Cocompactness and quasi-uniformizability of completely metrizable spaces

AbstractWe show that a metrizable topological space X is completely metrizable if and only if it admits a quasi-uniformity U such that the topology induced by the conjugate quasi-uniformity U−1 on X is compact

Weak regularity and consecutive topologizations and regularizations of pretopologies

AbstractL. Foged proved that a weakly regular topology on a countable set is regular. In terms of convergence theory, this means that the topological reflection Tξ of a regular pretopology ξ on a countable set is regular. It is proved that this still holds if ξ is a regular σ-compact pretopology. On the other hand, it is proved that for each n<ω there is a (regular) pretopology ρ (on a set of cardinality c) such that (RT)kρ>(RT)nρ for each k<n and (RT)nρ is a Hausdorff compact topology, where R is the reflector to regular pretopologies. It is also shown that there exists a regular pretopology of Hausdorff RT-order ⩾ω0. Moreover, all these pretopologies have the property that all the points except one are topological and regular

Sobrification and bicompletion of totally bounded quasi-uniform spaces

We observe that if is a compatible totally bounded quasi-uniformity on a T0-space (X,), then the bicompletion of (X, ) is a strongly sober, locally quasicompact space. It follows that the b-closure S of (X, ) in is homeomorphic to the sobrification of the space (X, ). We prove that S is equal to if and only if (X, ) is a core-compact space in which every ultrafilter has an irreducible convergence set and is the coarsest quasi-uniformity compatible with . If is the Pervin quasi-uniformity on X, then S is equal to if and only if X is hereditarily quasicompact, or equivalently, is the Pervin quasi-uniformity o

Schlachtkörper- und fleischqualität bei verschiedenen kombinationen von fleisch- und zweinutzungsrassen

International audienc

Beef breed bulls versus selected dual purpose bulls for meat production

International audienc

Complete partial metric spaces have partially metrizable computational models

We show that the domain of formal balls of a complete partial metric space (X, p) can be endowed with a complete partial metric that extends p and induces the Scott topology. This result, that generalizes well-known constructions of Edalat and Heckmann [A computational model for metric spaces, Theoret. Comput. Sci. 193 (1998), pp. 53-73] and Heckmann [Approximation of metric spaces by partial metric spaces, Appl. Cat. Struct. 7 (1999), pp. 71-83] for metric spaces and improves a recent result of Romaguera and Valero [A quantitative computational model for complete partial metric spaces via formal balls, Math. Struct. Comput. Sci. 19 (2009), pp. 541-563], motivates a notion of a partially metrizable computational model which allows us to characterize those topological spaces that admit a compatible complete partial metric via this model.The authors acknowledge the support of the Spanish Ministry of Science and Innovation, under grant MTM2009-12872-C02-01.Romaguera Bonilla, S.; Tirado Peláez, P.; Valero Sierra, Ó. (2012). Complete partial metric spaces have partially metrizable computational models. International Journal of Computer Mathematics. 89(3):284-290. https://doi.org/10.1080/00207160.2011.559229S284290893ALI-AKBARI, M., HONARI, B., POURMAHDIAN, M., & REZAII, M. M. (2009). The space of formal balls and models of quasi-metric spaces. Mathematical Structures in Computer Science, 19(2), 337-355. doi:10.1017/s0960129509007439Edalat, A., & Heckmann, R. (1998). A computational model for metric spaces. Theoretical Computer Science, 193(1-2), 53-73. doi:10.1016/s0304-3975(96)00243-5Edalat, A., & Sünderhauf, P. (1999). Computable Banach spaces via domain theory. Theoretical Computer Science, 219(1-2), 169-184. doi:10.1016/s0304-3975(98)00288-6Flagg, B., & Kopperman, R. (1997). Computational Models for Ultrametric Spaces. Electronic Notes in Theoretical Computer Science, 6, 151-159. doi:10.1016/s1571-0661(05)80164-1Heckmann, R. (1999). Applied Categorical Structures, 7(1/2), 71-83. doi:10.1023/a:1008684018933Kopperman, R., Künzi, H.-P. A., & Waszkiewicz, P. (2004). Bounded complete models of topological spaces. Topology and its Applications, 139(1-3), 285-297. doi:10.1016/j.topol.2003.12.001Krötzsch, M. (2006). Generalized ultrametric spaces in quantitative domain theory. Theoretical Computer Science, 368(1-2), 30-49. doi:10.1016/j.tcs.2006.05.037Künzi, H.-P. A. (2001). Nonsymmetric Distances and Their Associated Topologies: About the Origins of Basic Ideas in the Area of Asymmetric Topology. History of Topology, 853-968. doi:10.1007/978-94-017-0470-0_3LAWSON, J. (1997). Spaces of maximal points. Mathematical Structures in Computer Science, 7(5), 543-555. doi:10.1017/s0960129597002363Martin, K. (1998). Domain theoretic models of topological spaces. Electronic Notes in Theoretical Computer Science, 13, 173-181. doi:10.1016/s1571-0661(05)80221-xMatthews, S. G.Partial metric topology. Procedings of the 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. 728 (1994), pp. 183–197Rodríguez-López, J., Romaguera, S., & Valero, O. (2008). Denotational semantics for programming languages, balanced quasi-metrics and fixed points. International Journal of Computer Mathematics, 85(3-4), 623-630. doi:10.1080/00207160701210653Romaguera, S., & Valero, O. (2009). A quasi-metric computational model from modular functions on monoids. International Journal of Computer Mathematics, 86(10-11), 1668-1677. doi:10.1080/00207160802691652ROMAGUERA, S., & VALERO, O. (2009). A quantitative computational model for complete partial metric spaces via formal balls. Mathematical Structures in Computer Science, 19(3), 541-563. doi:10.1017/s0960129509007671ROMAGUERA, S., & VALERO, O. (2010). Domain theoretic characterisations of quasi-metric completeness in terms of formal balls. Mathematical Structures in Computer Science, 20(3), 453-472. doi:10.1017/s0960129510000010Rutten, J. J. M. M. (1998). Weighted colimits and formal balls in generalized metric spaces. Topology and its Applications, 89(1-2), 179-202. doi:10.1016/s0166-8641(97)00224-1Schellekens, M. P. (2003). A characterization of partial metrizability: domains are quantifiable. Theoretical Computer Science, 305(1-3), 409-432. doi:10.1016/s0304-3975(02)00705-3Smyth, M. B. (2006). The constructive maximal point space and partial metrizability. Annals of Pure and Applied Logic, 137(1-3), 360-379. doi:10.1016/j.apal.2005.05.032Waszkiewicz, P. (2003). Applied Categorical Structures, 11(1), 41-67. doi:10.1023/a:1023012924892WASZKIEWICZ, P. (2006). Partial metrisability of continuous posets. Mathematical Structures in Computer Science, 16(02), 359. doi:10.1017/s096012950600519

