2008
2008
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A note on k[z]Automorphisms in Two Variables
[OWP200817] (Mathematisches Forschungsinstitut Oberwolfach, 2008)We prove that for a polynomial $f \in k[x, y, z]$ equivalent are: (1)$f$ is a $k[z]$coordinate of $k[z][x,y]$, and (2) $k[x, y, z]/(f)\cong k^[2]$ and $f(x,y,a)$ is a coordinate in $k[x,y]$ for some $a \in k$. This solves ... 
On the Directionally Newtonnondegenerate Singularities of Complex Hypersurfaces
[OWP200816] (Mathematisches Forschungsinstitut Oberwolfach, 2008)We introduce a minimal generalization of Newtonnondegenerate singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called directionally Newtonnondegenerate if the local embedded ... 
On the δ=const Collisions of Singularities of Complex Plane Curves
[OWP200815] (Mathematisches Forschungsinstitut Oberwolfach, 2008)We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equinormalizable or ... 
WeylTitchmarsh Functions of VectorValued SturmLiouville Operators on the Unit Interval
[OWP200813] (Mathematisches Forschungsinstitut Oberwolfach, 2008)The matrixvalued WeylTitchmarsh functions $M(\lambda)$ of vectorvalued SturmLiouville operators on the unit interval with the Dirichlet boundary conditions are considered. The collection of the eigenvalues (i.e., poles ... 
Stratifying modular representations of finite groups
[OWP200820] (Mathematisches Forschungsinstitut Oberwolfach, 20080320)We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture ... 
Epsilonhypercyclic operators
[OWP200819] (Mathematisches Forschungsinstitut Oberwolfach, 20080319)For each fixed number $\varepsilon$ in $(0, 1)$ we construct a bounded linear operator on the Banach space $\ell_1$ having a certain orbit which intersects every cone of aperture $\varepsilon$, but with every orbit avoiding ... 
Quantities that frequencydependent selection maximizes
[OWP200818] (Mathematisches Forschungsinstitut Oberwolfach, 20080318)We consider a model of frequencydependent selection, to which we refer as the Wildcard Model, that accommodates as particular cases a number of diverse models of biologically specific situations. Two very different ... 
Nonlinear Optimization for Matroid Intersection and Extensions
[OWP200814] (Mathematisches Forschungsinstitut Oberwolfach, 20080317)We address optimization of nonlinear functions of the form $f(W_x)$ , where $f : \mathbb{R}^d \to \mathbb{R}$ is a nonlinear function, $W$ is a $d \times n$ matrix, and feasible $x$ are in some large finite set $\mathcal{F}$ ... 
Noncommutative topological entropy of endomorphismus of Cuntz Algebras
[OWP200812] (Mathematisches Forschungsinstitut Oberwolfach, 20080316)Noncommutative topological entropy estimates are obtained for ‘finite range’ endomorphisms of Cuntz algebras,generalising known results for the canonical shift endomorphisms. Exact values are computed for a class of ... 
A 3local characterization of Co2
[OWP200811] (Mathematisches Forschungsinstitut Oberwolfach, 20080315)Conway’s second largest simple group, $Co_2$, is characterized by the centralizer of an element of order 3 and certain fusion data. 
Nonlinear optimization over a Weighted Independence System
[OWP200810] (Mathematisches Forschungsinstitut Oberwolfach, 20080314)We consider the problem of optimizing a nonlinear objective function over a weighted independence system presented by a linearoptimization oracle. We provide a polynomialtime algorithm that determines an rbest solution ... 
The Nagata automorphism is shifted linearizable
[OWP200809] (Mathematisches Forschungsinstitut Oberwolfach, 20080313)A polynomial automorphism $F$ is called shifted linearizable if there exists a linear map $L$ such that $LF$ is linearizable. We prove that the Nagata automorphism $N:= (XY\DeltaZ\Delta^2,Y+Z\Delta,Z)$ where $\Delta=XZ+Y^2$ ... 
A Characterization of Semisimple Plane Polynomial Automorphisms
[OWP200808] (Mathematisches Forschungsinstitut Oberwolfach, 20080312)It is wellknown that an element of the linear group $GL_n(\mathbb{C})$ is semisimple if and only if its conjugacy class is Zariski closed. The aim of this paper is to show that the same result holds for the group of complex ... 
NonStandard Behavior of Density Estimators for Sums of Squared Observations
[OWP200807] (Mathematisches Forschungsinstitut Oberwolfach, 20080311)It has been shown recently that, under an appropriate integrability condition, densities of functions of independent and identically distributed random variables can be estimated at the parametric rate by a local Ustatistic, ... 
Urn Models & Operator Ordering Procedures
[OWP200806] (Mathematisches Forschungsinstitut Oberwolfach, 20080310)Ordering of operators is purely combinatorial task involving a number of commutators shuffling components of operator expression to desired form. Here we show how it can be illustrated by simple urn models in which normal ... 
Preconditioning of Block Tridiagonal Matrices
[OWP200805] (Mathematisches Forschungsinstitut Oberwolfach, 20080309)Preconditioning methods via approximate block factorization for block tridiagonal matrices are studied. Bounds for the resulting condition numbers are given, and two methods for the recursive construction of the approximate ... 
Interpolation in Bernstein and PaleyWiener Spaces
[OWP200804] (Mathematisches Forschungsinstitut Oberwolfach, 20080308)We construct closed sets S of arbitrarily small measure with the property: given any discrete set L, every lfunction on L can be interpolated by an Lfunction with spectrum on F. This should be contrasted against ... 
Hecke duality relations of Jacobi forms
[OWP200803] (Mathematisches Forschungsinstitut Oberwolfach, 20080307)In this paper we introduce a new subspace of Jacobi forms of higher degree via certain relations among Fourier coefficients. We prove that this space can also be characterized by duality properties of certain distinguished ... 
Upper tails for intersection local times of random walks in supercritical dimensions
[OWP200802] (Mathematisches Forschungsinstitut Oberwolfach, 20080306)We determine the precise asymptotics of the logarithmic upper tail probability of the total intersection local time of $p$ independent random walks in $\mathbb{Z}^d$ under the assumption $p(d2)>d$. Our approach allows a ... 
Formal punctured ribbons and twodimensional local fields
[OWP200801] (Mathematisches Forschungsinstitut Oberwolfach, 20080305)We investigate formal ribbons on curves. Roughly speaking, formal ribbon is a family of locally linearly compact vector spaces on a curve. We establish a onetoone correspondence between formal ribbons on curves plus some ...