275,610 research outputs found

    Weak lensing study of 16 DAFT/FADA clusters: substructures and filaments

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    While our current cosmological model places galaxy clusters at the nodes of a filament network (the cosmic web), we still struggle to detect these filaments at high redshifts. We perform a weak lensing study for a sample of 16 massive, medium-high redshift (0.4<z<0.9) galaxy clusters from the DAFT/FADA survey, that are imaged in at least three optical bands with Subaru/Suprime-Cam or CFHT/MegaCam. We estimate the cluster masses using an NFW fit to the shear profile measured in a KSB-like method, adding our contribution to the calibration of the observable-mass relation required for cluster abundance cosmological studies. We compute convergence maps and select structures within, securing their detection with noise re-sampling techniques. Taking advantage of the large field of view of our data, we study cluster environment, adding information from galaxy density maps at the cluster redshift and from X-ray images when available. We find that clusters show a large variety of weak lensing maps at large scales and that they may all be embedded in filamentary structures at megaparsec scale. We classify them in three categories according to the smoothness of their weak lensing contours and to the amount of substructures: relaxed (~7%), past mergers (~21.5%), recent or present mergers (~71.5%). The fraction of clusters undergoing merging events observationally supports the hierarchical scenario of cluster growth, and implies that massive clusters are strongly evolving at the studied redshifts. Finally, we report the detection of unusually elongated structures in CLJ0152, MACSJ0454, MACSJ0717, A851, BMW1226, MACSJ1621, and MS1621.Comment: 25 pages, accepted for publication in A&

    The German-Czech border region after the fall of the Iron Curtain: Effects on the labour market : an empirical study using the IAB Employment Sample (IABS)

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    "Using the IAB Employment Sample (IABS) covering 1980-2001 we investigate what impact the fall of the Iron Curtain has had on the skill structure of employment and wages in the western German districts neighbouring the Czech Republic. The introduction of free trade in this region, which has one of the world's largest spatial wage differentials, can be seen as a natural experiment. We presume that changes in skill and wage structures are particularly apparent in the regions situated immediately on the open border. Distinguishing three skill categories we obtain unexpected results. Though we observe a general shift from low-skilled jobs towards skilled jobs and a convergence trend of border regions towards the national average, we do not find a special effect for the period after the opening of the border, neither concerning the skill structure nor the wage differentials." (Author's abstract, IAB-Doku) ((en))Grenzgebiet, Qualifikationsstruktur, Lohnhöhe, osteuropäischer Transformationsprozess - Auswirkungen, IAB-Beschäftigtenstichprobe, Bayern, Tschechische Republik, Bundesrepublik Deutschland

    Quantale-valued Cauchy tower spaces and completeness

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    [EN] Generalizing the concept of a probabilistic Cauchy space, we introduce quantale-valued Cauchy tower spaces. These spaces encompass quantale-valued metric spaces, quantale-valued uniform (convergence) tower spaces and quantale-valued convergence tower groups. For special choices of the quantale, classical and probabilistic metric spaces are covered and probabilistic and approach Cauchy spaces arise. We also study completeness and completion in this setting and establish a connection to the Cauchy completeness of a quantale-valued metric space.Jäger, G.; Ahsanullah, TMG. (2021). Quantale-valued Cauchy tower spaces and completeness. Applied General Topology. 22(2):461-481. https://doi.org/10.4995/agt.2021.15610OJS461481222J. Adámek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1989.T. M. G. Ahsanullah and G. Jäger, Probabilistic uniform convergence spaces redefined, Acta Math. Hungarica 146 (2015), 376-390. https://doi.org/10.1007/s10474-015-0525-6T. M. G. Ahsanullah and G. Jäger, Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups, Math Slovaca 67 (2017), 985-1000. https://doi.org/10.1515/ms-2017-0027P. Brock and D. C. Kent, Approach spaces, limit tower spaces, and probabilistic convergence spaces, Appl. Cat. Structures 5 (1997), 99-110. https://doi.org/10.1023/A:1008633124960H. R. Fischer, Limesräume, Math. Ann. 137 (1959), 269-303. https://doi.org/10.1007/BF01360965R. C. Flagg, Completeness in continuity spaces, in: Category Theory 1991, CMS Conf. Proc. 13 (1992), 183-199.R. C. Flagg, Quantales and continuity spaces, Algebra Univers. 37 (1997), 257-276. https://doi.org/10.1007/s000120050018L. C. Florescu, Probabilistic convergence structures, Aequationes Math. 38 (1989), 123-145. https://doi.org/10.1007/BF01839999G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, Continuous lattices and domains, Cambridge University Press, 2003. https://doi.org/10.1017/CBO9780511542725D. Hofmann and C. D. Reis, Probabilistic metric spaces as enriched categories, Fuzzy Sets and Systems 210 (2013), 1-21. https://doi.org/10.1016/j.fss.2012.05.005U. Höhle, Commutative, residuated l-monoids, in: Non-classical logics and their applications to fuzzy subsets (U. Höhle, E. P. Klement, eds.), Kluwer, Dordrecht 1995, pp. 53-106. https://doi.org/10.1007/978-94-011-0215-5_5G. Jäger, A convergence theory for probabilistic metric spaces, Quaest. Math. 38 (2015), 587-599. https://doi.org/10.2989/16073606.2014.981734G. Jäger and T. M. G. Ahsanullah, Probabilistic limit groups under a tt-norm, Topology Proceedings 44 (2014), 59-74.G. Jäger and T. M. G. Ahsanullah, Characterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence, Applied Gen. Topology 19, no. 1 (2018), 129-144. https://doi.org/10.4995/agt.2018.7849G. Jäger, Quantale-valued uniform convergence towers for quantale-valued metric spaces, Hacettepe J. Math. Stat. 48, no. 5 (2019), 1443-1453. https://doi.org/10.15672/HJMS.2018.585G. Jäger, The Wijsman structure of a quantale-valued metric space, Iranian J. Fuzzy Systems 17, no. 1 (2020), 171-184.H. H. Keller, Die Limes-Uniformisierbarkeit der Limesräume, Math. Ann. 176 (1968), 334-341. https://doi.org/10.1007/BF02052894D. C. Kent and G. D. Richardson, Completions of probabilistic Cauchy spaces, Math. Japonica 48, no. 3 (1998), 399-407.F. W. Lawvere, Metric spaces, generalized logic, and closed categories, Rendiconti del Seminario Matematico e Fisico di Milano 43 (1973), 135-166. Reprinted in: Reprints in Theory and Applications of Categories} 1 (2002), 1-37. https://doi.org/10.1007/BF02924844R. Lowen, Index Analysis, Springer, London, Heidelberg, New York, Dordrecht 2015. https://doi.org/10.1007/978-1-4471-6485-2R. Lowen and Y. J. Lee, Approach theory in merotopic, Cauchy and convergence spaces. I, Acta Math. Hungarica 83, no. 3 (1999), 189-207. https://doi.org/10.1023/A:1006717022079R. Lowen and Y. J. Lee, Approach theory in merotopic, Cauchy and convergence spaces. II, Acta Math. Hungarica 83, no. 3 (1999), 209-229. https://doi.org/10.1023/A:1006769006149R. Lowen and B. Windels, On the quantification of uniform properties, Comment. Math. Univ. Carolin. 38, no. 4 (1997), 749-759.R. Lowen and B. Windels, Approach groups, Rocky Mountain J. Math. 30, no. 3 (2000), 1057-1073. https://doi.org/10.1216/rmjm/1021477259J. Minkler, G. Minkler and G. Richardson, Subcategories of filter tower spaces, Appl. Categ. Structures 9 (2001), 369-379. https://doi.org/10.1023/A:1011226611840H. Nusser, A generalization of probabilistic uniform spaces, Appl. Categ. Structures 10 (2002), 81-98. https://doi.org/10.1023/A:1013375301613H. Nusser, Completion of probabilistic uniform limit spaces, Quaest. 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    Convergence and quantale-enriched categories

