TY - JOUR A1 - Münch, Florentin T1 - Remarks on curvature dimension conditions on graphs JF - Calculus of variations and partial differential equations N2 - We show a connection between the CDE′ inequality introduced in Horn et al. (Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for nonnegative curvature graphs. arXiv:1411.5087v2, 2014) and the CDψ inequality established in Münch (Li–Yau inequality on finite graphs via non-linear curvature dimension conditions. arXiv:1412.3340v1, 2014). In particular, we introduce a CDφψ inequality as a slight generalization of CDψ which turns out to be equivalent to CDE′ with appropriate choices of φ and ψ. We use this to prove that the CDE′ inequality implies the classical CD inequality on graphs, and that the CDE′ inequality with curvature bound zero holds on Ricci-flat graphs. Y1 - 2017 U6 - https://doi.org/10.1007/s00526-016-1104-6 SN - 0944-2669 SN - 1432-0835 VL - 56 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Siska, Veronika A1 - Jones, Eppie Ruth A1 - Jeon, Sungwon A1 - Bhak, Youngjune A1 - Kim, Hak-Min A1 - Cho, Yun Sung A1 - Kim, Hyunho A1 - Lee, Kyusang A1 - Veselovskaya, Elizaveta A1 - Balueva, Tatiana A1 - Gallego-Llorente, Marcos A1 - Hofreiter, Michael A1 - Bradley, Daniel G. A1 - Eriksson, Anders A1 - Pinhasi, Ron A1 - Bhak, Jong A1 - Manica, Andrea T1 - Genome-wide data from two early Neolithic East Asian individuals dating to 7700 years ago JF - Science Advances N2 - Ancient genomes have revolutionized our understanding of Holocene prehistory and, particularly, the Neolithic transition in western Eurasia. In contrast, East Asia has so far received little attention, despite representing a core region at which the Neolithic transition took place independently ~3 millennia after its onset in the Near East. We report genome-wide data from two hunter-gatherers from Devil’s Gate, an early Neolithic cave site (dated to ~7.7 thousand years ago) located in East Asia, on the border between Russia and Korea. Both of these individuals are genetically most similar to geographically close modern populations from the Amur Basin, all speaking Tungusic languages, and, in particular, to the Ulchi. The similarity to nearby modern populations and the low levels of additional genetic material in the Ulchi imply a high level of genetic continuity in this region during the Holocene, a pattern that markedly contrasts with that reported for Europe. Y1 - 2017 U6 - https://doi.org/10.1126/sciadv.1601877 SN - 2375-2548 VL - 3 IS - 2 PB - American Assoc. for the Advancement of Science CY - Washington ER - TY - JOUR A1 - Guo, Li A1 - Paycha, Sylvie A1 - Zhang, Bin T1 - Algebraic Birkhoff factorization and the Euler–Maclaurin formula on cones JF - Duke mathematical journal N2 - We equip the space of lattice cones with a coproduct which makes it a cograded, coaugmented, connnected coalgebra. The exponential generating sum and exponential generating integral on lattice cones can be viewed as linear maps on this space with values in the space of meromorphic germs with linear poles at zero. We investigate the subdivision properties-reminiscent of the inclusion-exclusion principle for the cardinal on finite sets-of such linear maps and show that these properties are compatible with the convolution quotient of maps on the coalgebra. Implementing the algebraic Birkhoff factorization procedure on the linear maps under consideration, we factorize the exponential generating sum as a convolution quotient of two maps, with each of the maps in the factorization satisfying a subdivision property. A direct computation shows that the polar decomposition of the exponential generating sum on a smooth lattice cone yields an Euler-Maclaurin formula. The compatibility with subdivisions of the convolution quotient arising in the algebraic Birkhoff factorization then yields the Euler-Maclaurin formula for any lattice cone. This provides a simple formula for the interpolating factor by means of a projection formula. Y1 - 2017 U6 - https://doi.org/10.1215/00127094-3715303 SN - 0012-7094 SN - 1547-7398 VL - 166 IS - 3 SP - 537 EP - 571 PB - Duke Univ. Press CY - Durham ER - TY - JOUR A1 - Groschwitz, Jonas A1 - Szabo, Tibor T1 - Sharp Thresholds for Half-Random Games II JF - GRAPHS AND COMBINATORICS N2 - We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this work we focus on the case of Breaker playing randomly and Maker being "clever". The reverse scenario is treated in a separate paper. We determine the sharp