2015
2015
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Euler Reflexion Formulas for Motivic Multiple Zeta Functions
[OWP201517] (Mathematisches Forschungsinstitut Oberwolfach, 20151118)We introduce a new notion of *product of two integrable series with coeficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability and commuting with the limit of rational series. In the ... 
Prediction and Quantification of Individual Athletic Performance
[OWP201511] (Mathematisches Forschungsinstitut Oberwolfach, 20150827)We present a novel, quantitative view on the human athletic performance of individuals. We obtain a predictor for athletic running performances, a parsimonious model, and a training state summary consisting of three numbers, ... 
Time and band limiting for matrix valued functions, an example
[OWP201508] (Mathematisches Forschungsinstitut Oberwolfach, 20150729)The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the ... 
The algebra of differential operators for a Gegenbauer weight matrix
[OWP201507] (Mathematisches Forschungsinstitut Oberwolfach, 20150729)In this work we study in detail the algebra of differential operators $\mathcal{D}(W)$ associated with a Gegenbauer matrix weight. We prove that two second order operators generate the algebra, indeed $\mathcal{D}(W)$ is ... 
Right Unimodal and Bimodal Singularities inPositive Characteristic
[OWP201514] (Mathematisches Forschungsinstitut Oberwolfach, 20151118)The problem of classification of real and complex singularities was initiated by Arnol'd in the sixties who classified simple, unimodal and bimodal w.r.t. right equivalence. The classification of right simple singularities ... 
Milnor fibre homology via deformation
[OWP201522] (Mathematisches Forschungsinstitut Oberwolfach, 2015)In case of onedimensional singular locus, we use deformations in order toget refined information about the Betti numbers of the Milnor fibre. 
A nested family of ktotal effective rewards for positional games
[OWP201521] (Mathematisches Forschungsinstitut Oberwolfach, 2015)We consider Gillette's twoperson zerosum stochastic games with perfect information. For each $k \in \mathbb{Z}_+$ we introduce an effective reward function, called $k$total. For $k = 0$ and $1$ this function is known ... 
A PseudoPolynomial Algorithm for Mean Payoff Stochastic Games with Perfect Information and Few Random Positions
[OWP201520] (Mathematisches Forschungsinstitut Oberwolfach, 2015)We consider twoperson zerosum stochastic mean payoff games with perfect information, or BWRgames, given by a digraph $G = (V,E)$, with local rewards $r : E \to \mathbb{Z}$, and three types of positions: black $V_B$, ... 
A potential reduction algorithm for twoperson zerosum mean payoff stochastic games
[OWP201519] (Mathematisches Forschungsinstitut Oberwolfach, 2015)We suggest a new algorithm for twoperson zerosum undiscounted stochastic games focusing on stationary strategies. Given a positive real $\epsilon$, let us call a stochastic game $\epsilon$ergodic, if its values from any ... 
Simulation of Multibody Systems with Servo Constraints through Optimal Control
[OWP201518] (Mathematisches Forschungsinstitut Oberwolfach, 2015)We consider mechanical systems where the dynamics are partially constrained to prescribed trajectories. An example for such a system is a building crane with a load and the requirement that the load moves on a certain path. ... 
Noncommutative Marked Surfaces
[OWP201516] (Mathematisches Forschungsinstitut Oberwolfach, 20151118)The aim of the paper is to attach a noncommutative clusterlike structure to each marked surface $\Sigma$. This is a noncommutative algebra $\mathcal{A}_\Sigma$ generated by “noncommutative geodesics” between marked points ... 
Torsionfree Covers of Solvable Minimax Groups
[OWP201515] (Mathematisches Forschungsinstitut Oberwolfach, 20151118)We prove that every finitely generated solvable minimax group can be realized as a quotient of a torsionfree solvable minimax group. This result has an application to the investigation of random walks on finitely generated ... 
Graphical constructions for the sl(3), C2 and G2 invariants for virtual knots, virtual braids and free knots
[OWP201513] (Mathematisches Forschungsinstitut Oberwolfach, 20150731)We construct graphvalued analogues of the Kuperberg sl(3) and $G_2$ invariants for virtual knots. The restriction of the sl(3) and $G_2$ invariants for classical knots coincides with the usual Homflypt sl(3) invariant and ... 
Cocharacterclosure and spherical buildings
[OWP201512] (Mathematisches Forschungsinstitut Oberwolfach, 20150729)Let $k$ be a field, let $G$ be a reductive $k$group and $V$ an affine $k$variety on which $G$ acts. In this note we continue our study of the notion of cocharacterclosed $G(k)$orbits in $V$. In earlier work we used a ... 
Instability of point defects in a twodimensional nematic liquid crystal model
[OWP201505] (Mathematisches Forschungsinstitut Oberwolfach, 20150729)We study a class of symmetric critical points in a variational 2$D$ Landau  de Gennes model where the state of nematic liquid crystals is described by symmetric traceless $3 \times 3$ matrices. These critical points play ... 
Hight functions on quaternionic Stiefel manifolds
[OWP201510] (Mathematisches Forschungsinstitut Oberwolfach, 20150729)In this note, we study height functions on quaternionic Stiefel manifolds and prove that all these height functions are MorseBott. Among them, we characterize the Morse functions and give a lower bound for their number ... 
Discrete Translates in Lp (R)
[OWP201509] (Mathematisches Forschungsinstitut Oberwolfach, 20150618)A set $\Lambda$ is called $p$spectral if there is a function $g \in L^p (\mathbb{R})$ such that all $\Lambda$translates $\{g(t\lambda),\lambda \in \Lambda\}$ span $L^p(\mathbb{R})$. We prove that exponentially small ... 
Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation
[OWP201504] (Mathematisches Forschungsinstitut Oberwolfach, 20150518)We study the one dimensional periodic derivative nonlinear Schrödinger (DNLS) equation. This is known to be a completely integrable system, in the sense that there is an infinite sequence of formal integrals of motion $\int ... 
Maximal CohenMacaulay modules over nonisolated surface singularities and matrix problems
[OWP201506] (Mathematisches Forschungsinstitut Oberwolfach, 20150513)In this article we develop a new method to deal with maximal CohenMacaulay modules over nonisolated surface singularities. In particular, we give a negative answer on an old question of Schreyer about surface singularities ... 
Virtual Polytopes
[OWP201502] (Mathematisches Forschungsinstitut Oberwolfach, 20150410)Originating in diverse branches of mathematics, from polytope algebra and toric varieties to the theory of stressed graphs, virtual polytopes represent a natural algebraic generalization of convex polytopes. Introduced as ...