Analytic solutions of functional equations /:
The purpose of this volume is to examine bio-informatics and quantum information, which are growing rapidly at present, and to attempt to connect the two, with a view to enumerating and solving the many fundamental problems they entail. To this end, we look for interdisciplinary bridges in mathemati...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific,
©2008.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The purpose of this volume is to examine bio-informatics and quantum information, which are growing rapidly at present, and to attempt to connect the two, with a view to enumerating and solving the many fundamental problems they entail. To this end, we look for interdisciplinary bridges in mathematics, physics, and information and life sciences. In particular, research into a new paradigm for information science and life science on the basis of quantum theory is emphasized. |
| Beschreibung: | 1 online resource (xi, 284 pages) |
| Bibliographie: | Includes bibliographical references (pages 271-281) and index. |
| ISBN: | 9789812793355 9812793356 1281934240 9781281934246 |
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| 505 | 0 | |a 1. Prologue. 1.1. An example. 1.2. Basic definitions. 1.3. Notes -- 2. Sequences. 2.1. Lebesgue summable sequences. 2.2. Relatively summable sequences. 2.3. Uniformly summable sequences. 2.4. Properties of univariate sequences. 2.5. Properties of bivariate sequences. 2.6. Notes -- 3. Power series functions. 3.1. Univariate power series functions. 3.2. Univariate analytic functions. 3.3. Bivariate power series functions. 3.4. Bivariate analytic functions. 3.5. Multivariate power series and analytic functions. 3.6. Matrix power series and analytic functions. 3.7. Majorants. 3.8. Siegel's lemma. 3.9. Notes -- 4. Functional equations without differentiation. 4.1. Introduction. 4.2. Analytic implicit function theorem. 4.3. Polynomial and rational functional equations. 4.4. Linear equations. 4.5. Nonlinear equations. 4.6. Notes -- 5. Functional equations with differentiation. 5.1. Introduction. 5.2. Linear systems. 5.3. Neutral systems. 5.4. Nonlinear equations. 5.5. Cauchy-Kowalewski existence theorem. 5.6. Functional equations with first order derivatives. 5.7. Functional equations with higher order derivatives. 5.8. Notes. 6. Functional equations with iteration. 6.1. Equations without derivatives. 6.2. Equations with first order derivatives. 6.3. Equations with second order derivatives. 6.4 Equations with higher order derivatives. 6.5. Notes. | |
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| 650 | 0 | |a Power series. |0 http://id.loc.gov/authorities/subjects/sh85106004 | |
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| author | Cheng, S. S. (Sui Sun) |
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| contents | 1. Prologue. 1.1. An example. 1.2. Basic definitions. 1.3. Notes -- 2. Sequences. 2.1. Lebesgue summable sequences. 2.2. Relatively summable sequences. 2.3. Uniformly summable sequences. 2.4. Properties of univariate sequences. 2.5. Properties of bivariate sequences. 2.6. Notes -- 3. Power series functions. 3.1. Univariate power series functions. 3.2. Univariate analytic functions. 3.3. Bivariate power series functions. 3.4. Bivariate analytic functions. 3.5. Multivariate power series and analytic functions. 3.6. Matrix power series and analytic functions. 3.7. Majorants. 3.8. Siegel's lemma. 3.9. Notes -- 4. Functional equations without differentiation. 4.1. Introduction. 4.2. Analytic implicit function theorem. 4.3. Polynomial and rational functional equations. 4.4. Linear equations. 4.5. Nonlinear equations. 4.6. Notes -- 5. Functional equations with differentiation. 5.1. Introduction. 5.2. Linear systems. 5.3. Neutral systems. 5.4. Nonlinear equations. 5.5. Cauchy-Kowalewski existence theorem. 5.6. Functional equations with first order derivatives. 5.7. Functional equations with higher order derivatives. 5.8. Notes. 6. Functional equations with iteration. 6.1. Equations without derivatives. 6.2. Equations with first order derivatives. 6.3. Equations with second order derivatives. 6.4 Equations with higher order derivatives. 6.5. Notes. |
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| publisher | World Scientific, |
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| spelling | Cheng, S. S. (Sui Sun) https://id.oclc.org/worldcat/entity/E39PCjBmqcdFKPpGTTmP3rMGh3 http://id.loc.gov/authorities/names/no00020645 Analytic solutions of functional equations / Sui Sun Cheng, Wenrong Li. Singapore ; Hackensack, NJ : World Scientific, ©2008. 1 online resource (xi, 284 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda Includes bibliographical references (pages 271-281) and index. Print version record. The purpose of this volume is to examine bio-informatics and quantum information, which are growing rapidly at present, and to attempt to connect the two, with a view to enumerating and solving the many fundamental problems they entail. To this end, we look for interdisciplinary bridges in mathematics, physics, and information and life sciences. In particular, research into a new paradigm for information science and life science on the basis of quantum theory is emphasized. 1. Prologue. 1.1. An example. 1.2. Basic definitions. 1.3. Notes -- 2. Sequences. 2.1. Lebesgue summable sequences. 2.2. Relatively summable sequences. 2.3. Uniformly summable sequences. 