DOCSLIB.ORG

Mathematics CONTENTS

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Mathematics CONTENTS Editorial Board Supported by NSFC Honorary Editor General ZHOU GuangZhao (Zhou Guang Zhao) Editor General ZHU ZuoYan Institute of Hydrobiology, CAS, China Editor-in-Chief YUAN YaXiang Academy of Mathematics and Systems Science, CAS, China Associate Editors-in-Chief CHEN YongChuan Tianjin University, China GE LiMing Academy of Mathematics and Systems Science, CAS, China SHAO QiMan The Chinese University of Hong Kong, China XI NanHua Academy of Mathematics and Systems Science, CAS, China ZHANG WeiPing Nankai University, China Members BAI ZhaoJun LI JiaYu WANG YueFei University of California, Davis, USA University of Science and Technology Academy of Mathematics and Systems of China, China Science, CAS, China CAO DaoMin Academy of Mathematics and Systems LIN FangHua WU SiJue Science, CAS, China New York University, USA University of Michigan, USA LIU JianYa CHEN XiaoJun Shandong University, China WU SiYe The Hong Kong Polytechnic University, The University of Hong Kong, China China LIU KeFeng University of California, Los Angeles, USA XIAO Jie CHEN ZhenQing Zhejiang University, China Tsinghua University, China University of Washington, USA LIU XiaoBo XIN ZhouPing CHEN ZhiMing Peking University, China The Chinese University of Hong Kong, Academy of Mathematics and Systems University of Notre Dame, USA China Science, CAS, China MA XiaoNan XU Fei CHENG ChongQing University of Denis Diderot-Paris 7, Capital Normal University, China Nanjing University, China France MA ZhiMing XU Feng DAI YuHong University of California, Riverside, USA Academy of Mathematics and Systems Academy of Mathematics and Systems Science, CAS, China Science, CAS, China XU JinChao MOK NgaiMing Pennsylvania State University, USA DONG ChongYing The University of Hong Kong, China University of California, Santa Cruz, USA PUIG Lluis XU XiaoPing CNRS, Institute of Mathematics of Jussieu, Academy of Mathematics and Systems DUAN HaiBao France Science, CAS, China Academy of Mathematics and Systems Science, CAS, China QIN HouRong YAN Catherine H. F. Nanjing University, China Texas A&M University, USA E WeiNan Princeton University, USA RINGEL Claus M. YANG DaChun Peking University, China University of Bielefeld, Germany Beijing Normal University, China SHANG ZaiJiu FAN JianQing YE XiangDong Princeton University, USA Academy of Mathematics and Systems Science, CAS, China Sun Yat-sen University, China FENG Qi SHEN ZhongMin YU XingXing Academy of Mathematics and Systems Indiana University-Purdue University Georgia Institute of Technology, USA Science, CAS, China Indianapolis, USA ZHANG James J. FU JiXiang SHU Chi-Wang University of Washington, USA Fudan University, China Brown University, USA ZHANG JiPing GAO XiaoShan SIU Yum-Tong Peking University, China Academy of Mathematics and Systems Harvard University, USA Science, CAS, China ZHANG Ping SUN LiuQuan Academy of Mathematics and Systems GE GenNian Academy of Mathematics and Systems Science, CAS, China Zhejiang University, China Science, CAS, China GUO XianPing SUN XiaoTao ZHANG PingWen Sun Yat-sen University, China Academy of Mathematics and Systems Peking University, China Science, CAS, China HE XuMing ZHANG ShouWu University of Michigan, USA TAN Lei Columbia University, USA University of Angers, France HONG JiaXing ZHANG Xu Fudan University, China TANG ZiZhou Sichuan University, China Beijing Normal University, China HSU Elton P. ZHOU XiangYu Northwestern University, USA TEBOULLE Marc Academy of Mathematics and Systems Tel Aviv University, Israel Science, CAS, China JI LiZhen University of Michigan, USA WANG FengYu ZHU XiPing Beijing Normal University, China Sun Yat-sen University, China JING Bing-Yi The Hong Kong University of Science WANG HanSheng ZONG ChuanMing and Technology, China Peking University, China Peking University, China E ditorial Staff CHAI Zhao YANG ZhiHua ZHANG RuiYan [email protected] [email protected] [email protected] SCIENCE CHINA Mathematics . ARTICLES . June 2013 Vol. 56 No. 6: 1313–1330 doi: 10.1007/s11425-013-4582-4 Upper spectral bounds and a posteriori error analysis of several mixed finite element approximations for the Stokes eigenvalue problem YANG YiDu1,∗ & JIANG Wei2 1School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001,China; 2School of Physics and Mechanical & Electrical Engineering, Xiamen University, Xiamen 361005,China Email: [email protected], [email protected] Received November 21, 2011; accepted January 9, 2013; published online January 30, 2013 Abstract This paper discusses conforming mixed