Pairs of compact convex sets: fractional arithmetic with convex sets
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
2002
|
| Schriftenreihe: | Mathematics and its applications
548 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 287 - 295 |
| Beschreibung: | XII, 295 S. graph. Darst. |
| ISBN: | 1402009380 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | PAIRS OF COMPACT CONVEX SETS FRACTIONAL ARITHMETIC WITH CONVEX SETS BY
DIETHARD PALLASCHKE INSTITUTE FOR STATISTICS AND MATHEMATICAL ECONOMICS,
UNIVERSITY OF KARLSRUHE, KARLSRUHE, GERMANY AND RYSZARD URBARISKI
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, ADAM MICKIEWICZ UNIVERSITY,
POZNARI, POLAND KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
CONTENTS CONVEXITY 1 CONVEX SETS AND SUBLINEARITY 3 1.1 ORDERED SETS 3
1.2 SUBLINEAR FUNCTIONS 5 1.3 THE HAHN-BANACH THEOREM 7 1.4 THE
SEPARATION THEOREM 9 TOPOLOGICAL VECTOR SPACES 11 2.1 METRIC SPACES AND
TOPOLOGIES 11 2.2 LOCALLY CONVEX VECTOR SPACES 13 2.2.1 WEAK TOPOLOGIES
16 2.3 NORMED VECTOR SPACES 17 2.4 THE KREIN-MILMAN THEOREM 19 COMPACT
CONVEX SETS 23 3.1 NOTATIONS 23 3.2 THE ORDER CANCELLATION LAW 24 3.3
CALCULUS FOR CONVEX SETS 26 3.4 THE PINSKER-MINKOWSKI-RADSTROM-
HORMANDER LATTICE 29 3.4.1 THE MINKOWSKI DUALITY 31 3.4.2 DCH-FUNCTIONS
IN FINITE-DIMENSIONAL SPACES 36 3.5 MIXED VOLUMES 38 II MINIMAL PAIRS 47
4 MINIMAL PAIRS OF CONVEX SETS 49 4.1 MINIMAL PAIRS OF COMPACT CONVEX
SETS 49 4.2 MINIMAL PAIRS OF BOUNDED CLOSED CONVEX SETS 53 4.3
SUFFICIENT CONDITIONS FOR MINIMALITY 57 VI 4.4 PAIRS OF POLAR POLYTOPES
65 4.5 THE SEPARATION LAW FOR CONVEX SETS 67 4.6 GEOMETRIC AND ALGEBRAIC
EQUIVALENCES 73 4.6.1 THE SEPARATION OF CONVEX SETS 74 4.6.2 THE
EQUIVALENCE OF THE ORDER CANCELLATION AND THE SEPARATION LAW 78 4.7
REDUCTION OF PAIRS OF COMPACT CONVEX SETS 81 4.8 SUFFICIENT CONDITIONS
FOR NON-MINIMALITY 86 THE CARDINALITY OF MINIMAL PAIRS 91 5.1 PAIRS IN
COMPLEMENTARY SUBSPACES 91 5.2 MINIMAL PAIRS IN THE PLANE ARE UNIQUE UP
TO TRANSLATIONS . . . 97 5.2.1 A DIRECT PROOF 97 5.2.2 A PROOF BASED ON
MIXED VOLUMES 105 5.3 THE GENERAL CASE 110 5.4 A CONTINUUM OF MINIMAL
PAIRS 114 5.5 THE CARDINALITY OF MINIMAL PAIRS 120 MINIMALITY UNDER
CONSTRAINTS 127 6.1 SOME PROPERTIES OF CONVEX SETS 127 6.2 CONVEX PAIRS
130 6.3 MINIMAL CONVEX PAIRS 134 6.4 CONVEX CLASSES 140 6.5 C-MINIMAL
PAIRS 143 6.6 EQUIVALENCES OF MINIMALITY IN THE PLANE 148 6.7 REDUCTION
UNDER CONSTRAINTS 150 6.8 REDUCED PAIRS OF BOUNDED CLOSED CONVEX SETS
153 6.9 EXAMPLES 157 SYMMETRIES 169 7.1 SYMMETRIC PAIRS OF CONVEX
COMPACT SETS 169 7.2 ASYMMETRY CLASSES 173 7.3 THE MINIMALITY PROBLEM
175 7.4 STRONG ORDERING AND MINIMALITY 177 7.5 EXAMPLES 179
DECOMPOSITIONS 183 8.1 DECOMPOSITION OF POLYTOPES 183 8.2 SUMMANDS AND
ANTI-SUMMANDS 185 8.3 SUMMANDS AND ANTI-SUMMANDS OF POLYTOPES 188 8.4
SET THEORETIC DECOMPOSITIONS 191 VLL 8.5 CUTTING OF A FRUSTUM 193 8.6
FAMILIES OF PAIRWISE CONVEX SETS 196 9 INVARIANTS 199 9.1 THE INVARIANCE
OF THE DIMENSION 199 9.2 FLAT MINIMAL PAIRS 201 9.3 THE CONVEX HULL OF
PAIRS OF CONVEX COMPACT SETS 204 9.4 INVARIANT CONVEXIFICATORS 206 9.5
EXAMPLES 207 10 APPLICATIONS 213 10.1 PIECEWISE DIFFERENTIABLE FUNCTIONS
213 10.2 APPLICATION TO DCH-FUNCTIONS 218 10.2.1 QUASIDIFFERENTIABLE
