Defects of properties in mathematics: quantitative characterizations
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
c2002
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| Schriftenreihe: | Series on concrete and applicable mathematics
v. 5 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 337-348) and index "This book introduces a method of research which can be used in various fields of mathematics. It examines, in a systematic way, the quantitative characterizations of the "deviation from a (given) property", called the "defect of a property", in: set theory; topology; measure theory; real, complex and functional analysis; algebra; geometry; number theory; fuzzy mathematics"--P. [2] of cover Ch. 1. Introduction. 1.1. General description of the topic -- 1.2. On chapter 2: defect of property in set theory -- 1.3. On chapter 3: defect of property in topology -- 1.4. On chapter 4: defect of property in measure theory -- 1.5. On chapter 5: defect of property in real function theory -- 1.6. On chapter 6: defect of property in functional analysis -- 1.7. On chapter 7: defect of property in algebra -- 1.8. On chapter 8: miscellaneous -- ch. 2. Defect of property in set theory. 2.1. Measures of fuzziness -- 2.2. Intuitionistic entropies -- 2.3. Applications -- 2.4. Bibliographical remarks -- ch. 3. Defect of property in topology -- 3.1. Measures of noncompactness for classical sets -- 3.2. Random measures of noncompactness -- 3.3. Measures of noncompactness for fuzzy subsets in metric space -- 3.4. Measures of noncompactness for fuzzy subsets in topological space -- 3.5. Defects of opening and of closure for subsets in metric space -- - 3.6. Bibliographical remarks and open problems -- ch. 4. Defect of property in measure theory -- 4.1. Defect of additivity: basic definitions and properties -- 4.2. Defect of complementarity -- 4.3. Defect of monotonicity -- 4.4. Defect of subadditivity and of superadditivity -- 4.5. Defect of measurability -- 4.6. Bibliographical remarks -- ch. 5. Defect of property in real function theory -- 5.1. Defect of continuity, of differentiability and of integrability -- 5.2. Defect of monotonicity, of convexity and of linearity -- 5.3. Defect of equality for inequalities -- 5.4. Bibliographical remarks and open problems -- ch. 6. Defect of property in functional analysis. 6.1. Defect of orthogonality in real normed spaces -- 6.2. Defect of property for sets in normed spaces -- 6.3. Defect of property for functional -- 6.4. Defect of property for linear operators on normed spaces -- 6.5. Defect of fixed point -- 6.6. Bibliographical remarks and open problems -- - ch. 7. Defect of property in algebra -- 7.1. Defects of property for binary operations -- 7.2. Calculations of the defect of property -- 7.3. Defect of idempotency and distributivity of triangular norms -- 7.4. Applications -- 7.5. Bibliographical remarks -- ch. 8. Miscellaneous. 8.1. Defect of property in complex analysis -- 8.2. Defect of property in geometry -- 8.3. Defect of property in number theory -- 8.4. Defect of property in fuzzy logic -- 8.5. Bibliographical remarks and open problems |
| Beschreibung: | 1 Online-Ressource (xi, 352 p.) |
| ISBN: | 9789810249243 9789812777645 9810249241 9812777644 |
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| 245 | 1 | 0 | |a Defects of properties in mathematics |b quantitative characterizations |c Adrian I. Ban & Sorin G. Gal |
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| 500 | |a "This book introduces a method of research which can be used in various fields of mathematics. It examines, in a systematic way, the quantitative characterizations of the "deviation from a (given) property", called the "defect of a property", in: set theory; topology; measure theory; real, complex and functional analysis; algebra; geometry; number theory; fuzzy mathematics"--P. [2] of cover | ||
