In our previous publication we have shown a method for calculating series of even powers of $π$ based on the product representation of the $sinc$ function. We refer the readers to [1] for more details. In this work we apply the method to the product representation of the $cosine$ function and and thereby derive nice series formulas for even powers of the number $π$, such as \[ \frac{1}{2\,!} \left(\fracπ{2}\right)^2 = \sum_{\ell_1=1}^{\infty} \frac{1}{\left(2\,\ell_1-1\right)^2} \;;\quad \frac{1}{4\,!} \left(\fracπ{2}\right)^4 = \sum_{\ell_{2}=2}^{\infty} \left(\sum_{\ell_{1}=1}^{\ell_{2}-1} \frac{1}{ \left(2\,\ell_1-1\right)^2 \cdot \left(2\,\ell_2-1\right)^2} \right)\;; \] \[ \frac{1}{6\,!}\left(\fracπ{2}\right)^6 =\sum_{\ell_{3}=3}^{\infty} \left(\sum_{\ell_{2}=2}^{\ell_{3}-1} \left(\sum_{\ell_{1}=1}^{\ell_{2}-1} \frac{1}{ \left(2\,\ell_1-1\right)^2\cdot \left( 2\,\ell_2-1\right)^2 \cdot \left(2\,\ell_3-1\right)^2} \right)\right) \] Many of these formulas do not seem to be widely known. -- In unserer früheren Publikationen haben wir ein Verfahren vorgestellt, das die Berechnung von Reihen für geradzahlige $π$-Potenzen unter Verwendung der $sinc$-Funktion ermöglicht. Wir verweise
The energy transition is also about switching to electricity-based technologies such as heat pumps and electric mobility. They avoid heat as an intermediate step and are therefore much more efficient. This can significantly reduce the demand for primary energy in the future, which can then be fully covered by the expansion of renewable energies. Entropy and the maximum possible combustion temperature can be used to understand why combustion is so inefficient.
Which technologies are currently booming in power generation? The answer can clearly be seen in the trends in global electricity generation data. Analysing this data using the theory of diffusion of innovations reveals how photovoltaics and wind power are gaining ground worldwide. Other technologies - especially coal and nuclear power - are being displaced, with Germany playing a pioneering role.
We are in the process of creating a database of digital games from the DACH region. This article provides an insight into the context in which it was created and the underlying methodological considerations behind the games database. The database was compiled collaboratively and lists digital games developed in Germany, Austria and Switzerland up to the year 2000. In this report, we outline our initial considerations and the various stages of realisation as well as the input data on which the database was built, the aims of the data model and the difficulties we faced during the creation process. We then pin down the current status of the games database and give an outlook on the project's future plans. -- Unser Werkstattbericht gibt Einblick in den Entstehungskontext sowie die zugrundeliegenden methodischen Überlegungen hinter der von den Autor*innen publizierten Spieledatenbank. Diese wurde kollaborativ erarbeitet und führt digitale Spiele, die in Deutschland, Österreich und der Schweiz bis zum Jahr 2000 entwickelt wurden. In diesem Bericht skizzieren wir neben unseren Ausgangsüberlegungen und den verschiedenen Arbeitsschritten bei der Realisierung außerdem auch, auf welcher Date
In the course of the energy transition, energy generation from nuclear power - through nuclear fission and perhaps in the future through nuclear fusion - is often proposed as an alternative or supplement to renewable energy sources. There are already good reasons why electricity generation from nuclear energy is significantly more expensive than other forms of generation, while increasing dryness as a result of climate change is generally calling into question the reliability of thermal power plants. Nuclear energy is therefore unlikely to play a role in a future energy supply that relies on low costs and reliability.
The warmer temperatures of global climate change strengthen the water cycle, evaporation and precipitation increase. But the extremes of heavy rain, floods, dry periods and droughts will also increase. How does this fit together? Simple physical considerations show which factors mainly regulate the strength of the water cycle in the Earth system, and how this determines water availability on land. This can be used to interpret the observed changes in the water balance in Germany and explain the increasing dryness in Germany.
The wind blows stronger and more reliably over the sea than over land. Thus, offshore wind energy is expected to make a major contribution to the energy transition in Germany, especially in the German Bight. But what happens when a growing number of wind farms extract more and more wind energy from the atmosphere?
The more AI-assisted decisions affect people's lives, the more important the fairness of such decisions becomes. In this chapter, we provide an introduction to research on fairness in machine learning. We explain the main fairness definitions and strategies for achieving fairness using concrete examples and place fairness research in the European context. Our contribution is aimed at an interdisciplinary audience and therefore avoids mathematical formulation but emphasizes visualizations and examples. -- Je mehr KI-gestützte Entscheidungen das Leben von Menschen betreffen, desto wichtiger ist die Fairness solcher Entscheidungen. In diesem Kapitel geben wir eine Einführung in die Forschung zu Fairness im maschinellen Lernen. Wir erklären die wesentlichen Fairness-Definitionen und Strategien zur Erreichung von Fairness anhand konkreter Beispiele und ordnen die Fairness-Forschung in den europäischen Kontext ein. Unser Beitrag richtet sich dabei an ein interdisziplinäres Publikum und verzichtet daher auf die mathematische Formulierung sondern betont Visualisierungen und Beispiele.
