110,139 research outputs found
Baby Verma modules for rational Cherednik algebras
No full textThis paper introduces baby Verma modules for symplectic reflection algebras of complex reflection groups at parameter t = 0 (the so-called rational Cherednik algebras at parameter t = 0, and presents their most basic properties. Baby Verma modules are then used to answer several problems posed by Etingof and Ginzburg, and to give an elementary proof of a theorem of Finkelberg and Ginzburg. 2000 Mathematics Subject Classification 16Rxx, 16S38, 05E10
Vortex Vein Imaging: What Can It Tell Us?
No full textAditya Verma,1,2 Tommaso Bacci,3,4 David Sarraf,5 K Bailey Freund,3,4 SriniVas R Sadda1,2 1Doheny Eye Institute, Los Angeles, CA, USA; 2Department of Ophthalmology, David Geffen School of Medicine at UCLA, Los Angeles, CA, USA; 3Vitreous Retina Macula Consultants of New York, New York, NY, USA; 4Department of Ophthalmology, New York University Grossman School of Medicine, New York, NY, USA; 5Stein Eye Institute, David Geffen School of Medicine at University of California, Los Angeles, CA, 90095, USACorrespondence: SriniVas R Sadda Email [email protected]: This review article summarizes the patho-anatomy of the vortex veins, the major drainage channels for the choroid, and describes the various pathways of diseases associated with vortex vein abnormalities. This report also details the technical advancements to image the vortex veins, such as ultra-widefield indocyanine green angiography, which are critical to elucidate the importance of the vortices in various retino-choroidal disorders. Future applications of these advanced imaging systems to better understand the role of the vortex veins in health and disease are also discussed.Keywords: choroid, optical coherence tomography angiography, pachychoroid disease, ultra-widefield imaging, vortex vein
Sweeping has no effect on renormalized turbulent viscosity
No full textWe perform renormalization group analysis (RG) of the Navier-Stokes equation in the presence of constant mean velocity field , and show that the renormalized viscosity is unaffected by , thus negating the ``sweeping effect", proposed by Kraichnan [Phys. Fluids {\bf 7}, 1723 (1964)] using random Galilean invariance. Using direct numerical simulation, we show that the correlation functions for and differ from each other, but the renormalized viscosity for the two cases are the same. Our numerical results are consistent with the RG calculations
Verma kraftverk. Konsekvenser knyttet til planer for nytt kraftverk i Verma
No full textErikstad, L., Andersen, O., Halvorsen, G., Reitan, O., Risan, T. & Stabbetorp, O. 2008. Verma kraftverk - Konsekvenser knyttet til planer for nytt kraftverk i Verma. - NINA Rapport 357. 55 s.
Denne rapporten består av tre deler som hver for seg er knyttet til tre ulike stadier i arbeidet med konsekvensanalyse for tiltak knyttet til planene for opprusting av eksisterende Verma kraftverk. Det er alternativ beskrevet i del 3 som er aktuelle per 1/1 2008. Første delen av rapporten dekker utredningene i 2002/2003 for alternativene A1 og A2 som representerer en moderat opprustning av eksisterende Verma kraftverk Største forskjell i forhold til dagens situasjon (0-alternativ) er økt slukeevne, høyere inntaksdam og at et av alternativene vil slippe utløpsvann i Rauma nedenfor samløpet. Konsekvensene er vurdert å være negative, men små. Størst negativ konsekvens er knyttet til utslipp av utløpsvann nedstrøms et viktig gyte og oppvekstområde for laks ved Løkra. Del 2 i rapporten omfatter en utredning parallelt med del 1, men med mer omfattende planer for berørte elvestrekninger i både Verma og Rauma. Rauma med Verma er varig vernet mot kraftutbygging. Det er uklart hva dette vernet innebærer i detalj for nedre del av Verma der eksisterende kraftverk med regulering var etablert før vernet ble vedtatt. Del 3 omfatter en ny vurdering med spesiell vekt på biologisk mangfold og rødlistede arter knyttet til nye og reviderte opprustningsplaner. Planene ligger nær de opprinnelige planalternativene A1 og A 2, men det er også et alternativ som er en mellomting mellom disse. Konklusjonene er tilsvarende som de som ble trukket i del 1 av rapporten. En viktig biotop ved utløpet av Verma vurderes å bli lite berørt under forutsetning av at utløpstunneler ikke legges slik at skogsmark blir berørt. Nytt alternativ 6 som slipper vann umiddelbart nedstrøms samløpet mellom Verma og Rauma er klart bedre med hensyn til konsekvenser for fisk enn alternativ A2 og alternativ 4, men litt mer ugunstig enn alternativ A1 og alternativ 3. konsekvensanalyse, vassdrag, kraftverk, Verma, Rauma kommune, Møre og Romsdal fylke, environmental impact asessment, hydroelectric development, Verma, Rauma municipality, Møre & Romsdal count
Systems of Differential Operators and Generalized Verma Modules
No full textIn this paper we close the cases that were left open in our earlier works on the study of conformally invariant systems of second-order differential operators for degenerate principal series. More precisely, for these cases, we find the special values of the systems of differential operators, and determine the standardness of the homomorphisms between the generalized Verma modules, that come from the conformally invariant systems.The author was supported by the Global COE program at the Graduate School of Mathematical
Sciences, the University of Tokyo, Japan. He would like to be thankful for the referees for their
careful reading and invaluable comments
Branching laws for Verma modules and applications in parabolic geometry
No full textWe initiate a new study of differential operators with symmetries and combine this with the study of branching laws for Verma modules of reductive Lie algebras. By the criterion for discretely decomposable and multiplicity-free restrictions of generalized Verma modules [T. Kobayashi, Transf. Groups (2012)], we are brought to natural settings of parabolic geome-tries for which there exist unique equivariant differential operators to submanifolds. Then we apply a new method (F-method) relying on the Fourier transform to find singular vectors in generalized Verma modules, which significantly simplifies and generalizes many preceding works. In certain cases, it also determines the Jordan–Hölder series of the restriction for singular parameters. The F-method yields an explicit formula of such unique operators, for example, giving an intrinsic and new proof of Juhl’s conformally invariant differential operators [Juhl, Progr. Math. 2009] and its generalizations to spinor bundles. This article is the first in the series, and the next ones include their extension to curved cases together with more applications of the F-method to various settings in parabolic geometries
Letter, [Author unclear] to Paulina T. Merritt
No full textHandwritten letter to Paulina Merritt from an unknown author, October 1, 1876.
The F-method and a branching problem for generalized Verma modules associated to
No full textsummary:The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras , and generalized conformal -Verma modules of scalar type. As a result, we classify the -singular vectors for this class of -modules
Endomorphisms of verma modules for rational cherednik algebras
No full textWe study the endomorphism algebras of Verma modules for rational Cherednik algebras at t = 0. It is shown that, in many cases, these endomorphism algebras are quotients of the centre of the rational Cherednik algebra. Geometrically, they define Lagrangian subvarieties of the generalized Calogero–Moser space. In the introduction, we motivate our results by describing them in the context of derived intersections of Lagrangians
Supplemental Material - Disadvantaged communities have lower access to urban infrastructure
No full textSupplemental Material for Disadvantaged communities has lower access to urban infrastructure by Leonardo Nicoletti, Mikhail Sirenko and Trivik Verma in Environment and Planning B: Urban Analytics and City Science</p
- …
