2018/2
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- ItemPredicting football tables by a maximally parsimonious model(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2018) Haugen, Kjetil K.; Owren, BrynjulfThis paper presents some useful mathematical results concerned with football table prediction. In addition, some empirical results indicate that an alter- native methodology for football table prediction may produce high quality forecasts with far less resource usage than conventional methods.
- 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.
- 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 .