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

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

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

The innervation of the enthesis organ of the rat achilles tendon

PURPOSE: The enthesis (bony insertion of a tendon or ligament) is a common site of overuse injuries in sport. Because enthesopathies can be painful, it is often assumed that the enthesis is highly innervated-but with little evidence to support the assumption. The Achilles tendon has one of the most complex of attachment sites, for together with adjacent tissues, the enthesis itself forms part of an 'enthesis organ' which reduces stress concentration at the bony interface. These adjacent structures include a 'sesamoid fibrocartilage' in the tendon, a 'periosteal fibrocartilage' on the superior tuberosity of the calcaneus, and a fat pad which extends into the retrocalcaneal bursa during plantarflexion. The purpose of the present study is to investigate the innervation of the whole enthesis organ complex. METHODS: The tendon attachment site was removed from one leg of 3 male Wistar rats at each of the following ages-neonates, 4 weeks, 12 weeks, and 24 months. The tissue was fixed in 4% paraformaldehyde, prepared for routine indirect immunohistochemistry and cryosectioned in the sagittal plane. Serial sections were immunolabelled with polyclonal antibodies to protein gene product 9.5, substance P, calcitonin gene related peptide and neurofilament 200. Histology reference sections were stained with toluidine blue. RESULTS: No nerve fibers were detected at the enthesis itself or in the sesamoid and periosteal fib ro cartilages in rats of any age. However, the fat pad was richly supplied by nerve fibers which immunolabelled with all of the antibodies used. It also contained abundant mast cells. The innervation of the fat pad was confirmed in 10 human Achilles tendons obtained from the Department of Forensic Medicine at the Ludwig-Maximilians-Universität, in accordance with the ethical regulations of Munich University. The nerve fibers again immunolabelled with all antibodies and formed an intricate network in which the fibers lay between individual fat cells. CONCLUSION: We suggest that healthy entheses are not innervated because of the high levels of mechanical loading experienced at insertion sites. However, the striking innervation of the adjacent fat pad suggests that it may have an unheralded proprioceptive role monitoring changes in insertional angle between tendon and bone that occur as a result of foot movements

How U.S. Ocean Policy and Market Power Can Reform the Coral Reef Wildlife Trade

As the world’s largest importer of marine ornamental species for the aquaria, curio, home décor, and jewelry industries, the United States has an opportunity to leverage its considerable market power to promote more sustainable trade and reduce the effects of ornamental trade stress on coral reefs worldwide. Evidence indicates that collection of some coral reef animals for these trades has caused virtual elimination of local populations, major changes in age structure, and promotion of collection practices that destroy reef habitats. Management and enforcement of collection activities in major source countries such as Indonesia and the Philippines remain weak. Strengthening US trade laws and enforcement capabilities combined with increasing consumer and industry demand for responsible conservation can create strong incentives for improving management in source countries. This is particularly important in light of the March 2010 failure of the parties to the Convention on International Trade in Endangered Species (CITES) to take action on key groups of corals

Evolution of the Most Massive Galaxies to z=0.6: I. A New Method for Physical Parameter Estimation

We use principal component analysis (PCA) to estimate stellar masses, mean stellar ages, star formation histories (SFHs), dust extinctions and stellar velocity dispersions for ~290,000 galaxies with stellar masses greater than $10^{11}Msun and redshifts in the range 0.4<z<0.7 from the Baryon Oscillation Spectroscopic Survey (BOSS). We find the fraction of galaxies with active star formation first declines with increasing stellar mass, but then flattens above a stellar mass of 10^{11.5}Msun at z~0.6. This is in striking contrast to z~0.1, where the fraction of galaxies with active star formation declines monotonically with stellar mass. At stellar masses of 10^{12}Msun, therefore, the evolution in the fraction of star-forming galaxies from z~0.6 to the present-day reaches a factor of ~10. When we stack the spectra of the most massive, star-forming galaxies at z~0.6, we find that half of their [OIII] emission is produced by AGNs. The black holes in these galaxies are accreting on average at ~0.01 the Eddington rate. To obtain these results, we use the stellar population synthesis models of Bruzual & Charlot (2003) to generate a library of model spectra with a broad range of SFHs, metallicities, dust extinctions and stellar velocity dispersions. The PCA is run on this library to identify its principal components over the rest-frame wavelength range 3700-5500A. We demonstrate that linear combinations of these components can recover information equivalent to traditional spectral indices such as the 4000A break strength and HdA, with greatly improved S/N. This method is able to recover physical parameters such as stellar mass-to-light ratio, mean stellar age, velocity dispersion and dust extinction from the relatively low S/N BOSS spectra. We examine the sensitivity of our stellar mass estimates to the input parameters in our model library and the different stellar population synthesis models.Comment: 20 pages, 18 Figures, submitted to MNRA

Feedback and Recycled Wind Accretion: Assembling the z=0 Galaxy Mass Function

We analyse cosmological hydrodynamic simulations that include observationally-constrained prescriptions for galactic outflows. If these simulated winds accurately represent winds in the real Universe, then material previously ejected in winds provides the dominant source of gas infall for new star formation at redshifts z<1. This recycled wind accretion, or wind mode, provides a third physically distinct accretion channel in addition to the "hot" and "cold" modes emphasised in recent theoretical studies. Because of the interaction between outflows and gas in and around halos, the recycling timescale of wind material (t_rec) is shorter in higher-mass systems, which reside in denser gaseous environments. In these simulations, this differential recycling plays a central role in shaping the present-day galaxy stellar mass function (GSMF). If we remove all particles that were ever ejected in a wind, then the predicted GSMFs are much steeper than observed; galaxy masses are suppressed both by the direct removal of gas and by the hydrodynamic heating of their surroundings, which reduces subsequent infall. With wind recycling included, the simulation that incorporates our favoured momentum-driven wind scalings reproduces the observed GSMF for stellar masses 10^9 < M < 5x10^10 Msolar. At higher masses, wind recycling leads to excessive galaxy masses and excessive star formation rates relative to observations. In these massive systems, some quenching mechanism must suppress the re-accretion of gas ejected from star-forming galaxies. In short, as has long been anticipated, the form of the GSMF is governed by outflows; the unexpected twist here for our simulated winds is that it is not primarily the ejection of material but how the ejected material is re-accreted that governs the GSMF.Comment: 16 pages, 7 figures, accepted by MNRA

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.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

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