finite element approximations for the Stokes eigenvalue problem. Firstly, several mixed finite element identities are proved. Based on these identities, the following new results are given: (1) It is proved that the numerical eigenvalues obtained by mini-element, P1-P1 element and Q1-Q1 element approximate the exact eigenvalues from above. (2) As for the P1-P1, Q1-Q1 and Q1-P0 element eigenvalues, the asymptotically exact a posteriori error indicators are presented. (3) The reliable and efficient a posteriori error estimator proposed by Verf¨urth is applied to mini-element eigenfunctions. Finally, numerical experiments are carried out to verify the theoretical analysis. Keywords the Stokes eigenvalue, conforming mixed finite elements, upper spectral bounds, a posteriori error estimates MSC(2010) 65N25, 65N30 Citation: Yang Y D, Jiang W. Upper spectral bounds and a posteriori error analysis of several mixed finite el- ement approximations for the Stokes eigenvalue problem. Sci China Math, 2013, 56: 1313–1330, doi: 10.1007/s11425-013-4582-4 1 Introduction The finite element eigenvalues approximate the exact ones from above or from below is always an active topic in academic community. It is well known that the minimum-maximum principle insures that the conforming finite element eigenvalues approximate the exact eigenvalues from above (see [34]). Unfor- tunately, the classic result is not valid for the nonconforming finite elements. It has been proved that the numerical eigenvalues by many nonconforming element/nonconforming mixed elements approximate exact eigenvalues from below (see [1, 14, 22–24, 27, 40, 42, 43], etc.). Then how about the conforming mixed finite elements? It can be observed from some numerical examples that the numerical eigenvalues obtained by some conforming mixed finite elements have the properties of approximations from above, but there also have converse results. For example, as for the Stokes eigenvalue problem, the numerical results in [44] indicate that the mixed Bernadi-Raugel element eigenvalues approximate from below, while the mixed Q2-P1 element eigenvalues approximate from above. Moreover, the numerical results in [21] demonstrate that, for the Laplace operator eigenvalue problem, the approximate eigenvalues obtained by low order mixed Raviart-Thomas element approximate exact eigenvalues from above. However, there is ∗Corresponding author c Science China Press and Springer-Verlag Berlin Heidelberg 2013 math.scichina.com www.springerlink.com 1314 Yang Y D et al. Sci China Math June 2013 Vol. 56 No. 6 no theoretical proof for these phenomena. The first objective of this paper is to study the approximate properties of numerical eigenvalues obtained by some mixed finite elements for the Stokes eigenvalue problem. The a posteriori error estimates and adaptive computation in finite element methods were first pro- posed by Babuˇska and Rheinboldt in 1978 (see [3]), and have been developed into one of the main fields in finite element method. In the development of this field, a posteriori error estimate of finite element ap- proximation for eigenvalue problem is also an important topic. For elliptic eigenvalue problems, there are many research results (see, for example, [5,10,11,13,17,18,28,30,39]). For the Stokes eigenvalue problem, Lovadina et al. [26] have presented a suitable error indicator based on residual type. The second objective of this paper is to study a posteriori error estimates of some mixed finite element approximations for the Stokes eigenvalue problem further. To fulfill these two goals, the theory of Babuˇska-Brezzi (see [7]) and the theory of spectral approxima- tions (see [4, 8]) are adopted in this paper. Firstly, several mixed finite element identities for the Stokes eigenvalue problem are proved. Based on these identities, the following results are given: (1) It is proved that the numerical eigenvalues obtained by mini-element, P1-P1 element and Q1-Q1 element approxi- mate the exact eigenvalues from above. (2) As for the P1-P1, Q1-Q1 and Q1-P0 element eigenvalues, the asymptotically exact recovery type by post-processing interpolation a posteriori error indicators are presented, this is a new work, about which we have not seen the report until now. (3) The reliable and efficient a posteriori error estimator proposed by Verf¨urth [35] is applied to mini-element eigenfunctions. Finally, numerical experiments are carried out to verify the theoretical analysis. The rest of this paper is organized as follows. In the next section, some preliminaries needed in this paper are presented, and several mixed element identities are proved. In Sections 3 and 4, we prove the property of upper spectral bounds and present a posteriori error of mini-element and P1-P1 element, respectively. In Section 5, we analyze a posteriori error of Q1-P0 element. Finally, numerical experiments are presented to support the theoretical analysis. 