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Abstract—A coding scheme for the two-receivers Gaussian broadcast channel (BC) with feedback is proposed. For some asymmetric settings it achieves new rate pairs. Moreover, it achieves prelog 2 when the noises at the two receivers are fully positively correlated and of unequal variances, thus

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the difficulties of quantization on a curved manifold. At low temperatures our results are exact and allow direct comparisson with the planar Landau case. In this temperature limit we compute the magnetization and show it exhibit an oscillatory de Hass-Van Alphen type of behaviour.

1 Dedicated to Ludwig Elsner on the occasion of his sixtieth birthday We describe canonical forms for elements of a classical Lie group of matrices under similarity transformations in the group. Matrices in the associated Lie algebra and Jordan algebra of matrices inherit related forms under these similarity transforma-tions. In general, one cannot achieve diagonal or Schur form, but the form that can be achieved displays the eigenvalues of the matrix. We also discuss matrices in in-tersections of these classes and their Schur-like forms. Such multistructered matrices arise in applications from quantum physics and quantum chemistry. 1

Responses of soil biological processes to elevated atmospheric [CO2] and nitrogen addition in a poplar plantation

Abstract. We classify nonconstant entire local minimizers of the standard Ginzburg-Landau functional for maps in H 1 loc (R3; R 3) satisfying a natural energy bound. Up to translations and rotations, such solutions of the Ginzburg-Landau system are given by an explicit solution equivariant under

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ACKNOWLEDGMENTS I would like to give many thanks to Dr. Shengli Fu and Dr. Yan Huang as my advi-