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225300News from Boris Haase#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=68The determination of the number of elements of any (in-) finite set must consider exactly its construction before we can relate it to the set N|. This should be, due to its simple construction, used as basis. Without knowing the construction of a set, its number cannot be (uniquely) determined. If there are several construction options, we should use the most plausible one, i.e. it should represent (in-) finiteness in the best possible way, in the sense of differentiation ...#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 maximally in O(mn) and is strongly polynomial. Proof and algorithm: The normal method has the two phases of the simplex method and solves the LP, if possible, by moving in direction computed from O(n) orthogonal normal directions in the interior of the feasible domain as main step onto the potential maximum. Hereby, we solve all two-dimensional LPs (per direction) in each case by bisection method in O(m). Beginning and treating multiple vertices compare 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 two sequences n/2 for even n and 3n ± 1 end for odd n always in a cycle. We want to exclude unlimited growth of the sequences. Iterating once, we obtain according to (Jeffrey C. Lagarias, "The 3x+1 problem and its generalizations", American Mathematical Monthly 92 (1985), 3-23) the expectation value 3n/4 ± O(1) and thereof the assertion ...#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 ...#63: Completion Introduction and mathematics and Improvement Linear Optimisation on 15.04.2015
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Wed, 15 Apr 2015 20:00:00 +0200http://en.boris-haase.de/bh_rss.php?number=63In the following, we concern solving linear programmes (LP). The well-known simplex algorithm and its problems in the worst case is introduced as no longer strongly polynomial and a method is presented, which leaves fast each problematic multiple vertex. Then, this is opposed to the maximally quintic and strongly polynomial normal method as solution for the 9th Smale problem ...