In: Proceedings of the Third Arolla Conference on Algebraic Topology, 18-24 August 2008
We give a survey on geometric properties of the Witten genus. The survey focuses on relations between the Witten genus, group actions and positive curvature.
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In: Journal of Combinatorial Theory, Series A, 2009, vol. 116, no. 4, p. 875-902
We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram contains a unique dotted edge. We prove that such a polytope in d-dimensional hyperbolic space has at most d+3 facets. In view of results by Kaplinskaja [I.M. Kaplinskaya, Discrete groups generated by reflections in the faces of simplicial prisms in Lobachevskian spaces, Math. Notes 15 (1974) 88–91] and the second author [P....
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In: Journal of Algebra, 2009, vol. 322, no. 2, p. 429-448
We define a homology theory for a certain class of posets equipped with a pre-sheaf of modules. We show that when restricted to Boolean lattices this homology is isomorphic to the homology of the “cube” complex defined by Khovanov.
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In: Advances in Mathematics, 2009, vol. 222, no. 3, p. 920-936
We extend the classical Brunn theorem to symmetric moments of convex bodies and use it to prove the convexity of the Lp-intersection bodies of centered convex bodies.
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In: SIAM Journal on Applied Mathematics, 2008, vol. 68, no. 3, p. 869-889
A skeletal muscle is composed of motor units, each consisting of a motoneuron and the muscle fibers it innervates. The input to the motor units is formed of electrical signals coming from higher motor centers and propagated to the motoneurons along a network of nerve fibers. Because of its complexity, this network still escapes actual direct observations. The present model describes the steady...
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In: Applied and Computational Harmonic Analysis, 2007, vol. 23, no. 3, p. 307-320
We consider the Hermite trigonometric interpolation problem of order 1 for equidistant nodes, i.e., the problem of finding a trigonometric polynomial t that interpolates the values of a function and of its derivative at equidistant points. We give a formula for the Fourier coefficients of t in terms of those of the two classical trigonometric polynomials interpolating the values and those of the...
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Thèse de doctorat : Université de Fribourg, 2000 ; No 1313.
1995 wiederholten Besson, Courtois und Gallot [BCG] den Beweis eines bekannten Satzes, nämlich, dass jedes positive Mass µ auf dem Rand M(∞) eines lokal symmetrischen Raumes M vom Rang 1 einen Schwerpunkt p innerhalb des Raumes besitzt, der als Lösung p der Gleichung: beschrieben werden kann, wobei Bθ die Busemann Funktion für θ ∈ M(∞) ist. Wenn der Rang höher ist, ist es klar, dass...
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Thèse de doctorat : Université de Fribourg, 2001 ; no 1334.
Beaucoup de neurones et d’axones sont éliminés lors du développement du système nerveux. Ces cellules et leurs connexions sont en effet produites en surnombre et l’organisme est contraint à la destruction du surplus pour assurer son bon fonctionnement. Le mécanisme important assurant cette élimination semble être celui d’une compétition entre cellules pour l’appropriation d’une...
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In: Computer Physics Communications, 2004, vol. 163(3), p. 133-142
An algorithm for the generation of adaptive radial grids used in density functional theory or quantum chemical calculations is described. Our approach is general and can be applied for the integration over Slater or Gaussian type functions with only minor modifications. The relative error of the integration is fully controlled by the algorithm within a specified range of exponential parameters...
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In: Ecological Modelling
Levins and Ginzburg raised two paradoxes concerning the logistic equation of population growth. None of them received a satisfactory answer within the frame of the original equation. Here, we propose solutions to both paradoxes.
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