Dual sets of envelopes and characteristic regions of quasi-polynomials:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
©2009
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 225-226) and index 1. Prologue. 1.1. An example. 1.2. Basic definitions -- 2. Envelopes and dual sets. 2.1. Plane curves. 2.2. Envelopes. 2.3. Dual sets of plane curves. 2.4. Notes -- 3. Dual sets of convex-concave functions. 3.1. Quasi-tangent lines. 3.2. Asymptotes. 3.3. Intersections of quasi-tangent lines and vertical lines. 3.4. Distribution maps for dual points. 3.5. Intersections of dual sets of order 0. 3.6. Notes -- 4. Quasi-polynomials. 4.1. [symbol]- and [symbol]-polynomials. 4.2. Characteristic regions. 4.3. Notes -- 5. C\(0, [symbol])-characteristic regions of real polynomials. 5.1. Quadratic polynomials. 5.2. Cubic polynomials. 5.3. Quartic polynomials. 5.4. Quintic polynomials. 5.5. Notes -- 6. C\(0, [symbol])-characteristic regions of real [symbol]-polynomials. 6.1. [symbol]-polynomials involving one power. 6.2. [symbol]-polynomials involving two powers. 6.3. [symbol]-polynomials involving three powers. 6.4. Notes -- 7. C\R-characteristic regions of [symbol]-polynomials. 7.1. [symbol]-polynomials involving one power. 7.2. [symbol]-polynomials involving two powers. 7.3. [symbol]-polynomials involving three powers. 7.4. Notes Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations. For a wide class of functions called quasi-polynomials, the above problems can be transformed into the existence and nonexistence of tangents of the envelope curves associated with the functions under investigation. In this book, we present a formal theory of the Cheng-Lin envelope method, which is completely new, yet simple and precise. This method is both simple - since only basic Calculus concepts are needed for understanding - and precise, since necessary and sufficient conditions can be obtained for functions such as polynomials containing more than four parameters. Since the underlying principles are relatively simple, this book is useful to college students who want to see immediate applications of what they learn in Calculus; to graduate students who want to do research in functional equations; and to researchers who want references on roots of quasi-polynomials encountered in the theory of difference and differential equations |
| Beschreibung: | 1 Online-Ressource (viii, 227 pages) |
| ISBN: | 9789814277273 9789814277280 9814277274 9814277282 |
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| 245 | 1 | 0 | |a Dual sets of envelopes and characteristic regions of quasi-polynomials |c Sui Sun Cheng, Yi-Zhong Lin |
| 264 | 1 | |a Singapore |b World Scientific |c ©2009 | |
| 300 | |a 1 Online-Ressource (viii, 227 pages) | ||
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| 500 | |a Includes bibliographical references (pages 225-226) and index | ||
| 500 | |a 1. Prologue. 1.1. An example. 1.2. Basic definitions -- 2. Envelopes and dual sets. 2.1. Plane curves. 2.2. Envelopes. 2.3. Dual sets of plane curves. 2.4. Notes -- 3. Dual sets of convex-concave functions. 3.1. Quasi-tangent lines. 3.2. Asymptotes. 3.3. Intersections of quasi-tangent lines and vertical lines. 3.4. Distribution maps for dual points. 3.5. Intersections of dual sets of order 0. 3.6. Notes -- 4. Quasi-polynomials. 4.1. [symbol]- and [symbol]-polynomials. 4.2. Characteristic regions. 4.3. Notes -- 5. C\(0, [symbol])-characteristic regions of real polynomials. 5.1. Quadratic polynomials. 5.2. Cubic polynomials. 5.3. Quartic polynomials. 5.4. Quintic polynomials. 5.5. Notes -- 6. C\(0, [symbol])-characteristic regions of real [symbol]-polynomials. 6.1. [symbol]-polynomials involving one power. 6.2. [symbol]-polynomials involving two powers. 6.3. [symbol]-polynomials involving three powers. 6.4. Notes -- 7. C\R-characteristic regions of [symbol]-polynomials. 7.1. [symbol]-polynomials involving one power. 7.2. [symbol]-polynomials involving two powers. 7.3. [symbol]-polynomials involving three powers. 7.4. Notes | ||
| 500 | |a Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations. For a wide class of functions called quasi-polynomials, the above problems can be transformed into the existence and nonexistence of tangents of the envelope curves associated with the functions under investigation. In this book, we present a formal theory of the Cheng-Lin envelope method, which is completely new, yet simple and precise. This method is both simple - since only basic Calculus concepts are needed for understanding - and precise, since necessary and sufficient conditions can be obtained for functions such as polynomials containing more than four parameters. Since the underlying principles are relatively simple, this book is useful to college students who want to see immediate applications of what they learn in Calculus; to graduate students who want to do research in functional equations; and to researchers who want references on roots of quasi-polynomials encountered in the theory of difference and differential equations | ||
