关于Steiner树的一个不等式

本文部分地改进了堵丁柱、黄光明所证明的Gilbert-Pollak关于Steiner树的一个猜想,提出一个新的不等式。     

Spectral densities of infinite systems with strong electron correlations

Until now, solids with strongly correlated electrons can be treated only by model Hamiltonians. Even then a calculation of spectral densities is not simple, because the strong Coulomb interactions prevent us from treating correlations perturbatively. We show that projection and partitioning techniques are a very valuable tool here. The method is applied to computations of the density of states of transition metals, in particular, Ni. Here, the band narrowing and the sattlite peak at 6 eV due to correlations are reproduced. A second application concerns the spectral density of doped and undoped Cu(SINGLE BOND)O planes which are part of the high-T_c superconducting materials. © 1997 John Wiley & Sons, Inc. J Quant Chem 63: 645–653, 1997     

Conditions ensuring the applicability of cutting-plane methods for solving variational inequalities

Let VIP(F,C) denote the variational inequality problem associated with the mapping F and the closed convex set C. In this paper we introduce weak conditions on the mapping F that allow the development of a convergent cutting-plane framework for solving VIP(F,C). In the process we introduce, in a natural way, new and useful notions of generalized monotonicity for which first order characterizations are presented. Received: September 25, 1997 / Accepted: March 2, 1999?Published online July 20, 2000     

Characterisations of Flock Quadrangles

We characterise the Hermitian and Kantor flock generalized quadrangles of order (q ²,q), q even, (associated with the linear and Fisher–Thas–Walker flocks of a quadratic cone, and the Desarguesian and Betten–Walker translation planes) in terms of a self-dual subquadrangle. Equivalently, we show that a herd which contains a translation oval must be associated with the linear or Fisher–Thas–Walker flock. This result is a consequence of the determination of all functions which satisfy a certain absolute trace equation whose form is remarkably similar to that of an equation arising in recent studies of ovoids in three-dimensional projective space of finite order q.     

Characterization of Translation Planes by Orbit Lengths

The Desarguesian, Hall, and Hering translation planes of order q² are characterized as exactly those translation planes of odd order with spreads in PG (3,q) that admit a linear collineation group with infinite orbits one of length q+1 and i of length (q-q) /i for i=1 or 2.     

Polyesters with semifluorinated side chains: A proposal for the solid‐state structure

A proposal for the solid‐state structure of poly(p‐phenylene isophthalate) with oxydecylperfluorodecyl side chains is presented, which was calculated by the new Rietveld refinement program BGMN®. A triclinic unit cell with a = 0.575 nm, b = 4.06 nm, c = 2.1 nm, α = 91.2°, β = 85.7°, and γ = 66.1° was obtained using space group symmetry P1¯ (No. 2) with Z = 2. All fractional atom coordinates, reflections and structure factors F were determined. The results show that highly occupied netplanes lie in plane and perpendicularly to the side chains. It may be supposed that these net planes will form the low‐energy surface of the polymer. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1617–1625, 2000     

On divisible designs and twisted field planes

Starting from desarguesian and twisted field planes we construct and study some classes of divisible designs admitting an automorphism group which is 2-transitive on the set of point classes.     

On the density of foliations without algebraic solutions on weighted projective planes

We prove that a generic holomorphic foliation on a weighted projective plane has no algebraic solutions when the degree is big enough. We also prove an analogous result for foliations on Hirzebruch surfaces.