| 500 | |a Ch. 1. Introduction. 1.1. General description of the topic -- 1.2. On chapter 2: defect of property in set theory -- 1.3. On chapter 3: defect of property in topology -- 1.4. On chapter 4: defect of property in measure theory -- 1.5. On chapter 5: defect of property in real function theory -- 1.6. On chapter 6: defect of property in functional analysis -- 1.7. On chapter 7: defect of property in algebra -- 1.8. On chapter 8: miscellaneous -- ch. 2. Defect of property in set theory. 2.1. Measures of fuzziness -- 2.2. Intuitionistic entropies -- 2.3. Applications -- 2.4. Bibliographical remarks -- ch. 3. Defect of property in topology -- 3.1. Measures of noncompactness for classical sets -- 3.2. Random measures of noncompactness -- 3.3. Measures of noncompactness for fuzzy subsets in metric space -- 3.4. Measures of noncompactness for fuzzy subsets in topological space -- 3.5. Defects of opening and of closure for subsets in metric space -- | ||
| 500 | |a - 3.6. Bibliographical remarks and open problems -- ch. 4. Defect of property in measure theory -- 4.1. Defect of additivity: basic definitions and properties -- 4.2. Defect of complementarity -- 4.3. Defect of monotonicity -- 4.4. Defect of subadditivity and of superadditivity -- 4.5. Defect of measurability -- 4.6. Bibliographical remarks -- ch. 5. Defect of property in real function theory -- 5.1. Defect of continuity, of differentiability and of integrability -- 5.2. Defect of monotonicity, of convexity and of linearity -- 5.3. Defect of equality for inequalities -- 5.4. Bibliographical remarks and open problems -- ch. 6. Defect of property in functional analysis. 6.1. Defect of orthogonality in real normed spaces -- 6.2. Defect of property for sets in normed spaces -- 6.3. Defect of property for functional -- 6.4. Defect of property for linear operators on normed spaces -- 6.5. Defect of fixed point -- 6.6. Bibliographical remarks and open problems -- | ||
| 500 | |a - ch. 7. Defect of property in algebra -- 7.1. Defects of property for binary operations -- 7.2. Calculations of the defect of property -- 7.3. Defect of idempotency and distributivity of triangular norms -- 7.4. Applications -- 7.5. Bibliographical remarks -- ch. 8. Miscellaneous. 8.1. Defect of property in complex analysis -- 8.2. Defect of property in geometry -- 8.3. Defect of property in number theory -- 8.4. Defect of property in fuzzy logic -- 8.5. Bibliographical remarks and open problems | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Ban, Adrian I. |
| author_facet | Ban, Adrian I. |
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| building | Verbundindex |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
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| discipline | Mathematik |
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| id | DE-604.BV043129944 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:21Z |
| institution | BVB |
| isbn | 9789810249243 9789812777645 9810249241 9812777644 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028554135 |
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| physical | 1 Online-Ressource (xi, 352 p.) |
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| spelling | Ban, Adrian I. Verfasser aut Defects of properties in mathematics quantitative characterizations Adrian I. Ban & Sorin G. Gal Singapore World Scientific c2002 1 Online-Ressource (xi, 352 p.) txt rdacontent c rdamedia cr rdacarrier Series on concrete and applicable mathematics v. 5 Includes bibliographical references (p. 337-348) and index "This book introduces a method of research which can be used in various fields of mathematics. It examines, in a systematic way, the quantitative characterizations of the "deviation from a (given) property", called the "defect of a property", in: set theory; topology; measure theory; real, complex and functional analysis; algebra; geometry; number theory; fuzzy mathematics"--P. [2] of cover Ch. 1. Introduction. 1.1. General description of the topic -- 1.2. On chapter 2: defect of property in set theory -- 1.3. On chapter 3: defect of property in topology -- 1.4. On chapter 4: defect of property in measure theory -- 1.5. On chapter 5: defect of property in real function theory -- 1.6. On chapter 6: defect of property in functional analysis -- 1.7. On chapter 7: defect of property in algebra -- 1.8. On chapter 8: miscellaneous -- ch. 2. Defect of property in set theory. 