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| PART I.INTRODUCTORY REMARKS. SECT. 1.Steady Streamings in the Plane as an Interpretation of the Functions of x + iy 2.Consideration of the Infinities of w=f(z) 3.Rational Functions and their Integrals.Derivation of the Infinities of higher Order from those of lower Order 4.Experimental Production of these Streamings 5.Transition to the Surface of a Sphere.Streamings on arbitrary curved Surfaces 6.Connection between the foregoing Theory and the Functions of a complex Argument 7.Streamings on the Sphere resumed.Riemann's general Problem PART II. RIEMANN'S THEORY 8.Classification of closed Surfaces according to the Value of the Integer p 9.Preliminary Determination of steady Streamings on arbitrary Surikces 10.The most general steady Streaming.Proof of the Impossi- bility of other Streamings 11.Illustration of the Streamings by means of Examples 12.On the Composition of the most general Function of Position from single Summands 13.On the Multiformity of the Functions.Special Treatment of multiform Functions 14.The ordinary Riemann's Surfaces over the x+iy Plane 15.The Anchor-ring, n=1, and the two-sheeted Surface over the Plane with four Branch-points. 16.Functions of x+iy which correspond to the Streamings already investigated 17.Scope and Significance of the previous Investigations 18.Extension of the Theory PART III.CONCLUSIONS. 19.On the Moduli of Algebraical Equations 20.Conformal Representation of closed Surfaces upon themselves 21.Special Treatment of symmetrical Surfaces 22.Conformal Representation of different closed Surfaces upon each other 23.Surfaces with Boundaries and unifacial Surfaces 24.Conclusion |
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