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03528nam a22005655i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
978-0-8176-4436-9 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20161121230929.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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| fixed length control field |
cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
100301s2005 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780817644369 |
| -- |
978-0-8176-4436-9 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/0-8176-4436-9 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
T57-57.97 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBW |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
|---|
| Subject category code |
MAT003000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
519 |
| Edition number |
23 |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Free Energy and Self-Interacting Particles |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
edited by Takashi Suzuki. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
|---|
| Place of production, publication, distribution, manufacture |
Boston, MA : |
| Name of producer, publisher, distributor, manufacturer |
Birkhäuser Boston, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2005. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XIII, 370 p. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
|---|
| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
|---|
| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
|---|
| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Progress in Nonlinear Differential Equations and Their Applications ; |
| Volume/sequential designation |
62 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Summary -- Background -- Fundamental Theorem -- Trudinger-Moser Inequality -- The Green’s Function -- Equilibrium States -- Blowup Analysis for Stationary Solutions -- Multiple Existence -- Dynamical Equivalence -- Formation of Collapses -- Finiteness of Blowup Points -- Concentration Lemma -- Weak Solution -- Hyperparabolicity -- Quantized Blowup Mechanism -- Theory of Dual Variation. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc. |
This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary formation of blood vessels in angiogenesis. There are several methods to derive this system. One is the biased random walk of the individual, and another is the reinforced random walk of one particle modelled on the cellular automaton. In the context of statistical mechanics or chemical kinetics, this system of equations describes the motion of a mean ?eld of many particles, interacting under the gravitational inner force or the chemical reaction, and therefore this system is af?liated with a hierarchy of equations: Langevin, Fokker–Planck, Liouville–Gel’fand, and the gradient ?ow. All of the equations are subject to the second law of thermodynamics — the decrease of free energy. The mat- matical principle of this hierarchy, on the other hand, is referred to as the qu- tized blowup mechanism; the blowup solution of our system develops delta function singularities with the quantized mass. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematical analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Analysis (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Partial differential equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Applied mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Engineering mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Biomathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Physics. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Applications of Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Partial Differential Equations. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Analysis. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematical Methods in Physics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematical and Computational Biology. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Appl.Mathematics/Computational Methods of Engineering. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Suzuki, Takashi. |
| Relator term |
editor. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Relationship information |
Printed edition: |
| International Standard Book Number |
9780817643027 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Progress in Nonlinear Differential Equations and Their Applications ; |
| Volume/sequential designation |
62 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/0-8176-4436-9 |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
