Browsing 2009 by Issue Date
Now showing items 120 of 27

HeisenbergWeyl algebra revisited: combinatorics of words and paths
[OWP200902] (Mathematisches Forschungsinstitut Oberwolfach, 2009)The Heisenberg–Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a ... 
Proof mining in metric fixed point theory and ergodic theory
[OWP200905] (Mathematisches Forschungsinstitut Oberwolfach, 2009)In this survey we present some recent applications of proof mining to the fixed point theory of (asymptotically) nonexpansive mappings and to the metastability (in the sense of Terence Tao) of ergodic averages in uniformly ... 
Minimal Riesz energy on the sphere for axissupported external fields
[OWP200904] (Mathematisches Forschungsinstitut Oberwolfach, 2009)Abstract. We investigate the minimal Riesz $s$energy problem for positive measures on the ddimensional unit sphere $\mathbb{S}^d$ in the presence of an external field induced by a point charge, and more generally by ... 
Alternative iterative methods for nonexpansive mappings, rates of convergence and applications
[OWP200919] (Mathematisches Forschungsinstitut Oberwolfach, 2009)Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic ... 
Geometric quantization of integrable systems with hyperbolic singularities
[OWP200901] (Mathematisches Forschungsinstitut Oberwolfach, 2009)We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. ... 
On the nonanalyticity locus of an arcanalytic function
[OWP200903] (Mathematisches Forschungsinstitut Oberwolfach, 20090221)A function is called arcanalytic if it is real analytic on each real analytic arc. In real analytic geometry there are many examples of arcanalytic functions that are not real analytic. Arc analytic functions appear ... 
Pointwise hyperbolicity implies uniform hyperbolicity
[OWP200906] (Mathematisches Forschungsinstitut Oberwolfach, 20090223)We provide a general mechanism for obtaining uniform information from pointwise data. A sample result is that if a diffeomorphism of a compact Riemannian manifold has pointwise expanding and contracting continuous invariant ... 
Singer quadrangles
[OWP200907] (Mathematisches Forschungsinstitut Oberwolfach, 20090301) 
Classification of idempotent states on the compact quantum groups Uq(2), SUq(2) and SOq(3)
[OWP200908] (Mathematisches Forschungsinstitut Oberwolfach, 20090302)We give a simple characterisation of those idempotent states on compact quantum groups which arise as Haar states on quantum subgroups, show that all idempotent states on quantum groups $U_q(2)$, $SU_q(2)$, and $SO_q(3) ... 
Stein's method for dependent random variables occuring in statistical mechanics
[OWP200909] (Mathematisches Forschungsinstitut Oberwolfach, 20090303)We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the ... 
A study on gradient blow up for viscosity solutions of fully nonlinear, uniformly elliptic equations
[OWP200910] (Mathematisches Forschungsinstitut Oberwolfach, 20090304)We investigate sharp conditions for boundary and interior gradient estimates of continuous viscosity solutions to fully nonlinear, uniformly elliptic equations under Dirichlet boundary conditions. When these conditions are ... 
Homological properties of piecewise hereditary algebras
[OWP200911] (Mathematisches Forschungsinstitut Oberwolfach, 20090305)Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We will investigate homological properties of piecewise hereditary algebras $\Lambda$. In particular we give lower and upper bounds of ... 
Simple graded commutative algebras
[OWP200912] (Mathematisches Forschungsinstitut Oberwolfach, 20090306)We study the notion of $\Gamma$graded commutative algebra for an arbitrary abelian group $\Gamma$. The main examples are the Clifford algebras already treated in [2]. We prove that the Clifford algebras are the only ... 
An introduction to heavytailed and sibexponential distributions
[OWP200913] (Mathematisches Forschungsinstitut Oberwolfach, 20090307)This text studies heavytailed distributions in probability theory, and especially convolutions of such distributions. The mail goal is to provide a complete and comprehensive introduction to the theory of longtailed ... 
Tilting on noncommutative rational projective curves
[OWP200914] (Mathematisches Forschungsinstitut Oberwolfach, 20090308)In this article we introduce a new class of noncommutative projective curves and show that in certain cases the derived category of coherent sheaves on them has a tilting complex. In particular, we prove that the right ... 
On the geometry of the space of fibrations
[OWP200915] (Mathematisches Forschungsinstitut Oberwolfach, 20090309)We study geometrical aspects of the space of fibrations between two given manifolds $M$ and $B$, from the point of view of Fréchet geometry. As a first result, we show that any connected component of this space is the ... 
Control of Volterra systems with scalar kernels
[OWP200916] (Mathematisches Forschungsinstitut Oberwolfach, 20090310)Volterra observations systems with scalar kernels are studied. New sufficient conditions for admissibility of observation operators are developed and some examples are discussed. 
Approximation of discrete functions and size of spectrum
[OWP200917] (Mathematisches Forschungsinstitut Oberwolfach, 20090311)Let $\Lambda \subset \mathbb{R}$ be a uniformly discrete sequence and $S \subset \mathbb{R}$ a compact set. We prove that if there exists a bounded sequence of functions in PaleyWiener space $PW_s$, which approximates ... 
The contact polytope of the leech lattice
[OWP200918] (Mathematisches Forschungsinstitut Oberwolfach, 20090312)The contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we classify the facets of the contact polytope of the Leech lattice up to symmetry. There are 1, 197, 362, 269, 604, 214, 277, 200 ... 
Simple vector bundles on plane degenerations of an elliptic curve
[OWP200920] (Mathematisches Forschungsinstitut Oberwolfach, 20090313)In 1957 Atiyah classified simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classification by describing the simple vector bundles on all reduced plane cubic curves. Our main ...