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Geometry is part of the core of mathematics. It has been relevant ever since people have interacted with nature and its phenomena. Geometry’s relevance to the teaching and learning of mathematics can be emphasized, too. Nevertheless, a current potential shift in the topics of mathematics education to the detriment of geometry might be emerging. That is, other topics related to mathematics are seeming to grow in importance in comparison to geometry. Despite this, or perhaps because of it, geometry is an important component of current research in mathematics education. In the literature review, we elaborate relevant foci on the basis of current conference proceedings. By means of about 50 journal articles, five main topics are elaborated in more detail: geometric thinking and practices, geometric contents and topics, teacher education in geometry, argumentation and proof in geometry, as well as the use of digital tools for the teaching and learning of geometry. Conclusions and limitations for current and future research on geometry are formulated at the end of the article. In particular, the transfer to the practices of geometric teaching is explored on the basis of the elaborated research findings in order to combine both aspects of the teaching and learning of geometry.
Highlights
• We propose a framework to address landscape effects on ecosystem services.
• We expect ecosystem service flows to be modulated by the amount and configuration of supply and demand areas.
• We stress the role of neutral areas in facilitating or hindering ecosystem service flows.
• Supply/demand ratios, spatial overlap, and ES characteristics need to be accounted for when assessing flows.
• We propose a research agenda with challenges to couple the effects of landscape configuration on ES flow.
Abstract
Despite advances in understanding the effects of landscape structure on ecosystem services (ES), many challenges related to these complex spatial interactions remain. In particular, the integration of landscape effects on different components of the service provision chain (supply, demand, and flow) remains poorly understood and conceptualized. Here we propose a theoretical framework to further explore how the spatial flow of ES can vary according to landscape structure (i.e. composition and configuration) emphasizing the role played by the configuration of supply, demand, and neutral areas, as well as individual characteristics of ES (e.g., service rivalry). For this, we expand the discussion on how landscape changes can affect ES flows and propose a theoretical representation of ES flows variation led by different supply-demand ratios. Additionally, we expand this discussion by integrating the potential effects of neutral areas in the landscape as well as of supply/demand spatial overlap. This novel approach links the spatial arrangement (e.g. fragmentation, network complexity, matrix resistance) usually captured by landscape metrics, and ratios of ES supply and demand areas to potential effects on spatial flows of ES. We discuss the application of this model using widely studied ES, such as pollination, pest control by natural enemies, and microclimate regulation. Finally, we propose a research agenda to connect the presented ideas with other prominent research topics that must be further developed to support landscape management targeting ES provision. The prominence of ES science calls for contributions such as this to give the scientific community the opportunity to reflect on the underlying mechanisms of ES and avoid oversimplified spatial assessments.
Measurements of exclusive J/ψ, ψ(2s), and electron-positron (e+e−) pair photoproduction in Au+Au ultra-peripheral collisions are reported by the STAR experiment at √sNN=200 GeV. We report several first measurements at the Relativistic Heavy-Ion Collider, which are i) J/ψ photoproduction with large momentum transfer up to 2.2 (GeV/c)2, ii) coherent J/ψ photoproduction associated with neutron emissions from nuclear breakup, iii) the rapidity dependence of incoherent J/ψ photoproduction, iv) the ψ(2s) photoproduction cross section at mid-rapidity, and v) e+e− pair photoproduction up to high invariant mass of 6 GeV/c2. For measurement ii), the coherent J/ψ total cross section of γ∗+Au→J/ψ+Au as a function of the center-of-mass energy Wγ∗N has been obtained without photon energy ambiguities. The data are quantitatively compared with the Monte Carlo models STARlight, Sartre, BeAGLE, and theoretical calculations of gluon saturation with color glass condensate, nuclear shadowing with leading twist approximation, Quantum Electrodynamics, and the Next-to-Leading Order perturbative QCD. At the photon-nucleon center-of-mass energy of 25.0 GeV, the coherent and incoherent J/ψ cross sections of Au nuclei are found to be 71±10% and 36±7%, respectively, of that of free protons. These data provide an important experimental constraint for nuclear parton distribution functions and a unique opportunity to advance the understanding of the nuclear modification effect at the top RHIC energy.
For the search of the chiral magnetic effect (CME), STAR previously presented the results from isobar collisions (9644Ru+9644Ru, 9640Zr+9640Zr) obtained through a blind analysis. The ratio of results in Ru+Ru to Zr+Zr collisions for the CME-sensitive charge-dependent azimuthal correlator (Δγ), normalized by elliptic anisotropy (v2), was observed to be close to but systematically larger than the inverse multiplicity ratio. The background baseline for the isobar ratio, Y=(Δγ/v2)Ru(Δγ/v2)Zr, is naively expected to be (1/N)Ru(1/N)Zr; however, genuine two- and three-particle correlations are expected to alter it. We estimate the contributions to Y from those correlations, utilizing both the isobar data and HIJING simulations. After including those contributions, we arrive at a final background baseline for Y, which is consistent with the isobar data. We extract an upper limit for the CME fraction in the Δγ measurement of approximately 10% at a 95% confidence level on in isobar collisions at sNN−−−√=200 GeV.
