Hyper-(rank one) groups

A group $G$ is called a $\mathcal{P }_1$ -group if it has a normal series of finite length whose factors have rank $1$ , while $G$ is an $\mathcal{H }_1$ -group if it has an ascending normal series of the same type. This paper investigates properties of $\mathcal{P }_1$ -groups and $\mathcal{H }_1$ -groups which correspond to known properties of nilpotent and supersoluble groups.     

Optimization of Schwarz waveform relaxation over short time windows

Schwarz waveform relaxation algorithms (SWR) are naturally parallel solvers for evolution partial differential equations. They are based on a decomposition of the spatial domain into subdomains, and a partition of the time interval of interest into time windows. On each time window, an iteration, during which subproblems are solved in space-time subdomains, is then used to obtain better and better approximations of the overall solution. The information exchange between subdomains in space-time is performed through classical or optimized transmission conditions (TCs). We analyze in this paper the optimization problem when the time windows are short. We use as our model problem the optimized SWR algorithm with Robin TCs applied to the heat equation. After a general convergence analysis using energy estimates, we prove that in one spatial dimension, the optimized Robin parameter scales like the inverse of the length of the time window, which is fundamentally different from the known scaling on general bounded time windows, which is like the inverse of the square root of the time window length. We illustrate our analysis with a numerical experiment.     

Entropy for automorphisms of free groups

Let be the automorphism of the free group which is arising from a permutation of the free generators of The naturally induces the automorphism of the reduced -algebra and also the automorphism of the group factor We show that the Brown-Germain entropy is zero. This implies that the Brown-Voiculescu topological entropy the Connes-Narnhofer-Thirring dynamical entropy and the Connes-Størmer entropy are all zero.

     

Greedy approximation with respect to certain subsystems of the Walsh orthonormal system

In an article that appeared in 1967, J.J. Price has shown that there is a vast family of subsystems of the Walsh orthonormal system each of which is complete on sets of large measure. In the present work it is shown that the greedy algorithm, when applied to functions in , is surprisingly effective for these nearly-complete families. Indeed, if is such a subsystem of the Walsh system, then to each positive , however small, there corresponds a Lebesgue measurable set such that for every , Lebesgue integrable on , the greedy approximants to , associated with , converge, in the norm, to an integrable function that coincides with on .

     

A generic view of Dantzig-Wolfe decomposition in mixed integer programming

The Dantzig-Wolfe reformulation principle is presented based on the concept of generating sets. The use of generating sets allows for an easy extension to mixed integer programming. Moreover, it provides a unifying framework for viewing various column generation practices, such as relaxing or tightening the column generation subproblem and introducing stabilization techniques.     

Twistor Actions for Self-Dual Supergravities

We give holomorphic Chern-Simons-like action functionals on supertwistor space for self-dual supergravity theories in four dimensions, dealing with supersymmetries, the cases where different parts of the R-symmetry are gauged, and with or without a cosmological constant. The gauge group is formally the group of holomorphic Poisson transformations of supertwistor space where the form of the Poisson structure determines the amount of R-symmetry gauged and the value of the cosmological constant. We give a formulation in terms of a finite deformation of an integrable -operator on a supertwistor space, i.e., on regions in . For , we also give a formulation that does not require the choice of a background.     

Local time and Tanaka formula for a multitype Dawson–Watanabe superprocess

In [3] Dynkin defined the local time of a continuous superprocess as a stochastic integral and gave a criterion for existence of local time. Here we prove that the conditions in Dynkin's existence criterion are satisfied by the multitype Dawson–Watanabe superprocess, and give a Tanaka formula‐like representation of the local time which is used to show that the occupation measure of the multitype superprocess is absolutely continuous with respect to an appropriate reference measure, and that the corresponding density coincides a.s. with the local time. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generalized Bayes minimax estimators of the mean of multivariate normal distribution with unknown variance

We construct a broad class of generalized Bayes minimax estimators of the mean of a multivariate normal distribution with covariance equal to σ²I_p, with σ² unknown, and under the invariant loss δ(X)−θ²/σ². Examples that illustrate the theory are given. Most notably it is shown that a hierarchical version of the multivariate Student-t prior yields a Bayes minimax estimate.     

Conductance asymmetry of a slot gate Si‐MOSFET in a strong parallel magnetic field

We report measurements on a Si‐MOSFET sample with a slot in the upper gate, allowing for different electron densities n_1,2 across the slot. The dynamic longitudinal resistance was measured by the standard lock‐in technique, while maintaining a large DC current through the source‐drain channel. We find that the conductance of the sample in a strong parallel magnetic field is asymmetric with respect to the DC current direction. This asymmetry increases with magnetic field. The results are interpreted in terms of electron spin accumulation or depletion near the slot.     

How the SiC substrate impacts graphene's atomic and electronic structure

Graphene, the two‐dimensional form of carbon presents outstanding electronic and transport properties. This gives hope for the development of applications in nanoelectronics. However, for industrial purpose, graphene has to be supported by a substrate. We focus here on the graphene‐on‐SiC system to discuss how the SiC substrate interacts with the graphene layer and to show the effect of the interface on graphene atomic and electronic structures.