Star Decompositions of Cubes

 Let S _k denote the complete bipartite graph K _{1, k} and let Q _n denote the n-cube. We prove that the obvious necessary conditions for the existence of an S _k -decomposition of Q _n are sufficient. Received: July 21, 1999 Final version received: May 16, 2000     

Combinatorics,graph theory,and computing

Journal of Algebraic Combinatorics -     

Limits of minimal surfaces and Scherk's Fifth Surface

Communicated by J. C. C. Nitsche     

Glenn Theodore Seaborg: Contributions to Nuclear Science

The major contributions of G. T. Seaborg to nuclear science, including co-discovery of many isotopes with practical applications in medicine and industry, co-discovery of plutonium and nine more transuranium elements, the actinide hypothesis, and searches for superheavy elements are briefly summarized. His enduring interest in science education, the history of science, and public affairs are also noted.     

Efficient computation of mean drag for the subcritical flow past a circular cylinder using general Galerkin G2

General Galerkin (G2) is a new computational method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate weak solutions to the Navier–Stokes equations directly, without any filtering of the equations as in a standard approach to turbulence simulation, such as large eddy simulation, and thus no Reynolds stresses are introduced, which need modelling. In this paper, G2 is used to compute the drag coefficient c_D for the flow past a circular cylinder at Reynolds number Re=3900, for which the flow is turbulent. It is found that it is possible to approximate c_D to an accuracy of a few percent, corresponding to the accuracy in experimental results for this problem, using less than 10⁵ mesh points, which makes the simulations possible using a standard PC. The mesh is adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, which in this paper is c_D. Both the stopping criterion and the mesh‐refinement strategy are based on a posteriori error estimates, in the form of a space–time integral of residuals times derivatives of the solution of a dual problem, linearized at the approximate solution, and with data coupling to the output of interest. Copyright © 2008 John Wiley & Sons, Ltd.     

Spin-cluster effects and frustration in the uniaxial spin glass Fe2−xTi1+xO5

Transverse-field (TF) muon-spin-relaxation (μSR) and Mössbauer experiments on the uniaxial insulating spin glass Fe_2?xTi_1+xO₅ (x=0.25) have been performed near and below the spin-glass temperature (T _g). The effect of a transverse field on the spin-freezing process and spin-glass state has been investigated by measuring the field-and temperature-dependencies of the μSR parameters. Spin-cluster effects signaled by anomalous μ-spin relaxation have been observed in a temperature region just aboveT _g. An interpretation supported by recently developed theoretical models addressing non-linear relaxation in an intermediate Griffiths phase is offered.