2018/2
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- ItemSome new separation axioms in GenTop(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2018) Dourari, Khedidja; Lazaar, SamiIn this paper, we introduce some new separation axioms in the category of generalized topological spaces. Some characterizations of these axioms are given. Morphisms rendered invertible by the T 0 -reflection in GenTop are entirely deter- mined. Finally, some known results in the category Top are deduced.
- ItemThe quasitopos of b-uniform filter spaces(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2018) Leseberg, Dieter; Vaziry, ZohrehIn this paper a systematic study begins of the category b-UFIL of b- uniform filter spaces and b-uniformly continuous mappings. We will show that this construct forms a quasitopos in which quotients are stable under products. Consequently, it is extremely useful for further studies in the realm of Bounded topology.
- ItemOn real and complex convexity(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2018) Abidi, JamelWe show that the holomorphic differential equation k ′′ ( k + c ) = γ ( k ′ ) 2 is fundamental for the study of a special class of convex and strictly plurisubharmonic functions ( k : C → C be holomorphic and γ,c ∈ C ) . We characterize all the 4 holomorphic non-constant functions F 1 ,F 2 : C → C and g 1 ,g 2 : C n → C such that the function u is convex on C n × C , where u ( z,w ) = | F 1 ( w ) − g 1 ( z ) | 2 + | F 2 ( w ) − g 2 ( z ) | 2 , ( z,w ) ∈ C n × C .
- ItemExpected characteristic in Tunnels & Trolls character creation, with generalizations(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2018) Brander, TommiIn the roleplaying game Tunnels & Trolls the characteristics of player characters are determined by rolling dice in the following manner: First, one rolls three dice and calculates their sum. If the three dice all give the same result, another three dice are rolled and added to the total. This is continued until the three dice no longer match. We calculate the average result of the stochastic sum: 10 + 4 / 5. We also consider a generalized dice rolling scheme where we roll an arbitrary number of dice with an arbitrary number of sides. This generalization is motivated by various exotic dice that are used in many roleplaying games. We calculate the expectation, and how much it differs from the situation where we only roll the set of dice once, with no rerolling and adding. As the number of dice increases, or the number of sides the dice have increases, this difference approaches zero, unless there are two dice (with the number of sides increasing), in which case the difference approaches one.
- ItemEvent corruption: A game theoretic approach(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2018) Haugen, Kjetil K.; Solberg, Harry A.This article applies economics of doping theory (game theory) to corrup- tion. Similarities and significant differences between the two topics are identified. As a consequence of such differences, the corruptive action – the bribe – is introduced as a decision variable for the players. Nash equilibria of the “corruption game” are structurally similar to the doping situation – e.g. “everybody is corrupt”. However, the size of the bribe becomes, as a consequence of a significant revision of the basic models, “as high as possible”; indicating that the event corruption case should be at least as hard to handle as the doping problem and with possibly even more drastic adverse effects. Although the article focuses on corruption in sports and events, the results are also relevant for other types of corruptive action. Corruption in sports is a problem threatening the existence of professional sports. Hence, the methods for better understanding presented in this article are of vital importance for the professional sports business.