In the culture history of ancient Europe questions pertaining to its diverse relationships to advanced civilisations in the Mediterranean sphere look back upon a long tradition. Varyingly different single finds and groups of finds have repeatedly provided the prospect and scope for investigating the character and extent of contacts and influences as well as the consequences for cultural developments north of the Alps. In discussions on the genesis and significance of the Bronze Age in central and northern Europe, the perceived linkages between the eastern Mediterranean and the Carpathian Basin and via the Danube River as far as areas north of the Alps have played an important role. Without question, the Danube River represented a crucial axis of communication ever since the Neolithic period and in following times. Recent interdisciplinary studies, however, have broadened the scope and shown that further important communication routes existed along the Ionian-Adriatic Sea to Upper Italy and beyond the Alps, and via the Rhône valley and the West Alps to the North. Thereby, impulses of varying economic nature could be discerned, which were consequential for many aspects of the cultural development of the Early and Middle Bronze Age in Central Europe.
Matter-antimatter asymmetry is a research topic of fundamental interest, as it is the basis for the existence of the matter world, which survived annihilation with antimatter in the early Universe. High energy nuclear collisions create conditions similar to the Universe microseconds after the Big Bang, with comparable amounts of matter and antimatter. Much of the antimatter created escapes the rapidly expanding fireball without annihilation, making such collisions an effective experimental tool to create heavy antimatter nuclear objects and study their properties. In this paper, we report the first observation of the antimatter hypernucleus 4Λ¯H¯¯¯¯, composed of an Λ¯, an antiproton and two antineutrons. The discovery was made through its two-body decay after production in ultrarelativistic heavy ion collisions by the STAR experiment at the Relativistic Heavy Ion Collider. In total, 15.6 candidate 4Λ¯H¯¯¯¯ antimatter hypernuclei are obtained with an estimated background count of 6.4. Lifetimes of the antihypernuclei 3Λ¯H¯¯¯¯ and 4Λ¯H¯¯¯¯ are measured and compared with lifetimes of their corresponding hypernuclei, testing the symmetry between matter and antimatter. Various production yield ratios among (anti)hypernuclei and (anti)nuclei are also measured and compared with theoretical model predictions, shedding light on their production mechanism.
We report results on an elastic cross section measurement in proton-proton collisions at a center-of-mass energy s√=510 GeV, obtained with the Roman Pot setup of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The elastic differential cross section is measured in the four-momentum transfer squared range 0.23≤−t≤0.67 GeV2. We find that a constant slope B does not fit the data in the aforementioned t range, and we obtain a much better fit using a second-order polynomial for B(t). The t dependence of B is determined using six subintervals of t in the STAR measured t range, and is in good agreement with the phenomenological models. The measured elastic differential cross section dσ/dt agrees well with the results obtained at s√=546 GeV for proton--antiproton collisions by the UA4 experiment. We also determine that the integrated elastic cross section within the STAR t-range is σfidel=462.1±0.9(stat.)±1.1(syst.)±11.6(scale) μb.
We report a new measurement of the production of electrons from open heavy-flavor hadron decays (HFEs) at mid-rapidity (|y|< 0.7) in Au+Au collisions at sNN−−−√=200 GeV. Invariant yields of HFEs are measured for the transverse momentum range of 3.5<pT<9 GeV/c in various configurations of the collision geometry. The HFE yields in head-on Au+Au collisions are suppressed by approximately a factor of 2 compared to that in p+p collisions scaled by the average number of binary collisions, indicating strong interactions between heavy quarks and the hot and dense medium created in heavy-ion collisions. Comparison of these results with models provides additional tests of theoretical calculations of heavy quark energy loss in the quark-gluon plasma.
We report a new measurement of the production of electrons from open heavy-flavor hadron decays (HFEs) at mid-rapidity (|y|< 0.7) in Au+Au collisions at sNN−−−√=200 GeV. Invariant yields of HFEs are measured for the transverse momentum range of 3.5<pT<9 GeV/c in various configurations of the collision geometry. The HFE yields in head-on Au+Au collisions are suppressed by approximately a factor of 2 compared to that in p+p collisions scaled by the average number of binary collisions, indicating strong interactions between heavy quarks and the hot and dense medium created in heavy-ion collisions. Comparison of these results with models provides additional tests of theoretical calculations of heavy quark energy loss in the quark-gluon plasma.
