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225300News from Boris Haase#77: Extension Topology on 05.04.2019
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Fri, 05 Apr 2019 05:00:00 +0200https://en.boris-haase.de/bh_rss.php?number=77In the following, the terms of openness and closure of sets are reduced to absurdity. The Set Theory is presupposed. A disk without its boundary conventionally represents an open set, because then each point of it has a conventional neighbourhood that lies completely in this set ...#76: Improvement Linear Programming on 11.02.2019
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Mon, 11 Feb 2019 21:00:00 +0100https://en.boris-haase.de/bh_rss.php?number=76n the following section, we solve linear programmes (LPs) by the exponential simplex and the polynomial intex method (inter-/extrapolation). Diameter theorem for polytopes: The diameter of an n-dimensional polytope defined by m constraints is at most 2(m + n - 3). Proof: We can assemble at most m - 1 hyperplanes into an incomplete cycle (of dimension 2) and have to consider n - 2 alternatives sidewards (in the remaining dimensions) ...#75: Completion Set Theory on 10.11.2018
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Sat, 10 Nov 2018 05:00:00 +0100https://en.boris-haase.de/bh_rss.php?number=75When 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 ...#74: Renaming Representations Advice and Revision on 23.10.2018
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Tue, 23 Oct 2018 17:00:00 +0200https://en.boris-haase.de/bh_rss.php?number=74What can I tell you from my decades of mathematical experience? Real progress in mathematics is only possible with unusual ideas that result from intensive consideration. The fewest problems are solved with luck. We need a mathematical pool from which we can use the mathematical tools for our problems. Success only comes with a healthy dose of tenacity, with which we can pursue a problem for decades if necessary, before we can solve it
...#73: Improvement Linear Programming on 14.07.2018
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Sat, 14 Jul 2018 08:00:00 +0200https://en.boris-haase.de/bh_rss.php?number=73n the following section, we solve linear programmes (LPs) by the simplex and the intex method (inter-/extrapolation) as strongly polynomial solution to Smale's 9th problem. Diameter theorem for polytopes: The diameter of an n-dimensional polytope defined by m constraints is at most 2(m + n - 3). Proof: We can assemble at most m - 1 hyperplanes into an incomplete cycle (of dimension 2) and have to consider n - 2 alternatives sidewards (in the remaining dimensions) ...#72: Completion Nonstandard Analysis on 07.03.2018
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Wed, 07 Mar 2018 18:30:00 +0100https://en.boris-haase.de/bh_rss.php?number=72The counter-directional theorem holds. There is a simple formula with roots of unity that describes the zeta function for odd arguments dependently from the digamma function ...