Dual sets of envelopes and characteristic regions of quasi-polynomials
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 asso...
Saved in:
| Main Authors | , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
New Jersey
World Scientific Publishing Co. Pte. Ltd
2009
World Scientific World Scientific Publishing Company WORLD SCIENTIFIC |
| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9814277274 9789814277273 9789814277280 9814277282 |
| DOI | 10.1142/7338 |
Cover
| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. 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. |
| Author | Cheng, Sui Sun Lin, Yi-Zhong |
| Author_xml | – sequence: 1 fullname: Cheng, Sui Sun – sequence: 2 fullname: Cheng, Sui Sun – sequence: 3 fullname: Lin, Yi-Zhong |
| BackLink | https://cir.nii.ac.jp/crid/1130000794277805184$$DView record in CiNii |
| BookMark | eNo1kElPwzAQhY1YxNZfwCUHhOBQiLfYPkJZJSSQQHC0HGdaDMFO7RTEv8ehZQ7zNJrvvcPbRRs-eEBoH5enGDNyJiiVa2ikhFQy30IQWa6j3f9DsC20U2FKGaWCbqNRSu9lHspVydkOur5cmLZI0KciTAvwX9CGDlJhfFPYNxON7SG61DtbRJi54P-4-cIkN-5C--PDpzNt2keb0ywwWukeerm-ep7cju8fbu4m5_djw7lUYixxzZmQEhTlghBScQslblhDsW1MVUPFuGxKqiqhqlryijSY8YZIWQkLNaZ76GQZ_B1i2yTrwPdu6qyuQ_hIGpd6aEUPrWT2aMl2McwXkHoNA2WzJZpWX11MmBCY8AwerECILczCKkwyRaTI38Pl1zunrRs2xnQoUaihY1lyLFnGjpeYm3WLunXpzfmZ7qL7NPFHvz49Ti6yBWcP_QUiZ3-T |
| ContentType | eBook Book |
| DBID | WMAQA RYH YSPEL |
| DEWEY | 515/.5 |
| DOI | 10.1142/7338 |
| DatabaseName | World Scientific CiNii Complete Perlego |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISBN | 9789814277280 9814277282 9789814467599 9814467596 |
| Edition | 1 |
| ExternalDocumentID | 10.1142/7338 EBC477125 849287 BA91410075 WSPCB0001794 |
| Genre | Electronic books |
| GroupedDBID | -VQ -VX 089 20A 38. 92K 9WS A4I A4J AABBV AATMT ABARN ABCYV ABIAV ABMRC ABQPQ ACBYE ACLGV ACZWY ADVEM AERYV AFOJC AHWGJ AIXPE AJFER AKHYG ALMA_UNASSIGNED_HOLDINGS ALUEM AMYDA AZZ BBABE CZZ DUGUG EBSCA ECOWB GEOUK HF4 IWG J-X JJU MYL PE2 PQQKQ PVBBV TM9 WMAQA XI1 YSPEL RYH AVGCG |
| ID | FETCH-LOGICAL-a55897-81b54788e935722265ce01d4d31cda6be6458d0396796b8562d145d28867ceb13 |
| ISBN | 9814277274 9789814277273 9789814277280 9814277282 |
| IngestDate | Sat Mar 08 06:22:53 EST 2025 Wed Oct 01 01:19:58 EDT 2025 Tue Sep 30 18:31:17 EDT 2025 Thu Jun 26 21:24:31 EDT 2025 Mon Apr 07 05:00:56 EDT 2025 |
| IsPeerReviewed | false |
| IsScholarly | false |
| Keywords | Polynomial Root Quasi-Polynomial Function with Parameters Characteristic Function Characteristic Region Envelope Dual Point Dual Set |
| LCCallNum | QA351 |
| LCCallNum_Ident | QA351 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-a55897-81b54788e935722265ce01d4d31cda6be6458d0396796b8562d145d28867ceb13 |
| Notes | Includes bibliographical references and index |
| OCLC | 613343373 |
| PQID | EBC477125 |
| PageCount | 236 |
| ParticipantIDs | proquest_ebookcentral_EBC477125 nii_cinii_1130000794277805184 worldscientific_books_10_1142_7338 perlego_books_849287 igpublishing_primary_WSPCB0001794 |
| ProviderPackageCode | J-X |
| PublicationCentury | 2000 |
| PublicationDate | 2009. c2009 2009 20090500 |
| PublicationDateYYYYMMDD | 2009-01-01 2009-05-01 |
| PublicationDate_xml | – year: 2009 text: 2009 |
| PublicationDecade | 2000 |
| PublicationPlace | New Jersey |
| PublicationPlace_xml | – name: New Jersey – name: Singapore |
| PublicationYear | 2009 |
| Publisher | World Scientific Publishing Co. Pte. Ltd World Scientific World Scientific Publishing Company WORLD SCIENTIFIC |
| Publisher_xml | – name: World Scientific Publishing Co. Pte. Ltd – name: World Scientific – name: World Scientific Publishing Company – name: WORLD SCIENTIFIC |
| SSID | ssj0000359054 |
| Score | 1.9058626 |
| Snippet | Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations. For a wide class of... |
| SourceID | worldscientific proquest perlego nii igpublishing |
| SourceType | Publisher |
| SubjectTerms | Functions, Special General Mathematics Mathematical Logic and Foundations Numerical & Computational Mathematics Polynomials Pure Mathematics SCIENCE |
