Institute of Mathematics AS CR, v. v. i.
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Modular separating invariants for the dihedral groups
No full textsummary:Let be an algebraically closed field of odd prime characteristic . Using only transfers and norms, we describe a separating set for each indecomposable modular representation of the dihedral groups over the field . Our construction is recursive and the size of every separating set depends only on the dimension of the representation
News and Announcements
No full textsummary:Libuše Hozová (1939-2024). Vzpomínkové odpoledne a seminář ke 100. výročí narození profesora Miloše Zlámala
The Dirichlet-to-Neumann operator on rough domains with finite volume
No full textsummary:Using a variational formulation we consider the Dirichlet-to-Neumann operator on a connected open set of finite volume, assuming only that the surface measure is locally finite on the boundary. Then the boundary may have infinite measure and trace properties become delicate. We show that this has consequences for the kernel of the Dirichlet-to-Neumann operator and characterise the situation in which a trace on both exists and is unique
On weakly -ideals and weakly -ideals
No full textsummary:We study weakly -ideals and weakly -ideals in commutative rings. Let be a commutative ring with a nonzero identity and be a proper ideal of . Then is said to be a weakly -ideal (or weakly -ideal) if whenever for some nonunits (or for some , then either or (or or , respectively), where is the set of all nilpotent elements of . Many examples and properties of weakly -ideals and weakly -ideals are given. We characterize all rings in which every proper ideal is a weakly -ideal and weakly -ideal. Furthermore, we investigate both weakly -ideals and weakly -ideals in amalgamated algebras along an ideal
Unit nil-clean and singular clean group rings
No full textsummary:We study the unit nil-cleanness of group rings when is commutative or arbitrary. Furthermore, we investigate some properties of singular clean group rings. A necessary and sufficient condition for the group ring to be singular clean is provided
Composition operators on variable exponent Bloch spaces
No full textsummary:We consider the composition operator on the variable exponent Bloch space , which consists of all analytic functions on the unit disk such that Here, is a log-Hölder continuous function on . The boundedness and compactness of are characterized. Besides, we show that is Lipschitz continuous in terms of the pseudo-hyperbolic metric under the Lipschitz continuity of . By using this result, we study the bounded and compact difference of two composition operators on , and the boundedness from below of is partially described
A New result on stability analysis and dynamic output feedback controller for systems with time-varying delays
No full textsummary:The stability and stabilization of systems with time-varying delays and external disturbances are the subject of this study. To circumvent the limitation of the Bessel-Legendre inequality, which cannot treat a time-varying delay system because the resulting limit contains reciprocal convexity, the generalized free-matrix-based integral inequality is used to generate less conservative stability criteria. Improved stabilization requirements are proposed in the form of linear matrix inequalities by developing a new augmented Lyapuno-Krasovskii function. To achieve resolved controller gains, a method for designing a dynamic output feedback controller based on linear matrix inequalities is then provided. Finally, three examples are used to validate the advantages of the approach over existing methods
On conceptual understanding in mathematics
No full textsummary:Příspěvek vymezuje různé úrovně konceptuálního porozumění žáků v matematice (znalosti klasifikací, znalosti struktur a znalosti principů) a rozpracovává je pro oblast geometrie, konkrétně pro eukleidovské geometrické konstrukce. Pro tento účel představujeme nový design učebních úloh, který vede žáky ke „čtení“ již hotových konstrukcí. Na konkrétní úloze vhodné pro výuku geometrie na druhém stupni základní školy představujeme typické projevy různých úrovní konceptuálního porozumění a podáváme náměty učitelům matematiky, jak je možné míru konceptuálního porozumění žáků zjišťovat a jak ho dále rozvíjet.summary:The paper describes different levels of students’ conceptual understanding in mathematics (knowledge of classifications, knowledge of structures, and knowledge of principles) and elaborates on them for the field of geometry, specifically for Euclidean geometric constructions. For this purpose, we present a new design of learning tasks that lead students to “read” already completed constructions. With an illustrative task suitable for geometry education in lower secondary schools, we present typical displays of different levels of students’ conceptual understanding and provide mathematics teachers with suggestions of how such conceptual understanding can be assessed and further developed
Orbit-cone correspondence for the proalgebraic completion of normal toric varieties
Get PDFsummary:We prove that there is an orbit-cone correspondence for the proalgebraic completion of normal toric varieties, which is analogous to the classical orbit-cone correspondence for toric varieties
Almost complete convergence of a recursive kernel estimator of the density with complete and censored independent data
Get PDFsummary:In this paper, we firstly introduce a recursive kernel estimator of the density in the censored data case. Then, we establish its pointwise and uniform almost complete convergences, with rates, in both complete and censored independent data. Finally, we illustrate the accuracy of the proposed estimators throughout a simulation study