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225300News from Boris Haase#69: Extension Euclidean Geometry on 04.09.2017
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Mon, 04 Sep 2017 05:15:00 +0200http://en.boris-haase.de/bh_rss.php?number=69Toeplitz' conjecture: Every Jordan curve admits an inscribed square. Counterexamples: The right-angled triangle with two sides of length d0 and the obtuse triangle where we suitably move a vertex infinitesimally of at most one inscribed square. Theorem: There is a Jordan domain with more than one equichordal point. Proof: We suitably juxtapose equichordal points infinitesimally
...#68: Improvement Set Theory on 14.12.2016
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Wed, 14 Dec 2016 20:00:00 +0100http://en.boris-haase.de/bh_rss.php?number=68When counting the number of elements of a finite (infinite) set, we must pay careful attention to its construction before we compare it to the set of natural numbers. These latter sets may be taken as a basis thanks to their simple constructions. If we do not know the construction of a set, it cannot be (uniquely) counted. If there are multiple possible constructions, we should choose the most plausible, i.e. the one that best reflects the finiteness (infiniteness) of the set for the purpose of differentiating between these two cases ...#67: Improvement Linear Optimisation on 04.10.2016
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Tue, 04 Oct 2016 18:00:00 +0200http://en.boris-haase.de/bh_rss.php?number=67Theorem: The normal method solves the LP in at most O(mn) and is strongly polynomial. Proof and algorithm: The normal method includes the two phases of the simplex method and solves the LP if possible by moving in a direction calculated from one of O(n) orthogonal directions inside M as the next key step towards the potential maximum. We solve all two-dimensional LPs in O(m) by using the bisection method. The method begins and multiple vertices are handled identically to the simplex method ...#66: Insertion Number Theory on 29.06.2016
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Wed, 29 Jun 2016 09:00:00 +0200http://en.boris-haase.de/bh_rss.php?number=66The sequence n/2 for even n and 3n + 1 for odd n always ends at 1. After one iteration, by (Jeffrey C. Lagarias, "The 3x+1 problem and its generalizations", American Mathematical Monthly 92 (1985), 3-23), we obtain the expected value 3n/4 + O(1), from which the sequence cannot grow unlimitedly ...#65: Improvement Linear Optimisation on 22.05.2016
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Sun, 22 May 2016 19:00:00 +0200http://en.boris-haase.de/bh_rss.php?number=65Theorem: The normal method is maximally quartic and moreover strongly polynomial. Proof and algorithm: The normal method has the two phases of the simplex method, and determines the possible maximal value of the objective function by moving better than along the projections of the normal vector of the objective function at the boundary of the feasible domain onto the maximum. By this, the path is more effective determined than an optimal pivot rule without previous knowledge for the simplex method can be ...#64: Extension Set Theory on 17.11.2015
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Tue, 17 Nov 2015 20:00:00 +0100http://en.boris-haase.de/bh_rss.php?number=64In the h-homogeneous sets, only the transcendental numbers are that emerge by marking out h from the two selected and maybe minimal adjacent (hyper-) algebraic numbers to be specified. Herewith we approve the impreciseness, when (hyper-) algebraic numbers are between these points marked out. The deviation from the exact values maybe still further specified. Since it is infinitesimal, this is, however, less important ...