Escape rate and Hausdorff measure for entire functions

The escaping set of an entire function is the set of points that tend to infinity under iteration. We consider subsets of the escaping set defined in terms of escape rates and obtain upper and lower bounds for the Hausdorff measure of these sets with respect to certain gauge functions.Comment: 24 pages; some errors corrected, proof of Theorem 2 shortene

On the dimension of graphs of Weierstrass-type functions with rapidly growing frequencies

We determine the Hausdorff and box dimension of the fractal graphs for a general class of Weierstrass-type functions of the form $f(x) = \sum_{n=1}^\infty a_n \, g(b_n x + \theta_n)$, where $g$ is a periodic Lipschitz real function and $a_{n+1}/a_n \to 0$, $b_{n+1}/b_n \to \infty$ as $n \to \infty$. Moreover, for any $H, B \in [1, 2]$, $H \leq B$ we provide examples of such functions with \dim_H(\graph f) = \underline{\dim}_B(\graph f) = H, \bar{\dim}_B(\graph f) = B.Comment: 18 page

Boundaries of univalent Baker domains

Let $f$ be a transcendental entire function and let $U$ be a univalent Baker domain of $f$. We prove a new result about the boundary behaviour of conformal maps and use this to show that the non-escaping boundary points of $U$ form a set of harmonic measure zero with respect to $U$. This leads to a new sufficient condition for the escaping set of $f$ to be connected, and also a new general result on Eremenko's conjecture

9. ‘Without Any Violence’

Introduction: reflecting (‘vertically’) I was about to start preparing the written version of my ‘reading’ of the Nines, when two things happened that helped me give better order to my reflections. Among the PhD applications I was reviewing, I came across a powerful defence of interpreting the Commedia ‘vertically’. A few days later, after giving a lecture based on the current chapter at a prestigious North American department of Italian, the idea that Dante’s masterpiece might be read ‘verti..

Educational Implementation of a Sound Level Meter in the LabVIEW Environment

As a consequence of recent implementations of EU Directives related to noise protection more and more students of various AGH-UST programs are introduced to the basics of acoustic measurements. Students at various levels of theoretical background in the field of acoustic measurements are offered practical training in measurements using digital sound analyzers. The situation would be optimal if each student could have a device at his/her own disposal. Unfortunately, such a situation is not possible at the moment because of various reasons. With the above problem in mind, a dedicated software package has been developed, implemented in the LabVIEW environment, which allows detailed studies of problems related to the acoustic signal measurement using sound level meters, as well as tasks in spectral analysis (1/1 and 1/3 band filters) and narrow-band (FFT) analysis. With such organization during the introductory laboratory classes each student is offered a direct individual contact with a virtual device that is properly pre-programmed for realization of a well-constructed learning process. It definitely facilitates understanding of the essence of acoustic signal measurements and provides a good basis for further laboratory work carried out as a team-activity

Use of LabView Software for propulsion systems research

W artykule przedstawiono krótką charakterystykę programowania w środowisku LabVIEW. Opisano również ogólną budowę środowisko programu wraz z podstawowymi jego funkcjami. Ponadto, na przykładzie dwóch aplikacji, zaprezentowano technikę programowania w tym środowisku.The article describes shortly programming procedures in LabView software. General structure of the software and principal functions were also presented. Moreover, programming technique was shown on two examples

Computer aided stand for laboratory tests of HTPEM type fuel cells and electrolysers

W ramach projektu Lider finansowanego ze środków Narodowego Centrum Badań i Rozwoju zostało opracowane nowoczesne stanowisko do badania zarówno ogniw paliwowych jak i elektrolizerów. Zostało ono umieszczone w budynku Lubelskiego Parku Naukowo-Technologicznego, gdzie znajdują się doskonałe warunki do prowadzenia badań naukowych tego typu jak i komercjalizacji uzyskanych wyników. Zbudowane stanowisko badawcze jest typu uniwersalnego, przystosowane do badania membranowych ogniw paliwowych i elektrolizerów niskotemperaturowych (LTPEM) oraz wysokotemperaturowych (HTPEM). Jest to możliwe dzięki uniwersalnej badawczej jednostce sterującej zbudowanej na bazie modułu CompactRIO firmy National Instruments. Uzupełnieniem stanowiska są nowoczesne zasilacze oraz programowalne obciążenie prądowe. W przypadku ogniw/elektrolizerów HTPEM są one umieszczane w obudowie termicznej pozwalającej na pracę w temperaturach do 200 ⁰C. Prezentowane stanowisko zawiera całą niezbędną infrastrukturę dostarczania wodoru jak i system wykrywania nieszczelności. W artykule zostanie wykazane, że obecne badania ogniw paliwowych/elektrolizerów muszą być wspomagane innowacyjnymi technologiami komputerowymi.Within the Project Lider funded by the National Research and Development Centre the modern test stand for both, fuel cells and electrolysers has been designed. It has been placed at the Lublin Science and Technology Park joint stock co., where there are excellent conditions for conducting this type of research as well as for commercialization of the results. Built test stand is the universal stand, adapted for the study of Proton Exchange Membrane fuel cells and electrolysers as well as Low Temperature (LTPEM) as High Temperature (HTPEM). It is possible due to universal laboratory control unit based on CompactRIO module of National Instruments. Completion for the stand are modern power suppliers and programmable current load. In case of HTPEM fuel cells/electrolysers they are placed in thermal casing allowing them to operate at temperatures up to 200°C. Presented stand includes all the necessary infrastructure of hydrogen supply and leak detection system. In the article it is shown that the current fuel cell/electrolysers research must be supported by innovative computer technologies