2 The mixed finite element identities for the Stokes eigenvalue problem Consider the Stokes eigenvalue problem − Δu + ∇p = λu, in Ω, divu =0, in Ω, (2.1) u =0, on ∂Ω, ⊂ R2 where Ω is a polygonal domain, u =(u1,u2) is the velocity of the flow, and p is the pressure. 1 × 1 2 { ∈ 2 } 2 × 2 Denote U = H0 (Ω) H0 (Ω),V= L0(Ω) = v L (Ω) : Ω v =0 and H = L (Ω) L (Ω). In this paper, the above symbol denotes the element in product space U or H.SetD ⊂ Ω. For any function p in Hm(D), denote 1 2 α 2 pm,D = |∂ p| ,α=(α1,α2), |α| = α1 + α2. |α|m D For simplicity, write pm,Ω = pm. For the vector function u =(u1,u2), denote 1 1 2 2 2 2 2 2 um,D =(u1m,D + u2m,D) , |u|m,D =(|u1|m,D + |u2|m,D) .
Load more

Recommended publications
  • AROUND PERELMAN's PROOF of the POINCARÉ CONJECTURE S. Finashin After 3 Years of Thorough Inspection, Perelman's Proof of Th
    AROUND PERELMAN'S PROOF OF THE POINCARE¶ CONJECTURE S. Finashin Abstract. Certain life principles of Perelman may look unusual, as it often happens with outstanding people. But his rejection of the Fields medal seems natural in the context of various activities followed his breakthrough in mathematics. Cet animal est tr`esm¶echant, quand on l'attaque, il se d¶efend. Folklore After 3 years of thorough inspection, Perelman's proof of the Poincar¶eConjecture was ¯nally recognized by the consensus of experts. Three groups of researchers not only veri¯ed its details, but also published their own expositions, clarifying the proofs in several hundreds of pages, on the level \available to graduate students". The solution of the Poincar¶eConjecture was the central event discussed in the International Congress of Mathematicians in Madrid, in August 2006 (ICM-2006), which gave to it a flavor of a historical congress. Additional attention to the personality of Perelman was attracted by his rejec- tion of the Fields medal. Some other of his decisions are also non-conventional and tradition-breaking, for example Perelman's refusal to submit his works to journals. Many people ¯nd these decisions strange, but I ¯nd them logical and would rather criticize certain bad traditions in the modern organization of science. One such tradition is a kind of tolerance to unfair credit for mathematical results. Another big problem is the journals, which are often transforming into certain clubs closed for aliens, or into pro¯table businesses, enjoying the free work of many mathemati- cians. Sometimes the role of the \organizers of science" in mathematics also raises questions.
    [Show full text]
  • Grigori Yakovlevich Perelman “No Estoy Interesado En El Dinero O La Fama; No Quiero Estar Expuesto Como Un Animal En El Zoo
    Grigori Yakovlevich Perelman \No estoy interesado en el dinero o la fama; no quiero estar expuesto como un animal en el zoo. [...] no quiero que todo el mundo est´emir´andome." - Grigori Y. Perelman Asteroide El asteroide 50033-Perelman del cintur´onde asteroides del Sistema Solar, que fue descubierto el 3 de enero del 2000 por el astr´onomoaficionado Stefano Sposetti, lleva su nombre en su honor. Solo los/as matem´aticos/asm´asfamosos/as tienen un asteroide con su nombre; en contra de toda l´ogica,no hay ninguno con el nombre de Cauchy. Berkeley Perelman estuvo en la universidad p´ublicade California en Berkeley dos a~nos,entre 1993 y 1995, gracias a la prestigiosa beca Miller de investigaci´on.En ese periodo dio una demostraci´on concisa para la `conjetura del alma' de la geometr´ıade Riemann. Conjetura de Poincar´e Hernri Poincar´econjetur´oen 1904 el problema topol´ogicoque casi 100 a~nosm´astarde, en 2002, Perelman termin´odemostrando. Tras esto la conjetura adquiri´oel estatus de teorema. Diferente La comunidad matem´aticaen general, y m´asconcr´etamente la occidental, ha considerado su comportamiento como diferente por su decisi´onde anteponer las matem´aticasa la fama. El documental ruso El hombre que camina diferente: La lecci´onde Perelman, publicado en 2011, estudia la figura del matem´atico. Esfera La esfera en tres dimensiones es un objeto importante en los resultados sobre topolog´ıade Henri Poincar´e.Su extension a las cuatro dimensiones, la hiperesfera, es el objeto geom´etrico protagonista del teorema de Poincar´e. Flujo de Ricci Es un tipo de flujo geom´etrico,denominado as´ı en honor a Gregorio Ricci-Curbastro.
