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Lebesgue points and the fundamental convergence theorem for superharmonic functions on . . .
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Some conjectures and open problems on partition hook lengths
"... Abstract. We present some conjectures and open problems on partition hook lengths, which are all motivated by known results on the subject. The conjectures are suggested by extensive experimental calculations using a computer algebra system. The rst conjecture unies two classical results on the numb ..."
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Abstract. We present some conjectures and open problems on partition hook lengths, which are all motivated by known results on the subject. The conjectures are suggested by extensive experimental calculations using a computer algebra system. The rst conjecture unies two classical results on the number of standard Young tableaux and the number of pairs of standard Young tableaux of the same shape. The second unies the classical hook formula and the marked hook formula. The third includes the long standing Lehmer conjecture which says that the Ramanujan taufunction never takes the zero value. The fourth is a more precise version of the third one in the case of 3cores. We also list some open problems on partition hook lengths. 1.
Abstract Spin Dependent Transport in Magnetic Nanostructures
, 2003
"... Recent progress in physics on spin dependent transport in magnetic nanostructures is reviewed. Special attention is paid on the spin accumulation and spin current caused by spin injection into nonmagnetic metals and semiconductors and superconductors. A variety of phenomena induced in nanosupercon ..."
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Recent progress in physics on spin dependent transport in magnetic nanostructures is reviewed. Special attention is paid on the spin accumulation and spin current caused by spin injection into nonmagnetic metals and semiconductors and superconductors. A variety of phenomena induced in nanosuperconductor/ferromagnet devices are proposed, examining the spincharge separation in superconductors.
and
, 1993
"... We study the statistical equilibrium properties of the recently developed Antisymmetrized Molecular Dynamics model for heavyion reactions. We consider A noninteracting fermions in one dimension, either bound in a common harmonic potential or moving freely within an interval, and perform a Metropo ..."
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We study the statistical equilibrium properties of the recently developed Antisymmetrized Molecular Dynamics model for heavyion reactions. We consider A noninteracting fermions in one dimension, either bound in a common harmonic potential or moving freely within an interval, and perform a Metropolis sampling of the corresponding parameter space. Generally the average excitation and the specific heat, considered as functions of the imposed temperature, behave in a classical manner when the canonical weight is calculated in the meanfield approximation. However, it is possible to obtain results that are much closer to the quantal behavior by modifying the weight to take approximate account of the energy fluctuations within the individual wave packets.
Time Development of Axisymmetric ShockQuasiStationary Velocity Approximation
, 1971
"... Propagation formulae for axisymmetric shock wave in a continuous, inhomogeneous medium are newly derived through hydrodynamic considerations on state of the flow immediately behind the shock, with the use of orthogonality conditions between shockrays and their fronts as well as the shock relations ..."
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Propagation formulae for axisymmetric shock wave in a continuous, inhomogeneous medium are newly derived through hydrodynamic considerations on state of the flow immediately behind the shock, with the use of orthogonality conditions between shockrays and their fronts as well as the shock relations. Quasistationary velocity of isentropic flow in a steady gravitation is approximately assumed. The method is applied to an explosion of a highly rotating oblate star. From the computational results, we · see that the validity of our approximation of quasistationary velocity is restricted to the case in which incidenceangle of ray on an equidensity surface is comparatively small, less than the socalled critical angle. Within the validity, it is shown that shocks going to higher latitudes grow up more rapidly than to lower latitudes. Further, it is proposed that unsteady flow behind the steeply inclined strong shock will produce strong vorticity and the shock may become absolutely unstable. 83 Recently the propagation of shock wave due to a point explosion becomes
Å Ü¹ÈÐ Ò ¹ÁÒ×Ø ØÙØ für Mathematik in den Naturwissenschaften Leipzig Realizing homology classses by symplectic submanifolds Realizing homology classes by symplectic submanifolds
"... Abstract In this note we prove that a positive multiple of each evendimensional integral homology class of a compact symplectic manifold (M 2n , ω) can be represented as the difference of the fundamental classes of two symplectic submanifolds in (M 2n , ω). We also prove the realizability of some ..."
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Abstract In this note we prove that a positive multiple of each evendimensional integral homology class of a compact symplectic manifold (M 2n , ω) can be represented as the difference of the fundamental classes of two symplectic submanifolds in (M 2n , ω). We also prove the realizability of some integral homology classes by symplectic submanifolds in (M 2n , ω).
Giroux correspondence, confoliations, and symplectic structures on S 1 × M
, 2009
"... Let M be a closed oriented 3manifold such that S 1 × M admits a symplectic structure ω. The goal of this paper is to show that M is a fiber bundle over S 1. The basic idea is to use the obvious S 1action on S 1 × M by rotating the first factor of S 1 × M, and one of the key steps is to show that t ..."
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Let M be a closed oriented 3manifold such that S 1 × M admits a symplectic structure ω. The goal of this paper is to show that M is a fiber bundle over S 1. The basic idea is to use the obvious S 1action on S 1 × M by rotating the first factor of S 1 × M, and one of the key steps is to show that the S 1action on S 1 × M is actually symplectic with respect to a symplectic form cohomologous to ω. We achieve it by crucially using the recent result or its relative version of Giroux about onetoone correspondence between open book decompositions of M up to positive stabilization and cooriented contact structures on M up to contact isotopy. As a consequence, we can give an answer to a question of Kronheimer concerning the relation between symplectic structures on S 1 × MK and fibered knots K, where MK denotes the result of 0surgery on S 3 along a knot K in S 3. Moreover, a complete picture of the various intriguing implications between symplectic structures on
Honoring a Gift from
"... oday was an absolutely glorious day in Madison, Wisconsin. It is Christmas 2005, and everyone in the house is asleep after a long day of enjoying family, opening presents, and eating enormous portions of mashed potatoes and yule log cake. Yet powerful images keep me awake. Thirtysix hours ago I re ..."
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oday was an absolutely glorious day in Madison, Wisconsin. It is Christmas 2005, and everyone in the house is asleep after a long day of enjoying family, opening presents, and eating enormous portions of mashed potatoes and yule log cake. Yet powerful images keep me awake. Thirtysix hours ago I returned from a sixday whirlwind journey to a faroff place. I spent forty hours on airplanes, and I endured fourteen hours in cars