Anwendungen der Graphentheorie by Hansjoachim Walther PDF

By Hansjoachim Walther

Das vorgelegte Buch setzt die von Professor HORST SACHS geschriebenen Bucher "Einfuhrung in die Theorie der endlichen Graphen" I (1970), II (1972) castle und rundet sie durch seinen Anwendungscharakter abo Es wendet sich an Studierende aller Fachrichtungen, die sich mit mathematischen Methoden der Operations forschung beschaftigen, aber auch an Absolventen und Praktiker, um ihnen ein Handwerkszeug zu vermitteln, das ihnen bei der Modellierung und Losung von firms- und Optimierungsproblemen mit vornehmlich kombinatorischer Komponente helfen wird. Anwendung der Graphentheorie hat zwei Aspekte: Sie iet einerseits angewandte Graphentheorie, wobei im Vordergrund die numerische Ermittlung charakteristi scher GroJ3en eines vorgegebenen Graphen steht (z. B. die Frage, wie guy in einem Graphen eine minimale Bogenmenge finden kann, nach deren Entfernung der Graph kreisfrei ist; vgl. Kap. 9); sie ist andererseits Anwendung von Satzen und Algorithmen der Graphentheorie in anderen Wissensgebieten (bei der Festlegung einer optimalen Berechnungsfolge in einem Algorithmus spielen z. B. Schleifen eine entscheidende Rolle, und guy fragt, wie viele Ruckkehrbogen zerschnitten werden mussen, um die Abarbeitung schleifenfrei zu realisieren; vgl. ebenfalls Kap. 9). Beide Aspekte sind voneinander nicht zu trennen und finden im Buch ihren Niederschlag. In der kurz gehaltenen Einleitung werden die notwendigsten Begriffe der Graphentheorie zusammengestellt, die dann standig verwendet werden. Begriffe, die nur in einem Kapitel benotigt werden, werden dort definiert. Kapitel 1 legt die Grundlage fur aIle Kapitel, in denen wir es mit Stromproblemen zu tun haben; alle anderen Kapitel sind im wesentlichen unabhangig voneinander lesbar.

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In the first case, developed by Euler, there are no external forces, and the center of mass is fixed within the body. This is the case that describes the motion of the earth. In the second case, derived by Lagrange, the fixed point and the center of gravity both lie on the axis of symmetry of the body. This case describes the motion of the top. Sofya Kovalevsky developed the first of the solvable special cases for an unsymmetrical top. In this case the center of mass is no longer on an axis in the body.

Tidskr. 25/26 (1978), 5–32. 18. J. L¨utzen, Euler’s vision of a generalized partial differential calculus for a generalized kind of function, Math. Mag. 56 (1983), 299–306. 19. N. Luzin, Function (in Russian), The Great Soviet Encyclopedia, 59 (c. 1940), pp. 314–334. 20. A. F. Monna, The concept of function in the nineteenth and twentieth centuries, in particular with regard to the discussion between Baire, Borel and Lebesgue, Arch. Hist. Exact Sci. 9 (1972/73), 57–84. 21. G. H. Moore, Zermelo’s Axiom of Choice: Its Origins, Development, and Influence, Springer-Verlag, 1982.

She wrote to Weierstrass for advice. Weierstrass was excited by this letter, the first he had received from his pupil in three years. However, Kovalevsky’s return to mathematics was delayed by the birth of a daughter, Sofya Vladimirovna, in October 1878. On their return to Russia the Kovalevskys had assumed the obligations of a real marriage. This was done partly as an obligation to Sofya’s parents and partly because of their new politics. It was their feeling to end lying relationships of all kinds, and so the marriage was finally consummated.

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