Bifurcation Theory for Hexagonal Agglomeration in Economic Geography, 1st Edition

  • Published By:
  • ISBN-10: 4431542582
  • ISBN-13: 9784431542582
  • DDC: 330.900151
  • Grade Level Range: College Freshman - College Senior
  • 313 Pages | eBook
  • Original Copyright 2014 | Published/Released May 2014
  • This publication's content originally published in print form: 2014

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This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distributed places, and the symmetry of this lattice is expressed by a finite group. Several mathematical methodologies indispensable for tackling the present problem are gathered in a self-contained manner. The existence of hexagonal distributions is verified by group-theoretic bifurcation analysis, first by applying the so-called equivariant branching lemma and next by solving the bifurcation equation. This book offers a complete guide for the application of group-theoretic bifurcation analysis to economic agglomeration on the hexagonal lattice.

Table of Contents

Front Cover.
Half Title Page.
Other Frontmatter.
Title Page.
Copyright Page.
Preface to the Second Edition.
Preface to the First Edition.
1: Paul Erdős: Life and Work.
2: Erdős Magic.
3: Early Days.
4: Some of My Favorite Problems and Results.
5: Integers Uniquely Represented by Certain Ternary Forms.
6: Did Erdős Save Western Civilization?.
7: Encounters with Paul Erdős.
8: On Cubic Graphs of Girth at Least Five.
9: Number Theory.
10: Cross-Disjoint Pairs of Clouds in the Interval Lattice.
11: Classical Results on Primitive and Recent Results on Cross-Primitive Sequences.
12: Dense Difference Sets and Their Combinatorial Structure.
13: Integer Sets Containing No Solution to X + Y = 3z.
14: On Primes Recognizable in Deterministic Polynomial Time.
15: Ballot Numbers, Alternating Products, and the Erdős-Heilbronn Conjecture.
16: On Landau’s Function G(N).
17: On Divisibility Properties of Sequences of Integers.
18: On Additive Representative Functions.
19: Arithmetical Properties of Polynomials.
20: Some Methods of Erdős Applied to Finite Arithmetic Progressions.
21: Sur La Non-D´erivabilit´e De Fonctions P´eriodiques Associ´ees `a Certaines Formules Sommatoires.
22: 1105: First Steps in a Mysterious Quest.
23: Randomness and Applications.
24: Games, Randomness and Algorithms.
25: On Some Hypergraph Problems of Paul Erdős and the Asymptotics of Matchings, Covers and Colorings.
26: The Origins of the Theory of Random Graphs.
27: An Upper Bound for a Communication Game Related to Time-Space Tradeoffs.
28: How Abelian Is a Finite Group?.
29: On Small Size Approximation Models.
30: The Erdős Existence Argument.
31: Geometry.
32: Extension of Functional Equations.
33: Remarks on Penrose Tilings.
34: Distances in Convex Polygons.
35: Unexpected Applications of Polynomials in Combinatorics.
36: The Number of Homothetic Subsets.
37: On Lipschitz Mappings onto a Square∗.
38: A Remark on Transversal Numbers.
39: In Praise of the Gram Matrix.
40: On Mutually Avoiding Sets∗.