Continued fractions /:
This book is the first authoritative and up-to-date survey of the history of Iraq from earliest times to the present in any language. It presents a concise narrative of the rich and varied history of this land, drawing on political, social, economic, artistic, technological, and intellectual materia...
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| Sprache: | English |
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Hackensack, N.J. :
World Scientific,
©2006.
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| Zusammenfassung: | This book is the first authoritative and up-to-date survey of the history of Iraq from earliest times to the present in any language. It presents a concise narrative of the rich and varied history of this land, drawing on political, social, economic, artistic, technological, and intellectual material. It also includes excerpts from works of ancient, medieval, and modern literature written in Iraq, some of which are translated for the first time into English. The final chapters provide an introduction to the history of archaeology in Iraq, set in the wider context of the development of archaeology into a scientific discipline. A special section highlights selected objects from the Iraq Museum, with emphasis on their cultural significance and current status in the aftermath of the looting in April 2003. The last chapter offers a unique guide to the complex international and national legal regimes for the protection of cultural heritage. The American-led invasion and occupation of Iraq are a turning point in Iraq's modern history, with important cultural consequences for all periods of its past. For all who seek to understand more fully the current situation, this book includes discussion of cultural and legal issues of the war and occupation, placing recent events in their full context. |
| Beschreibung: | 1 online resource (xii, 245 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9812774688 9789812774682 1281919632 9781281919632 9786611919634 6611919635 |
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| 520 | |a This book is the first authoritative and up-to-date survey of the history of Iraq from earliest times to the present in any language. It presents a concise narrative of the rich and varied history of this land, drawing on political, social, economic, artistic, technological, and intellectual material. It also includes excerpts from works of ancient, medieval, and modern literature written in Iraq, some of which are translated for the first time into English. The final chapters provide an introduction to the history of archaeology in Iraq, set in the wider context of the development of archaeology into a scientific discipline. A special section highlights selected objects from the Iraq Museum, with emphasis on their cultural significance and current status in the aftermath of the looting in April 2003. The last chapter offers a unique guide to the complex international and national legal regimes for the protection of cultural heritage. The American-led invasion and occupation of Iraq are a turning point in Iraq's modern history, with important cultural consequences for all periods of its past. For all who seek to understand more fully the current situation, this book includes discussion of cultural and legal issues of the war and occupation, placing recent events in their full context. | ||
| 505 | 0 | |a Preface -- 1. Introduction. 1.1. The additive subgroup of the integers generated by a and b. 1.2. Continuants. 1.3. The continued fraction expansion of a real number. 1.4. Quadratic irrationals. 1.5. The tree of continued fraction expansions. 1.6. Diophantine approximation. 1.7. Other known continued fraction expansions -- 2. Generalizations of the gcd and the Euclidean algorithm. 2.1. Other gcd's. 2.2. Continued fraction expansions for complex numbers. 2.3. The lattice reduction algorithm of Gauss -- 3. Continued fractions with small partial quotients. 3.1. The sequence ({n[symbol]}) of multiples of a number. 3.2. Discrepancy. 3.3. The sum of {n[symbol]} from 1 to N -- 4. Ergodic theory. 4.1. Ergodic maps. 4.2. Terminology. 4.3. Nair's proof. 4.4. Generalization to E[symbol]. 4.5. A Natural extension of the dynamic system (E[symbol], [symbol], T) -- 5. Complex continued fractions. 5.1. The Schmidt regular chains algorithm. 5.2. The Hurwitz complex continued fraction. 