TY - JOUR A1 - Hedayat Mahmoudi, Mahdi A1 - Schulze, Bert-Wolfgang T1 - Corner boundary value problems JF - Asian-European journal of mathematics N2 - The paper develops some crucial steps in extending the first-order cone or edge calculus to higher singularity orders. We focus here on order 2, but the ideas are motivated by an iterative approach for higher singularities. KW - Mellin operators KW - Mellin oscillatory integrals KW - exit calculus KW - weighted Sobolev spaces Y1 - 2016 U6 - https://doi.org/10.1142/S1793557117500541 SN - 1793-5571 SN - 1793-7183 VL - 10 IS - 1 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Antonini, Paolo A1 - Azzali, Sara A1 - Skandalis, Georges T1 - Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations JF - Journal of functional analysis N2 - We construct equivariant KK-theory with coefficients in and R/Z as suitable inductive limits over II1-factors. We show that the Kasparov product, together with its usual functorial properties, extends to KK-theory with real coefficients. Let Gamma be a group. We define a Gamma-algebra A to be K-theoretically free and proper (KFP) if the group trace tr of Gamma acts as the unit element in KKR Gamma (A, A). We show that free and proper Gamma-algebras (in the sense of Kasparov) have the (KFP) property. Moreover, if Gamma is torsion free and satisfies the KK Gamma-form of the Baum-Connes conjecture, then every Gamma-algebra satisfies (KFP). If alpha : Gamma -> U-n is a unitary representation and A satisfies property (KFP), we construct in a canonical way a rho class rho(A)(alpha) is an element of KKR/Z1,Gamma (A A) This construction generalizes the Atiyah-Patodi-Singer K-theory class with R/Z-coefficients associated to alpha. (C) 2015 Elsevier Inc. All rights reserved. KW - Operator algebras KW - Bivariant K-theory KW - Rho invariants Y1 - 2016 U6 - https://doi.org/10.1016/j.jfa.2015.06.017 SN - 0022-1236 SN - 1096-0783 VL - 270 SP - 447 EP - 481 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Kollosche, David T1 - Criticising with Foucault: towards a guiding framework for socio-political studies in mathematics education JF - Educational studies in mathematics : an international journal N2 - Socio-political studies in mathematics education often touch complex fields of interaction between education, mathematics and the political. In this paper I present a Foucault-based framework for socio-political studies in mathematics education which may guide research in that area. In order to show the potential of such a framework, I discuss the potential and limits of Marxian ideology critique, present existing Foucault-based research on socio-political aspects of mathematics education, develop my framework and show its use in an outline of a study on socio-political aspects of calculation in the mathematics classroom. KW - Critique KW - Marx KW - Foucault KW - Critical mathematics education KW - Calculation Y1 - 2016 U6 - https://doi.org/10.1007/s10649-015-9648-5 SN - 0013-1954 SN - 1573-0816 VL - 91 SP - 73 EP - 86 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Nehring, Benjamin A1 - Rafler, Mathias A1 - Zessin, Hans T1 - Splitting-characterizations of the Papangelou process JF - Mathematische Nachrichten N2 - For point processes we establish a link between integration-by-parts-and splitting-formulas which can also be considered as integration-by-parts-formulas of a new type. First we characterize finite Papangelou processes in terms of their splitting kernels. The main part then consists in extending these results to the case of infinitely extended Papangelou and, in particular, Polya and Gibbs processes. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim KW - Papangelou processes KW - characterization of point processes KW - independent splittings KW - Gibbs processes Y1 - 2016 U6 - https://doi.org/10.1002/mana.201400384 SN - 0025-584X SN - 1522-2616 VL - 289 SP - 85 EP - 96 PB - Wiley-VCH CY - Weinheim ER - TY - JOUR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - Agmon estimates for the difference of exact and approximate Dirichlet eigenfunctions for difference operators JF - Asymptotic analysis N2 - We analyze a general class of difference operators H-epsilon = T-epsilon + V-epsilon on l(2)(((epsilon)Z)(d)), where V-epsilon is a multi-well potential and epsilon is a small parameter. We construct approximate eigenfunctions in neighbourhoods of the different wells and give weighted l(2)-estimates for the difference of these and the exact eigenfunctions of the associated Dirichlet-operators. Y1 - 2016 U6 - https://doi.org/10.3233/ASY-151343 SN - 0921-7134 SN - 1875-8576 VL - 97 SP - 61 EP - 89 PB - IOS Press CY - Amsterdam ER - TY - JOUR A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - The Earthquake History in a Fault Zone Tells Us Almost Nothing about m(max) JF - Seismological research letters N2 - In the present study, we summarize and evaluate the endeavors from recent years to estimate the maximum possible earthquake magnitude m(max) from observed data. In particular, we use basic and physically motivated assumptions to identify best cases and worst cases in terms of lowest and highest degree of uncertainty of m(max). In a general framework, we demonstrate that earthquake data and earthquake proxy data recorded in a fault zone provide almost no information about m(max) unless reliable and homogeneous data of a long time