- 2020/1

# 2020/1

## Browse

### Recent Submissions

Now showing 1 - 5 of 6

- ItemWho are the real top scorers: Algorithmically resorting a top scorer list by a limited set of preference assumptions(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2020) Hauge, Kjetil K.
Show more This article presents an algorithm, which by taking both goals scoredas well as matches played into account, is meant to provide “more sensible” topscorer lists in football. The algorithm computes Upper Hulls recursively in order toprovide a new and improved list. The complexity of the algorithm is reasonable, andshould imply practically feasible execution on a modern computer. The proposedalgorithm may also be an interesting alternative to academic scholar ranking. Ithas interesting properties for instance compared to the h-index.Show more - ItemCycle Systems(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2020) Pfaltz, John P.
Show more In this paper we show that the composition (symmetric difference) ofcycles is well-defined. So, such a collection {. . . , Ci, Ck, . . .} of cycles with a com-position operator,◦, is a matroid. As such, it has sets of independent, or basis,cycles that determine its rankr. This paper is concerned with independent anddependent sets of cycles within a cycle system. In particular, we enumerate thenumber of all possible basis sets in any cycle system of rankr≤6. Then we usea generating function to establish that the ratio of basis sets to all possiblerelementsets approachesc,0.287< c <0.289.Show more - ItemSome remarks about trunks and morphisms of neural codes(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2020) Christensen, Katie; Kulosman, Hamid
Show more We give intrinsic characterizations of neural rings and homomorphismsbetween them. Also we introduce the notion of a basic monomial code map andcharacterize monomial code maps as compositions of basic monomial code maps.Finally, we characterize monomial isomorphisms between neural codes. Our workis based on the 2015 paper by C. Curto and N. Youngs about neural ring homo-morphisms and maps between neural codes and on the 2018 paper by R. Amzi Jeffsabout morphisms of neural rings.Show more - ItemOn stability of delayed differential systems of arbitrary non-integer order(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2020) Kisela, Tomáš
Show more This paper summarizes and extends known results on qualitative behaviorof solutions of autonomous fractional differential systems with a time delay. Itutilizes two most common definitions of fractional derivative, Riemann–Liouvilleand Caputo one, for which optimal stability conditions are formulated via positionof eigenvalues in the complex plane. Our approach covers differential systems ofany non-integer orders of the derivative. The differences in stability and asymptoticproperties of solutions induced by the type of derivative are pointed out as well.Show more - ItemThe T0-reflection in the category V-PreTop(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2020) Lazaar, Sami; Mhemdi, Abdelwaheb; Tahri, Randa
Show more AV-pretopological space is a pair(X, a)whereXis a nonempty set andais aP(X)self map satisfyinga(∅) =∅,A⊆a(A)anda(A∪B) =a(A)∪a(B)foranyA, B∈ P(X). It is well known that the categoryTopof topological spaces isa reflective subcategory in the categoryV-PreTopwhose objects are pretopologicalspaces of typeV. In the present paper we give the construction of theT0-reflectionin the categoryV-PreTop. Hence, some new separation axioms are introducedand characterized. Finally, the orthogonal of some subcategories are studied.Show more