| SubjectTermsDisplay | Functions, Special Polynomials |
| TableOfContents | Dual sets of envelopes and characteristic regions of quasi-polynomials -- Preface -- Contents -- Chapter 1: Prologue -- Chapter 2: Envelopes and Dual Sets -- Chapter 3: Dual Sets of Convex-Concave Functions -- Chapter 4: Quasi-Polynomials -- Chapter 5: C; (0,)-Characteristic Regions of Real Polynomials -- Chapter 6: C; (0,)-Characteristic Regions of Real -Polynomials -- Chapter 7: C; R-Characteristic Regions of -Polynomials -- Appendix A: Intersections of Dual Sets of Order 0 -- Bibliography -- Index Intro -- Contents -- Preface -- 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 - and -Polynomials -- 4.2 Characteristic Regions -- 4.3 Notes -- 5. C\(0, )-Characteristic Regions of Real Polynomials -- 5.1 Quadratic Polynomials -- 5.2 Cubic Polynomials -- 5.3 Quartic Polynomials -- 5.3.1 First Description -- 5.3.2 Second Description -- 5.4 Quintic Polynomials -- 5.5 Notes -- 6. C\(0,1)-Characteristic Regions of Real -Polynomials -- 6.1 -Polynomials Involving One Power -- 6.1.1 (1, 0)-Polynomials -- 6.1.2 (0, 1)-Polynomials -- 6.1.3 (1, 1)-Polynomials -- 6.2 -Polynomials Involving Two Powers -- 6.2.1 (0, 0, 0)-Polynomials -- 6.2.2 (1, 0, 0)-Polynomials -- 6.2.3 (1, 1, 0)-Polynomials I . -- 6.2.4 (1, 1, 0)-Polynomials II -- 6.2.5 (n, n, 0)-Polynomials -- 6.3 -Polynomials Involving Three Powers -- 6.3.1 The Case 0 < -- < -- < -- -- 6.3.2 The Case < -- < -- < -- -1 -- 6.4 Notes -- 7. C\R-Characteristic Regions of r-Polynomials -- 7.1 r-Polynomials Involving One Power -- 7.1.1 (0, 0)-Polynomials -- 7.1.2 (1, 0)-Polynomials -- 7.1.3 (0, 1)-Polynomials -- 7.1.4 (1, 1)-Polynomials -- 7.1.5 (n, n)-Polynomials -- 7.2 -Polynomials Involving Two Powers -- 7.2.1 (0, 0, 0)-Polynomials -- 7.2.2 (1, 0, 0)-Polynomials -- 7.2.3 (1, 1, 0)-Polynomials -- 7.2.4 (n, n, 0)-Polynomials -- 7.3 r-Polynomials Involving Three Powers -- 7.3.1 (0, 0, 0, 0)-Polynomials -- 7.3.2 (1, 0, 0, 0)-Polynomials -- 7.4 Notes Appendix A Intersections of Dual Sets of Order 0 -- A.1 Intersections of Dual Sets of Order 0 -- Bibliography -- Index |
| Title | Dual sets of envelopes and characteristic regions of quasi-polynomials |
| URI | http://portal.igpublish.com/iglibrary/search/WSPCB0001794.html https://cir.nii.ac.jp/crid/1130000794277805184 https://www.perlego.com/book/849287/dual-sets-of-envelopes-and-characteristic-regions-of-quasipolynomials-pdf https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=477125 https://www.worldscientific.com/doi/10.1142/7338 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3fb9MwED6xIiGYNAED0bFBQLyhsKRxEvtx7TpNSEVIDBi8RHF83SJVSVnaB_jruYu9dC2TEDzUapIqVu5zfT9y9x3Am1BorY00fq608bls1tdRXPiImvuLJJHQHBqYfEhOP4v35_H5qqVhW12y0O-KX7fWlfwPqnSOcOUq2X9AtrspnaDvhC-NhDCNG8Zvd2jBPeaijwZtHgZWbd4PWrblYo2B-S03XnCpbj-WeVP683r2k0uR81lnTY8u0QWNlyV9Vkk6ll_gW-l_v6ydhrsOEKiNAIFNyml3ijb7aM2BVDIUg5RtmNu3U8H0rGlkCVg2iKmHR4qTRMnm2IKtNA16cJdU6XjShbiYHZAsQktztJqJfOPuQNyDbTfRIU_DhLEX8y4ARwq_KktyTeZ4NcOLes0N2Gk5ZZvuwW7YBWcPoce1Io_gDlaP4cGko8BtduGEMfIYI6-eeh1GHmHkrWPkOYz4d39g9AS-nIzPRqe-a1rh53EsFan8UDNHmkQVxSlZX0lcYBAaYaKwMHmiMRGxNEGkOIKnJdmfJhSxGUiZpAVpzugp9Kq6wmfgiaBIwild13LKXWFyzFHJaUB_IFQ40H14dVNa2dwSlGRfP30cDVsqJCX6cEAizIqSx5BfXhJiiqUvaT-WdH3XCTfjpdxkUijyovvw8lrSWfva3uUKZ-PhSKQpmcV9eL0BgLuBLXUfZIzn3l9mfw73V0t2H3qLqyUekJW30C_cavoN9nVLXw |
| linkProvider | ProQuest Ebooks |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.title=Dual+sets+of+envelopes+and+characteristic+regions+of+quasi-polynomials&rft.au=Cheng%2C+Sui+Sun&rft.au=Lin%2C+Yi-Zhong&rft.date=2009-01-01&rft.pub=World+Scientific&rft.isbn=9789814277273&rft_id=info:doi/10.1142%2F7338&rft.externalDocID=BA91410075 |
| thumbnail_l | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fwww.perlego.com%2Fbooks%2FRM_Books%2Fworld_scientific_pub_rlpceeul%2F9789814277280.jpg |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fportal.igpublish.com%2Figlibrary%2Famazonbuffer%2FWSPCB0001794_null_0_320.png http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fwww.worldscientific.com%2Faction%2FshowCoverImage%3Fdoi%3D10.1142%2F7338 |