 0 5 0 4 0 3 0 2

Contents

Preface i x

List o f Participant s x i

Non-uniform samplin g i n multipl y generate d shift-invarian t subspace s o f LP(Rd) A K R A M A L D R O U B I , Q I Y U S U N , AN D W A I - S H I N G T A N G 1

Multiwavelets, pseudodifferentia l operator s an d microloca l analysi s RYUICHI A S H I N O , C H R I S T O P H E R H E I L , M I C H I H I R O N A G A S E ,

AND R E M I VAILLANCOUR T 9

A maximu m entrop y criterio n fo r featur e extractio n S A N K A R B A S U , C H A R L E S A . M I C C H E L L I , AN D P E D E R O L S E N 2 1

Wavelet filter s an d infinite-dimensiona l unitar y group s O L A B R A T T E L I AN D P A L L E E . T . J O R G E N S E N 3 5

On th e Cohen-typ e condition s fo r th e stabilit y o f shift s o f a refinabl e function G. J . C H A E , H . O . K I M , AN D R . Y . K I M 6 7

Trigonometric Hermit e wavele t an d natura l integra l equation s fo r Stoke s problem W E N S H E N G C H E N AN D W E I L I N 7 3

Vision, harmoni c oscillato r an d wavelet s D A O - Q I N G D A I 8 7

Some propertie s o f refinabl e spline s T. N . T . G O O D M A N AN D S . L . L E E 9 3

On som e application s o f a clas s o f totall y positiv e base s L A U R A G O R I AN D F R A N C E S C A P I T O L L I 10 9

Interpolatory biorthogona l wavelet s an d CB C algorith m B I N H A N AN D S H E R M A N D . R I E M E N S C H N E I D E R 11 9

Constructing orthogona l refinabl e functio n vector s wit h prescribe d approximation orde r an d smoothnes s D O U G L A S P . H A R D I N AN D T H O M A S A . H O G A N 13 9

viii C O N T E N T S

On M-ban d wavelet s havin g thre e vanishin g moment s DAREN HUANG , ZHENW U WANG , AN D ZEYI N ZHAN G 14 9

Approximation powe r o f refinable vector s o f function s RONG-QING JI A AN D QING-TAN G JIAN G 15 5

Wavelet decompositio n unde r translat e JIN NIN G 17 9

Applications o f shift-invarian t spac e theor y t o som e problem s o f multi-resolution analysi s o f L 2(Rd) HONG O H KI M AN D JA E KU N LI M 18 3

On th e connectednes s an d classificatio n o f self-affine tile s IBRAHIM KIRA T AN D KA-SIN G LA U 19 3

Wavelet-Galerkin method s fo r secon d kin d integra l equation s XUE-ZHANG LIAN G AN D MING-CA I LI U 20 7

Convergence o f cascad e algorithm s i n L p(0 < p < 1) SONG L I 21 7

Asymptotics o f zero s o f Bernstei n polynomial s tha t ar e relate d t o modifie d Daubechies wavelet s I. YA . NOVIKO V 22 5

Homogeneous an d nonhomogeneou s refinabl e distribution s i n F qn

QIYU SU N 23 5

A wavelet transfor m base d fac e recognitio n syste m an d it s eapplication s JINSHAN TANG , SHINJIR O KAWATO , AN D JU N OHY A 24 5

Spline wavelet s i n numerica l resolutio n o f partia l differentia l equation s JIANZHONG WAN G 25 7

Basis an d convergenc e propertie s o f wavele t packet s MLADEN VICTO R WICKERHAUSE R 27 9

A wavelet-based characterizatio n o f curve s LIHUA YAN G AN D YUA N Y . TAN G 28 9

Face processin g an d recognitio n technolog y P. C . YUEN , G . C . FENG , J . H . LAI , AN D D . Q . DA I 29 7

The p-norm joint spectra l radiu s an d it s application s i n wavele t analysi s DING-XUAN ZHO U 30 5

Preface

Wavelet analysi s ha s bee n on e o f th e majo r researc h direction s i n scienc e i n th e last decade . Mor e an d more , mathematician s an d scientist s ar e joining thi s excitin g research area . Certainly , wavele t analysi s ha s ha d a grea t impac t o n area s suc h a s approximation theory , harmoni c analysis , an d scientifi c computation . Mor e impor -tantly, wavele t analysi s ha s show n grea t potentia l i n application s t o informatio n technology suc h a s signa l processing , imag e processing , an d compute r graphics .

