BUT Faculty of Civil Engineering,
Department of Mathematics and Descriptive Geometry
invites you to a lecture

On the symmetry in sharp oscillation criteria for second-order functional differential equations

Tuesday 2nd December 2025 at 10:00

Abstract. We study the oscillation of second-order half-linear functional differential equations under two fundamental dichotomies: the nature of deviating argument (delay vs. advance) and Trench’s canonical classification (canonical vs. non-canonical form). For each of the four resulting cases, sharp extensions of the classical Hille–Kneser oscillation criterion are obtained via an iterative monotonicity method. These criteria exhibit a notable symmetry: the canonical delay case pairs with the non-canonical advance case and vice versa for the canonical advance and non-canonical delay cases. We conclude by discussing possible extensions of the results to higher-order functional differential equations.

At the department meeting room (2^nd floor Z205), Žižkova 17.

THE LECTURE WILL BE GIVEN BY DR. IRENA JABLOVSKÁ,

Mathematical Institute, Slovak Academy of Science, extension in Košice, Košice, Slovak Republic

The lecture is intended for all those interested in these problems.

Ing. Jan Holešovský, Ph.D.

Head of the Institute of Mathematics and Descriptive Geometry

Handout

BUT Faculty of Civil Engineering,
Department of Mathematics and Descriptive Geometry
invites you to a lecture

On the Complexification of Linear Operators and its Applications

Wednesday 11th November 2025 at 14:15

Abstract. The aim of this talk is to demonstrate how the complexification procedure can be used to derive important properties of operators acting on a real Hilbert space from their counterparts in the complex setting. In particular, we will outline how the spectral representation theorem for real Hilbert spaces can be derived from its complex version. Although this result is often regarded as part of mathematical folklore, it nonetheless requires some explanation.

At the department meeting room (2^nd floor Z205), Žižkova 17.

THE LECTURE WILL BE GIVEN BY DR. WITOLD MAJDAK,

Department of Mathematical Analysis and Applications, Faculty of Applied Mathematics, AGH University of Krakow, Krakow, Poland

The lecture is intended for all those interested in these problems.

Ing. Jan Holešovský, Ph.D.

Head of the Institute of Mathematics and Descriptive Geometry

Handout

BUT Faculty of Civil Engineering,
Department of Mathematics and Descriptive Geometry
invites you to a lecture

Shadowing and hyperbolicity for linear delay difference equations

Wednesday 27th August 2025 at 13:00

Abstract. It is known that hyperbolic linear delay difference equations are shadowable on the half-line. In this talk, we prove the converse and hence the equivalence between hyperbolicity and the positive shadowing property for the following two classes of linear delay difference equations: (a) for non-autonomous equations with finite delays and uniformly bounded compact coefficient operators in Banach spaces, (b) for Volterra difference equations with infinite delay in finite dimensional spaces.

At the department meeting room (2^nd floor Z205), Žižkova 17.

THE LECTURE WILL BE GIVEN BY PROF. MIHÁLY PITUK,

Department of Mathematics, University of Pannonia, Egyetem út 10, 8200, Veszprém, Hungary

The lecture is intended for all those interested in these problems.

Ing. Jan Holešovský, Ph.D.

Head of the Institute of Mathematics and Descriptive Geometry

Handout

From 11^th to 17^th May 2025, as part of the Erasmus+ program, Ing. A. Derevianko and Professor J. Diblík stayed at the University of Bialystok, Poland. Also with this university, our department has had long-term contacts. As part of this teaching stay, a contract was initiated between the Faculty of Civil Engineering, Brno University of Technology and University of Bialystok on cooperation in teaching and research. Together with M. Růžičková from the University of Bialystok, Professor J. Diblík has published a number of research papers with the last one of 2024 having been published in the prestigious journal Advances in Nonlinear Analysis.