The STAR Collaboration presents measurements of the semi-inclusive distribution of charged-particle jets recoiling from energetic direct-photon γdir and neutral-pion (π0) triggers in p+p and central Au+Au collisions at √sNN=200 GeV over a broad kinematic range, for jet resolution parameters R=0.2 and 0.5. Medium-induced jet yield suppression is observed to be larger for R=0.2 than for 0.5, reflecting the angular range of jet energy redistribution due to quenching. The magnitude of suppression is similar for γdir- and π0-triggered data, which constrains the color-charge and path-length dependence of jet quenching. Theoretical model calculations incorporating jet quenching do not fully describe the measurements.
We report a measurement of exclusive J/ψ photoproduction in Au+Au ultra-peripheral collisions at sNN−−−√=200 GeV using the STAR detector. For the first time, i) the rapidity correlation between J/ψ photoproduction and neutron emission from nuclear breakups has been experimentally measured; ii) nuclear suppression factors are measured for both the coherent and incoherent J/ψ production. At photon-nucleon center-of-mass energy of 25.0 GeV, the coherent and incoherent J/ψ cross sections of Au nuclei are found to be 71±10% and 36±7%, respectively, of that of free protons. The stronger suppression observed in the incoherent production provides a new experimental handle to study the initial-state parton density in heavy nuclei. Data are compared with theoretical models quantitatively.
The establishment and maintenance of protected areas (PAs) is viewed as a key action in delivering post-2020 biodiversity targets. PAs often need to meet multiple objectives, ranging from biodiversity protection to ecosystem service provision and climate change mitigation, but available land and conservation funding is limited. Therefore, optimizing resources by selecting the most beneficial PAs is vital. Here, we advocate for a flexible and transparent approach to selecting protected areas based on multiple objectives, and illustrate this with a decision support tool on a global scale. The tool allows weighting and prioritization of different conservation objectives according to user-specified preferences, as well as real-time comparison of the selected areas that result from such different priorities. We apply the tool across 1347 terrestrial PAs and highlight frequent trade-offs among different objectives, e.g., between species protection and ecosystem integrity. Outputs indicate that decision makers frequently face trade-offs among conflicting objectives. Nevertheless, we show that transparent decision-support tools can reveal synergies and trade-offs associated with PA selection, thereby helping to illuminate and resolve land-use conflicts embedded in divergent societal and political demands and values.
The financial sector plays an important role in financing the green transformation. Various regulatory initiatives in the EU aim to improve transparency in relation to the sustainability of financial products and the sustainability of economic activities of non-financial and financial undertakings. For credit institutions, the Green Asset Ratio (GAR) has been established by the European regulatory authorities as a key performance indicator (KPI) for measuring the proportion of Taxonomy-aligned on-balance-sheet exposure in relation to the total assets. The breakdown of the total GAR by type of counterparty, environmental objective and type of asset provides in-depth information about the sustainability profile of a credit institution. This information, which has not been available to date, may also initiate discussions between management and shareholders or other stakeholders regarding the future sustainability strategy of credit institutions. This paper provides an overview of the regulatory background and the method of calculating the GAR along different dimensions. Finally, the potential benefits and limitations of the GAR are discussed.
The raccoon is listed among the invasive alien species of EU concern requiring management actions. Projections of its global distribution have been mainly based on climatic variables so far. In this study, we aim to address the impact of land cover (LC) on the raccoon distribution in North America and Europe. First, we identified the LC types in which the observation sites are predominantly located to derive preferred LC types. Second, we used an ecological niche modelling (ENM) approach to evaluate the predictive power of climatic and LC information on the current distribution patterns of raccoons in both ranges. Raccoons seem to be more often associated to forested areas and mixed landscapes, including cropland and urban areas, but underrepresented in vegetation-poor areas, with patterns largely coinciding in both ranges. In order to compare the predictive power of climate variables and land cover variables, we conducted principal component analyses of all variables in the respective variable sets (climate variables and land cover variables) and used all PC variables that together explain 90% of the total variance in the respective set as predictors. Land cover only models resulted in patchy patterns in the projected habitat suitabilities and showed a higher performance compared to the climate only models in both ranges. In Europe, the land cover habitat suitability seems to exceed the current observed occurrences, which could indicate a further spread potential of the raccoon in Europe. We conclude that information on land cover types are important drivers, which explain well the spatial patterns of the raccoon. Consideration of land cover could benefit efforts to control invasive carnivores and contribute to better management of biodiversity, but also human and animal health.
