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On Canonical Forms for Twoperson Zerosum Limit Average Payoff Stochastic Games
[OWP201135] (Mathematisches Forschungsinstitut Oberwolfach, 20110529)We consider twoperson zerosum mean payoff undiscounted stochastic games. We give a sufficient condition for the existence of a saddle point in uniformly optimal stationary strategies. Namely, we obtain sufficient ... 
On CoMinimal Pairs in Abelian Groups
[OWP201919] (Mathematisches Forschungsinstitut Oberwolfach, 20190709)A pair of nonempty subsets $(W,W')$ in an abelian group $G$ is a complement pair if $W+W'=G$. $W'$ is said to be minimal to $W$ if $W+(W'\setminus \{w'\}) \neq G, \forall \,w'\in W'$. In general, given an arbitrary subset ... 
On commuting varieties of nilradicals of borel subalgebras of reductive lie algebras
[OWP201214] (Mathematisches Forschungsinstitut Oberwolfach, 20121204)Let $G$ be a connected reductive algebraic group defined over an algebraically closed field $\mathbb{k}$ of characteristic zero. We consider the commuting variety $\mathcal{C}(\mathfrak{u})$ of the nilradical $\mathfrak{u}$ ... 
On Concentrators and Related Approximation Constants
[OWP201314] (Mathematisches Forschungsinstitut Oberwolfach, 20130610)Pippenger ([Pip77]) showed the existence of (6m, 4m, 3m, 6)concentrator for each positive integer m using a probabilistic method. We generalize his approach and prove existence of (6m, 4m, 3m, 5.05)concentrator (which ... 
On conjugacy of MASAs and the outer automorphism group of the Cuntz algebra
[OWP201321] (Mathematisches Forschungsinstitut Oberwolfach, 20131029)We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of MASAa in $\mathcal{O}_n$. In particular, we exhibit an uncountable family of MASAs, conjugate ... 
On densities of lattice arrangements intersecting every idimensional affine subspace
[OWP201608] (Mathematisches Forschungsinstitut Oberwolfach, 20160510)In 1978, Makai Jr. established a remarkable connection between the volumeproduct of a convex body, its maximal lattice packing density and the minimal density of a lattice arrangement of its polar body intersecting every ... 
On Generalizations of KacMoody Groups
[OWP201006] (Mathematisches Forschungsinstitut Oberwolfach, 20100310)In [7] we define a CurtisTits group as a certain generalization of a KacMoody group. We distinguish between orientable and nonorientable CurtisTits groups and identify all orientable CurtisTits groups as KacMoody ... 
On Local Combinatorial Formulas for Chern Classes of Triangulated Circle Bundle
[OWP201616] (Mathematisches Forschungsinstitut Oberwolfach, 20160817)Principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a ... 
On Logic, Choices and Games
[SNAP2019009EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190904)Can we always mathematically formalise our taste and preferences? We discuss how this has been done historically in the field of game theory, and how recent ideas from logic and computer science have brought an interesting ... 
On periodic solutions and global dynamics in a periodic differential delay equation
[OWP201408] (Mathematisches Forschungsinstitut Oberwolfach, 20140513)Several aspects of global dynamics and the existence of periodic solutions are studied for the scalar differential delay equation $x'(t) = a(t)f(x([tK]))$, where $f(x)$ is a continuous negative feedback function, $x \cdot ... 
On radial basis functions
[SNAP2019002EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190313)Many sciences and other areas of research and applications from engineering to economics require the approximation of functions that depend on many variables. This can be for a variety of reasons. Sometimes we have a ... 
On Reflection Subgroups of Finite Coxeter Groups
[OWP201106] (Mathematisches Forschungsinstitut Oberwolfach, 2011059)Let $W$ be a finite Coxeter group. We classify the reflection subgroups of $W$ up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup $R$ of $W$ the conjugacy class ... 
On Residuals of Finite Groups
[OWP201917] (Mathematisches Forschungsinstitut Oberwolfach, 20190528)A theorem of Dolfi, Herzog, Kaplan, and Lev [DHKL07, Thm. C] asserts that in a finite group with trivial Fitting subgroup, the size of the soluble residual of the group is bounded from below by a certain power of the group ... 
On Selfinjective Artin Algebras Having Generalized Standard Quasitubes
[OWP201018] (Mathematisches Forschungsinstitut Oberwolfach, 20100318)We give a complete description of the Morita equivalence classes of all connected selfinjective artin algebras for which the AuslanderReiten quiver admits a family of quasitubes having common composition factors, closed ... 
On Siegel modular forms of level p and their properties mod p
[OWP200923] (Mathematisches Forschungsinstitut Oberwolfach, 20090316)Using theta series we construct Siegel modular forms of level p which behave well modulo $p$ in all cusps. This construction allows us to show (under a mild condition) that all Siegel modular forms of level p and weight 2 ... 
On test sets for nonlinear integer maximization
[OWP200705] (Mathematisches Forschungsinstitut Oberwolfach, 20070323)A finite test set for an integer maximation problem enables us to verify whether a feasible point atains the global maximum. We establish in this paper several general results that apply to integer maximization problems ... 
On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces
[OWP201318] (Mathematisches Forschungsinstitut Oberwolfach, 20130723)Let $\Sigma_g$ be a closed hyperbolic surface of genus $g$ and let Ham($\Sigma_ g$) be the group of Hamiltonian diffeomorphisms of $\Sigma_g$. The most natural word metric on this group is the autonomous metric. It has ... 
On the autonomous metric on the group of areapreserving diffeomorphisms of the 2disc
[OWP201216] (Mathematisches Forschungsinstitut Oberwolfach, 2012)Let $D^2$ be the open unit disc in the Euclidean plane and let $G := Diff(D^2; area)$ be the group of smooth compactly supported areapreserving diffeomorphisms of $D^2$. For every natural number $k$ we construct an injective ... 
On the complement of the dense orbit for a quiver of type A
[OWP201011] (Mathematisches Forschungsinstitut Oberwolfach, 2010)Let $\mathbb{A}_t$ be the directed quiver of type $A$ with $t$ vertices. For each dimension vector $d$ there is a dense orbit in the corresponding representation space. The principal aim of this note is to use just rank ... 
On the Complement of the Richardson Orbit
[OWP201009] (Mathematisches Forschungsinstitut Oberwolfach, 20100313)We consider parabolic subgroups of a general algebraic group over an algebraically closed field $k$ whose Levi part has exactly $t$ factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup $P$ ...