    [Show full text]
  • ACD Fotocanvas Print
    Editorial Board Supported by NSFC Honorary Editor General ZHOU GuangZhao (Zhou Guang Zhao) Editor General ZHU ZuoYan Institute of Hydrobiology, CAS, China Editor-in-Chief YUAN YaXiang Academy of Mathematics and Systems Science, CAS, China Associate Editors-in-Chief CHEN YongChuan Tianjin University, China GE LiMing Academy of Mathematics and Systems Science, CAS, China SHAO QiMan The Chinese University of Hong Kong, China XI NanHua Academy of Mathematics and Systems Science, CAS, China ZHANG WeiPing Nankai University, China Members BAI ZhaoJun LI JiaYu WANG YueFei University of California, Davis, USA University of Science and Technology Academy of Mathematics and Systems of China, China Science, CAS, China CAO DaoMin Academy of Mathematics and Systems LIN FangHua WU SiJue Science, CAS, China New York University, USA University of Michigan, USA CHEN XiaoJun LIU JianYa WU SiYe The Hong Kong Polytechnic University, Shandong University, China The University of Hong Kong, China China LIU KeFeng XIAO Jie University of California, Los Angeles, USA Tsinghua University, China CHEN ZhenQing Zhejiang University, China University of Washington, USA XIN ZhouPing LIU XiaoBo The Chinese University of Hong Kong, CHEN ZhiMing Peking University, China China Academy of Mathematics and Systems University of Notre Dame, USA Science, CAS, China XU Fei MA XiaoNan Capital Normal University, China CHENG ChongQing University of Denis Diderot-Paris 7, Nanjing University, China France XU Feng University of California, Riverside, USA DAI YuHong MA ZhiMing Academy of Mathematics and Systems XU JinChao Academy of Mathematics and Systems Pennsylvania State University, USA Science, CAS, China Science, CAS, China MOK NgaiMing XU XiaoPing DONG ChongYing The University of Hong Kong, China Academy of Mathematics and Systems University of California, Santa Cruz, USA PUIG Lluis Science, CAS, China CNRS, Institute of Mathematics of Jussieu, YAN Catherine H.
    [Show full text]
  • 2017 年第 17 届 IEEE 通信技术国际会议 2017 17Th IEEE International Conference on Communication Technology (IEEE-ICCT2017)
    2017 年第 17 届 IEEE 通信技术国际会议 2017 17th IEEE International Conference on Communication Technology (IEEE-ICCT2017) 2017 年 10 月 27-30 四川成都 Oct. 27-30, 2017 Chengdu, China Conference Abstract Venue: 会议地址： 锦江宾馆/Sichuan Jinjiang Hotel 中国四川成都人民南路二段 80 号 No.80 Renmin Road South, Chengdu, Sichuan, China 电话/Tel：800-886-9898 网址/ Web：http://www.jjhotel.com/ 电子邮件/E-mail: [email protected] 1 Table of Contents Welcome Remarks----------------------------------------------------------------------------------------------- 4 Conference Committee----------------------------------------------------------------------------------------- 5-10 Instructions for Workshop ----------------------------------------------------------------------------------- 11 Conference Speakers-------------------------------------------------------------------------------------------- 12-22 Conference Schedule-------------------------------------------------------------------------------------------- 23-25 Session 1- Coding Theory and Technology----------------------------------------------------------------- 26-29 Session 2- Computer Science and Applied Technology-------------------------------------------------- 29-32 Session 3- Data Transmission and Security---------------------------------------------------------------- 33-36 Session 4 - Communication and Information System---------------------------------------------------- 36-39 Session 5- Modern Information Theory and Signal Analysis------------------------------------------- 40-43 Session 6- Network Architecture Design