China ha s playe d a significan t rol e i n thi s developmen t o f wavelet analysi s a s ev -idenced b y man y fruitfu l theoretica l result s an d practica l applie d projects . I n orde r to exchang e idea s an d result s wit h internationa l researc h groups , w e organize d a n international conferenc e o n wavele t analysi s an d it s application s durin g th e perio d of Novembe r 15-Novembe r 20 , 1999 , a t Zhongsha n University , Guangzhou , China . The conferenc e brough t togethe r mor e tha n 8 0 researcher s i n wavele t analysi s an d related area s fro m al l over th e world , includin g Australia , Canada , China , Germany , Hong Kong , Italy , Japan , Korea , Russia , Singapore , an d th e Unite d States .

The presen t proceeding s contai n twenty-si x selectiv e paper s fro m th e lecture s given i n th e conference . Thes e paper s cove r a wid e rang e o f researc h topic s o f current interes t an d includ e man y significan t result s i n th e stud y o f refinemen t equations an d refinabl e functions , propertie s an d constructio n o f wavelets , splin e wavelets, multi-wavelets , wavele t packets , shift-invarian t spaces , approximatio n schemes an d subdivisio n algorithms , an d tilings . Severa l paper s als o focu s o n ap -plications o f wavelet s t o numerica l solution s o f partia l differentia l equation s an d integral equations , imag e processin g an d facia l recognition , compute r vision , an d feature extractio n fro m data . W e than k al l th e author s fo r thei r contribution s an d believe tha t thes e paper s wil l stimulat e furthe r interes t i n wavele t analysi s an d it s applications.

This conferenc e wa s sponsore d b y th e Ministr y o f Educatio n o f China , th e Na -tional Scienc e Foundatio n o f China , Nanka i University , Pekin g University , Zhejian g University, an d Zhongsha n University . W e woul d lik e t o expres s ou r sincer e thank s to al l o f th e abov e organization s fo r thei r generou s financial suppor t t o th e confer -ence. Specia l thank s g o t o ou r host : th e Schoo l o f Mathematic s an d Computin g Science o f Zhongsha n University . I n particular , w e appreciat e th e efficien t wor k done b y Dr . Jianhuan g La i an d Ms . Shouzhuan g Lian g fo r th e conference .

x PREFAC E

During th e proces s o f editing these proceedings , we have received muc h neede d help fro m Drs . Bi n Ha n an d Qingtan g Jiang—w e ar e gratefu l fo r thei r assistance . We also thank the publisher, the International Press in Boston, fo r their cooperatio n in preparin g th e manuscript .

Donggao Deng , Dare n Huang , We i Li n Guangzhou, Guangdong , P . R . Chin a

Rong-Qing Ji a Edmonton, Alberta , Canad a

Jianzhong Wan g Huntsville, Texas , US A

December 20 , 200 0

Participants

A. Aldroubi , Departmen t o f Mathematics , Vanderbil t University , Nashville , T N 37240, USA [ aldroubi@math.vanderbilt.edu]

Ryuichi Ashino, Division of Mathematical Sciences , Osaka Kyoiku University, Kashi -wara, Osak a 582-8582 , Japa n [ ashino@cc.osaka-kyoiku.ac.jp]

Nin Bi, Department o f Applied Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, P . R . Chin a [ qsun@math.zju.edu.cn]

K. Bittner , Institut e o f Biomathemati k an d Biometrie , GS F Nationa l Researc h Center, German y [ bittner@gsf.de]

G. J . Chae , Division o f Applied Mathematics , Kore a Advance d Institut e o f Scienc e and Technology , 373- 1 Kusong-Dong Yusong-Gu , Taejo n 305-701 , Kore a

Hanlin Chen, Institute of Mathematics, Academia Sinica, Beijing 100080 , P. R. Chin a

