Dynkin graphs and quadrilateral singularities / / Tohsuke Urabe

• Record Nr.: UNISA996466601703316
• Autore: Urabe Tohsuke <1953-2011, >
• Pubbl/distr/stampa: Berlin ; ; Heidelberg : , : Springer-Verlag, , [1993]; ©1993
• ISBN: 3-540-47769-1
• Edizione: [1st ed. 1993.]
• Descrizione fisica: 1 online resource (CCXLVIII, 242 p.)
• Collana: Lecture Notes in Mathematics ; ; Volume 1548
• Disciplina: 516.35
• Soggetti: Singularities (Mathematics); Hypersurfaces
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: Quadrilateral singularities and elliptic K3 surfaces -- Theorems with the Ik-conditions for J 3,0, Z 1,0 and Q 2,0 -- Obstruction components -- Concept of co-root modules.
• Sommario/riassunto: The study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs will attract attention of researches.

Al-Kashi's Miftaḥ al-Ḥisab . Volume 3 : translation and commentary : Algebra / / Nuh Aydin, Lakhdar Hammoudi, Ghada Bakbouk

• Record Nr.: UNISA996466416903316
• Autore: Aydin Nuh
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 3-030-96615-1
• Descrizione fisica: 1 online resource (285 pages)
• Disciplina: 512
• Soggetti: Algebra; Àlgebra; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- Introduction -- A Biography of al-Kashı and a Brief History -- Al-Kashı's Letters: Invaluable Source -- Ulugh Beg in al-Kashı's Letters -- Samarkand in al-Kashı's letters: Center of Knowledge -- List of al-Kashı's Known Works -- Manuscript Copies of Miftah -- Pedagogical Aspects of Miftah -- Possible Future Projects -- Notes on Translation and the Purpose of This Work -- Original Table of Contents of The Fifth Treatise -- The Fifth Treatise -- First Chapter: On Algebra -- First Section: On Definitions and Terminology -- Second Section: On the Addition of Monomials -- Third Section: On Subtraction -- Fourth Section: On Multiplication of Polynomials -- Fifth Section: On the division of terms by each other -- Sixth Section: On the extraction of the roots of these expressions and the square root of any power -- Seventh Section: On Algebraic Problems -- Eight Section: On How to Find the Unknown in the Mentioned Six Known Problems -- Ninth Section: On How to Extract the Unknown -- Tenth Section: On What We Promised to Mention -- Second Chapter: On Finding the Unknown using the Rule of Double False Position -- Third Chapter: On Including some Arithmetic Rules that are much Needed for Finding the Unknowns -- The First Rule -- The Second Rule -- The Third Rule -- The Fourth Rule -- The Fifth Rule -- The Sixth Rule -- The Seventh Rule -- The Eighth Rule -- The Ninth Rule -- The Tenth-Twelfth Rules -- The ; Thirteenth-Fifteenth Rules -- The Sixteenth Rule -- The Seventeenth-Twenty-First Rules -- The Twenty-Second-Twenty-Sixth Rules -- The Twenty-Seventh-Twenty-Ninth Rules -- The Thirtieth-Thirty-Third Rules -- The Thirty-Fourth-Thirty-Seventh Rules -- The Thirty-Eighth-Thirty-Ninth Rules -- The Fortieth-Forty-First Rules -- The Forty-Second-Forty-Fifth Rules -- The Forty-Sixth-Forty-Ninth Rules -- The Fiftieth Rule.; Fourth Chapter: On Examples -- First Section: Twenty-Five Examples -- Second Section: Eight Examples on Wills -- Third Section: Eight Examples in Which the Unknown is Found Using Geometric Rules -- Glossary -- Bibliography.