    [Show full text]
  • Poincarévermutung
    4.9.2015 Poincaré­Vermutung – Wikipedia Poincaré­Vermutung aus Wikipedia, der freien Enzyklopädie Die Poincaré­Vermutung besagt, dass ein geometrisches Objekt, solange es kein Loch hat, zu einer Kugel deformiert (also geschrumpft, gestaucht, aufgeblasen o. ä.) werden kann. Und das gelte nicht nur im Fall einer zweidimensionalen Oberfläche im dreidimensionalen Raum, sondern auch für eine dreidimensionale Oberfläche im vierdimensionalen Raum. Die Poincaré­Vermutung gehört zu den bekanntesten, lange Zeit unbewiesenen mathematischen Sätzen, und galt als eines der bedeutendsten ungelösten Probleme der Topologie, eines Teilgebiets der Mathematik. Henri Poincaré hatte sie 1904 aufgestellt. Im Jahr 2000 zählte das Clay Mathematics Institute die Poincaré­Vermutung zu den sieben bedeutendsten ungelösten mathematischen Problemen, den Millennium­Problemen, und lobte für ihre Lösung eine Million US­Dollar aus. Grigori Perelman hat die Vermutung 2002 bewiesen. 2006 sollte er die Fields­Medaille für seinen Beweis erhalten, die er jedoch ablehnte. Am 18. März 2010 wurde ihm auch der Millennium­Preis des Clay­Instituts zugesprochen,[1] den er ebenfalls ablehnte.[2] Inhaltsverzeichnis 1 Wortlaut und Beschreibung 2 Erläuterungen In einem dreidimensionalen Raum ist eine Oberfläche dann 3 Die Vermutung in höheren Dimensionen homöomorph zu einer (nicht begrenzten zweidimensionalen) 4 Geschichte Kugeloberfläche, wenn sich jede geschlossene Schleife auf dieser 5 Beweis Fläche zu einem Punkt zusammenziehen lässt. 6 Bedeutung der Vermutung Die Poincaré­Vermutung behauptet, dass dies auch im Fall eines vier​­ 7 Literatur dimen​sio​nalen Raumes gilt, wenn also die Oberfläche durch eine 3­ 7.1 populärwissenschaftlich 8 Weblinks dimensionale Mannigfaltigkeit beschrieben wird, (also z. B. durch 9 Einzelnachweise und Fußnoten eine 3­Sphäre, eine unanschauliche „Oberfläche eines 4­ dimensionalen Kugeläquivalents“).
    [Show full text]
  • A Survey on Fourier Analysis Methods for Solving the Compressible Navier-Stokes Equations
    Editorial Board Supported by NSFC Honorary Editor General ZHOU GuangZhao (Zhou Guang Zhao) Editor General ZHU ZuoYan Institute of Hydrobiology, CAS Editor-in-Chief YANG Le (Yang Lo) Academy of Mathematics and Systems Science, CAS Executive Associate Editor-in-Chief LI WenLin Academy of Mathematics and Systems Science, CAS Members CAO DaoMin LI JianShu XI NanHua Academy of Mathematics and The Hong Kong University of Academy of Mathematics and Systems Science, CAS Science and Technology Systems Science, CAS CHEN ZhiMing LI KeZheng XIAO Jie Academy of Mathematics and Capital Normal University Tsinghua University Systems Science, CAS LIN FangHua XIN ZhouPing CHENG ChongQing New York University The Chinese University of Hong Kong Nanjing University LIU KeFeng XING ChaoPing University of California at Los Angeles DU DingZhu Nanyang Technological University University of Texas at Dallas LIU ZhangJu XU Fei Peking University DUAN HaiBao Academy of Mathematics and Academy of Mathematics and MA XiaoNan Systems Science, CAS Université Denis Diderot - Paris 7 Systems Science, CAS YAU Shing-Tung E WeiNan MA ZhiMing Harvard University Academy of Mathematics and Princeton University YE XiangDong Systems Science, CAS FAN JianQing University of Science and MOK NgaiMing Princeton University Technology of China The University of Hong Kong FENG KeQin YUAN YaXiang QIN HouRong Tsinghua University Academy of Mathematics and Nanjing University Systems Science, CAS FENG Qi SHI ZhongCi Academy of Mathematics and ZHANG JiPing Academy of Mathematics and Systems Science,
    [Show full text]