Jiming Chen, College of Sciences, Shanghai University, Shangha i 200233, P. R. Chin a

Lizhi Chen , Th e Sevent h Department , Nationa l Universit y o f Defens e Technology , Changsha 410073 , P. R . Chin a [ lzchen@nudt.edu.cn]

Ting Chen , Departmen t o f Communication Project , Shangha i University , Shangha i 201800, P . R . Chin a

Zhongying Chen , Departmen t o f Scientifi c Computin g & Compute r Applications , Zhongshan University , Guangzho u 510275 , P . R . Chin a [insczy@zsu.edu.cn]

Daoqing Dai , Departmen t o f Mathematics , Zhongsha n University , Guangzhou 510275 , P. R . Chin a [ stsddq@zsu.edu.cn]

Donggao Deng , Departmen t o f Mathematics , Zhongsha n University , Guangzhou 510275 , P . R . Chin a [ stsddg@zsu.edu.cn]

Lixin Ding , Stat e Ke y La b o f Softwar e Engineering , Wuha n University , Wuhan 430072 , P . R . Chin a [ ding@wipm.whenc.ac.cn]

Guocan Feng , Departmen t o f Mathematics , Zhongsha n University , Guangzhou 510275 , P . R . Chin a [ mcsfgc@zsu.edu.cn]

Xiangchu Feng , Departmen t o f Applie d Mathematics , Xi'A n Elecroni c Technolog y University, Xi'A n 710071 , P . R . Chin a

xii PARTICIPANT S

Yu Fu , Departmen t o f Applie d Mathematics , Xi'A n Elecroni c Technolog y Univer -sity, Xi 1 An 710071 , P . R . Chin a [ yfu@mail.xidian.edu.cn]

S. S. Goh, Department o f Mathematics, National University of Singapore, Singapor e 119260 [ matgohss@math.nus.edu.sg]

T. N . T . Goodman , Departmen t o f Mathematics , Universit y o f Dundee , Dunde e DD1 4HN, Scotland , U.K . [ tgoodman@mcs.dundee.ac.uk]

L. Gori , Dipartiment o d i Metod i e Modell i Matematici , Universit a degl i Stud i di Rom a "L a Sapienza" , Vi a Antoni a Scarp a 16-0016 1 Roma , Ital y [gor i@d mmm. uniromal. it]

Jianping Gu , Hube i University , P . R . Chin a

Bin Han , Applie d an d Computationa l Mathematics , Princeto n University , Prince -ton, N J 08544-1000 , USA , an d Departmen t o f Mathematica l Sciences , University o f Alberta , Edmonton , Canad a T6 G 2G 1 [ bhan@ualberta.ca]

Weidong Hao, Department o f Mathematics, Shangha i University , Shangha i 201800 , P. R . Chin a

D. Hardin, Department o f Mathematics, Vanderbil t University , Nashville , TN 37240, USA [ hardin@math.vanderbilt.edu]

Guoen Hu , Departmen t o f Applie d Mathematics , Institut e o f Informatio n Engi -neering, Zhengzho u 450002 , Henan , P . R . Chin a

Haiping Hu , Departmen t o f Mathematics , Shangha i University , Shangha i 201800 , P. R . Chin a

Junquan Hu , Departmen t o f Applied Mathematics , Zhejian g University , Hangzhou 310027 , Zhejiang , P . R . Chin a

Daren Huang , Departmen t o f Scientifi c Computation , Zhongsha n University , Guangzhou 510275 , P . R . Chin a

Rong-Qing Jia , Departmen t o f Mathematica l Sciences , Universit y o f Alberta , Edmonton, Canad a T6 G 2G 1 [ jia@xihu.math.ualberta.ca]

Huikun Jiang , Departmen t o f Mathematics , Nanjin g University , Nanjin g 210080 , Jiangsu, P . R . Chin a [ ata@nju.edu.cn]

Ning Jin , Departmen t o f Mathematics , Nanjin g University , Nanjin g 21008 0 Jiangsu, P . R . Chin a [ njin@nju.edu.cn]