From 30^th March to 5^th April 2025, as part of the Erasmus+ teaching-stay program, Professor Diblík stayed at the University of Pannonia, Veszprém, Hungary. With this university, our department has had long-term contacts involving both teaching and research. Professor M. Pituk, who works there, has visited our department several times, sharing with us his world-class results. In cooperation with Professor Diblík and Professor G. Szederkényi (Pázmány Péter Catholic University, Budapest, and Institute for Computer Science and Control, Budapest) he has also written a paper published last year in the prestigious journal Automatica.

Students are reminded,
that it is their duty, rather than their teachers’, to register for a course. Other problems such as those concerning individual study schedules, disabled registration for a mathematics course, etc. should be dealt with in cooperation with RNDr. Rudolf Schwarz, CSc. during his office hours – Wednesday 10.00 – 11.00.

Approved by: Ing Jan Holešovský, Ph.D.,
Head of the Institute of Mathematics and Descriptive Geometry.
Brno dated 1st February 2025.

BUT Faculty of Civil Engineering,
Department of Mathematics and Descriptive Geometry
invites you to a lecture

On the Systems of Nonlinear Evolution Equations – Existence and Uniqueness vie Theory of M-matrices

Tuesday 5th November 2024 at 12:30

Abstract. A system of nonlinear evolution equations with strictly monotone operators and perturbations satisfying certain counterpart of one-sided Lipschitz condition is considered. To reach the existence and uniqueness result, a certain remetrization method is proposed based on M-matrices theory and utilizing the Gelfand triple setting, which enables usage of a certain type of relaxed monotonicity. Asymptotic properties of the solution are also investigated by showing that any solution tends to the solution of a stationary problem. The results obtained are illustrated by considering a system of equations involving (q,p)-Laplacians and suitable non-monotone perturbations.

At the department meeting room (2^nd floor Z205), Žižkova 17.

The lecture will be given by Dr. Michał Bełdziński,

Institute of Mathematics, Lodz University of Technology, Lodz, Poland

The lecture is intended for all those interested in these problems.

Ing. Jan Holešovský, Ph.D.

Head of the Institute of Mathematics and Descriptive Geometry

Handout

BUT Faculty of Civil Engineering,
Department of Mathematics and Descriptive Geometry
invites you to a lecture

Shadowing, Hyers-Ulam stability and hyperbolicity for nonautonomous linear delay differential equations

Wednesday 28th August 2024 at 13:00

Abstract. It is known that hyperbolic nonautonomous linear delay differential equations in finite dimensional spaces are Hyers–Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this talk, we show the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the uniform boundedness assumption will be shown by an example.

This is a joint work with Professors Lucas Backes (Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil) and Davor Dragičević (University of Rijeka, Rijeka, Croatia).

At the department meeting room (2^nd floor Z205), Žižkova 17.

THE LECTURE WILL BE GIVEN BY PROF. MIHÁLY PITUK,

Department of Mathematics, University of Pannonia, Egyetem út 10, 8200, Veszprém, Hungary

The lecture is intended for all those interested in these problems.

Ing. Jan Holešovský, Ph.D.

Head of the Institute of Mathematics and Descriptive Geometry

Handout

BUT Faculty of Civil Engineering,
Department of Mathematics and Descriptive Geometry
invites you to a lecture

Spectral resolutions for non-self-adjoint convolution operators

Thursday 20th June 2024 at 11:00

Abstract. This talk presents a spectral theory for a class of non-self-adjoint convolution type operators. Particular attention is paid to spectral decomposition (in terms of suitable invariant chains) of the convolution operators under consideration, summing up the extension to them of the classical Schur theory on the triangular decomposition of matrices. It is considered the general case of operators defined on Banach spaces. Applications to the spectral theory of periodic Jacobi type operators that are applicable to mathematics, physics, mathematical physics and others will also be given.

At the department meeting room (2^nd floor Z205), Žižkova 17.

THE LECTURE WILL BE GIVEN BY DR. EWELINA ZALOT,

Faculty of Applied Mathematics, AGH University of Krakow, Al. A. Mickiewicza 30, 30-059 Kraków, Poland

The lecture is intended for all those interested in these problems.

Ing. Jan Holešovský, Ph.D.

Head of the Institute of Mathematics and Descriptive Geometry

Handout