Mutational analysis: a joint framework for cauchy problems in and beyond vector spaces
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Series: | Lecture notes in mathematics
1996 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIV, 509 S. Ill., graph. Darst., Kt. |
| ISBN: | 9783642124709 9783642124716 |
Staff View
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| 245 | 1 | 0 | |a Mutational analysis |b a joint framework for cauchy problems in and beyond vector spaces |c Thomas Lorenz |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XIV, 509 S. |b Ill., graph. Darst., Kt. | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1996 | |
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Record in the Search Index
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| adam_text |
CONTENTS PREFACE V ACKNOWLEDGMENTS VII 0 INTRODUCTION 1 0.1 DIVERSE
EVOLUTIONS COME TOGETHER UNDER THE SAME ROOF 1 0.2 SOME INTRODUCTORY
EXAMPLES 3 0.2.1 A REGION GROWING METHOD OF IMAGE SEGMENTATION 3 0.2.2
IMAGE SMOOTHING VIA ANISOTROPIE DIFFUSION 8 0.2.3 A STOCHASTIC
DIFFERENTIAL GAME WITHOUT PRECISELY KNOWN REALIZATIONS OF OPPONENTS 11
0.3 EXTENDING THE TRADITIONAL HORIZON: EVOLUTION EQUATIONS BEYOND VECTOR
SPACES 12 0.3.1 AUBIN'S INITIAL NOTION: REGARD AFFINE LINEAR MAPS JUST
AS A SPECIAL TYPE OF "ELEMENTARY DEFORMATIONS" 12 0.3.2 MUTATIONAL
ANALYSIS AS AN "ADAPTIVE BLACK BOX" FOR INITIAL VALUE PROBLEMS 15 0.3.3
THE INITIAL PROBLEM DECOMPOSITION AND THE FINAL LINK TO MORE POPULAR
MEANINGS OF ABSTRACT SOLUTIONS 17 0.3.4 THE NEW STEPS OF GENERALIZATION
18 0.4 MUTATIONAL INCLUSIONS 29 1 EXTENDING ORDINARY DIFFERENTIAL
EQUATIONS TO METRIC SPACES: AUBIN'S SUGGESTION 31 1 . 1 THE KEY FOR
AVOIDING (AFFINE) LINEAR STRUCTURES: TRANSITIONS 31 1.2 THE MUTATION AS
COUNTERPART OF TIME DERIVATIVE 37 1.3 FEEDBACK LEADS TO MUTATIONAL
EQUATIONS 38 1.4 PROOFS FOR EXISTENCE AND UNIQUENESS OF SOLUTIONS
WITHOUT STATE CONSTRAINTS 40 1.5 AN ESSENTIAL ADVANTAGE OF MUTATIONAL
EQUATIONS: SOLUTIONS TO SYSTEMS 44 1.6 PROOF FOR EXISTENCE OF SOLUTIONS
UNDER STATE CONSTRAINTS 47 1. BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1000753662 DIGITALISIERT DURCH X CONTENTS 1.9 EXAMPLE:
MORPHOLOGICAL EQUATIONS FOR COMPACT SETS IN R N 57 1.9.1 THE
POMPEIU-HAUSDORFF DISTANCE D 57 1.9.2 MORPHOLOGICAL TRANSITIONS ON
(JFR(R N ),D) 60 1.9.3 MORPHOLOGICAL PRIMITIVES AS REACHABLE SETS 64
1.9.4 SOME EXAMPLES OF MORPHOLOGICAL PRIMITIVES 66 1.9.5 SOME EXAMPLES
