edited by Thibaut Lery, Heather Tewkesbury, Mario Primicerio, Maria J. Esteban, Magnus Fontes, Yvon Maday, Volker Mehrmann, Gonçalo Quadros, Wil Schilders, Andreas Schuppert
出版情報:
Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2011
Why Would a Mathematician Care About Embryology? M.Gromov.- PART I.BIOLOGICAL BACKGROUND
Preface to the Biological Part
Pattern Formation in Regenerating Tissues. A.Hoffmann and P.A. Tsonis
Gradients and Regulatory Networks of Wnt Signalling in Hydra Pattern Formation. T.W. Holstein
Modeling of Planar Cell Polarity Signaling. J.D. Axelrod
Integrated Molecular Circuits for Stem Cell Activity in Arabidopsis Roots. B. Scheres
The Mechanics of Tissue Morphogenesis. T. Lecuit
Small Regulatory RNAs and Skeletal Muscle Cell Differentiation. A. Harel-Bellan, A.Polesskaya, I.Naguibneva, M.Ameyar-Zazoua, C.Degerny, J.Kropp, N.Nonne, M.Souidi, G.Kratassiouk, G.Pinna, L.L.Pritchard
Pattern Formation in Sea Urchin Endomesoderm as Instructed by Gene Regulatory Network Topologies. I.S. Peter and E.H. Davidson
PART II. MATHEMATICAL MODELS
Modelling Oscillator Synchronisation During Vertebrate Axis Segmentation. P.J. Murray, P.K. Maini, and R.E. Baker
Pattern Formation in Hybrid Models of Cell Populations. N. Bessonov, P. Kurbatova, V. Volpert.-An Integrative Approach to the Analysis of Pattern Formation in Butterfly Wings – Experiments and Models. T. Sekimura
Modeling Morphogenesis in Multicellular Structures with Cell Complexes and L-systems. P. Prusinkiewicz and B. Lane
Multistability and Hysteresis-based Mechanism of Pattern Formation in Biology. A. Marciniak-Czochra and A. Köthe
How to knock out feedback Circuits in Gene Networks? H. Gruber, A. Richard, C. Soulé
Formation of Evolutionary Patterns in Cancer Dynamics. M. Delitala and T. Lorenzi
How Cell Decides Between Life and Death: Mathematical Modeling of Epigenetic Landscapes of Cellular Fates. A. Zinovyev, L. Calzone, S. Fourquet and E. Barillot
PART III. IDEAS, HYPOTHESIS, SUGGESTIONS
From Hydra to Vertebrates: Models for the Transition from Radial- to Bilateral-symmetric Body Plans, H. Meinhardt
Cell Division and Hyperbolic Geometry. M. Gromov
Formalistic Representation of the Cellular Architecture in the Course of Plant Tissue Development. I.V. Rudskiy
The Geometry of Morphogenesis and the Morphogenetic Field Concept. N.Morozova and M.Shubin
Randomness and Geometric Structures in Biology. V. Capasso
Preface
Why Would a Mathematician Care About Embryology? M.Gromov.- PART I.BIOLOGICAL BACKGROUND
Some Reflections on Main Lines of Mathematical Development
Babylonian Number Theory and Trigonometric Functions: Trigonometric Table and Pythagorean Triples in the Mathematical Tablet Plimpton 322
Archimedes in China: Archimedes and His Works in Chinese Literature of the Ming and Qing Dynasties
The Nine Chapters on the Mathematical Procedures and Liu Hui’s Mathematical Theory
On the Alternative Algorithm of the 7th Problem in the Sea Island Mathematical Canon
A Comparative Study on Traditional Mathematics of Korea and Japan
The Axes of Mathematical Methodology in the Song and Yuan Dynasties: The Construction of Mathematical Models
The Suanxue Qimeng and Its Influence on Japanese Mathematics
Power Series Expansions in India Around A. D. 1400
An Early Japanese Work on Chinese Mathematics in Vietnam: Yoshio Mikami’s Study of the Vietnamese Mathematical Treatise Chi Minh Toan Phap
The Jinkōki of Yoshida Mitsuyoshi
Résumé of Works on Mathematics of Seki Takakazu
Seki Takakazu’s Measuring Process of the Volume of Solids Derived from Spheres
Seki Takakazu’s Method on the Remainder Problem
Seki Takakazu’s Method of Calculating the Volume of Solids of Revolution and His Mathematical Object
Leibniz’s Theory of Elimination and Determinants
Algebra, Elimination and the Complete Book of Mathematics
Some Questions and Observations Around the Mathematics of Seki Takakazu
Ming Antu and His Power Series Expansions
Standing on the Shoulders of the Giant Influence of Seki Takakazu on Takebe Katahiro’s Mathematical Achievements
Takebe Katahiro’s Algorithms for Finding the Circular Arc Length
The Method of Successive Divisions by Takebe Katahiro and Nakane Genkei
Manuscripts in the Edo Period: Preliminary Study on Manuscripts Written by Seki Takakazu
Influence of European Mathematics on Pre-Meiji Japan
On Contemporary Mathematics in Vietnam
Part II Supplements
Notes on Complete Book of Mathematics Vol. 4: Three Essentials
Complete Book of Mathematics Vol. 4: Three Essentials, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Fumiaki Ozaki and Hikosaburo Komatsu
