Dynamical properties of Metzler systems

Abstract. Spectral properties of nonnegative and Metzler matrices are considered. The conditions for existence of Metzler spectrum in dynamical systems have been established. An electric RL and GC ladder-network is presented as an example of dynamical Metzler system. The suitable conditions for parameters of these electrical networks are formulated. Numerical calculations were done in MATLAB

Discrete-time feedback stabilization

This paper presents an algorithm for designing dynamic compensator for infinitedimensional systems with bounded input and bounded output operators using finite dimensional approximation. The proposed method was then implemented in order to find the control function for thin rod heating process. The optimal sampling time was found depending on discrete output measurements

Two-site recognition of Staphylococcus aureus peptidoglycan by lysostaphin SH3b

Lysostaphin is a bacteriolytic enzyme targeting peptidoglycan, the essential component of the bacterial cell envelope. It displays a very potent and specific activity toward staphylococci, including methicillin-resistant Staphylococcus aureus. Lysostaphin causes rapid cell lysis and disrupts biofilms, and is therefore a therapeutic agent of choice to eradicate staphylococcal infections. The C-terminal SH3b domain of lysostaphin recognizes peptidoglycans containing a pentaglycine crossbridge and has been proposed to drive the preferential digestion of staphylococcal cell walls. Here we elucidate the molecular mechanism underpinning recognition of staphylococcal peptidoglycan by the lysostaphin SH3b domain. We show that the pentaglycine crossbridge and the peptide stem are recognized by two independent binding sites located on opposite sides of the SH3b domain, thereby inducing a clustering of SH3b domains. We propose that this unusual binding mechanism allows synergistic and structurally dynamic recognition of S. aureus peptidoglycan and underpins the potent bacteriolytic activity of this enzyme

Schodkowa funkcja bazowa w asymptotycznej homogenizacji systemu eliptycznego

The problem of asymptotic homogenization for one-dimensional stationary elliptic system was studied. The value of effective conductivity coefficient of homogeneous elliptic macroscopic system was determined for the basic cell approximated by a "stepped" function. The conditions to obtain given conductivity coefficient, in the considered homogenization problem, were shown. Results of numerical calculations were provided to illustrate discussed issues.W pracy rozważa się problem asymptotycznej homogenizacji dla jednowymiarowego stacjonarnego systemu eliptycznego. Dokonano aproksymacji "schodkowej" funkcji bazowej i wyznaczono przybliżoną wartość efektywnego współczynnika przewodności eliptycznego jednorodnego układu makroskopowego. Przedstawiono również jak w omawianym procesie homogenizacji uzyskać z góry zadany efektywny współczynnik przewodności. Rozważania zostały zilustrowane wynikami obliczeń numerycznych

Stabilization of control systems

W pracy przedstawiono kilka uwag na temat stabilizacji sterowanych układów dynamicznych. Wskazano różne obszary zastosowań praktycznych.The paper contains a remarks of the methods of stabilization of control systems. Examples of applications are presented

Approximation of Fractional Diffusion-Wave Equation

In this paper we consider the solution of the fractional differential equations. In particular, we consider the numerical solution of the fractional one dimensional diffusion-wave equation. Some improvements of computational algorithms are suggested. The considerations have been illustrated by examples

Analysis of undamped second order systems with dynamic feedback

In this paper the stabilization problem of undamped second order system is considered. The stabilization by first order dynamic feedback is studied. The global asymptotic stability of the respectively closed-loop system is proved by LaSalle's theorem. As an example of application of the proposed method an electric ladder network L and Ic type is presented. Numerical calculations were made using the Matlab/Simulink program

Finite-dimensional approximations of distributed RC networks

Spectral properties of ladder and spatial electrical networks are considered. Dynamic properties of the networks are characterised by eigenvalues of the Jacobi cyclic state matrix. The effective formulas for eigenvalues of appropriate uniform systems are given. Numerical calculations were made using MATLAB

Chaos in selected linear systems

W pracy przedstawiono wybrane liniowe układy o dynamice chaotycznej. Pokazano możliwość pojawienia się zachowań chaotycznych w symulacjach komputerowych liniowych aproksymacji układów o parametrach rozłożonych. Przeprowadzono oryginalną analizę dynamiki liniowego układu drabinkowego typu LC. Rozważania zilustrowano przykładami obliczeń numerycznych.In the paper selected linear systems displaying chaotic dynamics are presented. Particular attention is focused on numerical chaos and strange behaviour of the instantaneous voltage across suitable electrical capacitances in ladder networks of type LC. The possibility of arising the chaotic behaviour in numerical simulations of linear approximations of distributed parameters systems, with the so - called Lasota operator is shown. The original analysis of the linear LC ladder network dynamics is performed. Irregular trajectories arise in the systems of type LC as a result of mixing the time courses of incommensurable frequencies. The ladder network of type LC is approximation of an adequate hyperbolic system. The considered problems are illustrated with examples of numerical calculations. The comparative analysis for the LC ladder networks with different n, where n is a number of capacitance, is carried out

Mathematics at the AGH ust Electrical Faculty and comments on higher education

The paper presents the role of mathematics and mathematicians in the development of the Faculty of Electrical Engineering of the AGH in Krakow. The study was created on the 100th anniversary of the founding of the Mining Academy and the Polish Mathematical Society. The first chosen Rector of the AG in 1919 was Prof. A. Hoborski (mathematician), who together with S. Banach were co-founders of PTM in 1919 in Krakow.W pracy przedstawiono rolę matematyki i matematyków w rozwoju Wydziału Elektrycznego AGH w Krakowie. Opracowanie powstało w 1000lecie powstania Akademii Górniczej i Polskiego Towarzystwa Matematycznego. Pierwszym wybranym Rektorem AG w roku 1919 był Prof. A. Hoborski (matematyk), który wraz z S. Banachem byli współzałożycielami PTM w roku 1919, w Krakowie