OF CONTINGENT TRANSITION SETS 67 1.9.6 SOLUTIONS TO MORPHOLOGICAL
EQUATIONS 74 1.10 EXAMPLE: MORPHOLOGICAL TRANSITIONS FOR IMAGE
SEGMENTATION 79 1.10.1 ANALYTICAL TOOLS OF THE CONTINUOUS SEGMENTATION
PROBLEM . 80 1.10.2 SOLVING THE CONTINUOUS SEGMENTATION PROBLEM 83
1.10.3 THE APPLICATION TO COMPUTER IMAGES 90 1.11 EXAMPLE: MODIFIED
MORPHOLOGICAL EQUATIONS VIA BOUNDED ONE-SIDED LIPSCHITZ MAPS 96 2
ADAPTING MUTATIONAL EQUATIONS TO EXAMPLES IN VECTOR SPACES 103 2.1 THE
TOPOLOGICAL ENVIRONMENT OF THIS CHAPTER 104 2.2 SPECIFYING TRANSITIONS
AND MUTATION ON (E,{DJ)JE^,(\:\J)IEJ') * * * * 104 2.3 SOLUTIONS TO
MUTATIONAL EQUATIONS 107 2.3.1 CONTINUITY WITH RESPECT TO INITIAL STATES
AND RIGHT-HAND SIDE 108 2.3.2 LIMITS OF POINTWISE CONVERGING SOLUTIONS:
CONVERGENCE THEOREM 109 2.3.3 EXISTENCE FOR MUTATIONAL EQUATIONS WITHOUT
STATE CONSTRAINTS 112 2.3.4 CONVERGENCE THEOREM AND EXISTENCE FOR
SYSTEMS 116 2.3. CONTENTS XI 3 CONTINUITY OF DISTANCES REPLACES THE
TRIANGLE INEQUALITY 181 3.1 GENERAL ASSUMPTIONS OF THIS CHAPTER 182 3.2
THE ESSENTIAL FEATURES OF TRANSITIONS DO NOT CHANGE 185 3.3 SOLUTIONS TO
MUTATIONAL EQUATIONS 186 3.3.1 CONTINUITY WITH RESPECT TO INITIAL STATES
AND RIGHT-HAND SIDE 189 3.3.2 LIMITS OF GRAPHICALLY CONVERGING
SOLUTIONS: CONVERGENCE THEOREM 190 3.3.3 EXISTENCE FOR MUTATIONAL
EQUATIONS WITH DELAY AND WITHOUT STATE CONSTRAINTS 193 3.3.4 EXISTENCE
FOR SYSTEMS OF MUTATIONAL EQUATIONS WITH DELAY .198 3.3.5 EXISTENCE
UNDER STATE CONSTRAINTS FOR A SINGLE INDEX 202 3.3.6 EXPLOITING A
GENERALIZED FORM OF "WEAK" COMPACTNESS: CONVERGENCE AND EXISTENCE
WITHOUT STATE CONSTRAINTS 206 3.3.7 EXISTENCE OF SOLUTIONS DUE TO
COMPLETENESS: EXTENDING THE CAUCHY-LIPSCHITZ THEOREM 212 3.4 LOCAL
CO-CONTRACTIVITY OF TRANSITIONS CAN BECOME DISPENSABLE . 214 3.5
CONSIDERING TUPLES WITH A SEPARATE REAL TIME COMPONENT 221 3.6 EXAMPLE:
STRONG SOLUTIONS TO NONLOCAL STOCHASTIC DIFFERENTIAL EQUATIONS 231 3.6.1
THE GENERAL ASSUMPTIONS FOR THIS EXAMPLE 233 3.6.2 SOME STANDARD RESULTS
ABOUT ITO INTEGRALS AND STRONG SOLUTIONS TO STOCHASTIC ORDINARY
DIFFERENTIAL EQUATIONS . 233 3.6.3 A SHORT CUT TO EXISTENCE OF STRONG
SOLUTIONS 235 3.6.4 A SPECIAL CASE WITH FIXED ADDITIVE NOISE IN MORE
DETAIL . 238 3.7 EXAMPLE: STOCHASTIC MORPHOLOGICAL EQUATIONS FOR SQUARE
INTEGRABLE RANDOM CLOSED SETS IN R CONTENTS 3.9 EXAMPLE: NONLOCAL
PARABOLIC EQUATIONS IN CYLINDRICAL DOMAINS . 278 3.9.1 MOTIVATION:
