A Mathematical Approach to Research Problems of Science and Technology: Theoretical Basis and Developments in Mathematical Modeling PDF
Preview A Mathematical Approach to Research Problems of Science and Technology: Theoretical Basis and Developments in Mathematical Modeling
Mathematics for Industry 5 Ryuei Nishii Shin-ichiro Ei Miyuki Koiso Hiroyuki Ochiai Kanzo Okada Shingo Saito Tomoyuki Shirai Editors A Mathematical Approach to Research Problems of Science and Technology Theoretical Basis and Developments in Mathematical Modeling Mathematics for Industry Volume 5 For furthervolumes: http://www.springer.com/series/13254 Editor-in-Chief Masato Wakayama(Kyushu University, Japan) Scientific Board Members RobertS. Anderssen (CommonwealthScientific and IndustrialResearch Organisation, Australia) Heinz H.Bauschke (Kelowna, Canada) Philip Broadbridge (LaTrobe University, Australia) JinCheng(Fudan University, China) MoniqueChyba(University ofHawai’i atMa¯noa,USA) Georges-Henri Cottet (JosephFourier University, France) JoséAlberto Cuminato (University of São Paulo,Brazil) Shin-ichiro Ei(Hokkaido University, Japan) Yasuhide Fukumoto(KyushuUniversity, Japan) Jonathan R. M.Hosking(IBM T.J.Watson Research Center, USA) Alejandro Jofré (University ofChile, Chile) Kerry Landman(TheUniversity ofMelbourne, Australia) RobertMckibbin (Massey University, New Zealand) Geoff Mercer(Australian National University, Australia) (Deceased,2014) Andrea Parmeggiani (Montpellier,France) JillPipher(Brown University, USA) KonradPolthier(Free University ofBerlin,Germany) W.H.A.Schilders(Eindhoven Universityof Technology,The Netherlands) Zuowei Shen(National University ofSingapore, Singapore) Kim-Chuan Toh(National Universityof Singapore,Singapore) EvgenyVerbitskiy(Leiden University, Leiden, The Netherlands) NakahiroYoshida (The Universityof Tokyo,Japan) Aims & Scope Themeaningof‘‘MathematicsforIndustry’’(sometimesabbreviatedasMIorMfI)isdifferent from that of ‘‘Mathematics in Industry’’ (or of ‘‘Industrial Mathematics’’). The latter is restrictive:ittendstobeidentifiedwiththeactualmathematicsthatspecificallyarisesinthedaily managementandoperationofmanufacturing.Theformer,however,denotesanewresearchfield inmathematicsthatmayserveasafoundationforcreatingfuturetechnologies.Thisconceptwas bornfromtheintegrationandreorganizationofpureandappliedmathematicsinthepresentday into a fluid and versatile form capable of stimulating awareness of the importance of mathematics in industry, as well as responding to the needs of industrial technologies. The historyofthisintegrationandreorganizationindicatesthatthisbasicideawillsomedayfind increasingutility.Mathematicscanbeakeytechnologyinmodernsociety. The series aims to promote this trend by (1) providing comprehensive content on applicationsofmathematics,especiallytoindustrytechnologiesviavarioustypesofscientific research,(2)introducingbasic,useful,necessaryandcrucialknowledgeforseveralapplications through concrete subjects, and (3) introducing new research results and developments for applicationsofmathematicsintherealworld.Thesepointsmayprovidethebasisforopeninga newmathematics-orientedtechnologicalworldandevennewresearchfieldsofmathematics. Ryuei Nishii Shin-ichiro Ei • Miyuki Koiso Hiroyuki Ochiai • Kanzo Okada Shingo Saito • Tomoyuki Shirai Editors A Mathematical Approach to Research Problems of Science and Technology Theoretical Basis and Developments in Mathematical Modeling 123 Editors Ryuei Nishii Miyuki Koiso Kyushu University HiroyukiOchiai Fukuoka KanzoOkada Japan TomoyukiShirai Instituteof Mathematics forIndustry Shin-ichiro Ei Kyushu University Department of Mathematics Fukuoka Hokkaido University Japan Sapporo Japan Shingo Saito Faculty ofArts andScience Kyushu University Fukuoka Japan ISSN 2198-350X ISSN 2198-3518 (electronic) ISBN 978-4-431-55059-4 ISBN 978-4-431-55060-0 (eBook) DOI 10.1007/978-4-431-55060-0 Springer TokyoHeidelberg New YorkDordrecht London LibraryofCongressControlNumber:2014943753 (cid:2)SpringerJapan2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthe work. Duplication of this publication or parts thereof is permitted only under the provisions of theCopyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the CopyrightClearanceCenter.ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface TheInstituteofMathematicsforIndustry(IMI),KyushuUniversity,isarelatively new institute that will soon mark the fourth anniversary of its founding. In April 2013, the IMI received official recognition from the Ministry of Education, Culture, Sports, Science and Technology as Japan’s second Joint Usage/Research CenterinmathematicsfollowingtheResearchInstituteforMathematicalSciences of Kyoto University. Given the title of Center for Collaborative Research in Advanced and Fundamental Mathematics for Industry, the breadth of IMI activi- ties is widening in collaboration with the research community as a motivating force.TheIMIisalsothethirdnationalmathematicalscienceresearchinstitutein Japan if we include the Institute of Statistical Mathematics under the Research Organization of Information and Systems. Members of the IMI are researchers in what would traditionally be called industrial mathematics, (theoretical) applied mathematics, and pure mathematics, and they are divided about evenly among these fields. In addition, most of these members are currently engaged in joint research with industry while also being responsible for educating students majoring in mathematics including those in Master’s degree courses and Ph.D. programs. For this reason, I think it would be fair to say that this book has a feel different from a typical compilation on mathematical modeling. This book is based on a Japanese-language version prepared exactly one year ago, but its text has been revised and enhanced while adding contributions from new members in IMI. Instead of summarizing its contents, I will here quote from the preface to the Japanese edition. ‘‘ThisbookhasbeenachievedthroughthecooperationofIMImembersaswell as researchers in industry who have made time to give keynote addresses at researchgatheringssponsoredeithersolelyorjointlybyIMIortospeakattheIMI Colloquium held regularly on the third Wednesday of every month. The themes coveredinthebookwereselectedaccordingtothespecialtiesandinterestsofeach author,withattentiongiventooneormoreproblemswithineachtheme.Theidea here was to create a guide for solving those problems through mathematical modeling. The world of applied mathematics and industrial mathematics is, of course,quitevast,andonlyafewthemesfromthatworldaretakenupinthisbook. The purpose of the book, however, is to introduce those fields of mathematics— even if only a small portion of that world—that are now contributing to other scientific fields and to industry and that have the potential of contributing in the v vi Preface future. The readers that we have in mind begin with undergraduate students and graduate students with an interest in mathematics and mathematical science, followed by individuals in industry and finally researchers/faculty members in variousfieldsincludingmathematics.Itiswiththisorderinmindthataneditorial policy was established. In particular, the authors were asked to prepare their manuscripts assuming that readers would have a level of knowledge typical of second- and third-year undergraduate students majoring in mathematics for the Japanese standard. ‘‘Plansforpublishingthisbookgobacktothepreparatorystageinthefounding of IMI, but it has been a matter of ‘easier said than done’. Nevertheless, an editorial committee for preparing the book was established in IMI in April of last year with Prof. Ryuei Nishii taking on the responsibilities of chairman. The result of this committee’s efforts was a book consisting of 36 chapters. ‘‘AlthoughIcannotsayforsurethatthecontentsofthisbookhavecompletely satisfiedourobjective here,Isincerely hopethatit findsitsway intothe hands of manyreaders.Thepublishingofthisbookis,inaway,anexperimentalendeavor, andweplantousetheresultsthatwehaveachievedhereasabasisforenhancing the content of next year’s edition.’’ All of us at the IMI would be greatly pleased if this book created through the processdescribedaboveweretobreathenewlife,ifevenslightly,intotheresearch of industrial mathematics and mathematical modeling. At the same time, we look forward to the frank opinions and comments offered by reviewers and readers of this book. March 2014 Masato Wakayama Preface The purpose of this book is to introduce those fields of mathematics that are contributing to other fields and to industry and that have the potential of contributing in the future. The readers targeted by the book are upper-level undergraduate students, graduate students, and corporate individuals. The six peopleresponsibleforeditingtheBasicVolumeandAppliedVolumeofthebook and the person incharge ofoverall editing made up the Editorial Committee, and all members of the Institute of Mathematics for Industry (IMI) and individuals from industry and academia having a deep relationship with IMI made contribu- tions. The members of the Editorial Committee are listed below. Algebra: Takayuki Ochiai (IMI, Kyushu University) Geometry: Miyuki Koiso (IMI, Kyushu University) Analysis:Shin-ichiroEi(IMI,KyushuUniversity,nowatHokkaidoUniversity) Probability and Statistics: Tomoyuki Shirai (IMI, Kyushu University) Applied Mathematics: Ryuei Nishii (IMI, Kyushu University) Application of Mathematics: Kanzo Okada (IMI, Kyushu University) OverallEditing:ShingoSaito(FacultyofArtsandScience,KyushuUniversity) Onreadingthesubmittedmanuscripts,wecouldnothelpbutberemindedofthe wide dynamic range of mathematics and the great potential for its application to otherfieldsandindustry.Wefeelconfidentthatthegoalofpublishingthisbook— to help others become more knowledgeable about the great possibilities of mathematicalmodeling—willbeachieved,anditisourhopethatthisbookandits individual articles will prove useful in a variety of situations and scenarios. Finally, we would like to extend our deep appreciation to those in industry and academiawhotooktimefromtheirbusyschedulestopreparemanuscriptsforthis book. March 2014 Ryuei Nishii vii Contents Part I Algebra Mathematics: As an Infrastructure of Technology and Science. . . . . . 3 Hiroyuki Ochiai Remarks on Quantum Interaction Models by Lie Theory and Modular Forms via Non-commutative Harmonic Oscillators . . . . 17 Masato Wakayama Introduction to Public-Key Cryptography . . . . . . . . . . . . . . . . . . . . . 35 Tsuyoshi Takagi Code-Based Public-Key Encryption . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Kirill Morozov Gröbner Basis and Its Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Takafumi Shibuta Part II Geometry Stability Analysis for Variational Problems for Surfaces with Constraint. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Miyuki Koiso Discrete Models of Isoperimetric Deformation of Plane Curves. . . . . . 89 Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura and Yasuhiro Ohta Computing Optimal Cycles of Homology Groups. . . . . . . . . . . . . . . . 101 Emerson G. Escolar and Yasuaki Hiraoka Singularity Theory of Differentiable Maps and Data Visualization . . . 119 Osamu Saeki ix x Contents Part III Analysis Mathematical Analysis for Pattern Formation Problems. . . . . . . . . . . 133 Shin-ichiro Ei Models and Applications of Organism Transportation . . . . . . . . . . . . 141 Atsushi Tero The Renormalization Group Method for Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Hayato Chiba A Phase Field Approach to Mathematical Modeling of Crack Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Masato Kimura and Takeshi Takaishi Variational Methods in Differential Equations . . . . . . . . . . . . . . . . . . 171 Michiaki Onodera Part IV Probability and Statistics Finite Markov Chains and Markov Decision Processes. . . . . . . . . . . . 189 Tomoyuki Shirai Introduction to the Premium Principle Based on the Wang Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Shingo Saito Stochastic Process Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Hiroki Masuda Signal Detection and Model Selection. . . . . . . . . . . . . . . . . . . . . . . . . 239 Yoshiyuki Ninomiya Regression Analysis and Its Development. . . . . . . . . . . . . . . . . . . . . . 249 Ryuei Nishii Stochastic Analytical Models in Mathematical Finance. . . . . . . . . . . . 263 Setsuo Taniguchi An Introduction to the Minimum Description Length Principle . . . . . 279 Jun’ichi Takeuchi
The list of books you might like
