Normal functionals on Lipschitz spaces are weak∗^\ast continuous

Let $\operatorname{Lip}_0(M)$ be the space of Lipschitz functions on a complete metric space $M$ that vanish at a base point. We show that every normal functional in $\operatorname{Lip}_0(M)^\ast$ is weak$^*$ continuous, answering a question by N. Weaver.Comment: v2: Revised versio

Real-time estimation of zero crossings of sampled signals for timing using cubic spline interpolation

[EN] A scheme is proposed for hardware estimation of the location of zero crossings of sampled signals with sub-sample resolution for timing applications, that consists in interpolating the signal with a cubic spline near the zero crossing and then finding the root of the resulting polynomial. An iterative algorithm based on the bisection method is presented that obtains one bit of the result per step and admits an efficient FPGA implementation using fixed-point representation. In particular, the root estimation iteration involves only two additions, and the initial values can be obtained from FIR filters with certain symmetry properties. It is shown that this allows online, real-time estimation of timestamps in free-running sampling detector systems with improved accuracy with respect to the more common linear interpolation. The method is evaluated with simulations using ideal and real timing signals and estimates are given for the resource usage and speed of its implementation.This work was supported by the Generalitat Valenciana, Spain, under Grant PROMETEOII/2014/019.Aliaga, RJ. (2017). Real-time estimation of zero crossings of sampled signals for timing using cubic spline interpolation. IEEE Transactions on Nuclear Science. 64(8):2414-2422. https://doi.org/10.1109/TNS.2017.2721103S2414242264

Extreme points in Lipschitz-free spaces over compact metric spaces

We prove that all extreme points of the unit ball of a Lipschitz-free space over a compact metric space have finite support. Combined with previous results, this completely characterizes extreme points and implies that all of them are also extreme points in the bidual ball. For the proof, we develop some properties of an integral representation of functionals on Lipschitz spaces originally due to K. de Leeuw.Comment: v2: Corrected an embarrassing amount of small errors in the first draf

Transcending the Scottish Postmodern City: Ken MacLeod''s Future Urban Geographies

A place cannot exist if it has not been imagined, if it has not been perceived, as Alasdair Gray famously stated. Scottish science fiction (SF) goes a step further by emphasising the need not only to recognise and represent Scottish places, but also to recreate and to (re)imagine them in their possible futures. To (re)imagine Scotland and its places means to envision its potential spaces. Ken MacLeod is one of the figures who has successfully managed to set Scotland on the SF map. His novels Intrusion (2012) and Descent (2014) are remarkable examples of what some critics have called Transmodern fiction. Both are set in urban Scotland in the near-future and they portray new configurations of place. My analysis focuses on the interconnectedness of place as presented in the two novels, creating a new territory that transcends Scottish Postmodern urban geographies. In MacLeod''s fiction, a Transmodern urban place is conceived, where the glocal and the virtual meet in a new multifold reality without ever losing their local specificity

Supports and extreme points in Lipschitz-free spaces

[EN] For a complete metric space M, we prove that the finitely supported extreme points of the unit ball of the Lipschitz-free space F(M) are precisely the elementary molecules (¿(p)¿¿(q))/d(p,q) defined by pairs of points p,q in M such that the triangle inequality d(p,q)<d(p,r)+d(q,r) is strict for any r ¿ M different from p and q. To this end, we show that the class of Lipschitz-free spaces over closed subsets of M is closed under arbitrary intersections when M has finite diameter, and that this allows a natural definition of the support of elements of F(M).This work was supported by the grant GA. CR 18-00960Y. The first author was also partially supported by the Spanish Ministry of Economy and Competitiveness under Grant MTM2014-57838-C2-1-P.Aliaga, RJ.; Pernecka, E. (2020). Supports and extreme points in Lipschitz-free spaces. Revista Matemática Iberoamericana. 36(7):2073-2089. https://doi.org/10.4171/rmi/11912073208936

Points of differentiability of the norm in Lipschitz-free spaces

[EN] We consider convex series of molecules in Lipschitz-free spaces, i.e. elements of the form such that . We characterise these elements in terms of geometric conditions on the points , of the underlying metric space, and determine when they are points of Gâteaux differentiability of the norm. In particular, we show that Gâteaux and Fréchet differentiability are equivalent for finitely supported elements of Lipschitz-free spaces over uniformly discrete and bounded metric spaces, and that their tensor products with Gâteaux (resp. Fréchet) differentiable elements of a Banach space are Gâteaux (resp. Fréchet) differentiable in the corresponding projective tensor product.R. J. Aliaga was partially supported by the Spanish Ministry of Economy, Industry and Competitiveness under Grant MTM2017-83262-C2-2-P, and by a travel grant of the Institute of Mathematics (IEMath-GR) of the University of Granada, Spain. The research of Abraham Rueda Zoca was supported by Vicerrectorado de Investigación y Transferencia de la Universidad de Granada in the program ¿Contratos puente¿, by MICINN (Spain) Grant PGC2018-093794-B-I00 (MCIU, AEI, FEDER, UE), by Junta de Andalucía Grant A-FQM-484-UGR18 and by Junta de Andalucía Grant FQM-0185Aliaga, RJ.; Rueda Zoca, A. (2020). Points of differentiability of the norm in Lipschitz-free spaces. Journal of Mathematical Analysis and Applications. 489(2):1-17. https://doi.org/10.1016/j.jmaa.2020.124171S117489

Nebraska Population Projections to 2050 and Implications

This presentation features: How the projections were done; What the projections show; Limitations, potential issues; and Implications from these projections

Non-circular rotating beams and CMB experiments

This paper is concerned with small angular scale experiments for the observation of cosmic microwave background anisotropies. In the absence of beam, the effects of partial coverage and pixelisation are disentangled and analyzed (using simulations). Then, appropriate maps involving the CMB signal plus the synchrotron and dust emissions from the Milky Way are simulated, and an asymmetric beam --which turns following different strategies-- is used to smooth the simulated maps. An associated circular beam is defined to estimate the deviations in the angular power spectrum produced by beam asymmetry without rotation and, afterwards, the deviations due to beam rotation are calculated. For a certain large coverage, the deviations due to pure asymmetry and asymmetry plus rotation appear to be very systematic (very similar in each simulation). Possible applications of the main results of this paper to data analysis in large coverage experiments --as PLANCK-- are outlined.Comment: 13 pages, 9 figures, to appear in A&