5.3. Notation. 5.4. Growth of |qn| and the quality of the Hurwitz approximations. 5.5. Distribution of the remainders. 5.6. A class of algebraic approximants with atypical Hurwitz continued fraction expansions. 5.7. The Gauss-Kuz'min density for the Hurwitz algorithm -- 6. Multidimensional diophantine approximation. 6.1. The Hermite approximations to a real number. 6.2. The Lagarias algorithm in higher dimensions. 6.3. Convexity of expansion domains in the Lagarias algorithm -- 7. Powers of an algebraic integer. 7.1. Introduction. 7.2. Outline and plan of proof. 7.3. Proof of the existence of a unit [symbol][symbol][symbol]([symbol]) oF degree n. 7.4. The sequence v[k] of units with comparable conjugates. 7.5. Good units and good denominators. 7.6. Ratios of consecutive good q. 7.7. The surfaces associated with the scaled errors. 7.8. The general case of algebraic numbers in Q([symbol]) -- 8. Marshall Hall's theorem. 8.1. The binary trees of E[symbol]. 8.2. Sums of bridges covering [[symbol], [symbol]]. 8.3. The Lagrange and Markoff spectra -- 9. Functional-analytic techniques. 9.1. Continued fraction cantor sets. 9.2. Spaces and operators. 9.3. Positive operators. 9.4. An integral representation of g[symbol]. 9.5. A Hilbert space structure for G when s = [symbol] is real. 9.6. The uniform spectral gap. 9.7. Log convexity of [symbol][symbol] -- 10. The generating function method. 10.1. Entropy. 10.2. Notation. 10.3. A sampling of results -- 11. Conformal iterated function systems -- 12. Convergence of continued fractions. 12.1. Some general results and techniques. 12.2. Special analytic continued fractions. | |
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| author | Hensley, Doug (Douglas Austin), 1949- |
| author_GND | http://id.loc.gov/authorities/names/no2006094087 |
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| contents | Preface -- 1. Introduction. 1.1. The additive subgroup of the integers generated by a and b. 1.2. Continuants. 1.3. The continued fraction expansion of a real number. 1.4. Quadratic irrationals. 1.5. The tree of continued fraction expansions. 1.6. Diophantine approximation. 1.7. Other known continued fraction expansions -- 2. Generalizations of the gcd and the Euclidean algorithm. 2.1. Other gcd's. 2.2. Continued fraction expansions for complex numbers. 2.3. The lattice reduction algorithm of Gauss -- 3. Continued fractions with small partial quotients. 3.1. The sequence ({n[symbol]}) of multiples of a number. 3.2. Discrepancy. 3.3. The sum of {n[symbol]} from 1 to N -- 4. Ergodic theory. 4.1. Ergodic maps. 4.2. Terminology. 4.3. Nair's proof. 4.4. Generalization to E[symbol]. 4.5. A Natural extension of the dynamic system (E[symbol], [symbol], T) -- 5. Complex continued fractions. 5.1. The Schmidt regular chains algorithm. 5.2. The Hurwitz complex continued fraction. 5.3. Notation. 5.4. Growth of |qn| and the quality of the Hurwitz approximations. 5.5. Distribution of the remainders. 5.6. A class of algebraic approximants with atypical Hurwitz continued fraction expansions. 5.7. The Gauss-Kuz'min density for the Hurwitz algorithm -- 6. Multidimensional diophantine approximation. 6.1. The Hermite approximations to a real number. 6.2. The Lagarias algorithm in higher dimensions. 6.3. Convexity of expansion domains in the Lagarias algorithm -- 7. Powers of an algebraic integer. 7.1. Introduction. 7.2. Outline and plan of proof. 7.3. Proof of the existence of a unit [symbol][symbol][symbol]([symbol]) oF degree n. 7.4. The sequence v[k] of units with comparable conjugates. 7.5. Good units and good denominators. 7.6. Ratios of consecutive good q. 7.7. The surfaces associated with the scaled errors. 7.8. The general case of algebraic numbers in Q([symbol]) -- 8. Marshall Hall's theorem. 8.1. The binary trees of E[symbol]. 8.2. Sums of bridges covering [[symbol], [symbol]]. 8.3. The Lagrange and Markoff spectra -- 9. Functional-analytic techniques. 9.1. Continued fraction cantor sets. 9.2. Spaces and operators. 9.3. Positive operators. 9.4. An integral representation of g[symbol]. 9.5. A Hilbert space structure for G when s = [symbol] is real. 9.6. The uniform spectral gap. 9.7. Log convexity of [symbol][symbol] -- 10. The generating function method. 10.1. Entropy. 10.2. Notation. 10.3. A sampling of results -- 11. Conformal iterated function systems -- 12. Convergence of continued fractions. 12.1. Some general results and techniques. 12.2. Special analytic continued fractions. |
