Table Of ContentMathematics 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
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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