2.4. Properties of univariate sequences. 2.5. Properties of bivariate sequences. 2.6. Notes -- 3. Power series functions. 3.1. Univariate power series functions. 3.2. Univariate analytic functions. 3.3. Bivariate power series functions. 3.4. Bivariate analytic functions. 3.5. Multivariate power series and analytic functions. 3.6. Matrix power series and analytic functions. 3.7. Majorants. 3.8. Siegel's lemma. 3.9. Notes -- 4. Functional equations without differentiation. 4.1. Introduction. 4.2. Analytic implicit function theorem. 4.3. Polynomial and rational functional equations. 4.4. Linear equations. 4.5. Nonlinear equations. 4.6. Notes -- 5. Functional equations with differentiation. 5.1. Introduction. 5.2. Linear systems. 5.3. Neutral systems. 5.4. Nonlinear equations. 5.5. Cauchy-Kowalewski existence theorem. 5.6. Functional equations with first order derivatives. 5.7. Functional equations with higher order derivatives. 5.8. Notes. 6. Functional equations with iteration. 6.1. Equations without derivatives. 6.2. Equations with first order derivatives. 6.3. Equations with second order derivatives. 6.4 Equations with higher order derivatives. 6.5. Notes. Analytic functions. http://id.loc.gov/authorities/subjects/sh85004784 Functional equations. http://id.loc.gov/authorities/subjects/sh85052317 Power series. http://id.loc.gov/authorities/subjects/sh85106004 Fonctions analytiques. Équations fonctionnelles. Séries de puissances. MATHEMATICS Functional Analysis. bisacsh Analytic functions fast Functional equations fast Power series fast Li, Wenrong. https://id.oclc.org/worldcat/entity/E39PCjxkqtTT7KvrB77cBXgGDy http://id.loc.gov/authorities/names/nr90023276 has work: Analytic solutions of functional equations (Text) https://id.oclc.org/worldcat/entity/E39PCGcgQpvhrXCgYxwDYW9bMK https://id.oclc.org/worldcat/ontology/hasWork Print version: Cheng, S.S. (Sui Sun). Analytic solutions of functional equations. Singapore ; Hackensack, NJ : World Scientific, ©2008 9812793348 9789812793348 (DLC) 2008275073 (OCoLC)198759377 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=236112 Volltext |
| spellingShingle | Cheng, S. S. (Sui Sun) Analytic solutions of functional equations / 1. Prologue. 1.1. An example. 1.2. Basic definitions. 1.3. Notes -- 2. Sequences. 2.1. Lebesgue summable sequences. 2.2. Relatively summable sequences. 2.3. Uniformly summable sequences. 2.4. Properties of univariate sequences. 2.5. Properties of bivariate sequences. 2.6. Notes -- 3. Power series functions. 3.1. Univariate power series functions. 3.2. Univariate analytic functions. 3.3. Bivariate power series functions. 3.4. Bivariate analytic functions. 3.5. Multivariate power series and analytic functions. 3.6. Matrix power series and analytic functions. 3.7. Majorants. 3.8. Siegel's lemma. 3.9. Notes -- 4. Functional equations without differentiation. 4.1. Introduction. 4.2. Analytic implicit function theorem. 4.3. Polynomial and rational functional equations. 4.4. Linear equations. 4.5. Nonlinear equations. 4.6. Notes -- 5. Functional equations with differentiation. 5.1. Introduction. 5.2. Linear systems. 5.3. Neutral systems. 5.4. Nonlinear equations. 5.5. Cauchy-Kowalewski existence theorem. 5.6. Functional equations with first order derivatives. 5.7. Functional equations with higher order derivatives. 5.8. Notes. 6. Functional equations with iteration. 6.1. Equations without derivatives. 6.2. Equations with first order derivatives. 6.3. Equations with second order derivatives. 6.4 Equations with higher order derivatives. 6.5. Notes. Analytic functions. http://id.loc.gov/authorities/subjects/sh85004784 Functional equations. http://id.loc.gov/authorities/subjects/sh85052317 Power series. http://id.loc.gov/authorities/subjects/sh85106004 Fonctions analytiques. Équations fonctionnelles. Séries de puissances. MATHEMATICS Functional Analysis. bisacsh Analytic functions fast Functional equations fast Power series fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85004784 http://id.loc.gov/authorities/subjects/sh85052317 http://id.loc.gov/authorities/subjects/sh85106004 |
| title | Analytic solutions of functional equations / |
| title_auth | Analytic solutions of functional equations / |
| title_exact_search | Analytic solutions of functional equations / |
| title_full | Analytic solutions of functional equations / Sui Sun Cheng, Wenrong Li. |
| title_fullStr | Analytic solutions of functional equations / Sui Sun Cheng, Wenrong Li. |
| title_full_unstemmed | Analytic solutions of functional equations / Sui Sun Cheng, Wenrong Li. |
| title_short | Analytic solutions of functional equations / |
| title_sort | analytic solutions of functional equations |
| topic | Analytic functions. http://id.loc.gov/authorities/subjects/sh85004784 Functional equations. http://id.loc.gov/authorities/subjects/sh85052317 Power series. http://id.loc.gov/authorities/subjects/sh85106004 Fonctions analytiques. Équations fonctionnelles. Séries de puissances. MATHEMATICS Functional Analysis. bisacsh Analytic functions fast Functional equations fast Power series fast |
| topic_facet | Analytic functions. Functional equations. Power series. Fonctions analytiques. Équations fonctionnelles. Séries de puissances. MATHEMATICS Functional Analysis. Analytic functions Functional equations Power series |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=236112 |
| work_keys_str_mv | AT chengss analyticsolutionsoffunctionalequations AT liwenrong analyticsolutionsoffunctionalequations |