Yuhong Jin , Bo x 011 3 No. 339 , JiFang Road , Wuha n 430033 , P. R . Chin a

P. Jorgensen , Departmen t o f Mathematics , Th e Universit y o f Iowa , Iow a City , IA 52242-1419, US A [ pjorgen@blue.weeg.uiowa.edu]

H. O . Kim , Divisio n o f Applied Mathematics , Kore a Advance d Institut e o f Scienc e and Technology , 373- 1 Kusong-Dong Yusong-Gu , Taejo n 305-701 , Kore a

R. Y . Kim , Divisio n o f Applied Mathematics , Kore a Advance d Institut e o f Scienc e and Technology , 373- 1 Kusong-Dong Yusong-Gu , Taejo n 305-701 , Kore a

PARTICIPANTS xii i

Jianhuang Lai , Departmen t o f Mathematics , Zhongsha n University , Guangzhou 510275 , P . R . Chin a [ stsljh@zsu.edu.cn]

K. S . Lau , Departmen t o f Mathematics , Chines e Universit y o f Hon g Kong , Hon g Kong [ kslau@math.cuhk.edu.hk]

W. M . Lawton , Departmen t o f Mathematics , Nationa l Universit y o f Singapore , Singapore 11926 0 [ matwml@math.nus.edu.sg]

S. L . Lee , Departmen t o f Mathematics , Nationa l Universit y o f Singapopre , Singa -pore 11926 0 [ matleesl@math.nus.edu.sg]

Bingzheng Li , Department o f Applie d Mathematics , Zhejian g University , Hangzhou 310027 , Zhejiang , P . R . Chin a

Dengfeng Li , Southeas t University , Nanjin g 210096 , Jiangsu , P . R . Chin a

Jianping Li , Basi c Departmen t o f Chongqin g Logistic s Engineerin g University , Chongqing 410016 , P . R . Chin a [ jpli@cqleu.edu.cn]

Song Li , Departmen t o f Applie d Mathematics , Zhejian g University , Hangzhou 310027 , Zhejiang , P . R . Chin a

Wenming Li , Department o f Mathematics , Hebe i Norma l University , Shijiazhuang 050016 , Hebei , P . R . Chin a

Xuezhang Liang , Institut e o f Mathematics , Jili n University , Changchon g 130023 , Jilin, P . R . Chin a [ xzliang@mail.jiu.edu.cn]

J. K . Lim , Divisio n o f Applie d Mathematics , Kore a Advance d Institut e o f Scienc e and Technology , 373- 1 Kusong-Dong Yusong-Gu , Taejo n 305-701 , Kore a

Wei Lin , Departmen t o f Mathematics , Zhongsha n University , Guangzho u 510275 , P. R . Chin a [ stslw@zsu.edu.cn]

Heping Liu , Departmen t o f Mathematics , Pekin g University , Beijin g 100871 , P. R . Chin a

Jiufeng Liu , Departmen t o f Applied Mathematics , Zhejian g University , Hangzhou 310027 , Zhejiang , P . R . Chin a

Xiaodong Liu , Departmen t o f Mathematics , Hon g Kon g University , Hon g Kon g

Zhao Liu , Departmen t o f Applie d Mathematics , North-Wes t Industr y University , Xi'an 710071 , Shanxi , P . R . Chin a

Zhongxuan Luo , Dalian Scienc e & Engineering University , Dalia n 116026 , Liaonin , P. R . Chin a

Bolin Ma , Departmen t o f Mathematics , Huna n University , Changsh a 410082 , Hu -nan, P . R . Chin a [ Blma@mail.hun.edu.cn]

C. A. Micchelli, IBM Research Center , P . O. Box 218, Yorktown Heights, NY 10598, USA [ cam@watson.ibm.com]

Yongming Pei , Departmen t o f Applied Mathematics , North-Wes t Industr y Univer -sity, Xi'a n 710071 , Shanxi , P . R . Chin a

xiv PARTICIPANT S

Lizhong Peng , Departmen t o f Mathematics , Pekin g University , Bejing 100871 , P . R . Chin a [ lzpeng@pku.edu.cn]

Ruiren Peng , Colleg e of Sciences, Shangha i University , Shangha i 200233 , P. R. Chin a