| ctrlnum | (OCoLC)560445154 |
| dewey-full | 515.243 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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It presents a concise narrative of the rich and varied history of this land, drawing on political, social, economic, artistic, technological, and intellectual material. It also includes excerpts from works of ancient, medieval, and modern literature written in Iraq, some of which are translated for the first time into English. The final chapters provide an introduction to the history of archaeology in Iraq, set in the wider context of the development of archaeology into a scientific discipline. A special section highlights selected objects from the Iraq Museum, with emphasis on their cultural significance and current status in the aftermath of the looting in April 2003. The last chapter offers a unique guide to the complex international and national legal regimes for the protection of cultural heritage. The American-led invasion and occupation of Iraq are a turning point in Iraq's modern history, with important cultural consequences for all periods of its past. For all who seek to understand more fully the current situation, this book includes discussion of cultural and legal issues of the war and occupation, placing recent events in their full context.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Preface -- 1. Introduction. 1.1. The additive subgroup of the integers generated by a and b. 1.2. Continuants. 1.3. The continued fraction expansion of a real number. 1.4. Quadratic irrationals. 1.5. The tree of continued fraction expansions. 1.6. Diophantine approximation. 1.7. Other known continued fraction expansions -- 2. Generalizations of the gcd and the Euclidean algorithm. 2.1. Other gcd's. 2.2. Continued fraction expansions for complex numbers. 2.3. The lattice reduction algorithm of Gauss -- 3. Continued fractions with small partial quotients. 3.1. The sequence ({n[symbol]}) of multiples of a number. 3.2. Discrepancy. 3.3. The sum of {n[symbol]} from 1 to N -- 4. Ergodic theory. 4.1. Ergodic maps. 4.2. Terminology. 4.3. Nair's proof. 4.4. Generalization to E[symbol]. 4.5. A Natural extension of the dynamic system (E[symbol], [symbol], T) -- 5. Complex continued fractions. 5.1. The Schmidt regular chains algorithm. 5.2. The Hurwitz complex continued fraction. 5.3. Notation. 5.4. Growth of |qn| and the quality of the Hurwitz approximations. 5.5. Distribution of the remainders. 5.6. A class of algebraic approximants with atypical Hurwitz continued fraction expansions. 5.7. The Gauss-Kuz'min density for the Hurwitz algorithm -- 6. Multidimensional diophantine approximation. 6.1. The Hermite approximations to a real number. 6.2. The Lagarias algorithm in higher dimensions. 6.3. Convexity of expansion domains in the Lagarias algorithm -- 7. Powers of an algebraic integer. 7.1. Introduction. 7.2. Outline and plan of proof. 7.3. Proof of the existence of a unit [symbol][symbol][symbol]([symbol]) oF degree n. 7.4. The sequence v[k] of units with comparable conjugates. 7.5. Good units and good denominators. 7.6. Ratios of consecutive good q. 7.7. The surfaces associated with the scaled errors. 7.8. The general case of algebraic numbers in Q([symbol]) -- 8. Marshall Hall's theorem. 8.1. The binary trees of E[symbol]. 8.2. Sums of bridges covering [[symbol], [symbol]]. 8.3. The Lagrange and Markoff spectra -- 9. Functional-analytic techniques. 9.1. Continued fraction cantor sets. 9.2. Spaces and operators. 9.3. Positive operators. 9.4. An integral representation of g[symbol]. 9.5. A Hilbert space structure for G when s = [symbol] is real. 9.6. The uniform spectral gap. 9.7. Log convexity of [symbol][symbol] -- 10. The generating function method. 10.1. Entropy. 10.2. Notation. 10.3. A sampling of results -- 11. Conformal iterated function systems -- 12. Convergence of continued fractions. 12.1. Some general results and techniques. 12.2. 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| id | ZDB-4-EBA-ocn560445154 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:17:00Z |
| institution | BVB |
| isbn | 9812774688 9789812774682 1281919632 9781281919632 9786611919634 6611919635 |
| language | English |