Quantum physics is a long established content in high school curricula. More recently, alternative approaches based on information-theoretical formulations of quantum theory have been discussed, in which conceptual emphases change in comparison to established didactical approaches. In particular, the notions of "superposition" and "entanglement" are brought into the center of discussion in these approaches. Likewise, there is a broad public interest in the new applications of quantum physics such as quantum computing, which has led to a variety of popular depictions. In this paper we identify common inaccuracies and errors in these representations, explain the technical background and make first recommendations to avoid misunderstandings. Our initial focus is on the notion of "superposition". -- Die Quantenphysik ist seit vielen Jahren ein etablierter Inhalt der Oberstufenphysik. In jüngerer Zeit werden alternative Zugänge über die informationstheoretische Formulierung der Quantentheorie diskutiert, bei denen sich konzeptionelle und begriffliche Schwerpunkte im Vergleich zu etablierten Elementarisierungen verändern. Im Besonderen die Begriffe "Superposition" und "Verschränkung" wer
The transition of our energy system to renewable energies is necessary in order not to heat up the climate any further and to achieve climate neutrality. The use of wind energy plays an important role in this transition in Germany. But how much wind energy can be used and what are the possible consequences for the atmosphere if more and more wind energy is used?
With the increasing attention non-binary people receive in Western societies, strategies of gender-fair language have started to move away from binary (only female/male) concepts of gender. Nevertheless, hardly any approaches to take these identities into account into machine translation models exist so far. A lack of understanding of the socio-technical implications of such technologies risks further reproducing linguistic mechanisms of oppression and mislabelling. In this paper, we describe the methods and results of a workshop on gender-fair language and language technologies, which was led and organised by ten researchers from TU Wien, St. Pölten UAS, FH Campus Wien and the University of Vienna and took place in Vienna in autumn 2021. A wide range of interest groups and their representatives were invited to ensure that the topic could be dealt with holistically. Accordingly, we aimed to include translators, machine translation experts and non-binary individuals (as "community experts") on an equal footing. Our analysis shows that gender in machine translation requires a high degree of context sensitivity, that developers of such technologies need to position themselves cautious
Do our physics curricula provide the appropriate data management competences in a world where data are considered a crucial resource and substantial funding is available for building a national research data infrastructure (German: Nationale Forschungsdateninfrastuktur = NFDI)? Although basic data evaluation and systematic documentation are practiced when students first come into contact with data, particularly in experimental physics lab courses, they do not meet the increasing demands of research and professional practice to deal with the analysis of huge datasets. In many cases, the problem starts with the fact that there is no consensus on a suitable entry-level programming language. At the Department of Physics at Friedrich-Alexander-Universität Erlangen-Nürnberg, we have made minor adjustments to the physics curriculum in recent years, which we present in this article. We placed data management competences early in the bachelor curriculum, which has resulted in considerable advantages throughout the further course of studies. The authors feel that students are quickly moving into the fast lane in data management; we can already see in our research groups that they are becomin
The asteroid that wiped out the dinosaurs was likely an exceptionally rare CO chondrite from a distant region of the solar system。 Its unusual chemistry suggests that planet-cooling dust and debris, rather than sulfur inside the asteroid, may have delivered the deadliest blow
NASA's PACE satellite captured the Black Sea glowing turquoise during its annual phytoplankton bloom。 The vivid color comes from massive numbers of coccolithophores, microscopic organisms whose reflective shells brighten the water enough to be seen from space。 An astronaut aboard the International Space Station also photographed the bloom spreading
Scientists say new technologies have reopened the debate over whether Mars could someday be terraformed, turning a once impossible idea into a serious research topic。 Before anyone tries to reshape the Red Planet, though, researchers say we must understand the risks, including what might be lost if Mars already harbors its own forms of life
A giant planet had been hiding inside one of astronomy’s most closely studied planetary systems, concealed by a bright disk of cosmic dust。 Webb revealed Beta Pictoris d through atmospheric traces of carbon monoxide, water vapor, and methane, showcasing a promising new method for finding elusive exoplanets
Physicists from Heinrich Heine University Düsseldorf (HHU) have examined a fundamental property of quantum mechanics in collaboration with the German Aerospace Center (DLR)。 In the scientific journal Physical Review Letters, they show that this theory does not necessarily need to be formulated with imaginary numbers – real numbers can in fact also
NASA's James Webb Space Telescope has revealed new details about the blistering lava planet 55 Cancri e, where temperatures are high enough to melt rock。 The data indicate the planet likely has a hydrogen-rich atmosphere shaped by gases escaping from its molten interior, with signs that volcanic outgassing may even create temporary clouds
China’s Tianwen-1 orbiter captured a faint but remarkable view of 3I/ATLAS as the interstellar comet raced past Mars。 The images reveal its tail and glowing coma, offering scientists a glimpse of material born beyond our solar system