  • SOMMAIRE DU No 135
    SOMMAIRE DU No 135 SMF Mot de la Pr´esidente ................................. ............................... 3 MATHEMATIQUES´ La conjecture de Poincar´e, G. Besson .............................................. 5 Ce qu’Alan Turing nous a laiss´e, M. Margenstern .................................... 17 Alan Turing et la r´esolution num´erique des ´equations diff´erentielles, G. Dowek ...... 31 HISTOIRE Poincar´eet la logique, G. Heinzmann ................................................ 35 PRIX ET DISTINCTIONS Le prix Henri Poincar´epour Sylvia Serfaty, B. Helffer, R. Ignat ...................... 51 HOMMAGE A` PIERRE LELONG Quelques souvenirs autour de Pierre Lelong, J.-P. Ramis ............................ 57 Une œuvre fondatrice en analyse complexe et en g´eom´etrie analytique, J.-P. Demailly ................................................... ................................... 63 Short Tribute to Professor Pierre Lelong, S. Dineen ................................ 66 Hommage `aPierre Lelong, P. Dolbeault ............................................ 68 Pierre Lelong : souvenirs, P. Noverraz .............................................. 72 Pierre Lelong : un math´ematicien et un homme au service de l’Etat,´ H. Skoda ...... 74 INFORMATIONS Note d’information du comit´ed’experts pour les PES universitaires 2012, J. Garnier . 79 Nouvelles du CNRS, V. Bonnaillie-No¨el .............................................. 82 Bilan du congr`es SMF-VMS de Hu´e(20-24 aoˆut 2012), L. Schwartz ................ 84 2013, math´ematiques de la plan`ete Terre,
    [Show full text]
  • Global Existence for Slightly Compressible Hydrodynamic Flow of Liquid Crystals in Two Dimensions
    Editorial Board Supported by NSFC Honorary Editor General ZHOU GuangZhao (Zhou Guang Zhao) Editor General ZHU ZuoYan Institute of Hydrobiology, CAS, China Editor-in-Chief YUAN YaXiang Academy of Mathematics and Systems Science, CAS, China Associate Editors-in-Chief CHEN YongChuan Tianjin University, China GE LiMing Academy of Mathematics and Systems Science, CAS, China SHAO QiMan The Chinese University of Hong Kong, China XI NanHua Academy of Mathematics and Systems Science, CAS, China ZHANG WeiPing Nankai University, China Members BAI ZhaoJun LI JiaYu WANG YueFei University of California, Davis, USA University of Science and Technology Academy of Mathematics and Systems of China, China Science, CAS, China CAO DaoMin Academy of Mathematics and Systems LIN FangHua WU SiJue Science, CAS, China New York University, USA University of Michigan, USA CHEN XiaoJun LIU JianYa WU SiYe The Hong Kong Polytechnic University, Shandong University, China The University of Hong Kong, China China LIU KeFeng XIAO Jie University of California, Los Angeles, USA Tsinghua University, China CHEN ZhenQing Zhejiang University, China University of Washington, USA XIN ZhouPing LIU XiaoBo The Chinese University of Hong Kong, CHEN ZhiMing Peking University, China China Academy of Mathematics and Systems University of Notre Dame, USA Science, CAS, China XU Fei MA XiaoNan Capital Normal University, China CHENG ChongQing University of Denis Diderot-Paris 7, Nanjing University, China France XU Feng University of California, Riverside, USA DAI YuHong MA ZhiMing Academy of Mathematics and Systems XU JinChao Academy of Mathematics and Systems Pennsylvania State University, USA Science, CAS, China Science, CAS, China MOK NgaiMing XU XiaoPing DONG ChongYing The University of Hong Kong, China Academy of Mathematics and Systems University of California, Santa Cruz, USA PUIG Lluis Science, CAS, China CNRS, Institute of Mathematics of Jussieu, YAN Catherine H.