| oclc_num | 560445154 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xii, 245 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Hensley, Doug (Douglas Austin), 1949- http://id.loc.gov/authorities/names/no2006094087 Continued fractions / Doug Hensley. Hackensack, N.J. : World Scientific, ©2006. 1 online resource (xii, 245 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references and index. Print version record. This book is the first authoritative and up-to-date survey of the history of Iraq from earliest times to the present in any language. It presents a concise narrative of the rich and varied history of this land, drawing on political, social, economic, artistic, technological, and intellectual material. It also includes excerpts from works of ancient, medieval, and modern literature written in Iraq, some of which are translated for the first time into English. The final chapters provide an introduction to the history of archaeology in Iraq, set in the wider context of the development of archaeology into a scientific discipline. A special section highlights selected objects from the Iraq Museum, with emphasis on their cultural significance and current status in the aftermath of the looting in April 2003. The last chapter offers a unique guide to the complex international and national legal regimes for the protection of cultural heritage. The American-led invasion and occupation of Iraq are a turning point in Iraq's modern history, with important cultural consequences for all periods of its past. For all who seek to understand more fully the current situation, this book includes discussion of cultural and legal issues of the war and occupation, placing recent events in their full context. Preface -- 1. Introduction. 1.1. The additive subgroup of the integers generated by a and b. 1.2. Continuants. 1.3. The continued fraction expansion of a real number. 1.4. Quadratic irrationals. 1.5. The tree of continued fraction expansions. 1.6. Diophantine approximation. 1.7. Other known continued fraction expansions -- 2. Generalizations of the gcd and the Euclidean algorithm. 2.1. Other gcd's. 2.2. Continued fraction expansions for complex numbers. 2.3. The lattice reduction algorithm of Gauss -- 3. Continued fractions with small partial quotients. 3.1. The sequence ({n[symbol]}) of multiples of a number. 3.2. Discrepancy. 3.3. The sum of {n[symbol]} from 1 to N -- 4. Ergodic theory. 4.1. Ergodic maps. 4.2. Terminology. 4.3. Nair's proof. 4.4. Generalization to E[symbol]. 4.5. A Natural extension of the dynamic system (E[symbol], [symbol], T) -- 5. Complex continued fractions. 5.1. The Schmidt regular chains algorithm. 5.2. The Hurwitz complex continued fraction. 5.3. Notation. 5.4. Growth of |qn| and the quality of the Hurwitz approximations. 5.5. Distribution of the remainders. 5.6. A class of algebraic approximants with atypical Hurwitz continued fraction expansions. 5.7. The Gauss-Kuz'min density for the Hurwitz algorithm -- 6. Multidimensional diophantine approximation. 6.1. The Hermite approximations to a real number. 6.2. The Lagarias algorithm in higher dimensions. 6.3. Convexity of expansion domains in the Lagarias algorithm -- 7. Powers of an algebraic integer. 7.1. Introduction. 7.2. Outline and plan of proof. 7.3. Proof of the existence of a unit [symbol][symbol][symbol]([symbol]) oF degree n. 7.4. The sequence v[k] of units with comparable conjugates. 7.5. Good units and good denominators. 7.6. Ratios of consecutive good q. 7.7. The surfaces associated with the scaled errors. 7.8. The general case of algebraic numbers in Q([symbol]) -- 8. Marshall Hall's theorem. 8.1. The binary trees of E[symbol]. 8.2. Sums of bridges covering [[symbol], [symbol]]. 8.3. The Lagrange and Markoff spectra -- 9. Functional-analytic techniques. 9.1. Continued fraction cantor sets. 9.2. Spaces and operators. 9.3. Positive operators. 9.4. An integral representation of g[symbol]. 9.5. A Hilbert space structure for G when s = [symbol] is real. 9.6. The uniform spectral gap. 9.7. Log convexity of [symbol][symbol] -- 10. The generating function method. 10.1. Entropy. 10.2. Notation. 10.3. A sampling of results -- 11. Conformal iterated function systems -- 12. Convergence of continued fractions. 12.1. Some general results and techniques. 12.2. Special analytic continued fractions. English. Continued fractions. http://id.loc.gov/authorities/subjects/sh85051149 Series. http://id.loc.gov/authorities/subjects/sh85120237 Fractions continues. Séries (Mathématiques) series (mathematics) aat MATHEMATICS Infinity. bisacsh Continued fractions fast Series fast has work: Continued fractions (Text) https://id.oclc.org/worldcat/entity/E39PCGCbjC9GjmVJCdHKR86HqP https://id.oclc.org/worldcat/ontology/hasWork Print version: Hensley, Doug (Douglas Austin), 1949- Continued fractions. Hackensack, N.J. : World Scientific, ©2006 (DLC) 2006281718 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210849 Volltext |