threshold bias of classical games played on the edge set of the complete graph , such as connectivity, perfect matching, Hamiltonicity, and minimum degree-1 and -2. In all of these games, the threshold is equal to the trivial upper bound implied by the number of edges needed for Maker to occupy a winning set. Moreover, we show that CleverMaker can not only win against asymptotically optimal bias, but can do so very fast, wasting only logarithmically many moves (while the winning set sizes are linear in n). KW - Positional games KW - Randomized strategy KW - Sharp threshold KW - Fast win KW - Hamiltonicity KW - Connectivity Y1 - 2017 U6 - https://doi.org/10.1007/s00373-016-1753-4 SN - 0911-0119 SN - 1435-5914 VL - 33 SP - 387 EP - 401 PB - Springer CY - Tokyo ER - TY - JOUR A1 - Kolasinski, Slawomir A1 - Menne, Ulrich T1 - Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds JF - Nonlinear Differential Equations and Applications NoDEA N2 - This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the quadratic tilt-excess is completed by establishing the precise decay rate for two-dimensional integral varifolds of locally bounded first variation. In order to obtain the exact decay rate, a coercive estimate involving a height-excess quantity measured in Orlicz spaces is established. Moreover, counter-examples to pointwise power decay rates almost everywhere of the super-quadratic tilt-excess are obtained. These examples are optimal in terms of the dimension of the varifold and the exponent of the integrability condition in most cases, for example if the varifold is not two-dimensional. These examples also demonstrate that within the scale of Lebesgue spaces no local higher integrability of the second fundamental form, of an at least two-dimensional curvature varifold, may be deduced from boundedness of its generalised mean curvature vector. Amongst the tools are Cartesian products of curvature varifolds. KW - Integral varifold KW - First variation KW - Generalised mean curvature vector KW - Quadratic tilt-excess KW - Super-quadratic tilt-excess KW - Orlicz space height-excess KW - Curvature varifold KW - Second fundamental form KW - Cartesian product of varifolds Y1 - 2017 U6 - https://doi.org/10.1007/s00030-017-0436-z SN - 1021-9722 SN - 1420-9004 VL - 24 PB - Springer CY - Basel ER - TY - JOUR A1 - Khalil, Sara A1 - Schulze, Bert-Wolfgang T1 - Boundary problems on a manifold with edge JF - Asian-European Journal of Mathematics N2 - We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel’s theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices. KW - manifolds with edge and boundary KW - distribution with asymptotics KW - ellipticity KW - Fredholm property Y1 - 2017 U6 - https://doi.org/10.1142/S1793557117500875 SN - 1793-5571 SN - 1793-7183 VL - 10 IS - 2 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Dereudre, David A1 - Roelly, Sylvie T1 - Path-dependent infinite-dimensional SDE with non-regular drift BT - an existence result JF - Annales de l'Institut Henri Poincaré : B, Probability and statistics N2 - We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither bounded or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy and a finite second moment. The originality of our method leads in the use of the specific entropy as a tightness tool and in the description of such infinite-dimensional stochastic process as solution of a variational problem on the path space. Our result clearly improves previous ones obtained for free dynamics with bounded drift. N2 - Nous établissons, dans cet article, l’existence de solutions faibles pour un système infini-dimensionnel de diffusions browniennes. Le terme de dérive est véritablement général, au sens où il est supposé n’être ni borné, ni continu, ni Markovien. Nous supposons cependant que la loi initiale admet une entropie spécifique finie. L’originalité de notre méthode consiste en l’utilisation de la bornitude de l’entropie spécifique comme critère de tension et en l’identification des solutions du système comme solutions d’un problème variationnel sur l’espace des trajectoires. Notre résultat améliore clairement ceux préexistants concernant des dynamiques libres perturbées par des dérives bornées. KW - Infinite-dimensional SDE KW - Non-Markov drift KW - Non-regular drift KW - Variational principle KW - Specific entropy Y1 - 2017 U6 - https://doi.org/10.1214/15-AIHP728 SN - 0246-0203 VL - 53 IS - 2 SP - 641 EP - 657 PB - Inst. of Mathematical Statistics CY - Bethesda