2.1. Measures of fuzziness -- 2.2. Intuitionistic entropies -- 2.3. Applications -- 2.4. Bibliographical remarks -- ch. 3. Defect of property in topology -- 3.1. Measures of noncompactness for classical sets -- 3.2. Random measures of noncompactness -- 3.3. Measures of noncompactness for fuzzy subsets in metric space -- 3.4. Measures of noncompactness for fuzzy subsets in topological space -- 3.5. Defects of opening and of closure for subsets in metric space -- - 3.6. Bibliographical remarks and open problems -- ch. 4. Defect of property in measure theory -- 4.1. Defect of additivity: basic definitions and properties -- 4.2. Defect of complementarity -- 4.3. Defect of monotonicity -- 4.4. Defect of subadditivity and of superadditivity -- 4.5. Defect of measurability -- 4.6. Bibliographical remarks -- ch. 5. Defect of property in real function theory -- 5.1. Defect of continuity, of differentiability and of integrability -- 5.2. Defect of monotonicity, of convexity and of linearity -- 5.3. Defect of equality for inequalities -- 5.4. Bibliographical remarks and open problems -- ch. 6. Defect of property in functional analysis. 6.1. Defect of orthogonality in real normed spaces -- 6.2. Defect of property for sets in normed spaces -- 6.3. Defect of property for functional -- 6.4. Defect of property for linear operators on normed spaces -- 6.5. Defect of fixed point -- 6.6. Bibliographical remarks and open problems -- - ch. 7. Defect of property in algebra -- 7.1. Defects of property for binary operations -- 7.2. Calculations of the defect of property -- 7.3. Defect of idempotency and distributivity of triangular norms -- 7.4. Applications -- 7.5. Bibliographical remarks -- ch. 8. Miscellaneous. 8.1. Defect of property in complex analysis -- 8.2. Defect of property in geometry -- 8.3. Defect of property in number theory -- 8.4. Defect of property in fuzzy logic -- 8.5. Bibliographical remarks and open problems MATHEMATICS / Essays bisacsh MATHEMATICS / Pre-Calculus bisacsh MATHEMATICS / Reference bisacsh Deviation (Mathematics) fast Fuzzy mathematics fast Mathematics fast Mathematik Mathematics Fuzzy mathematics Deviation (Mathematics) Gal, Sorin G. Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=210662 Aggregator Volltext |
| spellingShingle | Ban, Adrian I. Defects of properties in mathematics quantitative characterizations MATHEMATICS / Essays bisacsh MATHEMATICS / Pre-Calculus bisacsh MATHEMATICS / Reference bisacsh Deviation (Mathematics) fast Fuzzy mathematics fast Mathematics fast Mathematik Mathematics Fuzzy mathematics Deviation (Mathematics) |
| title | Defects of properties in mathematics quantitative characterizations |
| title_auth | Defects of properties in mathematics quantitative characterizations |
| title_exact_search | Defects of properties in mathematics quantitative characterizations |
| title_full | Defects of properties in mathematics quantitative characterizations Adrian I. Ban & Sorin G. Gal |
| title_fullStr | Defects of properties in mathematics quantitative characterizations Adrian I. Ban & Sorin G. Gal |
| title_full_unstemmed | Defects of properties in mathematics quantitative characterizations Adrian I. Ban & Sorin G. Gal |
| title_short | Defects of properties in mathematics |
| title_sort | defects of properties in mathematics quantitative characterizations |
| title_sub | quantitative characterizations |
| topic | MATHEMATICS / Essays bisacsh MATHEMATICS / Pre-Calculus bisacsh MATHEMATICS / Reference bisacsh Deviation (Mathematics) fast Fuzzy mathematics fast Mathematics fast Mathematik Mathematics Fuzzy mathematics Deviation (Mathematics) |
| topic_facet | MATHEMATICS / Essays MATHEMATICS / Pre-Calculus MATHEMATICS / Reference Deviation (Mathematics) Fuzzy mathematics Mathematics Mathematik |
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