The maximal tubes under the deformations of a class of 3-dimensional hyperbolic cone-manifolds

Recently, Hodgson and Kerckhoff found a small bound on Dehn surgered 3-manifolds from hyperbolic knots not admitting hyperbolic structures using deformations of hyperbolic cone-manifolds. They asked whether the area normalized meridian length squared of maximal tubular neighborhoods of the singular locus of the cone-manifold is decreasing and that summed with the cone angle squared is increasing as we deform the cone-angles. We confirm this near 0 cone-angles for an infinite family of hyperbolic cone-manifolds obtained by Dehn surgeries along the Whitehead link complements. The basic method is based on explicit holonomy computations using the A-polynomials and finding the maximal tubes. One of the key tool is the Taylor expression of a geometric component of the zero set of the A-polynomial in terms of the cone-angles. We also show a sequence of Taylor expressions for Dehn surgered manifolds converges to one for the limit hyperbolic manifold.Comment: 27 pages, 10 figure

Analysis of two-player quantum games in an EPR setting using geometric algebra

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of Clifford geometric algebra (GA). In this setting, the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, which is then obtained as proper subset of the corresponding quantum game. As examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt when played in the EPR type setting.Comment: 20 pages, no figure, revise

N-player quantum games in an EPR setting

The $N$-player quantum game is analyzed in the context of an Einstein-Podolsky-Rosen (EPR) experiment. In this setting, a player's strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players' strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find the relations for the probability distribution for $N$-qubit GHZ and W-type states, subject to general measurement directions, from which the expressions for the mixed Nash equilibrium and the payoffs are determined. Players' payoffs are then defined with linear functions so that common two-player games can be easily extended to the $N$-player case and permit analytic expressions for the Nash equilibrium. As a specific example, we solve the Prisoners' Dilemma game for general $N \ge 2$. We find a new property for the game that for an even number of players the payoffs at the Nash equilibrium are equal, whereas for an odd number of players the cooperating players receive higher payoffs.Comment: 26 pages, 2 figure

Perioperatives Management im Rahmen der CRS und HIPEC

Cytoreductive surgery (CRS) and hyperthermic intraperitoneal chemotherapy (HIPEC) are therapeutic options for the treatment of intra-abdominal neoplasms. Following the resection of all visible tumor areas by CRS, microscopic tumor areas are treated with HIPEC. This procedure increases the quality of life and survival. The CRS with HIPEC is a complex surgical procedure in which the mainly younger and often otherwise healthy patients undergo several pathophysiological changes during the operation. The main concern of the anesthesiologist is the massive volume loss, volume shift and metabolic alterations. Patients with a high comorbidity should undergo preoperative optimization to reduce the perioperative morbidity and mortality especially by protracted interventions

The Effect of Si Doping on the Electrical Properties of B12As2 Thin Films on (0001) 6H-SiC Substrates

The ability to control the resistivity of the wide band gap semiconductor B12As2 by doping with silicon was verified. The electrical properties of nominally undoped and Si-doped rhombohedral B12As2 thin films on semi-insulating 6H-SiC (0001) substrates prepared by chemical vapor deposition were subjected to Hall effect measurements. Varying the Si concentration in the B12As2 thin films from 7×1018 to 7×1021 at./cm3 (as measured by secondary ion mass spectrometry) decreased the resistivities of the p-type B12As2 films from 2×105 to 10 Ω cm. The resistivities of the B12As2 films were decreased by one to two orders of magnitude after rapid thermal annealing for 30 s in argon. The spatial distribution of the hydrogen concentration was measured before and after annealing. No changes were detected, casting doubt on hydrogen as being the cause for the change in the resistivities of the B12As2 films with annealing