    [Show full text]
  • Essentials of Mathematical Thinking
    i \K31302_FM" | 2017/9/4 | 18:10 | page 2 | #2 i i i ESSENTIALS OF MATHEMATICAL THINKING i i i i i \K31302_FM" | 2017/9/4 | 18:10 | page 4 | #4 i i i TEXTBOOKS in MATHEMATICS Series Editors: Al Boggess and Ken Rosen PUBLISHED TITLES ABSTRACT ALGEBRA: A GENTLE INTRODUCTION Gary L. Mullen and James A. Sellers ABSTRACT ALGEBRA: AN INTERACTIVE APPROACH, SECOND EDITION William Paulsen ABSTRACT ALGEBRA: AN INQUIRY-BASED APPROACH Jonathan K. Hodge, Steven Schlicker, and Ted Sundstrom ADVANCED LINEAR ALGEBRA Hugo Woerdeman ADVANCED LINEAR ALGEBRA Nicholas Loehr ADVANCED LINEAR ALGEBRA, SECOND EDITION Bruce Cooperstein APPLIED ABSTRACT ALGEBRA WITH MAPLE™ AND MATLAB®, THIRD EDITION Richard Klima, Neil Sigmon, and Ernest Stitzinger APPLIED DIFFERENTIAL EQUATIONS: THE PRIMARY COURSE Vladimir Dobrushkin APPLIED DIFFERENTIAL EQUATIONS WITH BOUNDARY VALUE PROBLEMS Vladimir Dobrushkin APPLIED FUNCTIONAL ANALYSIS, THIRD EDITION J. Tinsley Oden and Leszek Demkowicz A BRIDGE TO HIGHER MATHEMATICS Valentin Deaconu and Donald C. Pfaff COMPUTATIONAL MATHEMATICS: MODELS, METHODS, AND ANALYSIS WITH MATLAB® AND MPI, SECOND EDITION Robert E. White A COURSE IN DIFFERENTIAL EQUATIONS WITH BOUNDARY VALUE PROBLEMS, SECOND EDITION Stephen A. Wirkus, Randall J. Swift, and Ryan Szypowski A COURSE IN ORDINARY DIFFERENTIAL EQUATIONS, SECOND EDITION Stephen A. Wirkus and Randall J. Swift i i i i i \K31302_FM" | 2017/9/4 | 18:10 | page 6 | #6 i i i PUBLISHED TITLES CONTINUED DIFFERENTIAL EQUATIONS: THEORY, TECHNIQUE, AND PRACTICE, SECOND EDITION Steven G. Krantz DIFFERENTIAL EQUATIONS: THEORY, TECHNIQUE, AND PRACTICE WITH BOUNDARY VALUE PROBLEMS Steven G. Krantz DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES, THIRD EDITION George F. Simmons DIFFERENTIAL EQUATIONS WITH MATLAB®: EXPLORATION, APPLICATIONS, AND THEORY Mark A.
    [Show full text]
  • Mathematics CONTENTS
    Editorial Board Supported by NSFC Honorary Editor General ZHOU GuangZhao (Zhou Guang Zhao) Editor General ZHU ZuoYan Institute of Hydrobiology, CAS, China Editor-in-Chief YUAN YaXiang Academy of Mathematics and Systems Science, CAS, China Associate Editors-in-Chief CHEN YongChuan Tianjin University, China GE LiMing Academy of Mathematics and Systems Science, CAS, China SHAO QiMan The Chinese University of Hong Kong, China XI NanHua Academy of Mathematics and Systems Science, CAS, China ZHANG WeiPing Nankai University, China Members BAI ZhaoJun LI JiaYu WANG YueFei University of California, Davis, USA University of Science and Technology Academy of Mathematics and Systems of China, China Science, CAS, China CAO DaoMin Academy of Mathematics and Systems LIN FangHua WU SiJue Science, CAS, China New York University, USA University of Michigan, USA LIU JianYa CHEN XiaoJun Shandong University, China WU SiYe The Hong Kong Polytechnic University, The University of Hong Kong, China China LIU KeFeng University of California, Los Angeles, USA XIAO Jie CHEN ZhenQing Zhejiang University, China Tsinghua University, China University of Washington, USA LIU XiaoBo XIN ZhouPing CHEN ZhiMing Peking University, China The Chinese University of Hong Kong, Academy of Mathematics and Systems University of Notre Dame, USA China Science, CAS, China MA XiaoNan XU Fei CHENG ChongQing University of Denis Diderot-Paris 7, Capital Normal University, China Nanjing University, China France MA ZhiMing XU Feng DAI YuHong University of California, Riverside, USA Academy of Mathematics and Systems Academy of Mathematics and Systems Science, CAS, China Science, CAS, China XU JinChao MOK NgaiMing Pennsylvania State University, USA DONG ChongYing The University of Hong Kong, China University of California, Santa Cruz, USA PUIG Lluis XU XiaoPing CNRS, Institute of Mathematics of Jussieu, Academy of Mathematics and Systems DUAN HaiBao France Science, CAS, China Academy of Mathematics and Systems Science, CAS, China QIN HouRong YAN Catherine H.
