We investigate how the inverse degree index of graphs depends on their cyclomatic number. In particular, we provide sharp lower bounds on the inverse degree index over all graphs on a given number of vertices with a given cyclomatic number. We also deduce some structural properties of extremal graphs. Some open questions regarding the upper bound over the same class of graphs are discussed and some possible further developments are indicated.

In dieser Arbeit wird eine Strategie zur Bewertung des Zuverlässigkeitsniveaus von gemauerten Gründerzeithäusern im Erdbebenlastfall vorgestellt. Die Nachbemessungsstrategie ermöglicht eine normgerechte Bewertung der Schubtragfähigkeit, des Erdbebenerfüllungsfaktors sowie des personenbezogenen Risikos einzelner Schubwände (aussteifende Zwischenwände) in Form von Nachbemessungstafeln. Die Nachbemessungstafeln ergeben sich im Wesentlichen durch die einschlägigen Normen, der aktuell angewandten Pushover-Berechnungsmethode im gemauerten Altbestand, der gründerzeitlichen Bauwerkscharakteristika und der Standortgegebenheiten im Raum Wien. Die methodische Herangehensweise umfasste eine ausführliche Bestandsanalyse von mehr als 200 Gründerzeithäuser, die Nachweisführung der betrachteten Bestandsobjekte im Erdbebenlastfall, eine Sensitivitätsanalyse der Einflussparameter auf das sich einstellende Sicherheitsniveau und die Ableitung sowie Vorstellung der Nachbemessungstafeln. Die Mauerwerksqualität konnte anhand von umfangreichen Mauerwerksuntersuchungen von 125 gründerzeitlichen Objekten in der vorgestellten Strategie berücksichtigt werden.

The paper considers the possibility of improving the technical characteristics of gas surge arresters for the co-ordination of insulation at low voltage, medium voltage and high voltage levels. The idea for improving the characteristics of a gas surge arrester is based on the application of the radioactive source 241Am in the area of the surge arrester cathode. Intensive ionization with alpha particles significantly increases the number of free electrons in the space between electrodes, which shortens the time of their transition to initial electrons. This changes the Paschen curve of the gas surge arrester, narrows and flattens its impulse characteristic and reduces the stochasticity of the response of the gas surge arrester. All this results in a significant improvement in the characteristics of the gas surge arrester at all voltage levels. This improvement is particularly noticeable in the case of low voltage surge arresters. The paper is basically theoretical-experimental research. The experiments were performed under well-controlled laboratory conditions. The combined measurement uncertainty of all measurements was acceptable.

The study of aerosol dispersion in indoor environments is essential to understanding and mitigating airborne virus transmission, such as SARS-CoV-2. Computational Fluid Dynamics (CFD) has emerged as a valuable tool for investigating aerosol dispersion, providing an alternative to costly experimental methods. In this study, we investigated the performance of four (4) Reynolds-averaged Navier-Stokes (RANS) turbulence models in predicting aerosol dispersion from a human body coughing in a small, ventilated indoor environment. We compared the Standard, RNG, Realizable k-ϵ models and the SST k- ω model using the same boundary conditions. We initially observed that the horizontal distance of the coughed aerosols after 10.2s dispersion time was substantially shorter with the standard k-ϵ turbulence compared to the other three turbulence models compared to the SST k-ω model, the RNG, and realizable k-ϵ models exhibit a high degree of similarity in their dispersion patterns. Specifically, we observed that the aerosols dispersed horizontally faster with the RNG and Realizable k-ϵ models. In conclusion, when compared to qualitative data from the literature, our observations exclude the standard k-ϵ turbulence. However, to select the most appropriate turbulence model for capturing the cough flow and aerosol dispersion dynamics, further detailed validation against both quantitative and qualitative data is needed.

The acoustic adaptation hypothesis (AAH) is often tested between species from open and closed habitats. However, the acoustic differences are rather small and thus the evidence is ambiguous. We tested the AAH between subterranean and surface-dwelling species living in very different acoustic environments. Lower frequencies (<1 kHz) are transmitted best in subterranean burrows and there is a high-frequency cut off around 3 kHz. The other important factor influencing the frequencies of vocal signals is body size. Acoustic allometry – a negative relationship between body size and frequency of acoustic signals – indicates that larger species tend to produce sounds of lower frequencies than smaller species, due to their larger vocal apparatus. The present study shows, that acoustic allometry applies to subterranean as well as surface-dwelling rodents and that the environment influences the main frequency of their vocalization. Besides, the subterranean species tend to have lower vocal signals than surface-dwelling species.

Everyone is born with the right to life and the right to live that life with the dignity of a human being and a citizen, to have the right to choose education, place of residence, the right but not the obligation to start a family, the right to earn money and the freedom to dispose of it. Every man and citizen is a woman. However, it hasn't always been like that: The work deals with the position of women in society, and what is reflected on her position and status in the family throughout history and modern times. The main goal of the work is, through a cross-section of the past with a comparative analysis of the contemporary era, to realize productivity and full equality of the sexes in the near future. The work is based on the analysis of a heterogeneous family (the family of a man and a woman).