2017/1
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- ItemHigher-dimensional general Jacobi identities I(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Nishimura, H.It was shown by the author [International Journal of Theoretical Physics 36 (1997), 1099{1131] that what is called the general Jacobi identity, obtaining in microcubes, underlies the Jacobi identity of vector elds. It is well known in the theory of Lie algebras that a plethora of higher-dimensional generalizations of the Jacobi identity hold, though they are usually established not as a derivation on the nose from the axioms of Lie algebras but by making an appeal to the socalled Poincar e{Birkho {Witt theorem and the like. The general Jacobi identity was rediscovered by Kirill Mackenzie in the second decade of this century [Geometric Methods in Physics, Birkh auser/Springer, 2013, 357{366]. The principal objective of this paper is to investigate a four-dimensional generalization of the general Jacobi identity in detail. In a subsequent paper we will propose a uniform method for establishing a bevy of higher-dimensional generalizations of the general Jacobi identity under a single umbrella.
- ItemOn an equation related to nonadditive entropies in information theory(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Nath, P.; Singh, D. K.The paper provides the general solutions of a sum form functional equa- tion containing three unknown mappings with some of the solutions related to the nonadditive entropies in information theory
- ItemClassification trees in a box extent lattice(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Veres, L.In this paper we show that, during an elementary extension of a context, each of the classi cation trees of the newly created box extent lattice can be obtained by modifying the classi cation trees of the box extent lattice of the original, smaller context. We also devise an algorithm which, starting from a classi cation tree of the box extent lattice of the smaller context (H;M; I \H M); gives a classi cation tree of the extended context (G;M; I) which contains the new elements inserted. The e ciency of the method is given by the fact that it is su cient to know the original context, the classi cation tree of the box extent lattice and its box extents while the knowledge of a new box extension of the extended context mesh elements is not required (except for one, which is the new element box extension).
- ItemA note on some generalized closure and interior operators in a topological space(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Gupta, A.; Sarma, R. D.If X is a topological space and A X, then the number of distinct sets that can be obtained from A by using all possible compositions for operators i , c (where = ; ; ; ) introduced by Cs asz ar is at the most 25. Explicit expressions for these sets are provided. An example is provided where all the 25 di erent sets are determined. The result is also discussed for special cases such as when the space is extremally disconnected, resolvable, open-unresolvable, and partition spaces.
- ItemProfessor Ladislav Skula is eighty(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Kureš, M.; Šlapal, J.30 June 1937 is the birthday of Professor Ladislav Skula, our colleague at the Institute of Mathematics of the BUT Faculty of Mechanical Engineering, a distinguished editorial board member of this journal, and an outstanding Brno mathematician of world renown.