H. Hamburger: Uber Kurvennetze mit isolierten Singularitaten auf geschlossenen Flachen. Mathematische Zeitschrift 19 (1924) 50-66.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of S, then the index of the umbilic point p is defined as times the increase of the angle of L 1 (x) or L 2 (x) when x runs once around p, along a small loop and in the positive direction with respect to the orientation of S. See Blaschke [1, p. 287] the original definition of Hamburger [3] is slightly different. Hamburger [3] proved that if S is a compact oriented surface, immersed in R with only isolated umbilic points, then the sum of the indices of the umbilic points is equal to 2 = 2 (2 Gamma 2 g) where and g denote the Euler characteristic and the genus of S, ....

....point p is defined as times the increase of the angle of L 1 (x) or L 2 (x) when x runs once around p, along a small loop and in the positive direction with respect to the orientation of S. See Blaschke [1, p. 287] the original definition of Hamburger [3] is slightly different. Hamburger [3] proved that if S is a compact oriented surface, immersed in R with only isolated umbilic points, then the sum of the indices of the umbilic points is equal to 2 = 2 (2 Gamma 2 g) where and g denote the Euler characteristic and the genus of S, respectively. For our purpose, of relating the ....

H. Hamburger: Uber Kurvennetze mit isolierten Singularitaten auf geschlossenen Flachen. Mathematische Zeitschrift 19 (1924) 50-66.

....symbolische Gleichung bewiesen werden kann. p. 61) The obvious historical question here is, what did Hilbert know about Brouwer s views. In [12] the following papers are listed, when the impact of Brouwer and Weyl in 1920 is discussed: 18] 19] 20] and [21] by Brouwer and [104] and [105] by Weyl. One should recall in this context also that in 1919 Brouwer had been o#ered a professorship in G ottingen. More precisely, according to a private communication of Dirk van Dalen, the decision of the G ottingen faculty to put Brouwer no. 1 on the list for the chair was made on ....

....Existenzbehauptung hat hier uberhaupt nur einen Sinn als ein Hinweis auf ein Verfahren der Au#ndung, welches man besitzt, das man aber f ur gew ohnlich nicht n aher anzugeben braucht, weil es im allgemeinen gen ugt, zu wissen, dass man es besitzt. pp. 67 8) HILBERT S PROGRAMS: 1917 1922 29 in [105]. 56 With this understanding of quantifiers the conclusion concerning the non validity of the law of the excluded middle is again obtained. Hilbert points out: Thus we see that, for a strict foundation of mathematics, the usual inference methods of analysis must not be taken as logically ....

[Article contains additional citation context not shown here]

, Uber die neue Grundlagenkrise der Mathematik, Mathematische Zeitschrift, vol. 10 (1921), pp. 39--79.

....Similarly [#x # X.Px] #x : X. Px] where #x : A. Px] is the Cartesian product of the [Px] because a proof of #x # A.Px consists of a function that assigns to each element x # A a proof of Px. In this way proof objects become isomorphic with the intuitionistic natural deduction proofs of [48]. Using this interpretation, a proof of #y # A.Py # Py is #y : A#x : Py.x. Here #x : A.B(x) denotes the function that assigns to input x # A the output B(x) A proof of (A # A # B) # A # B is #p : A # A # B)#q : A.pqq. A description of the typed lambda calculi in which these ....

, Untersuchungen uber das logische Schliessen, Mathematische Zeitschrift, vol. 39 (1935), pp. 176--210, 405--431, also available in [111], pp 68--131.

....of S, then the index of the umbilic point p is defined as 1 times the increase of the angle of L 1 (x) or L 2 (x) when x runs once around p, along a small loop and in the positive direction with respect to the orientation of S. See Blaschke [1, p. 287] the original definition of Hamburger [3] is slightly different. Hamburger [3] proved that if S is a compact oriented surface, immersed in R 3 with only isolated umbilic points, then the sum of the indices of the umbilic points is equal to 2 = 2 (2 Gamma 2 g) where and g denote the Euler characteristic and the genus of S, ....

....point p is defined as 1 times the increase of the angle of L 1 (x) or L 2 (x) when x runs once around p, along a small loop and in the positive direction with respect to the orientation of S. See Blaschke [1, p. 287] the original definition of Hamburger [3] is slightly different. Hamburger [3] proved that if S is a compact oriented surface, immersed in R 3 with only isolated umbilic points, then the sum of the indices of the umbilic points is equal to 2 = 2 (2 Gamma 2 g) where and g denote the Euler characteristic and the genus of S, respectively. For our purpose, of relating ....

H. Hamburger: Uber Kurvennetze mit isolierten Singularitaten auf geschlossenen Flachen. Mathematische Zeitschrift 19 (1924) 50-66.

....and Eisenstein, among others. The poster Solving the Quintic with Mathematica [12] gives a nice introduction to these classical techniques and underlines their relevance for symbolic computation. The state of the art in the first half of our century appears in works of Richard Birkeland [2] and Karl Mayr [10] They proved that the roots are multivariate hypergeometric functions (in the sense of Horn) in all of the coefficients and they gave series expansions for the roots and their powers. The purpose of this note is to refine the these results. Our point of departure is the fact ....

R. Birkeland: Uber die Auflosung algebraischer Gleichungen durch hypergeometrische Funktionen, Mathematische Zeitschrift 26 (1927) 565--578.

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