Rapid meridional transport of tropical airmasses to the Arctic during the major stratospheric warming in January 2003

International audienceWe present observations of unusually high values of ozone and N2O in the middle stratosphere that were observed by the airborne submillimeter radiometer ASUR in the Arctic. The observations took place in the meteorological situation of a major stratospheric warming that occurred in mid-January 2003 and was dominated by a wave 2 event. On 23 January 2003 the observed N2O and O3 mixing ratios around 69° N in the middle stratosphere reached maximum values of ~190 ppb and ~10 ppm, respectively. The similarities of these N2O profiles in a potential temperature range between 800 and 1200 K with N2O observations around 20° N on 1 March 2003 by the same instrument suggest that the observed Arctic airmasses were transported from the tropics quasi-isentropically. This is confirmed by 5-day back trajectory calculations which indicate that the airmasses between about 800 and 1000 K had been located around 20° N 3?5 days prior to the measurement in the Arctic. Calculations with a linearized ozone chemistry model along calculated as well as idealized trajectories, initialized with the low-latitude ASUR ozone measurements, give reasonable agreement with the Arctic ozone measurement by ASUR. PV distributions suggest that these airmasses did not stay confined in the Arctic region which makes it unlikely that this dynamical situation lead to the formation of dynamically caused pockets of low ozone

New results on the mathematical foundations of asymptotic complexity analysis of algorithms via complexity spaces