In this paper, we use the “gender as a social structure” framework to assess macro-, interactional-, and micro-level mechanisms explaining the stalled revolution in gender ideologies. Using the European Values Study 2008 data and latent class analysis, we look at the spread of gender ideologies and examine their association with national levels of gendered ascription of work and care roles, work–family compatibility, social inequality and societal affluence, individual characteristics, and cross-level interactions with gender and education in 36 (post-)industrialized countries. By including a large number of Central, Eastern, and South-Eastern European countries, we provide a new and comprehensive picture of the gender ideology landscapes of Europe, reflected in two unidimensional classes—egalitarian and traditional—and four multidimensional classes, covering more than 60 percent of respondents—family oriented, choice egalitarian, intensive motherhood, and neotraditional. By modeling key features of macro-level variation, we show how the spread of gender ideologies is associated with distinct contextual conditions. We consolidate previous findings on multidimensional gender ideologies, which were based on fewer countries.
Background/aim: The aim of this study was to analyze a population of patients who had suffered from traumatic dental injuries (TDIs) by using different patient-, trauma- and treatment-related parameters.
Material and methods: All dental records of patients ≥ 3 years old who had presented at the dental emergency service between Jan 1, 2009 and Dec 31, 2016 for the treatment of dental trauma were analyzed. A total of 2758 patients were invited for a recall examination at the Department for Dental Surgery and Implantology, ZZMK Carolinum, Goethe University Frankfurt, Germany; of these, 269 patients attended their recall appointments.
Results: The enrolled patient population consisted of 1718 males and 1040 females, with a mean age of 19.63 years (median 12.00 ± 17.354 years). A total of 4909 injured teeth were assessed, with a mean of 1.78 injured teeth per patient (median 2.00 ± 1.279). Males were found to be more frequently affected by TDIs compared to females (1.65:1). The majority of these injuries occurred in the first two decades of life (66.1%; n = 1824). The majority of the patients presented for initial treatment within 24 h of their accident (95.7%). The most frequent TDIs were isolated luxation injuries 49.4% (n = 2426) and isolated crown fractures 30% (n = 1472). Combination injuries were diagnosed in 20.6% of the cases (n = 1011).
Conclusions: Based on the findings of the present analysis, it can be concluded that males were more frequently affected by TDIs than females. Most patients had suffered from TDI before they had turned 10 years of age. Overall, the enamel–dentin fracture was found to be the most frequent injury, followed by concussions and lateral luxations.
We consider ground state solutions u ∈ H2(RN) of biharmonic (fourth-order) nonlinear Schrodinger equations of the form ¨2u + 2au + bu − |u| p−2u = 0 in RN with positive constants a, b > 0 and exponents 2 < p < 2∗, where 2∗ = 2N N−4 if N > 4 and 2∗ = ∞ if N ≤ 4. By exploiting a connection to the adjoint Stein–Tomas inequality on the unit sphere and by using trial functions due to Knapp, we prove a general symmetry breaking result by showing that all ground states u ∈ H2(RN) in dimension N ≥ 2 fail to be radially symmetric for all exponents 2 < p < 2N+2 N−1 in a suitable regime of a, b > 0. As applications of our main result, we also prove symmetry breaking for a minimization problem with constrained L2-mass and for a related problem on the unit ball in RN subject to Dirichlet boundary conditions.
The topic of the article is the status of translation and homophony in philosophy, psychoanalysis and philology. The article focuses on the question of how translation is carried out using the basic principle of equivalence of meaning by homophony and what effects this can produce. The analysis of two case studies by Freud and Lacan shows that homophonic transfer from one language to another can be extremely productive for the subjective traversal of a phantasm. It is then shown that this is not, however, of purely subjective interest. Werner Hamacher has sketched the future of philology starting from such homophonic translations; Lacan has tried to advance to another theory of language through homophonic formations.
Using 𝑒+𝑒− collision data with an integrated luminosity of 7.33 fb−1 collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector operating at the BEPCII collider, the branching fraction of the leptonic decay 𝐷+ 𝑠→𝜇+𝜈𝜇 is measured to be (0.5294±0.0108stat±0.0085syst)%. Based on this, the product of the 𝐷+ 𝑠 decay constant 𝑓𝐷+ 𝑠 and the magnitude of the 𝑐→𝑠 quark mixing matrix element |𝑉𝑐𝑠| is determined to be 𝑓𝐷+ 𝑠|𝑉𝑐𝑠| = 241.8±2.5stat±2.2syst MeV. Using the value of |𝑉𝑐𝑠| given by the global standard model fit, 𝑓𝐷+ 𝑠 is found to be 248.4±2.5stat±2.2syst MeV. Alternatively, using the value of 𝑓𝐷+ 𝑠 from a recent lattice quantum chromodynamics calculation, |𝑉𝑐𝑠| is determined to be 0.968±0.010stat±0.009syst.