interval, including several earthquakes with magnitude close to m(max), are available. Even if detailed earthquake information from some centuries including historic and paleoearthquakes are given, only very few, namely the largest events, will contribute at all to the estimation of m(max), and this results in unacceptably high uncertainties. As a consequence, estimators of m(max) in a fault zone, which are based solely on earthquake-related information from this region, have to be dismissed. Y1 - 2016 U6 - https://doi.org/10.1785/0220150176 SN - 0895-0695 SN - 1938-2057 VL - 87 SP - 132 EP - 137 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Menne, Ulrich T1 - Weakly Differentiable Functions on Varifolds JF - Indiana University mathematics journal N2 - The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration-by-parts identities for certain compositions with smooth functions. In this class, the idea of zero boundary values is realised using the relative perimeter of superlevel sets. Results include a variety of Sobolev Poincare-type embeddings, embeddings into spaces of continuous and sometimes Holder-continuous functions, and point wise differentiability results both of approximate and integral type as well as coarea formulae. As a prerequisite for this study, decomposition properties of such varifolds and a relative isoperimetric inequality are established. Both involve a concept of distributional boundary of a set introduced for this purpose. As applications, the finiteness of the geodesic distance associated with varifolds with suitable summability of the mean curvature and a characterisation of curvature varifolds are obtained. KW - Rectifiable varifold KW - (generalised) wealdy differentiable function KW - distributional boundary KW - decomposition KW - relative isoperimetric inequality KW - Sobolev Poincare inequality KW - approximate differentiability KW - coarea formula KW - geodesic distance KW - curvature varifold Y1 - 2016 U6 - https://doi.org/10.1512/iumj.2016.65.5829 SN - 0022-2518 SN - 1943-5258 VL - 65 SP - 977 EP - 1088 PB - Indiana University, Department of Mathematics CY - Bloomington ER - TY - JOUR A1 - Gregory, A. A1 - Cotter, C. J. A1 - Reich, Sebastian T1 - MULTILEVEL ENSEMBLE TRANSFORM PARTICLE FILTERING JF - SIAM journal on scientific computing N2 - This paper extends the multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, multilevel Monte Carlo is applied to a certain variant of the particle filter, the ensemble transform particle filter (EPTF). A key aspect is the use of optimal transport methods to re-establish correlation between coarse and fine ensembles after resampling; this controls the variance of the estimator. Numerical examples present a proof of concept of the effectiveness of the proposed method, demonstrating significant computational cost reductions (relative to the single-level ETPF counterpart) in the propagation of ensembles. KW - multilevel Monte Carlo KW - sequential data assimilation KW - optimal transport Y1 - 2016 U6 - https://doi.org/10.1137/15M1038232 SN - 1064-8275 SN - 1095-7197 VL - 38 SP - A1317 EP - A1338 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Tinpun, Kittisak A1 - Koppitz, Jörg T1 - Generating sets of infinite full transformation semigroups with restricted range JF - Acta scientiarum mathematicarum N2 - In the present paper, we consider minimal generating sets of infinite full transformation semigroups with restricted range modulo specific subsets. In particular, we determine relative ranks. KW - generating sets KW - transformation semigroups KW - restricted range KW - relative ranks Y1 - 2016 U6 - https://doi.org/10.14232/actasm-015-502-4 SN - 0001-6969 VL - 82 SP - 55 EP - 63 PB - Institutum Bolyaianum Universitatis Szegediensis CY - Szeged ER - TY - JOUR A1 - Bomanson, Jori A1 - Janhunen, Tomi A1 - Schaub, Torsten H. A1 - Gebser, Martin A1 - Kaufmann, Benjamin T1 - Answer Set Programming Modulo Acyclicity JF - Fundamenta informaticae N2 - Acyclicity constraints are prevalent in knowledge representation and applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity, offers a rich set of primitives to express constraints related to recursive structures. In the technical results of the paper, we relate the new generalization with standard ASP by showing (i) how acyclicity extensions translate into normal rules, (ii) how weight constraint programs can be instrumented by acyclicity extensions to capture stability in analogy to unfounded set checking, and (iii) how the gap between supported and stable models is effectively closed in the presence of such an extension. Moreover, we present an efficient implementation of acyclicity constraints by incorporating a respective propagator into the state-of-the-art ASP solver CLASP. The implementation provides a unique combination of traditional unfounded set checking with acyclicity propagation. In the experimental part, we evaluate the interplay of these orthogonal checks by equipping logic programs with supplementary acyclicity constraints. The performance results show that native support for acyclicity constraints is a worthwhile addition, furnishing a complementary modeling construct in ASP itself as well as effective means for translation-based ASP solving. Y1 - 2016 U6 - https://doi.org/10.3233/FI-2016-1398 SN - 0169-2968 SN - 1875-8681 VL - 147 SP - 63 EP - 91 PB - IOS Press CY - Amsterdam ER -