ER - TY - JOUR A1 - Lazarides, Rebecca A1 - Rubach, Charlott T1 - Instructional characteristics in mathematics classrooms BT - relationships to achievement goal orientation and student engagement JF - Mathematics Education Research Journal N2 - This longitudinal study examined relationships between student-perceived teaching for meaning, support for autonomy, and competence in mathematic classrooms (Time 1), and students’ achievement goal orientations and engagement in mathematics 6 months later (Time 2). We tested whether student-perceived instructional characteristics at Time 1 indirectly related to student engagement at Time 2, via their achievement goal orientations (Time 2), and, whether student gender moderated these relationships. Participants were ninth and tenth graders (55.2% girls) from 46 classrooms in ten secondary schools in Berlin, Germany. Only data from students who participated at both timepoints were included (N = 746 out of total at Time 1 1118; dropout 33.27%). Longitudinal structural equation modeling showed that student-perceived teaching for meaning and support for competence indirectly predicted intrinsic motivation and effort, via students’ mastery goal orientation. These paths were equivalent for girls and boys. The findings are significant for mathematics education, in identifying motivational processes that partly explain the relationships between student-perceived teaching for meaning and competence support and intrinsic motivation and effort in mathematics. KW - Mathematics classrooms KW - Instruction KW - Intrinsicmotivation KW - Achievement goal orientation KW - Effort KW - Gender Y1 - 2017 U6 - https://doi.org/10.1007/s13394-017-0196-4 SN - 1033-2170 SN - 2211-050X VL - 29 SP - 201 EP - 217 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Makhmudov, K. O. A1 - Makhmudov, O. I. A1 - Tarkhanov, Nikolai Nikolaevich T1 - A nonstandard Cauchy problem for the heat equation JF - Mathematical Notes N2 - We consider the Cauchy problem for the heat equation in a cylinder C (T) = X x (0, T) over a domain X in R (n) , with data on a strip lying on the lateral surface. The strip is of the form S x (0, T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S, we derive an explicit formula for solutions of this problem. Y1 - 2017 U6 - https://doi.org/10.1134/S0001434617070264 SN - 0001-4346 SN - 1573-8876 VL - 102 SP - 250 EP - 260 PB - Pleiades Publ. CY - New York ER - TY - JOUR A1 - Wicha, Sebastian G. A1 - Huisinga, Wilhelm A1 - Kloft, Charlotte T1 - Translational pharmacometric evaluation of typical antibiotic broad-spectrum combination therapies against staphylococcus aureus exploiting in vitro information JF - CPT: pharmacometrics & systems pharmacology N2 - Broad-spectrum antibiotic combination therapy is frequently applied due to increasing resistance development of infective pathogens. The objective of the present study was to evaluate two common empiric broad-spectrum combination therapies consisting of either linezolid (LZD) or vancomycin (VAN) combined with meropenem (MER) against Staphylococcus aureus (S. aureus) as the most frequent causative pathogen of severe infections. A semimechanistic pharmacokinetic-pharmacodynamic (PK-PD) model mimicking a simplified bacterial life-cycle of S. aureus was developed upon time-kill curve data to describe the effects of LZD, VAN, and MER alone and in dual combinations. The PK-PD model was successfully (i) evaluated with external data from two clinical S. aureus isolates and further drug combinations and (ii) challenged to predict common clinical PK-PD indices and breakpoints. Finally, clinical trial simulations were performed that revealed that the combination of VAN-MER might be favorable over LZD-MER due to an unfavorable antagonistic interaction between LZD and MER. Y1 - 2017 U6 - https://doi.org/10.1002/psp4.12197 SN - 2163-8306 VL - 6 SP - 512 EP - 522 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Shaki, Samuel A1 - Pinhas, Michal A1 - Fischer, Martin H. T1 - Heuristics and biases in mental arithmetic BT - revisiting and reversing operational momentum JF - Thinking & Reasoning N2 - Mental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum (OM) effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems (e.g., 3+0, 3-0) but reverse OM with non-zero problems (e.g., 2+1, 4-1). In a third experiment, we tested the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving. KW - Heuristics KW - mental arithmetic KW - mental number line KW - operational momentum KW - problem-solving Y1 - 2017 U6 - https://doi.org/10.1080/13546783.2017.1348987 SN - 1354-6783 SN - 1464-0708 VL - 24 IS - 2 SP - 138 EP - 156 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Bandara, Lashi A1 - McIntosh, Alan A1 - Rosen, Andreas T1 - Riesz continuity of the Atiyah BT - singer dirac operator under perturbations of the metric JF - Mathematische Annalen N2 - We prove that the Atiyah–Singer Dirac operator in L2 depends Riesz continuously on L∞ perturbations of complete metrics g on a smooth manifold. The Lipschitz bound for the map depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Calderón’s first commutator and the Kato square root problem. We also show perturbation results for more general functions of general Dirac-type operators on vector bundles. Y1 - 2017 U6 - https://doi.org/10.1007/s00208-017-1610-7 SN - 0025-5831 SN - 1432-1807 VL - 370 IS - 1-2 SP - 863 EP - 915 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Gerlach, Moritz Reinhardt A1 - Glück, Jochen T1 - On a convergence theorem for semigroups of positive integral operators JF - Comptes Rendus Mathematique N2 - We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result. Y1 - 2017 U6 - https://doi.org/10.1016/j.crma.2017.07.017 SN - 1631-073X SN - 1778-3569 VL - 355 SP - 973 EP - 976 PB - Elsevier CY - Paris ER - TY - JOUR A1 - Taghvaei, Amirhossein A1 - de Wiljes, Jana A1 - Mehta, Prashant G. A1 - Reich, Sebastian T1 - Kalman filter and its modern extensions for the continuous-time nonlinear filtering problem JF - Journal of dynamic systems measurement and control N2 - This paper is concerned with the filtering problem in continuous time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter, which provides an exact solution for the linear Gaussian problem; (ii) the ensemble Kalman-Bucy filter (EnKBF), which is an approximate filter and represents an extension of the Kalman-Bucy filter to nonlinear problems; and (iii) the feedback particle filter (FPF), which represents an extension of the EnKBF and furthermore provides for a consistent solution in the general nonlinear, non-Gaussian case. The common feature of the three algorithms is the gain times error formula to implement the update step (to account for conditioning due to the observations) in the filter. In contrast to the commonly used sequential Monte Carlo methods, the EnKBF and FPF avoid the resampling of the particles in the importance sampling update step. Moreover, the feedback control structure provides for error correction potentially leading to smaller simulation variance and improved stability properties. The paper also discusses the issue of nonuniqueness of the filter update formula and formulates a novel approximation algorithm based on ideas from optimal transport and coupling of measures. Performance of this and other algorithms is illustrated for a numerical example. Y1 - 2017 U6 - https://doi.org/10.1115/1.4037780 SN - 0022-0434 SN - 1528-9028 VL - 140 IS - 3 PB - ASME CY - New York ER - TY - JOUR A1 - Lesur, Vincent A1 - Wardinski, Ingo A1 - Bärenzung, Julien A1 - Holschneider, Matthias T1 - On the frequency spectra of the core magnetic field Gauss coefficients JF - Physics of the earth and planetary interiors N2 - From monthly mean observatory data spanning 1957-2014, geomagnetic field secular variation values were calculated by annual differences. Estimates of the spherical harmonic Gauss coefficients of the core field secular variation were then derived by applying a correlation based modelling. Finally, a Fourier transform was applied to the time series of the Gauss coefficients. This process led to reliable temporal spectra of the Gauss coefficients up to spherical harmonic degree 5 or 6, and down to periods as short as 1 or 2 years depending on the coefficient. We observed that a k(-2) slope, where k is the frequency, is an acceptable approximation for these spectra, with possibly an exception for the dipole field. The monthly estimates of the core field secular variation at the observatory sites also show that large and rapid variations of the latter happen. This is an indication that geomagnetic jerks are frequent phenomena and that significant secular variation signals at short time scales - i.e. less than 2 years, could still be extracted from data to reveal an unexplored part of the core dynamics. KW - Geomagnetism KW - Core field KW - Secular variation rate of change KW - Geomagnetic jerks KW - Correlation based modelling