    [Show full text]
  • Finding the Spectral Radius of a Nonnegative Tensor
    Editorial Board Supported by NSFC Honorary Editor General ZHOU GuangZhao (Zhou Guang Zhao) Editor General ZHU ZuoYan Institute of Hydrobiology, CAS, China Editor-in-Chief YUAN YaXiang Academy of Mathematics and Systems Science, CAS, China Associate Editors-in-Chief CHEN YongChuan Tianjin University, China GE LiMing Academy of Mathematics and Systems Science, CAS, China SHAO QiMan The Chinese University of Hong Kong, China XI NanHua Academy of Mathematics and Systems Science, CAS, China ZHANG WeiPing Nankai University, China Members BAI ZhaoJun LI JiaYu WANG YueFei University of California, Davis, USA University of Science and Technology Academy of Mathematics and Systems of China, China Science, CAS, China CAO DaoMin Academy of Mathematics and Systems LIN FangHua WU SiJue Science, CAS, China New York University, USA University of Michigan, USA CHEN XiaoJun LIU JianYa WU SiYe The Hong Kong Polytechnic University, Shandong University, China The University of Hong Kong, China China LIU KeFeng XIAO Jie University of California, Los Angeles, USA Tsinghua University, China CHEN ZhenQing Zhejiang University, China University of Washington, USA XIN ZhouPing LIU XiaoBo The Chinese University of Hong Kong, CHEN ZhiMing Peking University, China China Academy of Mathematics and Systems University of Notre Dame, USA Science, CAS, China XU Fei MA XiaoNan Capital Normal University, China CHENG ChongQing University of Denis Diderot-Paris 7, Nanjing University, China France XU Feng University of California, Riverside, USA DAI YuHong MA ZhiMing Academy of Mathematics and Systems XU JinChao Academy of Mathematics and Systems Pennsylvania State University, USA Science, CAS, China Science, CAS, China MOK NgaiMing XU XiaoPing DONG ChongYing The University of Hong Kong, China Academy of Mathematics and Systems University of California, Santa Cruz, USA PUIG Lluis Science, CAS, China CNRS, Institute of Mathematics of Jussieu, YAN Catherine H.
    [Show full text]
  • Mathematics CONTENTS
    Editorial Board Supported by NSFC Honorary Editor General ZHOU GuangZhao (Zhou Guang Zhao) Editor General ZHU ZuoYan Institute of Hydrobiology, CAS, China Editor-in-Chief YUAN YaXiang Academy of Mathematics and Systems Science, CAS, China Associate Editors-in-Chief CHEN YongChuan Tianjin University, China GE LiMing Academy of Mathematics and Systems Science, CAS, China SHAO QiMan The Chinese University of Hong Kong, China XI NanHua Academy of Mathematics and Systems Science, CAS, China ZHANG WeiPing Nankai University, China Members BAI ZhaoJun LI JiaYu WANG YueFei University of California, Davis, USA University of Science and Technology Academy of Mathematics and Systems of China, China Science, CAS, China CAO DaoMin Academy of Mathematics and Systems LIN FangHua WU SiJue Science, CAS, China New York University, USA University of Michigan, USA CHEN XiaoJun LIU JianYa WU SiYe The Hong Kong Polytechnic University, Shandong University, China The University of Hong Kong, China China LIU KeFeng XIAO Jie University of California, Los Angeles, USA Tsinghua University, China CHEN ZhenQing Zhejiang University, China University of Washington, USA XIN ZhouPing LIU XiaoBo The Chinese University of Hong Kong, CHEN ZhiMing Peking University, China China Academy of Mathematics and Systems University of Notre Dame, USA Science, CAS, China XU Fei MA XiaoNan Capital Normal University, China CHENG ChongQing University of Denis Diderot-Paris 7, Nanjing University, China France XU Feng University of California, Riverside, USA DAI YuHong MA ZhiMing Academy of Mathematics and Systems XU JinChao Academy of Mathematics and Systems Pennsylvania State University, USA Science, CAS, China Science, CAS, China MOK NgaiMing XU XiaoPing DONG ChongYing The University of Hong Kong, China Academy of Mathematics and Systems University of California, Santa Cruz, USA PUIG Lluis Science, CAS, China CNRS, Institute of Mathematics of Jussieu, YAN Catherine H.
    [Show full text]