Enriques surfaces and Jacobian elliptic K3 surfaces

This paper proposes a new geometric construction of Enriques surfaces. Its starting point are K3 surfaces with Jacobian elliptic fibration which arise from rational elliptic surfaces by a quadratic base change. The Enriques surfaces obtained in this way are characterised by elliptic fibrations with a rational curve as bisection which splits into two sections on the covering K3 surface. The construction has applications to the study of Enriques surfaces with specific automorphisms. It also allows us to answer a question of Beauville about Enriques surfaces whose Brauer groups show an exceptional behaviour. In a forthcoming paper, we will study arithmetic consequences of our construction.     

Order and chaos in Hofstadter's Q(n) sequence

A number of observations are made on Hofstadter's integer sequence defined by Q(n) = Q(n − Q(n − 1)) + Q(n − Q(n − 2)), for n > 2, and Q(1) = Q(2) = 1. On short scales, the sequence looks chaotic. It turns out, however, that the Q(n) can be grouped into a sequence of generations. The k‐th generation has 2^k members that have “parents” mostly in generation k − 1 and a few from generation k − 2. In this sense, the sequence becomes Fibonacci type on a logarithmic scale. The variance of S(n) = Q(n) − n/2, averaged over generations, is ≅2^αk, with exponent α = 0.88(1). The probability distribution p*(x) of x = R(n) = S(n)/n^α, n ≫ 1, is well defined and strongly non‐Gaussian, with tails well described by the error function erfc. The probability distribution of x_m = R(n) − R(n − m) is given by p_m(x_m) = λ_m p*(x_m/λ_m), with λ_m → √2 for large m. © 1999 John Wiley & Sons, Inc.     

Minimal ideals of n-homogeneous polynomials on Banach spaces

The minimal kernel of a p-Banach ideal of n-homogeneous polynomials between Banach spaces is defined as a composition ideal, characterized to be the smallest ideal which coincides with the given one on finite-dimensional spaces and represented through tensor products with appropriate norms.     

Torsion of differentials on toric varieties

We introduce an invariant for semigroups with cancellation property. When the semigroup equals the set of lattice points in a rational, polyhedral cone, then this invariant describes the torsion of the differential sheaf on the associated toric variety. Finally, as an example, we present the case of two-dimensional cones (corresponding to two-dimensional cyclic quotient singularities).     

Inert gas clusters ejected from bursting bubbles during sputtering

Ar(+)(n) cluster ions (n相似文献   

Modeling and Simulation of Damage Processes based on a Gradient-Enhanced Free Energy Function

Taking into account softening effects in connection with conventional inelastic material models can cause ill-posed boundary value problems. These problems can be established by obtaining no unique solution for the resulting algebraic system or by having a strong mesh dependence of the numerical results. This is the consequence of losing ellipticity of the governing field equations. A possible approach to solve these problems is to introduce a non-local field function in the model which includes an internal material length scale. For this purpose a gradient-enhanced free energy function is used for the current continuum damage model from which two variational equations are resulting. Calculations with less effort can be achieved due to the enhancement of the free energy function in comparison to other approaches. The mentioned model is applied to a material with locally varying damage properties (yield limits). Furthermore, the model is able to describe crack propagation in cases of completely damaged material. Therewith, a matrix material including precipitates, such as carbides, is modeled. This allows to investigate ship screws, which usually exhibit the mentioned composition, with regard to the influence of cavitation. Cavitation describes the implosion of risen vapor bubbles, whereby the impact on screws causes heavy damages which can lead to a complete destruction. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rigidity of flat surfaces under the boundary measure

Consider a closed marked flat surface S of genus g ≥ 2 and its universal cover ~S endowed with the pulled back metric. We show that the measure class induced by the Hausdorff measure of the Gromov boundary of ~S uniquely determines S up to rescaling.     

Bidirectional molecular dynamics: Interpretation in terms of a modern formulation of classical mechanics

The validity and applicability of bidirectional molecular dynamics is shown in terms of modern classical mechanics. A simple interpretation of bidirectional molecular dynamics is given. This interpretation justifies an easy approach to start from an equilibrium configuration, to perform simulations in parallel in “forward” and “backward” time direction, and to combine the two obtained trajectories into a single one for proper evaluation of statistical quantities. Practical results, obtained for liquid ammonia, are presented. © 1996 by John Wiley & Sons, Inc.     

Preparation of Cr2O3-Al2O3 Solid Solutions by Reactive Magnetron Sputtering

 (Al,Cr)₂O₃ layers were deposited on cemented carbide insert tips at a substrate temperature of 500 °C by means of reactive magnetron sputtering. An Al target was sputtered in RF mode and a Cr target in DC mode simultaneously in an oxygen/argon plasma. The influence of the Al and Cr sputter power and of the oxygen partial pressure on composition and structure of the (Al,Cr)₂O₃ layers as well as on the binding states of their components were investigated. Special attention was paid to the interpretation of the O ls and O-KLL fine structure and peak shifts. For the binary phases γ-Al₂O₃ and Cr₂O₃, a good agreement with literature values was observed in each case. In case of the ternary phases a continuous shift of the energetic position of the O1s peak, the O-KL₂₃L₂₃ transition and the modified Auger parameter α ′ of oxygen between the two binary phases γ-Al₂O₃ and Cr₂O₃ could be detected, indicating a wide range of solid solubility between Al₂O₃ and Cr₂O₃. As revealed by grazing incidence X-ray diffraction, the crystallinity of the ternary phases is less pronounced as compared to the binaries and increases with increasing oxygen flow rate.     

Synthesis of α-N-Ethylamino Acids and their Derivatives

 A new synthesis of α-N-ethylamino acids starting from α-amino acids using hexafluoroacetone as protecting and activating agent is described. The hexafluoroacetone-protected N-ethylamino acid derivatives obtained are activated lactons. Therefore, they can be directly transformed without the need of an additional activation step with various nucleophiles into the corresponding carboxylic acid derivatives.