The emergence of 4-cycles in polynomial maps over the extended integers

Let $f(x) \in \mathbb{Z}[x]$; for each integer $\alpha$ it is interesting to consider the number of iterates $n_{\alpha}$, if possible, needed to satisfy $f^{n_{\alpha}}(\alpha) = \alpha$. The sets $\{\alpha, f(\alpha), \ldots, f^{n_{\alpha} - 1}(\alpha), \alpha\}$ generated by the iterates of $f$ are called cycles. For $\mathbb{Z}[x]$ it is known that cycles of length 1 and 2 occur, and no others. While much is known for extensions to number fields, we concentrate on extending $\mathbb{Z}$ by adjoining reciprocals of primes. Let $\mathbb{Z}[1/p_1, \ldots, 1/p_n]$ denote $\mathbb{Z}$ extended by adding in the reciprocals of the $n$ primes $p_1, \ldots, p_n$ and all their products and powers with each other and the elements of $\mathbb{Z}$. Interestingly, cycles of length 4, called 4-cycles, emerge for polynomials in $\mathbb{Z}\left[1/p_1, \ldots, 1/p_n\right][x]$ under the appropriate conditions. The problem of finding criteria under which 4-cycles emerge is equivalent to determining how often a sum of four terms is zero, where the terms are $\pm 1$ times a product of elements from the list of $n$ primes. We investigate conditions on sets of primes under which 4-cycles emerge. We characterize when 4-cycles emerge if the set has one or two primes, and (assuming a generalization of the ABC conjecture) find conditions on sets of primes guaranteed not to cause 4-cycles to emerge.Comment: 14 pages, 1 figur

Kohleausstieg : Analyse von aktuellen Diskussionsvorschlägen und Studien ; Kurzstudie

Die deutschen Braun- und Steinkohlekraftwerke produzieren 40 % des deutschen Stroms - sind aber für 80 % der Treibhausgasemissionen in diesem Sektor verantwortlich. Ein sukzessiver Ausstieg aus der Kohleverstromung kann daher einen entscheidenden Beitrag leisten, die deutschen Klimaziele zu erreichen und den Pfad zur Einhaltung der Klimaziele von Paris offen zu halten. Vor diesem Hintergrund hat sich in den letzten Jahren in Deutschland eine Debatte um einen möglichen nationalen Kohleausstieg entsponnen. Der Naturschutzbund Deutschland (NABU) hat das Wuppertal Institut daher beauftragt, zentrale wissenschaftliche Studien und politische Positionspapiere zum Thema Kohleausstieg zu analysieren. In der nun vorliegenden Metastudie fassen die Autoren den aktuellen Diskussionsstand zu wichtigen Eckpfeilern eines beschleunigten Kohleausstiegs in Deutschland zusammen. Analysiert wurden insbesondere Aussagen zur klimapolitischen Notwendigkeit und zur energiewirtschaftlichen Machbarkeit unterschiedlicher Zeithorizonte eines Kohleausstiegs sowie Optionen für eine sozialverträgliche Gestaltung des damit einhergehenden Strukturwandels

Suffizienzansätze in der nationalen Energie- und Klimapolitik in Deutschland : Kurzanalyse

Steigende Energiepreise und die Importabhängigkeit von fossilen Energieträgern - unter anderem aufgrund des Krieges in der Ukraine - erfordern eine politische und gesellschaftliche Reaktion. Wie kann es gelingen, weniger Energie zu verbrauchen? Hier kann die Energiesuffizienz als Nachhaltigkeitsstrategie Ansatzpunkte liefern. Der vorliegende Beitrag widmet sich der Frage, welche Pläne und Instrumente für Energiesuffizienz die politischen Institutionen in Deutschland vorlegen

Paediatric drowning: a standard operating procedure to aid the prehospital management of paediatric cardiac arrest resulting from submersion

Objectives: Drowning is one of the leading causes of death in children. Resuscitating a child following submersion is a highpressure situation, and standard operating procedures can reduce error. Currently, the Resuscitation Council UK guidance does not include a standard operating procedure on paediatric drowning. The objective of this project was to design a standard operating procedure to improve outcomes of drowned children. Methods: A literature review on the management of paediatric drowning was conducted. Relevant publications were used to develop a standard operating procedure for management of paediatric drowning. Results: A concise standard operating procedure was developed for resuscitation following paediatric submersion. Specific recommendations include: the Heimlich manoeuvre should not be used in this context; however, prolonged resuscitation and therapeutic hypothermia are recommended. Conclusions: This standard operating procedure is a potentially useful adjunct to the Resuscitation Council UK guidance and should be considered for incorporation into its next iteration

