| 000 -LEADER |
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| fixed length control field |
04606nam a22006731i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
8661826 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
IEEE |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
|---|
| control field |
20200413152931.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS |
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| fixed length control field |
m eo d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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| fixed length control field |
cr bn |||m|||a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
|---|
| fixed length control field |
190402s2019 cau foab 000 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781681735061 |
| Qualifying information |
electronic |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| Canceled/invalid ISBN |
9781681735078 |
| Qualifying information |
hardcover |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| Canceled/invalid ISBN |
9781681735054 |
| Qualifying information |
paperback |
| 024 7# - OTHER STANDARD IDENTIFIER |
|---|
| Standard number or code |
10.2200/S00898ED1V01Y201902MAS023 |
| Source of number or code |
doi |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(CaBNVSL)thg00978683 |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(OCoLC)1091193877 |
| 040 ## - CATALOGING SOURCE |
|---|
| Original cataloging agency |
CaBNVSL |
| Language of cataloging |
eng |
| Description conventions |
rda |
| Transcribing agency |
CaBNVSL |
| Modifying agency |
CaBNVSL |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA374 |
| Item number |
.R367 2019eb |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
518/.64 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Ramm, A. G. |
| Fuller form of name |
(Alexander G.), |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Symmetry problems : |
| Remainder of title |
the Navier-Stokes problem / |
| Statement of responsibility, etc. |
Alexander G. Ramm. |
| 246 30 - VARYING FORM OF TITLE |
|---|
| Title proper/short title |
Navier-Stokes problem. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
|---|
| Place of production, publication, distribution, manufacture |
[San Rafael, California] : |
| Name of producer, publisher, distributor, manufacturer |
Morgan & Claypool, |
| Date of production, publication, distribution, manufacture, or copyright notice |
[2019] |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
1 PDF (xiv, 71 pages). |
| 336 ## - CONTENT TYPE |
|---|
| Content type term |
text |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
|---|
| Media type term |
electronic |
| Source |
isbdmedia |
| 338 ## - CARRIER TYPE |
|---|
| Carrier type term |
online resource |
| Source |
rdacarrier |
| 490 1# - SERIES STATEMENT |
|---|
| Series statement |
Synthesis lectures on mathemathics and statistics, |
| International Standard Serial Number |
1938-1743 ; |
| Volume/sequential designation |
#23 |
| 538 ## - SYSTEM DETAILS NOTE |
|---|
| System details note |
Mode of access: World Wide Web. |
| 538 ## - SYSTEM DETAILS NOTE |
|---|
| System details note |
System requirements: Adobe Acrobat Reader. |
| 500 ## - GENERAL NOTE |
|---|
| General note |
Part of: Synthesis digital library of engineering and computer science. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc. note |
Includes bibliographical references (pages 65-69). |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
1. Introduction -- 2. Necessary and sufficient conditions for a scatterer to be spherically symmetric -- 2.1. Scattering by potentials -- 2.2. Scattering by obstacles |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
3. Symmetry problems for the Helmholtz equation -- 3.1. A general symmetry problem -- 3.2. Old symmetry problem -- 3.3. Necessary and sufficient conditions for S to be a sphere -- 3.4. The Pompeiu problem |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
4. Other symmetry problems -- 4.1. Volume potential -- 4.2. Surface potential -- 4.3. Invisible obstacles |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
5. Solution to the Navier-Stokes problem -- 5.1. A new approach -- 5.2. Construction of G -- 5.3. Solution to integral equation for v satisfies NS equations -- 5.4. Uniqueness of the solution to the integral equation -- 5.5. Existence of the solution to integral equation -- 5.6. Energy of the solution -- 5.7. Auxiliary estimates -- 5.8. Proof of the uniqueness of the solution -- 5.9. Proof of the existence of the solution -- 5.10. Convolution and positiveness of distributions |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
6. Inverse problem of potential theory -- 6.1. Statement of the problem -- 6.2. Proofs. |
| 506 ## - RESTRICTIONS ON ACCESS NOTE |
|---|
| Terms governing access |
Abstract freely available; full-text restricted to subscribers or individual document purchasers. |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Compendex |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
INSPEC |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Google scholar |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Google book search |
| 520 3# - SUMMARY, ETC. |
|---|
| Summary, etc. |
This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier-Stokes problem in R3. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier-Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies. |
| 530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE |
|---|
| Additional physical form available note |
Also available in print. |
| 588 ## - SOURCE OF DESCRIPTION NOTE |
|---|
| Source of description note |
Title from PDF title page (viewed on April 2, 2019). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Helmholtz equation. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Navier-Stokes equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Scattering (Mathematics) |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Helmholtz equation |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
symmetry problems |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Navier--Stokes problem |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Inverse problem of potential theory |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Relationship information |
Print version: |
| International Standard Book Number |
9781681735078 |
| -- |
9781681735054 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Synthesis digital library of engineering and computer science. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Synthesis lectures on mathemathics and statistics ; |
| Volume/sequential designation |
#23. |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
Abstract with links to resource |
| Uniform Resource Identifier |
https://ieeexplore.ieee.org/servlet/opac?bknumber=8661826 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
Abstract with links to full text |
| Uniform Resource Identifier |
https://doi.org/10.2200/S00898ED1V01Y201902MAS023 |