SMOOTHING AN IMAGE, BUT PRESERVING ITS EDGES . 278 3.9.2 THE MAIN RESULT
279 3.9.3 THE UNDERLYING DETAILS IN TERMS OF MUTATIONAL ANALYSIS . 282
3.10 EXAMPLE: SEMILINEAR EVOLUTION EQUATIONS IN ANY BANACH SPACES . 291
3.10.1 THE DISTANCE FUNCTIONS (D) * C *+,(E/) I - (= *+ ONX =M XX . .
293 3.10.2 THE VARIATION OF CONSTANTS INDUCES TRANSITIONS ON X 298
3.10.3 MILD SOLUTIONS TO SEMILINEAR EVOLUTION EQUATIONS IN X * USING AN
IMMEDIATELY COMPACT SEMIGROUP 300 3.10.4 EXPLOITING RELATIVELY COMPACT
TERMS OF INHOMOGENEITY . 306 3.11 EXAMPLE: PARABOLIC DIFFERENTIAL
EQUATIONS IN NONCYLINDRICAL DOMAINS 311 3.11.1 THE GENERAL ASSUMPTIONS
FOR THIS EXAMPLE 311 3.11.2 SOME RESULTS OF LUMER AND SCHNAUBELT 313
3.11.3 SEMILINEAR PARABOLIC DIFFERENTIAL EQUATIONS IN A FIXED
NONCYLINDRICAL DOMAIN 317 3.11.4 THE TUSK CONDITION FOR APPROXIMATIVE
CAUCHY BARRIERS . 326 3.11.5 SUCCESSIVE COUPLING OF NONLINEAR
PARABOLIC PROBLEM AND MORPHOLOGICAL EQUATION 329 INTRODUCING
DISTRIBUTION-LIKE SOLUTIONS TO MUTATIONAL EQUATIONS 331 4.1 GENERAL
ASSUMPTIONS OF THIS CHAPTER 334 4.2 COMPARING WITH "TEST ELEMENTS" OF @
CONTENTS XIII 4.5 FURTHER EXAMPLE: MUTATIONAL EQUATIONS FOR COMPACT SETS
DEPENDING ON NORMAL CONES 372 4.5.1 SPECIFYING SETS AND DISTANCE
FUNCTIONS 373 4.5.2 REACHABLE SETS INDUCE TIMED TRANSITIONS 376 4.5.3
EXISTENCE DUE TO STRONG-WEAK TRANSITIONAL EULER COMPACTNESS 381 4.5.4
UNIQUENESS OF TIMED SOLUTIONS 383 5 MUTATIONAL INCLUSIONS IN METRIC
SPACES 385 5.1 MUTATIONAL INCLUSIONS WITHOUT STATE CONSTRAINTS 386 5.1.1
SOLUTIONS TO MUTATIONAL INCLUSIONS: DEFINITION AND EXISTENCE 386 5.1.2 A
SELECTION PRINCIPLE GENERALIZING THE THEOREM OF ANTOSIEWICZ-CELLINA 388
5.1.3 PROOFS ON THE WAY TO EXISTENCE THEOREM 5.4 395 5.2 MORPHOLOGICAL
INCLUSIONS WITH STATE CONSTRAINTS: A VIABILITY THEOREM 399 5.2.1
(WELL-KNOWN) VIABILITY THEOREM FOR DIFFERENTIAL INCLUSIONS 400 5.2.2
ADAPTING THIS CONCEPT TO MORPHOLOGICAL INCLUSIONS: THE MAIN THEOREM 401
5.2.3 THE STEPS FOR PROVING THE MORPHOLOGICAL VIABILITY THEOREM 403 5.3
MORPHOLOGICAL CONTROL PROBLEMS FOR COMPACT SETS IN R^ WITH STATE
CONSTRAINTS 413 5.3.1 FORMULATION 415 5.3.2 THE LINK TO MORPHOLOGICAL
INCLUSIONS 416 5.3.3 APPLICATION TO CONTROL PROBLEMS WITH STATE
CONSTRAINTS 418 5.3.4 RELAXED CONTROL PROBLEMS WITH STATE CONSTRAINTS
420 5.3.5 CLARKE TANGENT CONE IN THE MORPHOLOGICAL FRAMEWORK: THE
CIRCATANGENT TRANSITION SET 426 5.3.6 THE HYPERTANGENT TRANSITION SET
433 5.3.7 CLOSED CONTROL LOOPS FOR PROBLEMS WITH STATE CONSTRAINTS. 436
TOOL CONTENTS A.5 REGULARITY OF REACHABLE SETS OF DIFFERENTIAL
INCLUSIONS 454 A.5.1 NORMAL CONES AND COMPACT SETS: DEFINITIONS AND
NOTATION . 454 A.5.2 ADJOINT ARCS FOR EVOLVING NORMAL CONES TO REACHABLE
SETS 456 A.5.3 HAMILTONIAN SYSTEM HELPS PRESERVING C 1 ' 1 BOUNDARIES
. 458 A.5.4 HOW TO GUARANTEE REVERSIBILITY OF REACHABLE SETS IN TIME
. 461 A.5.5 HOW TO MAKE POINTS EVOLVE INTO CONVEX SETS OF POSITIVE
EROSION 463 A.5.6 REACHABLE SETS OF BALLS AND THEIR COMPLEMENTS 469
A.5.7 THE (UNIFORM) TUSK CONDITION FOR GRAPHS OF REACHABLE SETS 473 A.6
REYNOLDS TRANSPORT THEOREM FOR DIFFERENTIAL INCLUSIONS WITH CARATHEODORY
MAPS 476 A.7 DIFFERENTIAL INCLUSIONS WITH ONE-SIDED LIPSCHITZ CONTINUOUS
MAPS. 480 A.8 STOCHASTIC DIFFERENTIAL INCLUSIONS IN M. N 482 A.8.1
FILIPPOV-LIKE THEOREM OF DA PRATO AND FRANKOWSKA 482 A.8.2 A SUFFICIENT
CONDITION ON INVARIANT SUBSETS 486 A.9 PROXIMAL NORMALS OF SET SEQUENCES
IN R N 487 A.10 TOOLS FOR SET-VALUED MAPS 489 A.10.1 MEASURABLE
SET-VALUED MAPS 489 A. 10.2 PARAMETERIZATION OF SET-VALUED MAPS 491 A.I
1 COMPACTNESS OF CONTINUOUS FUNCTIONS BETWEEN METRIC SPACES . 491 A.
