Riemann b bernhard (3 Ergebnisse)

Leipzig, Johann Ambrosius Barth, 1855. Contemp. hcalf, raised bands, gilt spine. A few scratches to spine. Small stamps to verso of titlepages and verso of plates. In "Annalen der Physik und Chemie. Hrsg. von J.C. Poggendorff", Bd. 95. (Entire volume offered). (2),X,628 pp. and 6 engraved plates, partly folded. Riemann's paper: pp. 130-139. Clean and fine. First appearance of an importent paper in mathematical physics, dealing with the foudations of electricity. Here Riemann uses semiconvergent (asymptotic) series, an approach which motivated the subsequent works of Weber and Henkel. …

Berlin, Georg Reimer, 1857. 4to. Spine gone. Covers loose. In: "Journal für die reine und angewandte Mathematik Crelle/Borchardt", 54. Band. IV,388 pp. (Entire volume offered). Internally clean and fine. The memoir: pp. 115-155. First appearance of these groundbreaking papers on Abelian functions and hypergeometric series, introducing the use of cross cuts to define the n-fold connectivity of a surface and extending many of the ideas from his dissertation of 1851 (Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse). "His famous theory of Abelian functions" the theory itself, ONE OF THE MOST NOTABLE MASTERWORKS OF MATHEMATICS."(DSB)"While four importent papers repeat many of the ideas in his dissertation, they are primarely devoted to Abelian integrals and functions. The fourth paper is the one that gave the subject its major development (Theorie der Abel'schen Functionen). All four were difficilt to understand" "they were a book with seven seals". Fortunately many fine mathematicians later elaborated on and explained the material."(Kline "Mathematical Thought from Ancient to Modern Times", p. 663)"His courses in 1855-1856, in which, he expounded his now famous theory of Abelian functions, were attended by C. A. Bjerknes, Dedekind, and Ernst Schering" the theory itself, one of the most notable masterworks of mathematics, was published in 1857." DSB)Abelian functions were studied by Abel and Jacobi" they are a generalization of elliptic functions. Building on the ideas introduced in his thesis, particularly that of a Riemann surface, Riemann developed a very powerful geometric theory that resolved a number of outstanding problems. This work established Riemann as an important mathematician, but it was not without controversy. Riemann made extensive use, without proof, of a variational principle called the Dirichlet principle. Weierstrass had his doubts about it, and after Riemann's death it fell into disrepute. This state of affairs eventually had fruitful consequences. Several mathematicians successfully found proofs of Riemann's results without using the Dirichlet principle, and the principle itself was given a rigorous proof in 1899 by Hilbert. The three other Riemann-papers (all in first edition) are: 1. "Allgemeine Voraussetzungen und Hülfsmittel für die Untersuchung von Functionen unbeschränkt veränderlichen Grössen", pp. 101-104. - 2. "Lehrsätze aus der analysis situs für die Theorie der Integrale von zweigliedrigen vollständigen Differentialen", pp. 105-110, with 4 textillustr. - 3. "Bestimmung einer Function einer veränderlichen complexen Grösse durch Grenz- und Unstetigkeitsbedingungen.", pp. 111-114.The volume contains further importent mathematical papers by Dedekind, Cayley, Lipschitz, Clebsch.Parkinson "Breakthroughs" 1857 M.…

Leipzig, Johann Ambrosius Barth, 1867. Contemp. hcalf, raised bands, gilt spinewith gilt lettering. A few scratches to binding. In "Annalen der Physik und Chemie. Hrsg.von Poggendorff", Bd. 131. (Entire volume offered). (2),X,660 pp. and 5 engraved plates. Small stamps to verso of titlepage and to verso of plates. Clean and fine. First German edition (which originally appeared the same year in Danish in "Oversigt over det Kongelige Danske Viidenskabernes Selskabs Forhandlinger") of Lorenz' paper, which contains his important studies on the electromagnetic theory of light in which he - less than two years after, but independently of, Maxwell - found that LIGHT MIGHT BE INTERPRETED AS ELECTROMAGNETIC WAVES, and that his equations lead to the CORRECT VALUE FOR THE VELOCITY OF LIGHT. AND: First appearance of RIEMANN'S important paper (issued posthumously) in which he introduces the concept of "RETARDED POTENTIALS". Riemann suggests that Poisson's equation be modified by introducing terms which, though too small to be appreciable in ordinary experiments, would be capable of accounting for the propagation of electrical effects through space with a finite velocity c. This, so far as it goes, is in agreement with the view now accepted as correct."The procedure which Lorenz followed was that of which Riemann had suggested in 1858 (the present paper by Riemann, which was published for the first time in 1867), namely, to modify the accepted formula of electrodynamics by introducing terms which, though too small to be appreciable in ordinary laboratory experiments, would be capable of accounting for the propagation of electrical effects through space with a finite velocity.The (Lorenz-) equations are, however, the fundamental equations of Maxwell's theory" and therefore the theory of L. Lorenz is practically equivalent to that of Maxwell, so far as concerns the propagation of electromagnetic disturbances through free aether.he suggested that ALL LUMINOUS VIBRATIONS MIGHT BE CONSTITUTED BY ELECTRIC CURRENTS, and hence that there was 'no longer any reason for maintaining the hypothesis of an aether, since we can admit that space contains sufficient ponderable matter to enable the disturbance to be propagated" (Edmund Whittaker in "A History of the Theories of Aether and Electricity I", p. 267-70)."Maxwell seems to have considered the great paper of L. Lorenz on retarded potentials (published simultaneously in 1867 with a paper written in 1858 by B. Riemann on the same theme) as insufficiently supportive of his vision of a dynamical theory of theelectromagnetic field, whereas the present attitude is that Riemann and Lorenz made important contributions to the Maxwellian view." (Kirk T. McDonald in "Maxwell's Objection to Lorenz' Retarded Potentials").…