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【转贴】(英-Math)On Riemann’s Theory Of Algebraic Functions
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(英-Math)On Riemann’s Theory Of Algebraic Functions Djvu with OCR, 1.64 MB pages 60-62 http://www.filefactory.com/file/a9740d/n/onriemannstheory_djvu http://rapidshare.com/files/1430 ... lgebraic_Functions_< wind_code_2 > On Riemann’s Theory Of Algebraic Functions By Felix Klein Publisher: Rough Draft Printing Number Of Pages: 96 Publication Date: 2007-10-19 ISBN-10 / ASIN: 1603860541 ISBN-13 / EAN: 9781603860543 Binding: Paperback Originally Titled: On Riemann’s Theory Of Algebraic Functions And Their Integrals; A Supplement To The Usual Treatises - From The Unabridged Translation By Frances Hardcastle CONTENTS: PART I. INTRODUCTORY REMARKS. SECT. PAGE 1. Steady Streamings in the Plane as an Interpretation of the Functions of x iy 1 2. Consideration of the Infinities of w=f(z) …. 5 3. Kational Functions and their Integrals. Derivation of the Infinities of higher Order from those of lower Order . 9 4. Experimental Production of these Streamings . . . 12 5. Transition to the Surface of a Sphere. Streamings on arbitrary curved Surfaces . . . . . . 15 6. Connection between the foregoing Theory and the Functions of a complex Argument 19 7. Streamings on the Sphere resumed. Riemann’s general Problem 21 PART II. RIEMANN’S THEORY. 8. Classification of closed Surfaces according to the Value of the Integer p 23 9. Preliminary Determination of steady Streamings on arbitrary Surfaces 26 10. The most general steady Streaming. Proof of the Impossi- bility of other Streamings 29 11. Illustration of the Streamings by means of Examples . . 32 12. On the Composition of the most general Function of Position from single Summands 37 13. On the Multiformity of the Functions. Special Treatment of multiform Functions 40 14. The ordinary Riemann’s Surfaces over the x iy Plane . 43 15. The Anchor-ring, p=I, and the two-sheeted Surface over the Plane with four Branch-points 46 16. Functions of x iy which correspond to the Streamings already investigated 51 17. Scope and Significance of the previous Investigations . . 55 18. Extension of the Theory 56 PART III. CONCLUSIONS. 19. On the Moduli of Algebraical Equations …. 59 20. Conformal Representation of closed Surfaces upon themselves 64 21. Special Treatment of symmetrical Surfaces …. 66 22. Conformal Representation of different closed Surfaces upon each other 70 23. Surfaces with Boundaries and unifacial Surfaces … 72 24. Conclusion 75 [ Last edited by laizuliang on 2008-9-12 at 12:45 ] |
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