12 BOCHNER INTEGRALS AND WEAK COMPACTNESS IN L) 492 BIBLIOGRAPHICAL
NOTES 493 REFERENCE |
| any_adam_object | 1 |
| author | Lorenz, Thomas 1974- |
| author_GND | (DE-588)131512617 |
| author_facet | Lorenz, Thomas 1974- |
| author_role | aut |
| author_sort | Lorenz, Thomas 1974- |
| author_variant | t l tl |
| building | Verbundindex |
| bvnumber | BV036520006 |
| classification_rvk | SI 850 |
| classification_tum | MAT 356f MAT 347f MAT 606f |
| ctrlnum | (OCoLC)845676191 (DE-599)DNB1000753662 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-20T10:40:24Z |
| institution | BVB |
| isbn | 9783642124709 9783642124716 |
| language | English |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Lorenz, Thomas 1974- Verfasser (DE-588)131512617 aut Mutational analysis a joint framework for cauchy problems in and beyond vector spaces Thomas Lorenz Berlin [u.a.] Springer 2010 XIV, 509 S. Ill., graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1996 Verallgemeinerte Differentialgleichung (DE-588)4187509-6 gnd rswk-swf Nichtglatte Analysis (DE-588)4379207-8 gnd rswk-swf Mengenwertige Abbildung (DE-588)4270772-9 gnd rswk-swf Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Verallgemeinerte Differentialgleichung (DE-588)4187509-6 s Nichtlineare Evolutionsgleichung (DE-588)4221363-0 s Nichtglatte Analysis (DE-588)4379207-8 s Mengenwertige Abbildung (DE-588)4270772-9 s DE-604 Lecture notes in mathematics 1996 (DE-604)BV000676446 1996 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3439853&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020442023&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lorenz, Thomas 1974- Mutational analysis a joint framework for cauchy problems in and beyond vector spaces Lecture notes in mathematics Verallgemeinerte Differentialgleichung (DE-588)4187509-6 gnd Nichtglatte Analysis (DE-588)4379207-8 gnd Mengenwertige Abbildung (DE-588)4270772-9 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd |
| subject_GND | (DE-588)4187509-6 (DE-588)4379207-8 (DE-588)4270772-9 (DE-588)4221363-0 (DE-588)4113937-9 |
| title | Mutational analysis a joint framework for cauchy problems in and beyond vector spaces |
| title_auth | Mutational analysis a joint framework for cauchy problems in and beyond vector spaces |
| title_exact_search | Mutational analysis a joint framework for cauchy problems in and beyond vector spaces |
| title_full | Mutational analysis a joint framework for cauchy problems in and beyond vector spaces Thomas Lorenz |
| title_fullStr | Mutational analysis a joint framework for cauchy problems in and beyond vector spaces Thomas Lorenz |
| title_full_unstemmed | Mutational analysis a joint framework for cauchy problems in and beyond vector spaces Thomas Lorenz |
| title_short | Mutational analysis |
| title_sort | mutational analysis a joint framework for cauchy problems in and beyond vector spaces |
| title_sub | a joint framework for cauchy problems in and beyond vector spaces |
| topic | Verallgemeinerte Differentialgleichung (DE-588)4187509-6 gnd Nichtglatte Analysis (DE-588)4379207-8 gnd Mengenwertige Abbildung (DE-588)4270772-9 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd |
| topic_facet | Verallgemeinerte Differentialgleichung Nichtglatte Analysis Mengenwertige Abbildung Nichtlineare Evolutionsgleichung Hochschulschrift |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3439853&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020442023&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT lorenzthomas mutationalanalysisajointframeworkforcauchyproblemsinandbeyondvectorspaces |