F. Pitolli , Dipartiment o d i Metod i e Modell i Matematici , Universit a degl i Stud i di Rom a "L a Sapienza" , Vi a Antoni a Scarp a 16-0016 1 Roma , Ital y [gori@dmmm.uniromal.it]

L. W . Qian , Departmen t o f Computationa l Science , Nationa l Universit y o f Singa -pore, Singapor e 11926 0 [ qianlw@cz3.nus.edu.sg]

Shuxi Qiu , Departmen t o f Mathematics , Xiame n University , Xiame n 361005 , Fu -jian, P . R . Chin a

Qiwen Ran , Departmen t o f Mathematics , Harbi n Inst i tut e o f Technology , Harbi n 150001. Heilongjiang , P . R . Chin a

T. A . Ridsdill-Smith , Roo m 4.5 9 Physic s Building , Departmen t o f Geolog y an d Geophysics, Th e Universit y o f Wester n Australia , Nedlands , W A 6907 , Australia [ tridsdil@geol.uwa.edu.au]

S. D . Riemenschneider , Departmen t o f Mathematics , Wes t Virgini a University , Morgantown, W V 26506-6310 , US A [ sherm@math.wvu.edu]

Qiuhui Sheng , Insti tut e o f Computationa l Mathematic s an d Scientifi c Engineerin g Computing, Academi a Sinica , Beijin g 10008 0 P. R . Chin a [ qhsheng@lsec.cc.ac.cn]

Qingyun Shi , Cente r o f Infofmatio n Science , Pekin g University , Beijing 100871 , P . R . Chin a

Guoxiang Song , Departmen t o f Applie d Mathematics , Xi 'A n Elecroni c Technolog y University, Xi 'A n 710071 , P . R . Chin a

Weifeng Su , Mathematic s Institute , Nanka i University , Tianji n 300071 , P. R . Chin a

Qiyu Sun , Departmen t o f Mathematics , Nationa l Universit y o f Singapore , Singa -pore 11926 0 [ matsunqy@math.nus.edu.sg]

Wenchang Sun , Mathematic s Institute , Nanka i University , Tianji n 300071 , P. R . Chin a [ wenchsun@263.net]

J. S . Tang , Researche r AT R Medi a Integratio n & Communication s Researc h Lab -oratories 2-2 , Hikaridai , Seika-cho , Soraku-Gu n Kyoto , 619-0288 , Japa n [stang@mic.atr.co.jp]

Yuan Y . Tang , Departmen t o f Compute r Science , Hon g Kon g Baptis t University , Kowloon Tong , Hon g Kon g

Guoqiu Wang , Th e Sevent h Dept. , Nationa l Universit y o f Defens e Technology , Changsha 410073 , P . R . Chin a [ guoqiun@public.cs.hn.cn]

J. Z . Wang , Departmen t o f Mathematics , Compute r Sciences , an d Statistics , Sa m Huston Stat e University , Huntsville , T X 77341 , US A [mth-jxw@shsu.edu]

PARTICIPANTS x v

Ling Wang, Department o f Computing Science, Sichuan Normal University, Chengd u 610066, Sichuan , P . R . Chin a [ lwang@sicnu.edu.cn]

Minghui Wang , Departmen t o f Mathematics , Pekin g University , Beijing 100871 , P . R . Chin a

Yongge Wang , Departmen t o f Mathematics , Pekin g University , Beijing 100871 , P . R . Chin a

Zhenwu Wang , Departmen t o f Applied Mathematics , Zhejian g University , Hangzhou 310027 , Zhejiang , P . R . Chin a

Joseph D . Ward , Departmen t o f Mathematics , Texa s A& M University , College Station , Texa s 77843-3368 , USA [ jward@math.tamu.edu]

Yuchuan Wei , Departmen t o f Electrica l Engineering , Bo x 202 , Beijin g Universit y of Aeronautic s an d Astronautics , Beijin g 100083 , P . R . Chin a [yuchuan -wei@21cn.com]

Chenglin Wen , Departmen t o f Applied Mathematics , Hena n University , Xinxiang 475001 , Henan , P . R . Chin a [ wencl@mail.henu.edu.cn]

