Weak and cyclic amenability for Fourier algebras of connected Lie groups

Using techniques of non-abelian harmonic analysis, we construct an explicit, non-zero cyclic derivation on the Fourier algebra of the real $ax+b$ group. In particular this provides the first proof that this algebra is not weakly amenable. Using the structure theory of Lie groups, we deduce that the Fourier algebras of connected, semisimple Lie groups also support non-zero, cyclic derivations and are likewise not weakly amenable. Our results complement earlier work of Johnson (JLMS, 1994), Plymen (unpublished note) and Forrest--Samei--Spronk (IUMJ 2009). As an additional illustration of our techniques, we construct an explicit, non-zero cyclic derivation on the Fourier algebra of the reduced Heisenberg group, providing the first example of a connected nilpotent group whose Fourier algebra is not weakly amenable.Comment: v4: AMS-LaTeX, 26 pages. Final version, to appear in JFA. Includes an authors' correction added at proof stag

Surface temperatures in New York City: Geospatial data enables the accurate prediction of radiative heat transfer

Three decades into the research seeking to derive the urban energy budget, the dynamics of the thermal exchange between the densely built infrastructure and the environment are still not well understood. We present a novel hybrid experimental-numerical approach for the analysis of the radiative heat transfer in New York City. The aim of this work is to contribute to the calculation of the urban energy budget, in particular the stored energy. Improved understanding of urban thermodynamics incorporating the interaction of the various bodies will have implications on energy conservation at the building scale, as well as human health and comfort at the urban scale. The platform presented is based on longwave hyperspectral imaging of nearly 100 blocks of Manhattan, and a geospatial radiosity model that describes the collective radiative heat exchange between multiple buildings. The close comparison of temperature values derived from measurements and the computed surface temperatures (including streets and roads) implies that this geospatial, thermodynamic numerical model applied to urban structures, is promising for accurate and high resolution analysis of urban surface temperatures.Comment: 11 pages, 5 figure

Projections in L1(G)L^1(G); the unimodular case

We consider the issue of describing all self-adjoint idempotents (projections) in $L^1(G)$ when $G$ is a unimodular locally compact group. The approach is to take advantage of known facts concerning subspaces of the Fourier-Stieltjes and Fourier algebras of $G$ and the topology of the dual space of $G$. We obtain an explicit description of any projection in $L^1(G)$ which happens to also lie in the coefficient space of a finite direct sum of irreducible representations. This leads to a complete description of all projections in $L^1(G)$ for $G$ belonging to a class of groups that includes $SL(2,R)$ and all almost connected nilpotent locally compact groups.Comment: 13 page

Ocena skali ABCD2 u pacjentów z napadem przemijającego niedokrwienia mózgu lub udarem mózgu

Background and purpose Stroke risk prediction scores have been designed to stratify risk of recurrent cerebrovascular events in patients with transient ischaemic attack (TIA) or minor ischaemic stroke (MIS). Material and methods Consecutive patients with TIA or MIS referring to Ghaem Hospital, Mashhad presenting within 24 hours from the onset of symptoms were recruited to the prospective cohort study between 2010 and 2011. MIS was defined as an ischaemic stroke with National Institutes of Health Stroke Scale (NIHSS) score < 4. The end-point of the study was a new ischaemic cerebrovascular event or vascular death at 90 days and, additionally, at 3 days after the index TIA or MIS. The decision to admit and of method of treatment in each case was left to the discretion of the stroke neurologist. The predictive accuracy of the ABCD2 scoring system for recurrent stroke or TIA was quantified by the area under the curve (AUC), using the c-statistics. Results The study included 393 patients with TIA (238 males, 155 females) and 118 patients with MIS (77 males, 41 females). Among 511 patients with minor ischaemic events, 117 strokes (23.2%), 99 TIAs (19.6%), and 11 vascular deaths (2.2%) occurred within 3 months after the index event. The ABCD2 score had a weak predictive value for 3-month and 3-day recurrent stroke in patients with TIA (AUC = 0.599 and 0.591, respectively), but a high predictive value for 3-month and 3-day recurrent stroke in patients with MIS (AUC = 0.727 and 0.728, respectively). Conclusions The ABCD2 score is highly predictive for short-term recurrent stroke in patients with MIS but not in patients with TIA, although it was originally designed for patients with TIA.Wstęp i cel pracy Punktację oceny ryzyka wystąpienia udaru mózgu opracowano w celu stratyfikacji ryzyka nawrotowego incydentu naczyniowego mózgu u pacjentów z napadem przemijającego niedokrwienia mózgu (transient ischaemic attack – TIA) lub niewielkim udarem niedokrwiennym mózgu (minor ischaemic stroke – MIS). Materiał i metody Do badania włączono kolejnych chorych zgłaszających się w latach 2010–2011 do szpitala Ghaem w Mashad w ciągu 24 godzin od wystąpienia TIA lub MIS. Niewielki udar niedokrwienny mózgu definiowano jako udar niedokrwienny mózgu powodujący ubytkowe objawy neurologiczne ocenione w skali National Institutes of Health Stroke Scale (NIHSS) na < 4 pkt. Punktem końcowym badania było wystąpienie kolejnego incydentu naczyniowego mózgu lub zgon w ciągu 90 dni, a dodatkowo również w ciągu 3 dni od pierwszego zachorowania. Decyzję o przyjęciu do szpitala i o sposobie leczenia podejmował neurolog specjalizujący się w chorobach naczyniowych mózgu. Dokładność rokowniczą skali ABCD2 w przewidywaniu wystąpienia nawrotowego udaru mózgu lub TIA oceniono liczbowo i określono ilościowo metodą pola pod krzywą (area under the curve – AUC) z użyciem statystyki c. Wyniki W badaniu wzięło udział 393 chorych na TIA (238 mężczyzn i 155 kobiet) oraz 118 chorych na MIS (77 mężczyzn i 41 kobiet). W grupie obejmującej łącznie 511 chorych z lekkimi incydentami naczyniowymi mózgu w okresie 3 miesięcy od wystąpienia pierwszego incydentu naczyniowego mózgu wystąpiło 117 udarów mózgu (23,2%), 99 TIA (19,6%) i 11 zgonów z przyczyn naczyniowych (2,2%). Wartość predykcyjna punktacji ABCD2 w odniesieniu do wystąpienia nawrotowego udaru mózgu w okresie 3 miesięcy lub 3 dni po pierwotnym incydencie naczyniowym była niewielka u pacjentów z TIA (wartość AUC odpowiednio 0,599 i 0,591), a duża u pacjentów z MIS (wartość AUC odpowiednio 0,727 i 0,728). Wniosek Punktacja ABCD2 ma dużą wartość predykcyjną wczesnego wystąpienia nawrotowego udaru mózgu u pacjentów z MIS, ale nie z TIA, chociaż pierwotnie została zaprojektowana do użycia w drugiej z tych populacji

Covering a closed curve with a given total curvature

http://archive.org/details/coveringclosedcu00ghanN