Institute of Mathematics AS CR, v. v. i.
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Card Shuffling and Combinatorial Sequences
No full textsummary:V článku se věnujeme několika metodám míchání karet. Připomeneme klasický Fisherův-Yatesův algoritmus a popíšeme některé jeho modifikace. Tyto nestandardní metody míchání jsou z pohledu matematiky mnohem zajímavější a souvisejí s některými známými kombinatorickými posloupnostmi
Strong convergence for weighted sums of WOD random variables and its application in the EV regression model
No full textsummary:The strong convergence for weighted sums of widely orthant dependent (WOD) random variables is investigated. As an application, we further investigate the strong consistency of the least squares estimator in EV regression model for WOD random variables. A simulation study is carried out to confirm the theoretical results
Symmetric and reversible properties of bi-amalgamated rings
No full textsummary:Let and be two ring homomorphisms and let and be two ideals of and , respectively, such that . We investigate unipotent, symmetric and reversible properties of the bi-amalgamation ring of with along with respect to
Two results of -exangulated categories
No full textsummary:M. Herschend, Y. Liu, H. Nakaoka introduced -exangulated categories, which are a simultaneous generalization of -exact categories and -angulated categories. This paper consists of two results on -exangulated categories: (1) we give an equivalent characterization of axiom (EA2); (2) we provide a new way to construct a closed subfunctor of an -exangulated category
Condition numbers of Hessenberg companion matrices
No full textsummary:The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition number than any Fiedler companion matrix. We finish by exploring the condition number of a class of matrices obtained from perturbing a Frobenius companion matrix while preserving the characteristic polynomial.\looseness -
Strong endomorphism kernel property for finite Brouwerian semilattices and relative Stone algebras
Get PDFsummary:We show that all finite Brouwerian semilattices have strong endomorphism kernel property (SEKP), give a new proof that all finite relative Stone algebras have SEKP and also fully characterize dual generalized Boolean algebras which possess SEKP
Multi-type synchronization of impulsive coupled oscillators via topology degree
No full textsummary:The existence of synchronization is an important issue in complex dynamical networks. In this paper, we study the synchronization of impulsive coupled oscillator networks with the aid of rotating periodic solutions of impulsive system. The type of synchronization is closely related to the rotating matrix, which gives an insight for finding various types of synchronization in a united way. We transform the synchronization of impulsive coupled oscillators into the existence of rotating periodic solutions in a relevant impulsive system. Some existence theorems about rotating periodic solutions for a non-homogeneous linear impulsive system and a nonlinear perturbation system are established by topology degree theory. Finally, we give two examples to show synchronization behaviors in impulsive coupled oscillator networks
Representation of uni-nullnorms and null-uninorms on bounded lattices
Get PDFsummary:In this paper, we present the representation for uni-nullnorms with disjunctive underlying uninorms on bounded lattices. It is shown that our method can cover the representation of nullnorms on bounded lattices and some of existing construction methods for uni-nullnorms on bounded lattices. Illustrative examples are presented simultaneously. In addition, the representation of null-uninorms with conjunctive underlying uninorms on bounded lattices is obtained dually
A new approach to construct uninorms via uninorms on bounded lattices
Get PDFsummary:In this paper, on a bounded lattice , we give a new approach to construct uninorms via a given uninorm on the subinterval (or ) of under additional constraint conditions on and . This approach makes our methods generalize some known construction methods for uninorms in the literature. Meanwhile, some illustrative examples for the construction of uninorms on bounded lattices are provided
Data transformation technique in the data informativity approach via algebraic sequences
Get PDFsummary:The data-informativity approach in data-driven control focuses on data and their matching model sets for system design and analysis. The approach offers a new mathematical formulation different from model-based control and is expected to progress. In model-based control, the introduction of equivalent transformations has made system analysis and design easier and facilitated theoretical development. In this study, we focus on data transformations and their transformation of matching model sets. We first introduce an algebraic sequence representing the relationship between the data and model set, and using this algebraic approach, we utilize propositions from homology theory, such as kernel universality, to analyze data and model transformations. This technique is significant not only mathematically but also in engineering. Further, we demonstrate how this technique can be applied to derive controllability judgments for data informativity-based analysis. Finally, we prove that design problems can be reduced to analysis problems involving controller inclusion