V. Wickerhauser , Departmen t o f Mathematics , Washingto n University , St. Louis , M O 63130 , USA [ victor@math.wustl.edu]

Shaoquan Wu , Departmen t o f Applied Mathematics , Zhejian g University , Hangzhou 310027 , Zhejiang , P . R . Chin a

Yan Wu , A I La b Institut e o f Automatio n Chines e Academ y o f Sciences , Beijing , P. R . Chin a

Guiwei Xing , Cente r o f Infofmation Science , Pekin g University , Beijin g 100871, P . R . Chin a

Zhengfeng Xiong , Departmen t o f Applied Mathematics , Zhejian g University , Hangzhou 310027 , Zhejiang , P . R . Chin a

Chuanxiang Xu , Departmen t o f Mathematics , Pekin g University , Beijin g 100871 , P. R . Chin a

Huiying Xu , Departmen t o f Electroni c Projection , Xiame n University , Xiame n 361005, Fujian , P . R . Chin a [zpcai@jingxi'an.xmu.edu.cn ]

Shuzhen Xu , Shangha i Jiaoton g University , P . R . Chin a

Y. S . Xu , Departmen t o f Mathematics , Nort h Dakot a Sat e University , Fargo , N D 58105, USA [ xu@plains.nodak.edu]

I. Novikov, Department o f Mathematics, Voronezh State University, 394693 Voronezh, Russia [ mail@igorno.vrn.ru]

xvi PARTICIPANT S

Jingwen Yan , Departmen t o f Electroni c Projection , Xiame n University , Xiame n 361005, Fujian , P . R . Chin a [yfwen@jingxi'an.xmu. edu.cn]

Lihua Yang , Departmen t o f Scientifi c Computin g & Computer Applications , Zhongshan University , Guangzho u 510275 , P . R . Chin a [mcsylh@zsu.edu.cn]

Yirong Ying , Departmen t o f Applie d Mathematics , Xi'A n Electroni c Technolog y University, Xi'A n 710071 , P . R . Chin a

Xinge You , Hube i University , P . R . Chin a

Zhendong Yuan, Department o f Mathematics, Eas t Chin a Normal University, Shang -hai 200062 , P . R . Chin a [ zdyuan@Mathematicsecuu.edu.cn]

Pongchi Yuen , Departmen t o f Compute r Science , Hon g Kon g Baptis t University , Hong Kon g [ pcyuen@comp.hkbu.edu.hk]

Xiaoming Zeng , Departmen t o f Mathematics , Xiame n University , Xiame n 361005 , Fujian, P . R . Chin a [xmzeng@jingxi'an. xmu.edu.en]

Jingyuan Zhang , Bo x 50 3 No. 339 , JiFan g Road , 43003 3 Wuhan, P . R . Chin a

Zeyin Zhang , Departmen t o f Applied Mathematics , Zhejian g University , Hangzhou 310027 , P . R . Chin a [ yzhang@Mathematicszju.edu.cn]

Ruizhen Zhao , Departmen t o f Applied Mathematics , Xi'A n Electroni c Technolog y University, Xi'A n 710071 , P . R . Chin a

Yan Zhao , Departmen t o f Applie d Mathematics , Zhejian g University , Hangzhou 310027 , Zhejiang , P . R . Chin a

D. X . Zhou , Departmen t o f Mathematics , Cit y Universit y o f Hon g Kong , Hon g Kong [ mazhou@math.cityu.edu.hk]

Xiaolin Zhou , Departmen t o f Mathematics , Scienc e College , Xi'a n Jiaoton g Uni -versity, Xi'a n 710049 , Shanxi , P . R . Chin a

Xingwei Zhou , Departmen t o f Mathematics , Nanka i University , Tianjin 300071 , P . R . Chin a [ xwzhou@sun.nankai.edu.cn]

Yueping Zhu , Departmen t o f Mathematics , Nanton g Teacher s College , Nantong 226007 , P . R . Chin a [ zyp@nttc.edu.cn]

Jin Zou , Departmen t o f Mathematics , Sichua n Lesha n Teacher s College , Sichuan , P. R . Chin a