Shintani functions, real spherical manifolds, and symmetry breaking operators

For a pair of reductive groups $G \supset G'$, we prove a geometric criterion for the space $Sh(\lambda, \nu)$ of Shintani functions to be finite-dimensional in the Archimedean case. This criterion leads us to a complete classification of the symmetric pairs $(G,G')$ having finite-dimensional Shintani spaces. A geometric criterion for uniform boundedness of $dim Sh(\lambda, \nu)$ is also obtained. Furthermore, we prove that symmetry breaking operators of the restriction of smooth admissible representations yield Shintani functions of moderate growth, of which the dimension is determined for $(G, G') = (O(n+1,1), O(n,1))$.Comment: to appear in Progress in Mathematics, Birkhause

Eigenfunctions of the Laplacian and associated Ruelle operator

Let $\Gamma$ be a co-compact Fuchsian group of isometries on the Poincar\'e disk \DD and $\Delta$ the corresponding hyperbolic Laplace operator. Any smooth eigenfunction $f$ of $\Delta$, equivariant by $\Gamma$ with real eigenvalue $\lambda=-s(1-s)$, where $s={1/2}+ it$, admits an integral representation by a distribution \dd_{f,s} (the Helgason distribution) which is equivariant by $\Gamma$ and supported at infinity \partial\DD=\SS^1. The geodesic flow on the compact surface \DD/\Gamma is conjugate to a suspension over a natural extension of a piecewise analytic map T:\SS^1\to\SS^1, the so-called Bowen-Series transformation. Let $\ll_s$ be the complex Ruelle transfer operator associated to the jacobian $-s\ln |T'|$. M. Pollicott showed that \dd_{f,s} is an eigenfunction of the dual operator $\ll_s^*$ for the eigenvalue 1. Here we show the existence of a (nonzero) piecewise real analytic eigenfunction $\psi_{f,s}$ of $\ll_s$ for the eigenvalue 1, given by an integral formula \psi_{f,s} (\xi)=\int \frac{J(\xi,\eta)}{|\xi-\eta|^{2s}} \dd_{f,s} (d\eta), \noindent where $J(\xi,\eta)$ is a $\{0,1\}$-valued piecewise constant function whose definition depends upon the geometry of the Dirichlet fundamental domain representing the surface \DD/\Gamma

On Kostant's partial order on hyperbolic elements

We study Kostant's partial order on the elements of a semisimple Lie group in relations with the finite dimensional representations. In particular, we prove the converse statement of [3, Theorem 6.1] on hyperbolic elements.Comment: 7 page

Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type

We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them

Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from the Satake diagram, in a way that is suited for the use with computer algebra systems. As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified. The submission also contains an example implementation of the algorithms and formulas of the paper as a package for Maple 10, the technical documentation for this implementation, and a worksheet carrying out the computations for the space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical documentatio

Extremal Black Attractors in 8D Maximal Supergravity

Motivated by the new higher D-supergravity solutions on intersecting attractors obtained by Ferrara et al. in [Phys.Rev.D79:065031-2009], we focus in this paper on 8D maximal supergravity with moduli space [SL(3,R)/SO(3)]x[SL(2,R)/SO(2)] and study explicitly the attractor mechanism for various configurations of extremal black p- branes (anti-branes) with the typical near horizon geometries AdS_{p+2}xS^{m}xT^{6-p-m} and p=0,1,2,3,4; 2<=m<=6. Interpretations in terms of wrapped M2 and M5 branes of the 11D M-theory on 3-torus are also given. Keywords: 8D supergravity, black p-branes, attractor mechanism, M-theory.Comment: 37 page

d=4 Attractors, Effective Horizon Radius and Fake Supergravity

We consider extremal black hole attractors (both BPS and non-BPS) for N=3 and N=5 supergravity in d=4 space-time dimensions. Attractors for matter-coupled N=3 theory are similar to attractors in N=2 supergravity minimally coupled to Abelian vector multiplets. On the other hand, N=5 attractors are similar to attractors in N=4 pure supergravity, and in such theories only 1\N-BPS non-degenerate solutions exist. All the above mentioned theories have a simple interpretation in the first order (fake supergravity) formalism. Furthermore, such theories do not have a d=5 uplift. Finally we comment on the "duality" relations among the attractor solutions of N\geq2 supergravities sharing the same full bosonic sector.Comment: 1+47 pages, 2 Tables. v2: Eqs. (2.3),(2.4) and Footnote 3 added; minor cosmetic changes; to appear in PR

Symmetric spaces of higher rank do not admit differentiable compactifications

Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank one spaces, this topological compactification can be endowed with a differentiable structure such that the action of the isometry group is differentiable. Moreover, the restriction of the action on the boundary leads to a flat model for some geometry (conformal, CR or quaternionic CR depending of the space). One can ask whether such a differentiable compactification exists for higher rank spaces, hopefully leading to some knew geometry to explore. In this paper we answer negatively.Comment: 13 pages, to appear in Mathematische Annale