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    Generalising Nachbin's theory of "topology and order", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these V\mathcal{V}-categorical compact Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that the presence of a compact Hausdorff topology guarantees Cauchy completeness and (suitably defined) codirected completeness of the underlying quantale enriched category

    Compactly Generated Domain Theory

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    The enriched Vietoris monad on representable spaces

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    Employing a formal analogy between ordered sets and topological spaces, over the past years we have investigated a notion of cocompleteness for topological, approach and other kind of spaces. In this new context, the down-set monad becomes the filter monad, cocomplete ordered set translates to continuous lattice, distributivity means disconnectedness, and so on. Curiously, the dual(?) notion of completeness does not behave as the mirror image of the one of cocompleteness; and in this paper we have a closer look at complete spaces. In particular, we construct the "up-set monad" on representable spaces (in the sense of L. Nachbin for topological spaces, respectively C. Hermida for multicategories); we show that this monad is of Kock-Z\"oberlein type; we introduce and study a notion of weighted limit similar to the classical notion for enriched categories; and we describe the Kleisli category of our "up-set monad". We emphasize that these generic categorical notions and results can be indeed connected to more "classical" topology: for topological spaces, the "up-set monad" becomes the upper Vietoris monad, and the statement "XX is totally cocomplete if and only if XopX^\mathrm{op} is totally complete" specialises to O. Wyler's characterisation of the algebras of the Vietoris monad on compact Hausdorff spaces.Comment: One error in Example 1.9 is corrected; Section 4 works now without the assuming core-compactnes

    A categorical approach to the maximum theorem

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    Berge's maximum theorem gives conditions ensuring the continuity of an optimised function as a parameter changes. In this paper we state and prove the maximum theorem in terms of the theory of monoidal topology and the theory of double categories. This approach allows us to generalise (the main assertion of) the maximum theorem, which is classically stated for topological spaces, to pseudotopological spaces and pretopological spaces, as well as to closure spaces, approach spaces and probabilistic approach spaces, amongst others. As a part of this we prove a generalisation of the extreme value theorem.Comment: 45 pages. Minor changes in v2: this is the final preprint for publication in JPA

    Some open problems in mathematical two-dimensional conformal field theory

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    We discuss some open problems in a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras.Comment: 16 pages. Typos are corrected and some sentences are adjusted. Final version to appear in the proceedings of the Conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, held at University of Notre Dame, Notre Dame, Indiana, August 14-18, 201

    Approximation in quantale-enriched categories

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    Our work is a fundamental study of the notion of approximation in V-categories and in (U,V)-categories, for a quantale V and the ultrafilter monad U. We introduce auxiliary, approximating and Scott-continuous distributors, the way-below distributor, and continuity of V- and (U,V)-categories. We fully characterize continuous V-categories (resp. (U,V)-categories) among all cocomplete V-categories (resp. (U,V)-categories) in the same ways as continuous domains are characterized among all dcpos. By varying the choice of the quantale V and the notion of ideals, and by further allowing the ultrafilter monad to act on the quantale, we obtain a flexible theory of continuity that applies to partial orders and to metric and topological spaces. We demonstrate on examples that our theory unifies some major approaches to quantitative domain theory.Comment: 17 page

    Normed groupoids with dilations

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    We study normed groupoids with dilations and their induced deformations.Comment: arXiv admin note: this contains the content of arXiv:0911.130
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