Y1 - 2017 U6 - https://doi.org/10.1016/j.pepi.2017.05.017 SN - 0031-9201 SN - 1872-7395 VL - 276 SP - 145 EP - 158 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Pathiraja, Sahani Darschika A1 - Anghileri, Daniela A1 - Burlando, P. A1 - Sharma, A. A1 - Marshall, L. A1 - Moradkhani, H. T1 - Insights on the impact of systematic model errors on data assimilation performance in changing catchments JF - Advances in water resources N2 - The global prevalence of rapid and extensive land use change necessitates hydrologic modelling methodologies capable of handling non-stationarity. This is particularly true in the context of Hydrologic Forecasting using Data Assimilation. Data Assimilation has been shown to dramatically improve forecast skill in hydrologic and meteorological applications, although such improvements are conditional on using bias-free observations and model simulations. A hydrologic model calibrated to a particular set of land cover conditions has the potential to produce biased simulations when the catchment is disturbed. This paper sheds new light on the impacts of bias or systematic errors in hydrologic data assimilation, in the context of forecasting in catchments with changing land surface conditions and a model calibrated to pre-change conditions. We posit that in such cases, the impact of systematic model errors on assimilation or forecast quality is dependent on the inherent prediction uncertainty that persists even in pre-change conditions. Through experiments on a range of catchments, we develop a conceptual relationship between total prediction uncertainty and the impacts of land cover changes on the hydrologic regime to demonstrate how forecast quality is affected when using state estimation Data Assimilation with no modifications to account for land cover changes. This work shows that systematic model errors as a result of changing or changed catchment conditions do not always necessitate adjustments to the modelling or assimilation methodology, for instance through re-calibration of the hydrologic model, time varying model parameters or revised offline/online bias estimation. Y1 - 2017 U6 - https://doi.org/10.1016/j.advwatres.2017.12.006 SN - 0309-1708 SN - 1872-9657 VL - 113 SP - 202 EP - 222 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Brungs, Hans H. A1 - Gräter, Joachim T1 - On central extensions of SL(2, F) admitting left-orderings JF - Journal of Algebra N2 - For an arbitrary euclidean field F we introduce a central extension (G(F), Phi) of SL(2, F) admitting a left-ordering and study its algebraic properties. The elements of G(F) are order preserving bijections of the convex hull of Q in F. If F = R then G(F) is isomorphic to the classical universal covering group of the Lie group SL(2, R). Among other results we show that G(F) is a perfect group which possesses a rank 1 cone of exceptional type. We also prove that its centre is an infinite cyclic group and investigate its normal subgroups. KW - Universal covering group KW - Central extensions of groups KW - Perfect groups KW - Ordered fields KW - Left-ordered groups KW - Order-preserving bijections KW - Euclidean fields Y1 - 2017 U6 - https://doi.org/10.1016/j.jalgebra.2017.05.025 SN - 0021-8693 SN - 1090-266X VL - 486 SP - 288 EP - 327 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Elin, Mark A1 - Shoikhet, David A1 - Tarkhanov, Nikolai Nikolaevich T1 - Analytic Semigroups of Holomorphic Mappings and Composition Operators JF - Computational Methods and Function Theory N2 - In this manuscript we provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. KW - Non-linear semigroups KW - Composition operators KW - Analytic extension KW - Holomorphic mappings Y1 - 2017 U6 - https://doi.org/10.1007/s40315-017-0227-x SN - 1617-9447 SN - 2195-3724 VL - 18 IS - 2 SP - 269 EP - 294 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Gairing, Jan A1 - Högele, Michael A1 - Kosenkova, Tetiana T1 - Transportation distances and noise sensitivity of multiplicative Levy SDE with applications JF - Stochastic processes and their application N2 - This article assesses the distance between the laws of stochastic differential equations with multiplicative Levy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Levy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate. KW - Stochastic differential equations KW - Multiplicative Levy noise KW - Levy type processes KW - Heavy-tailed distributions KW - Model selection KW - Wasserstein distance KW - Time series Y1 - 2017 U6 - https://doi.org/10.1016/j.spa.2017.09.003 SN - 0304-4149 SN - 1879-209X VL - 128 IS - 7 SP - 2153 EP - 2178 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Rado theorem for the porous medium equation JF - Boletin de la Sociedad Matemática Mexicana N2 - We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi. KW - Quasilinear equations KW - Removable sets KW - Porous medium equation Y1 - 2017 U6 - https://doi.org/10.1007/s40590-017-0169-3 SN - 1405-213X SN - 2296-4495 VL - 24 IS - 2 SP - 427 EP - 437 PB - Springer CY - Cham ER - TY - JOUR A1 - Kollosche, David T1 - Entdeckendes Lernen BT - eine Problematisierung JF - Journal für Mathematik-Didaktik N2 - Trotz der nachweislichen Popularität des Entdeckenden Lernens in der deutschsprachigen Mathematikdidaktik finden sich aktuell keine kritischen Beiträge, die dazu beitragen könnten, dieses grundlegende Unterrichtskonzept zu hinterfragen und auszuschärfen. In diesem Diskussionsbeitrag werden zunächst die Theorie und einige Umsetzungsbeispiele des Entdeckenden Lernens herausgearbeitet, um aufzuzeigen, dass das Entdeckende Lernen einem vagen Sammelbegriff gleicht, unter dem oft fragwürdige Unterrichtsumgebungen legitimiert werden. Anschließend werden an Hand erkenntnistheoretischer, lerntheoretischer, didaktischer und soziokultureller Betrachtungen Probleme des Entdeckenden Lernens im Mathematikunterricht und Möglichkeiten ihrer Überwindung thematisiert. Dabei zeigt sich, dass die Konzeption des Entdeckenden Lernens hinter dem aktuellen mathematikdidaktischen Erkenntnisstand zurückfällt und Lehrer sowie Schüler mit unmöglichen Forderungen konfrontiert, dass lerntheoretische Vorteile des Entdeckenden Lernens oft nicht nachweisbar sind, dass die Idee des Entdeckens auf einem problematischen platonistischen Verständnis von Erkenntnis beruht und dass Entdeckendes Lernen bildungsferne Schüler zu benachteiligen droht. Abschließend werden Forschungsdesiderata abgeleitet, deren Bearbeitung dazu beitragen könnte, die aufgezeigten Problemfelder zu überwinden. N2 - Despite the attested popularity of discovery learning in germanophone research on mathematics education, we contemporarily lack critical contributions which may contribute to questioning and sharpening this fundamental teaching concept. Here, in this discussion paper the theory and some implementations of discovery learning are being discussed in order to show that discovery learning constitutes a vague umbrella term, with which often questionable learning environments are being legitimised. Afterwards, it is outlined which objections from the perspectives of epistemology, learning theory, didactics and social theory may be brought forward against discovery learning in mathematics education, and how these objections may be overcome. Thereby it becomes obvious that the conception of discovery learning falls behind the current level of knowledge in mathematics education research and confronts teachers as well as students with impossible demands; that learning benefits of discovery learning often cannot be substantiated; that the idea of discovery rests on a problematic platonic understanding of insight; and that discovery learning threatens to disadvantage educationally alienated students. As a last point, research desiderata, whose study may contribute to the negotiation of the described obstacles, are deduced. T2 - Discovery learning: A problematization KW - Discovery learning KW - Inquiry-based learning KW - Epistemology KW - Learning theory KW - Sociolinguistics KW - Entdeckendes Lernen KW - Epistemologie KW - Lerntheorie KW - Soziolinguistik Y1 - 2017 U6 - https://doi.org/10.1007/s13138-017-0116-x SN - 0173-5322 SN - 1869-2699 VL - 38 SP - 209 EP - 237 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Chang, Der-Chen A1 - Schulze, Bert-Wolfgang T1 - Ellipticity on spaces with higher singularities JF - Science China Mathematics N2 - We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata. KW - pseudo-differential operators KW - operator-valued symbols KW - Fourier and Mellin transforms Y1 - 2017 U6 - https://doi.org/10.1007/s11425-016-0519-9 SN - 1674-7283 SN - 1869-1862 VL - 60 IS - 11 SP - 2053 EP - 2076 PB - Science China Press CY - Beijing ER - TY - JOUR A1 - Dimitrova, Ilinka A1 - Koppitz, Jörg T1 - On the semigroup of all partial fence-preserving injections on a finite set JF - Journal of Algebra and Its Applications N2 - For n∈N , let Xn={a1,a2,…,an} be an n-element set and let F=(Xn;