Seki’s Trilogy: Methods of Solving Explicit Problems, Methods of Solving Implicit Problems and Methods of Solving Concealed Problems
Methods of Solving Explicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu
Methods of Solving Implicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu
Methods of Solving Concealed Problems, by Seki Takakazu, collated by Hikosaburo Komatsu
Notes on Complete Book of Mathematics Vol. 10: Geometry
Complete Book of Mathematics Vol. 10: Geometry, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Hikosaburo Komatsu
Seki’s Theory of Elimination as Compared with the Others’
Part I Contributed papers
Seki Takakazu, His Life and Bibliography
Some Reflections on Main Lines of Mathematical Development
C. Bisi, C. Stoppato: Regular vs. classical Mobius transformations of the quaternionic unit ball
F. Brackx, H. De Bie, Hennie De Schepper: Distributional Boundary Values of Harmonic Potentials in Euclidean Half-space as Fundamental Solutions of Convolution Operators in Clifford Analysis
F. Colombo, J.O. Gonzalez-Cervantes, M.E. Luna-Elizarraras, I. Sabadini, M. Shapiro: On two approaches to the Bergman theory for slice regular functions
C. Della Rocchetta, G. Gentili, G. Sarfatti: A Bloch- Landau Theorem for slice regular functions
M. Ku, U. Kahler, P. Cerejeiras: Dirichlet-type problems for the iterated Dirac operator on the unit ball in Clifford analysis
A. Perotti: Fueter regularity and slice regularity: meeting points for two function theories
D.C. Struppa: A note on analytic functionals on the complex light cone
M.B. Vajiac: The S-spectrum for some classes of matrices
F. Vlacci: Regular Composition for SliceRegular Functions of Quaternionic Variable
C. Bisi, C. Stoppato: Regular vs. classical Mobius transformations of the quaternionic unit ball
F. Brackx, H. De Bie, Hennie De Schepper: Distributional Boundary Values of Harmonic Potentials in Euclidean Half-space as Fundamental Solutions of Convolution Operators in Clifford Analysis
F. Colombo, J.O. Gonzalez-Cervantes, M.E. Luna-Elizarraras, I. Sabadini, M. Shapiro: On two approaches to the Bergman theory for slice regular functions
The shifted wave equation on Damek–Ricci spaces and on homogeneous trees.- Invariance of capacity under quasisymmetric maps of the circle: an easy proof.- A Koksma–Hlawka inequality for simplices.- A dual interpretation of the Gromov–Thurston proof of Mostow rigidity and volume rigidity for representations of hyperbolic lattices.- The algebras generated by the Laplace operators in a semi-homogeneous tree.- Surjunctivity and reversibility of cellular automata over concrete categories.- Pointwise convergence of Bochner–Riesz means in Sobolev spaces.- Sub-Finsler geometry and finite propagation speed.- On the boundary behavior of holomorphic and harmonic functions.- Constructing Laplacians on limit spaces of self-similar groups.- Some remarks on generalized Gaussian noise
Eigenvalues of the vertex set Hecke algebra of an affine building.- A Liouville type theorem for Carnot groups: a case study.- Stochastic properties of Riemannian manifolds and applications to PDE’s
Characterization of Carleson measures for Besov spaces on homogeneous trees.- Atomic and maximal Hardy spaces on a Lie group of exponential growth.- The maximal singular integral: estimates in terms of the singular integral
The shifted wave equation on Damek–Ricci spaces and on homogeneous trees.- Invariance of capacity under quasisymmetric maps of the circle: an easy proof.- A Koksma–Hlawka inequality for simplices.- A dual interpretation of the Gromov–Thurston proof of Mostow rigidity and volume rigidity for representations of hyperbolic lattices.- The algebras generated by the Laplace operators in a semi-homogeneous tree.- Surjunctivity and reversibility of cellular automata over concrete categories.- Pointwise convergence of Bochner–Riesz means in Sobolev spaces.- Sub-Finsler geometry and finite propagation speed.- On the boundary behavior of holomorphic and harmonic functions.- Constructing Laplacians on limit spaces of self-similar groups.- Some remarks on generalized Gaussian noise
Eigenvalues of the vertex set Hecke algebra of an affine building.- A Liouville type theorem for Carnot groups: a case study.- Stochastic properties of Riemannian manifolds and applications to PDE’s
Characterization of Carleson measures for Besov spaces on homogeneous trees.- Atomic and maximal Hardy spaces on a Lie group of exponential growth.- The maximal singular integral: estimates in terms of the singular integral