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- ItemExtremal configurations of polygonal linkages(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Khimshiashvili, G.; Panina, G.; Siersma, D.; Zhukova, A.[no abstract available]
- ItemInfeasibility certificates for linear matrix inequalities(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Klep, Igor; Schweighofer, MarkusFarkas' lemma is a fundamental result from linear programming providing linear certi cates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear algebraic certificates for all infeasible linear matrix inequalities in the spirit of real algebraic geometry. More precisely, we show that a linear matrix inequality L(x)⪰0 is infeasible if and only if −1 lies in the quadratic module associated to L. We prove exponential degree bounds for the corresponding algebraic certificate. In order to get a polynomial size certi cate, we use a more involved algebraic certificate motivated by the real radical and Prestel's theory of semiorderings. Completely different methods, namely complete positivity from operator algebras, are employed to consider linear matrix inequality domination.
- ItemLegendrian knots in Lens spaces(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Onaran, Sinem CelikIn this note, we first classify all topological torus knots lying on the Heegaard torus in Lens spaces, and then we classify Legendrian representatives of torus knots. We show that all Legendrian torus knots in universally tight contact structures on Lens spaces are determined up to contactomorphism by their knot type, rational Thurston-Bennequin invariant and rational rotation number.
- ItemNew representations of matroids and generalizations(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Izhakian, Zur; Rhodes, JohnWe extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This idea of representations is naturally generalized to include hereditary collections (also known as abstract simplicial complexes). We show that a matroid that can be directly decomposed as matroids, each of which is representable over a field, has a boolean representation, and more generally that any arbitrary hereditary collection is superboolean-representable.
- ItemLocalized endomorphisms of graph algebras(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Conti, Roberto; Hong, Jeong Hee; Szyma´nski, WojciechEndomorphisms of graph C*-algebras are investigated. A combinatorial ap- proach to analysis of permutative endomorphisms is developed. Then invertibility criteria for localized endomorphisms are given. Furthermore, proper endomor- phisms which restrict to automorphisms of the canonical diagonal MASA are analyzed. The Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. Criteria of outerness for automorphisms in the restricted Weyl group are found.
- ItemBraid equivalences and the L-moves(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Lambropoulou, SofiaIn this survey paper we present the L–moves between braids and how they can adapt and serve for establishing and proving braid equivalence theorems for various diagrammatic settings, such as for classical knots, for knots in knot complements, in c.c.o. 3–manifolds and in handlebodies, as well as for virtual knots, for flat virtuals, for welded knots and for singular knots. The L–moves are local and they provide a uniform ground for formulating and proving braid equivalence theorems for any diagrammatic setting where the notion of braid and diagrammatic isotopy is defined, the statements being first geometric and then algebraic.
- ItemThe Weyl group of the Cuntz algebra(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Conti, Roberto; Hong, Jeong Hee; Szyma´nski, WojciechThe Weyl group of the Cuntz algebra On is investigated. This is (isomorphic to) the group of polynomial automorphisms λu of On, namely those induced by unitaries u that can be written as finite sums of words in the canonical generating isometries Si and their adjoints. A necessary and sufficient algorithmic combinatorial condition is found for deciding when a polynomial endomorphism λu restricts to an automorphism of the canonical diagonal MASA. Some steps towards a general criterion for invertibility of λu on the whole of On are also taken. A condition for verifying invertibility of a certain subclass of polynomial endomorphisms is given. First examples of polynomial automorphisms of On not inner related to permutative ones are exhibited, for every n≥2. In particular, the image of the Weyl group in the outer automorphism group of On is strictly larger than the image of the reduced Weyl group analyzed in previous papers. Results about the action of the Weyl group on the spectrum of the diagonal are also included.
- ItemFormal adjoints of linear DAE operators and their role in optimal control(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Kunkel, Peter; Mehrmann, VolkerFor regular strangeness-free linear differential-algebraic equations (DAEs) the definition of an adjoint DAE is straightforward. This definition can be formally extended to general linear DAEs. In this paper, we analyze the properties of the formal adjoints and their implications in solving linear-quadratic optimal control problems with DAE constraints.
- ItemA note on delta hedging in markets with jumps(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Mijatovi´c, Aleksandar; Urusov, MikhailModelling stock prices via jump processes is common in financial markets. In practice, to hedge a contingent claim one typically uses the so-called delta-hedging strategy. This strategy stems from the Black–Merton–Scholes model where it perfectly replicates contingent claims. From the theoretical viewpoint, there is no reason for this to hold in models with jumps. However in practice the delta-hedging strategy is widely used and its potential shortcoming in models with jumps is disregarded since such models are typically incomplete and hence most contingent claims are non-attainable. In this note we investigate a complete model with jumps where the delta-hedging strategy is well-defined for regular payoff functions and is uniquely determined via the risk-neutral measure. In this setting we give examples of (admissible) delta-hedging strategies with bounded discounted value processes, which nevertheless fail to replicate the respective bounded contingent claims. This demonstrates that the deficiency of the delta-hedging strategy in the presence of jumps is not due to the incompleteness of the model but is inherent in the discontinuity of the trajectories.
- ItemAnalytic varieties with finite volume amoebas are algebraic(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Madani, Farid; Nisse, MounirIn this paper, we study the amoeba volume of a given k-dimensional generic analytic variety V of the complex algebraic torus (C∗)n. When n>=2k, we show that V is algebraic if and only if the volume of its amoeba is finite. Moreover, in this case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the k-linear spaces will be given.