Institute of Mathematics AS CR, v. v. i.
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Extension methods for nullnorms on bounded lattices
No full textsummary:After nullnorms were defined on bounded lattices by Karaçal et al., construction methods for nullnorms on bounded lattices have been widely studied in which the existence of t-norms (t-conorms) on sublattices of the bounded lattice has generally been exploited. Extension methods of nullnorms are important as they also play a significant role for ordinal sum construction of nullnorms on bounded lattices. In this paper, we introduce extension construction methods for nullnorms on a bounded lattice by exploiting the existence of a nullnorm on a sublattice of . Then, we demonstrate that our new construction methods are also different from the existing construction methods in the literature. Additionally, some illustrative examples are provided. Finally, we also give modified versions of our construction method by induction
Structure of the unit group of the group algebras of non-metabelian groups of order 128
Full text linksummary:We characterize the unit group for the group algebras of non-metabelian groups of order 128 over the finite fields whose characteristic does not divide the order of the group. Up to isomorphism, there are 2328 groups of order 128 and only 14 of them are non-metabelian. We determine the Wedderburn decomposition of the group algebras of these non-metabelian groups and subsequently characterize their unit groups
On -Pell numbers which are sum of two Narayana's cows numbers
Full text linksummary:For any positive integer , let be the -generalized Pell sequence which starts with ( terms) with the linear recurrence Let be Narayana's sequence given by The purpose of this paper is to determine all -Pell numbers which are sums of two Narayana's numbers. More precisely, we study the Diophantine equation in nonnegative integers , , and
Finite logarithmic order meromorphic solutions of linear difference/differential-difference equations
Full text linksummary:Firstly we study the growth of meromorphic solutions of linear difference equation of the form where and are meromorphic functions of finite logarithmic order, are distinct nonzero complex constants. Secondly, we deal with the growth of solutions of differential-difference equation of the form where and are meromorphic functions of finite logarithmic order, are distinct complex constants. We extend some previous results obtained by Zhou and Zheng and Biswas to the logarithmic lower order.\looseness -
On almost periodicity defined via non-absolutely convergent integrals
No full textsummary:We investigate some properties of the normed space of almost periodic functions which are defined via the Denjoy-Perron (or equivalently, Henstock-Kurzweil) integral. In particular, we prove that this space is barrelled while it is not complete. We also prove that a linear differential equation with the non-homogenous term being an almost periodic function of such type, possesses a solution in the class under consideration
On the behaviour of the solutions of a -order cyclic-type system of max difference equations
No full textsummary:We investigate the behaviour of the solutions of a -dimensional cyclic system of difference equations with maximum. More precisely, we study the existence and the number of the equilibria in the case when is an odd or an even positive integer, but also for the various values of the exponents of the terms of the difference equations of this system. In addition, we find invariant intervals for our system and we invistegate the convergence of the solutions to the unique positive equilibrium. Finally, we study the asymptotic behavior of the positive solutions of the system in the case, where and
Local equivalence of some maximally symmetric -distributions II
Full text linksummary:We show the change of coordinates that maps the maximally symmetric -distribution given by solutions to the and generalised Chazy equation to the flat Cartan distribution. This establishes the local equivalence between the maximally symmetric and generalised Chazy distribution and the flat Cartan or Hilbert-Cartan distribution. We give the set of vector fields parametrised by solutions to the and generalised Chazy equation and the corresponding Ricci-flat conformal scale that bracket-generate to give the split real form of
Metrization of powers of the Jensen-Shannon divergence
Full text linksummary:Metrization of statistical divergences is valuable in both theoretical and practical aspects. One approach to obtaining metrics associated with divergences is to consider their fractional powers. Motivated by this idea, Osán, Bussandri, and Lamberti (2018) studied the metrization of fractional powers of the Jensen-Shannon divergence between multinomial distributions and posed an open problem. In this short note, we provide an affirmative answer to their conjecture. Moreover, our method is also applicable to fractional powers of -divergences between Cauchy distributions