| 650 | 7 | |a MATHEMATICS / Calculus |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Mathematical Analysis |2 bisacsh | |
| 650 | 4 | |a Functions, Special | |
| 650 | 4 | |a Polynomials | |
| 700 | 1 | |a Lin, Yi-Zhong |e Sonstige |4 oth | |
| 710 | 2 | |a World Scientific (Firm) |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804175600955424768 |
|---|---|
| any_adam_object | |
| author | Cheng, S. S., (Sui Sun) |
| author_facet | Cheng, S. S., (Sui Sun) |
| author_role | aut |
| author_sort | Cheng, S. S., (Sui Sun) |
| author_variant | s s s s c ssss ssssc |
| building | Verbundindex |
| bvnumber | BV043146337 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)613343373 (DE-599)BVBBV043146337 |
| dewey-full | 515.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.5 |
| dewey-search | 515.5 |
| dewey-sort | 3515.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043146337 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:52Z |
| institution | BVB |
| isbn | 9789814277273 9789814277280 9814277274 9814277282 |
| language | English |
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| spelling | Cheng, S. S., (Sui Sun) Verfasser aut Dual sets of envelopes and characteristic regions of quasi-polynomials Sui Sun Cheng, Yi-Zhong Lin Singapore World Scientific ©2009 1 Online-Ressource (viii, 227 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 225-226) and index 1. Prologue. 1.1. An example. 1.2. Basic definitions -- 2. Envelopes and dual sets. 2.1. Plane curves. 2.2. Envelopes. 2.3. Dual sets of plane curves. 2.4. Notes -- 3. Dual sets of convex-concave functions. 3.1. Quasi-tangent lines. 3.2. Asymptotes. 3.3. Intersections of quasi-tangent lines and vertical lines. 3.4. Distribution maps for dual points. 3.5. Intersections of dual sets of order 0. 3.6. Notes -- 4. Quasi-polynomials. 4.1. [symbol]- and [symbol]-polynomials. 4.2. Characteristic regions. 4.3. Notes -- 5. C\(0, [symbol])-characteristic regions of real polynomials. 5.1. Quadratic polynomials. 5.2. Cubic polynomials. 5.3. Quartic polynomials. 5.4. Quintic polynomials. 5.5. Notes -- 6. C\(0, [symbol])-characteristic regions of real [symbol]-polynomials. 6.1. [symbol]-polynomials involving one power. 6.2. [symbol]-polynomials involving two powers. 6.3. [symbol]-polynomials involving three powers. 6.4. Notes -- 7. C\R-characteristic regions of [symbol]-polynomials. 7.1. [symbol]-polynomials involving one power. 7.2. [symbol]-polynomials involving two powers. 7.3. [symbol]-polynomials involving three powers. 7.4. Notes Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations. For a wide class of functions called quasi-polynomials, the above problems can be transformed into the existence and nonexistence of tangents of the envelope curves associated with the functions under investigation. In this book, we present a formal theory of the Cheng-Lin envelope method, which is completely new, yet simple and precise. This method is both simple - since only basic Calculus concepts are needed for understanding - and precise, since necessary and sufficient conditions can be obtained for functions such as polynomials containing more than four parameters. Since the underlying principles are relatively simple, this book is useful to college students who want to see immediate applications of what they learn in Calculus; to graduate students who want to do research in functional equations; and to researchers who want references on roots of quasi-polynomials encountered in the theory of difference and differential equations MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Functions, Special Polynomials Lin, Yi-Zhong Sonstige oth World Scientific (Firm) Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=305323 Aggregator Volltext |
| spellingShingle | Cheng, S. S., (Sui Sun) Dual sets of envelopes and characteristic regions of quasi-polynomials MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Functions, Special Polynomials |
| title | Dual sets of envelopes and characteristic regions of quasi-polynomials |
| title_auth | Dual sets of envelopes and characteristic regions of quasi-polynomials |
| title_exact_search | Dual sets of envelopes and characteristic regions of quasi-polynomials |
| title_full | Dual sets of envelopes and characteristic regions of quasi-polynomials Sui Sun Cheng, Yi-Zhong Lin |
| title_fullStr | Dual sets of envelopes and characteristic regions of quasi-polynomials Sui Sun Cheng, Yi-Zhong Lin |
| title_full_unstemmed | Dual sets of envelopes and characteristic regions of quasi-polynomials Sui Sun Cheng, Yi-Zhong Lin |
| title_short | Dual sets of envelopes and characteristic regions of quasi-polynomials |
| title_sort | dual sets of envelopes and characteristic regions of quasi polynomials |
| topic | MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Functions, Special Polynomials |
| topic_facet | MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Functions, Special Polynomials |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=305323 |
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