| spellingShingle | Hensley, Doug (Douglas Austin), 1949- Continued fractions / Preface -- 1. Introduction. 1.1. The additive subgroup of the integers generated by a and b. 1.2. Continuants. 1.3. The continued fraction expansion of a real number. 1.4. Quadratic irrationals. 1.5. The tree of continued fraction expansions. 1.6. Diophantine approximation. 1.7. Other known continued fraction expansions -- 2. Generalizations of the gcd and the Euclidean algorithm. 2.1. Other gcd's. 2.2. Continued fraction expansions for complex numbers. 2.3. The lattice reduction algorithm of Gauss -- 3. Continued fractions with small partial quotients. 3.1. The sequence ({n[symbol]}) of multiples of a number. 3.2. Discrepancy. 3.3. The sum of {n[symbol]} from 1 to N -- 4. Ergodic theory. 4.1. Ergodic maps. 4.2. Terminology. 4.3. Nair's proof. 4.4. Generalization to E[symbol]. 4.5. A Natural extension of the dynamic system (E[symbol], [symbol], T) -- 5. Complex continued fractions. 5.1. The Schmidt regular chains algorithm. 5.2. The Hurwitz complex continued fraction. 5.3. Notation. 5.4. Growth of |qn| and the quality of the Hurwitz approximations. 5.5. Distribution of the remainders. 5.6. A class of algebraic approximants with atypical Hurwitz continued fraction expansions. 5.7. The Gauss-Kuz'min density for the Hurwitz algorithm -- 6. Multidimensional diophantine approximation. 6.1. The Hermite approximations to a real number. 6.2. The Lagarias algorithm in higher dimensions. 6.3. Convexity of expansion domains in the Lagarias algorithm -- 7. Powers of an algebraic integer. 7.1. Introduction. 7.2. Outline and plan of proof. 7.3. Proof of the existence of a unit [symbol][symbol][symbol]([symbol]) oF degree n. 7.4. The sequence v[k] of units with comparable conjugates. 7.5. Good units and good denominators. 7.6. Ratios of consecutive good q. 7.7. The surfaces associated with the scaled errors. 7.8. The general case of algebraic numbers in Q([symbol]) -- 8. Marshall Hall's theorem. 8.1. The binary trees of E[symbol]. 8.2. Sums of bridges covering [[symbol], [symbol]]. 8.3. The Lagrange and Markoff spectra -- 9. Functional-analytic techniques. 9.1. Continued fraction cantor sets. 9.2. Spaces and operators. 9.3. Positive operators. 9.4. An integral representation of g[symbol]. 9.5. A Hilbert space structure for G when s = [symbol] is real. 9.6. The uniform spectral gap. 9.7. Log convexity of [symbol][symbol] -- 10. The generating function method. 10.1. Entropy. 10.2. Notation. 10.3. A sampling of results -- 11. Conformal iterated function systems -- 12. Convergence of continued fractions. 12.1. Some general results and techniques. 12.2. Special analytic continued fractions. Continued fractions. http://id.loc.gov/authorities/subjects/sh85051149 Series. http://id.loc.gov/authorities/subjects/sh85120237 Fractions continues. Séries (Mathématiques) series (mathematics) aat MATHEMATICS Infinity. bisacsh Continued fractions fast Series fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85051149 http://id.loc.gov/authorities/subjects/sh85120237 |
| title | Continued fractions / |
| title_auth | Continued fractions / |
| title_exact_search | Continued fractions / |
| title_full | Continued fractions / Doug Hensley. |
| title_fullStr | Continued fractions / Doug Hensley. |
| title_full_unstemmed | Continued fractions / Doug Hensley. |
| title_short | Continued fractions / |
| title_sort | continued fractions |
| topic | Continued fractions. http://id.loc.gov/authorities/subjects/sh85051149 Series. http://id.loc.gov/authorities/subjects/sh85120237 Fractions continues. Séries (Mathématiques) series (mathematics) aat MATHEMATICS Infinity. bisacsh Continued fractions fast Series fast |
| topic_facet | Continued fractions. Series. Fractions continues. Séries (Mathématiques) series (mathematics) MATHEMATICS Infinity. Continued fractions Series |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210849 |
| work_keys_str_mv | AT hensleydoug continuedfractions |