Convex cones: geometry and probability
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2022]
|
| Schriftenreihe: | Lecture notes in mathematics
Volume 2319 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 347 Seiten |
| ISBN: | 9783031151262 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV048527782 | ||
| 003 | DE-604 | ||
| 005 | 20221110 | ||
| 007 | t | ||
| 008 | 221024s2022 |||| 00||| eng d | ||
| 020 | |a 9783031151262 |9 978-3-031-15126-2 | ||
| 035 | |a (OCoLC)1347779895 | ||
| 035 | |a (DE-599)HBZHT021561995 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-188 |a DE-824 |a DE-83 | ||
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a 52A22 |2 msc | ||
| 084 | |a 60D05 |2 msc | ||
| 100 | 1 | |a Schneider, Rolf |d 1940- |0 (DE-588)129512877 |4 aut | |
| 245 | 1 | 0 | |a Convex cones |b geometry and probability |c Rolf Schneider |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2022] | |
| 264 | 4 | |c © 2022 | |
| 300 | |a X, 347 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v Volume 2319 | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Probabilities | |
| 650 | 4 | |a Convex geometry | |
| 650 | 4 | |a Discrete geometry | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-15127-9 |w (DE-604)BV048495916 |
| 830 | 0 | |a Lecture notes in mathematics |v Volume 2319 |w (DE-604)BV000676446 |9 2319 | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033904570&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-033904570 | ||
Datensatz im Suchindex
| _version_ | 1804184518857326592 |
|---|---|
| adam_text | Contents
1 Basic notions and facts coolen 1
1 1 Notation and prerequisites 2 2 co c nennen 1
1 2 Incidence algebras 2 22 ccnoee een 4
1 3 Convex Comes „u nennen nennen erreenn 7
1 4 Polyhedra 0 cece cence cece een nees 22
1 5 Recession cones 00 c cece ec c ee ccce eee eneeeennaee 29
1 6 Valuations 2 0 eee ccc cece een eee neeeees 33
1 7 Identities for characteristic functions 02 e000 49
1 8 Polarity as a valuation 022er 59
19A characterization of polarity 2 2 once 64
2 Angle functions 0 00 00 c cece cece cece eennaes 71
2 1 Invariant measures 2 cece cece cece eee ee cree 71
2 2 Angles 20 ccc cece eee tence tence eer enes 77
2 3 Conic intrinsic volumes and Grassmann angles 82
2 4 Polyhedral Gauss~Bonnet theorems 000 cee 98
25A tube formula for compact general polyhedra 105
3 Relations to spherical geometry 22222oc nenn 113
3 1 Basic facts 0 0 ccc eee c ete ee ennenees 113
3 2 The gnomonic map 00c cece cece cece eens 120
3 3 Spherical and conic valuations 06 000 cee eee 122
3 4 Inequalities in spherical space 0 0 cee cece cc ueaee 129
4 Steiner and kinematic formulas 00 0 00005 135
41A general Steiner formula for polyhedral cones 136
4 2 Support measures of general convex cones 0005 147
4 3 Kinematic formulas 0000 cece ccc cece ene 157
4 4 Concentration of the conic intrinsic volumes 170
4 5 Inequalities and monotonicity properties 183
4 6 Observations about the conic support measures 188
x Contents
i ed cones 195
5 Central hyperplane arrangements and Induced cones «+++ 196
livans-Swartz formula - ere eee eee eeee
32 Absorption probabilities via central arrangements 206
Random cones generated by central arrangements op
5 4 Volume weighted Schlafli cones ---- +++: +++ +e reer esse ress 2
5 5 Typical faces ---e een een ernennen en ernennen on
5 6 Intersections of random cones -- +--+ + sere etree eee e eens
6 Miscellanea on random cones -- rerreeeereeeeenenn an
6 1 Random projections --- 0 2 see eee eee ee eee eee eee 1
6 2 Gaussian images of cones nen renee e test ents eee ee es 243
6 3 Wendel probabilities in high dimensions 247
6 4 Donoho-Tanner cones in high dimensions 251
6 5 Cover—Efron cones in high dimensions 000 260
6 6 Random cones in halfspaces 0 c cee eee ce eee ee cease 277
7 Convex hypersurfaces adapted to cones 283
7 1 Coconvex sets 0 0 eee cc ene ee neeeeeeeeee 284
7 2 Mixed volumes involving bounded coconvex sets 288
7 3 Wulff shapes im cones 2 cc nen 294
74 A Minkowski-type existence theorem 299
y
75A Brunn-Minkowski theorem for coconvex sets 306
7 6 Mixed volumes of general coconvex sets 310
7 7 Minkowski’s theorem for general coconvex sets 313
78 The cone-volume measure 2 22 2222 nn 320
8 Appendix: Open questions 325
References 329
Notati
Ofation Index 339
Author Index
En 343
Subject Index
|
| adam_txt |
Contents
1 Basic notions and facts coolen 1
1 1 Notation and prerequisites 2 2 co c nennen 1
1 2 Incidence algebras 2 22 ccnoee een 4
1 3 Convex Comes „u nennen nennen erreenn 7
1 4 Polyhedra 0 cece cence cece een nees 22
1 5 Recession cones 00 c cece ec c ee ccce eee eneeeennaee 29
1 6 Valuations 2 0 eee ccc cece een eee neeeees 33
1 7 Identities for characteristic functions 02 e000 49
1 8 Polarity as a valuation 022er 59
19A characterization of polarity 2 2 once 64
2 Angle functions 0 00 00 c cece cece cece eennaes 71
2 1 Invariant measures 2 cece cece cece eee ee cree 71
2 2 Angles 20 ccc cece eee tence tence eer enes 77
2 3 Conic intrinsic volumes and Grassmann angles 82
2 4 Polyhedral Gauss~Bonnet theorems 000 cee 98
25A tube formula for compact general polyhedra 105
3 Relations to spherical geometry 22222oc nenn 113
3 1 Basic facts 0 0 ccc eee c ete ee ennenees 113
3 2 The gnomonic map 00c cece cece cece eens 120
3 3 Spherical and conic valuations 06 000 cee eee 122
3 4 Inequalities in spherical space 0 0 cee cece cc ueaee 129
4 Steiner and kinematic formulas 00 0 00005 135
41A general Steiner formula for polyhedral cones 136
4 2 Support measures of general convex cones 0005 147
4 3 Kinematic formulas 0000 cece ccc cece ene 157
4 4 Concentration of the conic intrinsic volumes 170
4 5 Inequalities and monotonicity properties 183