Nitrogen cycling in root associated soils at bolting, flowering and seed pod filling across eight diverse Brassica napus (canola) genotypes

Non-Peer ReviewedNitrogen (N) mineralization and nitrification can be used predict the amount of N that is available to crops. Brassica napus L. (canola) production is N intensive; therefore, to improve and sustain yields, a better understanding of N cycling patterns for fertilization application is needed. The objective of this study is to examine N cycling after urea fertilization at the three major canola growth stages: bolting, flowering and seed pod filling; and how N cycling may differ between diverse canola lines grown in different soil types. Eight diverse B. napus lines were grown on Dark Brown Chernozemic soil and Black Chernozemic soil in Saskatchewan, Canada. Root-associated soils were collected from each line at bolting, flowering and seed pod filling, and this soil was analyzed for potential nitrification and mineralization, as well as soil nitrate and ammonium content. We predict that potential nitrification will be higher during the bolting and flowering stages of canola growth because the urea fertilizer that was applied to the field would have been converted to nitrate-N, which is plant available. We predict that potential mineralization will be higher during flowering and seed pod filling, because the demand for N to make protein-rich seeds is high enough to deplete much of the inorganic fertilizer N. We also predict that both nitrate-N and ammonium-N will decrease over the growing season, with significant differences between the canola lines and the soil environments. Mixed effect analyses and ANOVA will be used to analyze N cycling in the soil in relation to soil type differences, canola line differences, and growth stage differences. By characterizing soil N processes, this research will advance efforts to understand and improve N uptake for B. napus lines

Changes in patients’ need of treatment at the Faculty of Odontology, University of Iceland, in the years 1992, 1997 and 2002

Neðst á síðunni er hægt að nálgast greinina í heild sinni með því að smella á hlekkinn View/OpenObjectives: To evaluate if there has been a change in patients’ needs of dental treatment over a 10-year period. Methods: 604 panoramic radiographs from patients’ records from 1992, 1997 and 2002 were evaluated. The panoramic radiographs were evaluated by three observers in consensus. The occurrence of the following were studied; number of teeth, number of teeth needing treatment, number of decays and number of extra radiographs needed to make a confident diagnosis (bitewings and/or periapical). Third molars were not included in this study. Chi-square tests and t-tests were used. Results: When looking at patients with 20 or more teeth, male patients were in higher need of treatment than female patients in the age group 46-50 years (p=0.031). No significant difference was found in treatment need among patients in 1992 and 1997 or 1997 and 2002. However, between 1992 and 2002 the treatment need of the youngest age group (20 years and younger) had significantly risen from 0.60 teeth to 4.88 teeth (p=0.026). Conclusion: There seems to be an increase in numbers of teeth that need dental treatment in the youngest patient group seeking dental service at the Faculty of Odontology, University of Iceland.Tilgangur: Kannað var hvort breyting hefði orðið á meðferðarþörf sjúklinga Tannlæknadeildar Háskóla Íslands á 10 ára tímabili. Vísbendingar benda til aukinnar tannátu og að aukinnar meðferðar sé þörf meðal yngri sjúklinga tannlæknadeildar (20 ára og yngri). Efniviður: 604 kjálkabreiðmyndir úr sjúkraskrám, frá árunum 1992, 1997 og 2002 voru skoðaðar. Þrír tannlæknar greindu kjálkabreiðmyndirnar í sameiningu með tilliti til fjölda tanna, fjölda tanna sem þörfnuðust meðferðar, fjölda tannskemmda og fjölda viðbóta röntgenmynda (bitewings og/eða periapical) sem gera myndu greininguna marktækari. Meðferðarþörf endajaxla var ekki metin í þessari rannsókn. Kí-kvaðrat próf og t-próf voru notuð. Niðurstöður: Þegar litið var á sjúklinga með 20 eða fleiri tennur, þá voru karlmenn oftast í meiri meðferðarþörf en konur en það var marktækt (p=0.031) í aldurshópnum 46-50 ára. Ekki var markækur munur á meðferðarþörf sjúklinga sem komu til meðferðar á árunum 1992 og 1997, eða 1997 og 2002 en milli áranna 1992 og 2002 hafði meðal meðferðarþörf yngsta hópsins (20 ára og yngri) marktækt aukist úr 0.60 tönnum árið 1992 í 4.88 tennur árið 2002 (p=0.026). Niðurstöður: Í yngsta sjúklingahópnum sem leitar til tannlæknadeildar Háskóla Íslands virðist vera aukin meðferðarþörf