FUNCTIONS 221 10.2.2 STRONG DIRECTIONAL DERIVATIVES OF SET-VALUED
FUNCTIONS 229 10.3 QUADRATURE FORMULAS FOR THE AUMANN INTEGRAL 231 III
SEMIGROUPS 237 11 FRACTIONS 239 11.1 SEMIGROUPS WITH CANCELLATION
PROPERTY 239 11.2 CONVEX FRACTIONS 243 11.3 C-MINIMAL AND MINIMAL CONVEX
FRACTIONS 245 11.4 AMOUNT OF MINIMAL FRACTIONS 248 11.5 EXAMPLES 250 12
PIECEWISE LINEAR FUNCTIONS 255 12.1 THE COMBINATORIAL PICARD GROUP 255
12.2 THE MORSE-FAN S N 256 12.2.1 THE TWO-DIMENSIONAL CASE 2 259 12.2.2
THE THREE-DIMENSIONAL CASE E3 265 OPEN QUESTIONS 279 LIST OF SYMBOLS 281
INDEX 283 BIBLIOGRAPHY 287
|
| any_adam_object | 1 |
| author | Pallaschke, Diethard Urbański, Ryszard |
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| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.08 |
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| dewey-sort | 3516 18 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019418032 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:59:51Z |
| institution | BVB |
| isbn | 1402009380 |
| language | English |
| lccn | 2002034352 |
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| owner | DE-703 DE-634 |
| owner_facet | DE-703 DE-634 |
| physical | XII, 295 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Pallaschke, Diethard Verfasser aut Pairs of compact convex sets fractional arithmetic with convex sets by Diethard Pallaschke and Ryszard Urbański Dordrecht [u.a.] Kluwer Acad. Publ. 2002 XII, 295 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 548 Literaturverz. S. 287 - 295 Convex sets Kompakte konvexe Menge (DE-588)4164844-4 gnd rswk-swf Kompakte konvexe Menge (DE-588)4164844-4 s DE-604 Urbański, Ryszard Verfasser aut Mathematics and its applications 548 (DE-604)BV008163334 548 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012879776&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pallaschke, Diethard Urbański, Ryszard Pairs of compact convex sets fractional arithmetic with convex sets Mathematics and its applications Convex sets Kompakte konvexe Menge (DE-588)4164844-4 gnd |
| subject_GND | (DE-588)4164844-4 |
| title | Pairs of compact convex sets fractional arithmetic with convex sets |
| title_auth | Pairs of compact convex sets fractional arithmetic with convex sets |
| title_exact_search | Pairs of compact convex sets fractional arithmetic with convex sets |
| title_full | Pairs of compact convex sets fractional arithmetic with convex sets by Diethard Pallaschke and Ryszard Urbański |
| title_fullStr | Pairs of compact convex sets fractional arithmetic with convex sets by Diethard Pallaschke and Ryszard Urbański |
| title_full_unstemmed | Pairs of compact convex sets fractional arithmetic with convex sets by Diethard Pallaschke and Ryszard Urbański |
| title_short | Pairs of compact convex sets |
| title_sort | pairs of compact convex sets fractional arithmetic with convex sets |
| title_sub | fractional arithmetic with convex sets |
| topic | Convex sets Kompakte konvexe Menge (DE-588)4164844-4 gnd |
| topic_facet | Convex sets Kompakte konvexe Menge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012879776&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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