4 6 Observations about the conic support measures 188
x Contents
i ed cones 195
5 Central hyperplane arrangements and Induced cones «+++ 196
livans-Swartz formula - ere eee eee eeee
32 Absorption probabilities via central arrangements 206
Random cones generated by central arrangements op
5 4 Volume weighted Schlafli cones ---- +++: +++ +e reer esse ress 2
5 5 Typical faces ---e een een ernennen en ernennen on
5 6 Intersections of random cones -- +--+ + sere etree eee e eens
6 Miscellanea on random cones -- rerreeeereeeeenenn an
6 1 Random projections --- 0 2 see eee eee ee eee eee eee 1
6 2 Gaussian images of cones nen renee e test ents eee ee es 243
6 3 Wendel probabilities in high dimensions 247
6 4 Donoho-Tanner cones in high dimensions 251
6 5 Cover—Efron cones in high dimensions 000 260
6 6 Random cones in halfspaces 0 c cee eee ce eee ee cease 277
7 Convex hypersurfaces adapted to cones 283
7 1 Coconvex sets 0 0 eee cc ene ee neeeeeeeeee 284
7 2 Mixed volumes involving bounded coconvex sets 288
7 3 Wulff shapes im cones 2 cc nen 294
74 A Minkowski-type existence theorem 299
y
75A Brunn-Minkowski theorem for coconvex sets 306
7 6 Mixed volumes of general coconvex sets 310
7 7 Minkowski’s theorem for general coconvex sets 313
78 The cone-volume measure 2 22 2222 nn 320
8 Appendix: Open questions 325
References 329
Notati
Ofation Index 339
Author Index
En 343
Subject Index |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Schneider, Rolf 1940- |
| author_GND | (DE-588)129512877 |
| author_facet | Schneider, Rolf 1940- |
| author_role | aut |
| author_sort | Schneider, Rolf 1940- |
| author_variant | r s rs |
| building | Verbundindex |
| bvnumber | BV048527782 |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)1347779895 (DE-599)HBZHT021561995 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01463nam a2200397 cb4500</leader><controlfield tag="001">BV048527782</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20221110 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">221024s2022 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783031151262</subfield><subfield code="9">978-3-031-15126-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1347779895</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)HBZHT021561995</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-188</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">52A22</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60D05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Schneider, Rolf</subfield><subfield code="d">1940-</subfield><subfield code="0">(DE-588)129512877</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Convex cones</subfield><subfield code="b">geometry and probability</subfield><subfield code="c">Rolf Schneider</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cham, Switzerland</subfield><subfield code="b">Springer</subfield><subfield code="c">[2022]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2022</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 347 Seiten</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">Volume 2319</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probabilities</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convex geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Discrete geometry</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-031-15127-9</subfield><subfield code="w">(DE-604)BV048495916</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">Volume 2319</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">2319</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033904570&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-033904570</subfield></datafield></record></collection> |
| id | DE-604.BV048527782 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T20:51:26Z |
| indexdate | 2024-07-10T09:40:37Z |
| institution | BVB |
| isbn | 9783031151262 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033904570 |
| oclc_num | 1347779895 |
| open_access_boolean | |
| owner | DE-188 DE-824 DE-83 |
| owner_facet | DE-188 DE-824 DE-83 |
| physical | X, 347 Seiten |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Schneider, Rolf 1940- (DE-588)129512877 aut Convex cones geometry and probability Rolf Schneider Cham, Switzerland Springer [2022] © 2022 X, 347 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics Volume 2319 Geometry Probabilities Convex geometry Discrete geometry Erscheint auch als Online-Ausgabe 978-3-031-15127-9 (DE-604)BV048495916 Lecture notes in mathematics Volume 2319 (DE-604)BV000676446 2319 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033904570&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schneider, Rolf 1940- Convex cones geometry and probability Lecture notes in mathematics Geometry Probabilities Convex geometry Discrete geometry |
| title | Convex cones geometry and probability |
| title_auth | Convex cones geometry and probability |
| title_exact_search | Convex cones geometry and probability |
| title_exact_search_txtP | Convex cones geometry and probability |
| title_full | Convex cones geometry and probability Rolf Schneider |
| title_fullStr | Convex cones geometry and probability Rolf Schneider |
| title_full_unstemmed | Convex cones geometry and probability Rolf Schneider |
| title_short | Convex cones |
| title_sort | convex cones geometry and probability |
| title_sub | geometry and probability |
| topic | Geometry Probabilities Convex geometry Discrete geometry |
| topic_facet | Geometry Probabilities Convex geometry Discrete geometry |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033904570&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT schneiderrolf convexconesgeometryandprobability |