Schellekens [The Smyth completion: A common foundation for denotational semantics and complexity analysis, Electron. Notes Theor. Comput. Sci. 1 (1995), pp. 211-232.] introduced the theory of complexity (quasi-metric) spaces as a part of the development of a topological foundation for the asymptotic complexity analysis of programs and algorithms in 1995. The applicability of this theory to the asymptotic complexity analysis of divide and conquer algorithms was also illustrated by Schellekens in the same paper. In particular, he gave a new formal proof, based on the use of the Banach fixed-point theorem, of the well-known fact that the asymptotic upper bound of the average running time of computing of Mergesort belongs to the asymptotic complexity class of n log(2) n. Recently, Schellekens' method has been shown to be useful in yielding asymptotic upper bounds for a class of algorithms whose running time of computing leads to recurrence equations different from the divide and conquer ones reported in Cerda-Uguet et al. [The Baire partial quasi-metric space: A mathematical tool for the asymptotic complexity analysis in Computer Science, Theory Comput. Syst. 50 (2012), pp. 387-399.]. However, the variety of algorithms whose complexity can be analysed with this approach is not much larger than that of algorithms that can be analysed with the original Schellekens method. In this paper, on the one hand, we extend Schellekens' method in order to yield asymptotic upper bounds for a certain class of recursive algorithms whose running time of computing cannot be discussed following the techniques given by Cerda-Uguet et al. and, on the other hand, we improve the original Schellekens method by introducing a new fixed-point technique for providing, contrary to the case of the method introduced by Cerda-Uguet et al., lower asymptotic bounds of the running time of computing of the aforementioned algorithms and those studied by Cerda-Uguet et al. We illustrate and validate the developed method by applying our results to provide the asymptotic complexity class (asymptotic upper and lower bounds) of the celebrated algorithms Quicksort, Largetwo and Hanoi.The authors are thankful for the support from the Spanish Ministry of Science and Innovation, grant MTM2009-12872-C02-01.Romaguera Bonilla, S.; Tirado Peláez, P.; Valero Sierra, Ó. (2012). New results on the mathematical foundations of asymptotic complexity analysis of algorithms via complexity spaces. International Journal of Computer Mathematics. 89(13-14):1728-1741. https://doi.org/10.1080/00207160.2012.659246S172817418913-14Cerdà-Uguet, M. A., Schellekens, M. P., & Valero, O. (2011). The Baire Partial Quasi-Metric Space: A Mathematical Tool for Asymptotic Complexity Analysis in Computer Science. Theory of Computing Systems, 50(2), 387-399. doi:10.1007/s00224-010-9310-7Cull, P., & Ecklund, E. F. (1985). Towers of Hanoi and Analysis of Algorithms. The American Mathematical Monthly, 92(6), 407. doi:10.2307/2322448García-Raffi, L. M., Romaguera, S., & Sánchez-Pérez, E. A. (2002). Sequence spaces and asymmetric norms in the theory of computational complexity. Mathematical and Computer Modelling, 36(1-2), 1-11. doi:10.1016/s0895-7177(02)00100-0García-Raffi, L. M., Romaguera, S., & Schellekens, M. P. (2008). Applications of the complexity space to the General Probabilistic Divide and Conquer Algorithms. Journal of Mathematical Analysis and Applications, 348(1), 346-355. doi:10.1016/j.jmaa.2008.07.026Künzi, H.-P. A. (2001). Nonsymmetric Distances and Their Associated Topologies: About the Origins of Basic Ideas in the Area of Asymmetric Topology. History of Topology, 853-968. doi:10.1007/978-94-017-0470-0_3Rodríguez-López, J., Romaguera, S., & Valero, O. (2008). Denotational semantics for programming languages, balanced quasi-metrics and fixed points. International Journal of Computer Mathematics, 85(3-4), 623-630. doi:10.1080/00207160701210653Rodríguez-López, J., Schellekens, M. P., & Valero, O. (2009). An extension of the dual complexity space and an application to Computer Science. Topology and its Applications, 156(18), 3052-3061. doi:10.1016/j.topol.2009.02.009Romaguera, S., & Schellekens, M. (1999). Quasi-metric properties of complexity spaces. Topology and its Applications, 98(1-3), 311-322. doi:10.1016/s0166-8641(98)00102-3Romaguera, S., & Valero, O. (2008). On the structure of the space of complexity partial functions. International Journal of Computer Mathematics, 85(3-4), 631-640. doi:10.1080/00207160701210117Romaguera, S., Schellekens, M. P., & Valero, O. (2011). The complexity space of partial functions: a connection between complexity analysis and denotational semantics. International Journal of Computer Mathematics, 88(9), 1819-1829. doi:10.1080/00207161003631885Schellekens, M. (1995). The Smyth Completion. Electronic Notes in Theoretical Computer Science, 1, 535-556. doi:10.1016/s1571-0661(04)00029-5Scott, D. S. 1970. Outline of a mathematical theory of computation. Proceedings of the 4th Annual Princeton Conference on Information Sciences and Systems. March26–271970, Princeton, NJ. pp.169–176

Normally preordered spaces and utilities

In applications it is useful to know whether a topological preordered space is normally preordered. It is proved that every $k_\omega$-space equipped with a closed preorder is a normally preordered space. Furthermore, it is proved that second countable regularly preordered spaces are perfectly normally preordered and admit a countable utility representation.Comment: 17 pages, 1 figure. v2 contains a second proof to the main theorem with respect to the published version. The last section of v1 is not present in v2. It will be included in a different wor

Processing second-order stochastic dominance models using cutting-plane representations

This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-VerlagSecond-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).This study was funded by OTKA, Hungarian National Fund for Scientific Research, project 47340; by Mobile Innovation Centre, Budapest University of Technology, project 2.2; Optirisk Systems, Uxbridge, UK and by BRIEF (Brunel University Research Innovation and Enterprise Fund)