Changes in pain and nutritional intake modulate ultra-running performance: a case report

Ultra-endurance running provides numerous physiological, psychological, and nutritional challenges to the athlete and supporting practitioners. We describe the changes in physiological status, psychological condition, and nutritional intake over the course of two 100-mile running races, with differing outcomes: non-completion and completion. Athlete perception of pain, freshness, and motivation differed between events, independent of rating of perceived exertion. Our data suggest that the integration of multiple sensations (freshness, motivation, hunger, pain, and thirst) produce performance. Increases in carbohydrate feeding (+5 g·h −1) and protein intake (+0.3 g·kg −1) also likely contributed to successful completion of a 100-mile race, by reducing the fractional utilization of maximal oxygen uptake and satiating hunger, respectively. Nutritional data support the notion that the gut is a trainable, and critical organ with respect to ultra-endurance performance. Finally, we propose future research to investigate the rate at which peak feeding occurs throughout ultra-endurance events, as this may further serve to personalize sports nutrition strategies

Exploring energy sufficiency : new challenges and options in times of crisis

The war in Ukraine is changing the political landscape at breakneck speed. How should politics and society react to high energy prices and a precarious dependence on fossil fuels imports? Can modern societies get by with much less energy? Energy sufficiency can play an important role in answering these questions. The contributions in this Special topic explore sufficiency as an interdisciplinary research topic for energy modeling, scenarios, and policy

Das Gebot der Stunde : Energiesparen durch Energiesuffizienz

Energiesparen ist durch den Krieg in der Ukra­ine das Gebot der Stunde, um uns unabhängig von russischen Energieträgern zu machen; vor Kriegsbeginn spielte dieses Thema keine allzu große Rolle in der breiteren politischen Diskus­sion. In Szenarien und Strategien, wie mittel­- und langfristige Klimaziele erreicht werden könnten, gewann das Thema Energiesparen durch Ener­giesuffizienz in den vergangenen Jahren hinge­gen immer mehr an Bedeutung, wobei die tech­nischen Strategien Effizienz und Konsistenz, also die Umstellung auf erneuerbare Energien, noch immer maßgebend sind. In diesem Beitrag zeigen wir, welche Rol­le das Senken des Energieverbrauches spielt, um Klimaziele zu erreichen, und warum dies eine ge­eignete Möglichkeit ist, multiple Krisen gleich­zeitig zu lösen. In Hinblick darauf ist Energie­suffizienz unabdingbarer Bestandteil möglicher Lösungsstrategien. Außerdem skizzieren wir, welche kurz­, mittel­- und langfristigen Politikin­strumente derzeit diskutiert werden, und ergän­zen dies um weitere Ideen zu Einsparpotenzialen sowie um Umsetzungsbeispiele

Disordered RNA chaperones can enhance nucleic acid folding via local charge screening

This work is licensed under a Creative Commons Attribution 4.0 International License.RNA chaperones are proteins that aid in the folding of nucleic acids, but remarkably, many of these proteins are intrinsically disordered. How can these proteins function without a well-defined three-dimensional structure? Here, we address this question by studying the hepatitis C virus core protein, a chaperone that promotes viral genome dimerization. Using single-molecule fluorescence spectroscopy, we find that this positively charged disordered protein facilitates the formation of compact nucleic acid conformations by acting as a flexible macromolecular counterion that locally screens repulsive electrostatic interactions with an efficiency equivalent to molar salt concentrations. The resulting compaction can bias unfolded nucleic acids towards folding, resulting in faster folding kinetics. This potentially widespread mechanism is supported by molecular simulations that rationalize the experimental findings by describing the chaperone as an unstructured polyelectrolyte.Swiss National Science FoundationEuropean Molecular Biology OrganizationIntramural Research Program of the NIDDK at the National Institutes of Healt

Analysis of the historical structural change in the German hard coal mining Ruhr area (case study)

This case study examined the structural change in the Ruhr area caused by the low international competitiveness of German hard coal mining over the period from the late 1950s to 2015. It analysed the structural change process and the structural policies implemented as a reaction to this process with the objective to make this knowledge available for future structural change processes in other (coal) regions by deploying various qualitative and quantitative methods of empirical social and economic research. A discourse analysis helped to recognise who supported which structural policy approaches and why - and thus gives indications of the possible relevance of experiences for other regions