The Hahn–Banach Theorem for Partially Ordered Totally Convex, Positively Convex and Superconvex Modules

The Hahn–Banach Theorem for partially ordered totally convex modules [3] and a necessary and sufficient condition for the existence of an extension of a morphism from a submodule C ₀ of a partially ordered totally convex module C (with the ordered unit ball of the reals as codomain) to C, are proved. Moreover, the categories of partially ordered positively convex and superconvex modules are introduced and for both categories the Hahn–Banach Theorem is proved.     

Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

Structure of solid monolayers and multilayers of n -hexane on graphite

We present all-atom molecular dynamics simulations ofn-hexane on the basal plane of graphite at monolayer and multilayer coverages. In keeping with experimental data, we find the presence of ordered adsorbed layers both at single monolayer coverage and when the adsorbed layer coexists with excess liquid adsorbate. Using a simulation method that does not impose any particular periodicity on the adsorbed layer, we quantitatively compare our results to the results of neutron diffraction experiments and find a structural transition from a uniaxially incommensurate lattice to a fully commensurate structure on increasing the coverage from a monolayer to a multilayer. The zig-zag backbone planes of all the alkane molecules lie parallel to the graphite surface at the multilayer coverage, while a few molecules are observed to attain the perpendicular orientation at monolayer coverage. Dedicated to Professor C N R Rao on his 70th birthday     

On the Embedding of Ordered Semigroups into Ordered Group

It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of L-maher and R-maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered L or R-maher semigroup can be embedded into an ordered group.     

Synthesis and characterization of polyaniline/graphite conducting nanocomposites

A new method for the synthesis of exfoliated graphite and polyaniline (PANI)/graphite nanocomposites was developed. Exfoliated graphite nanosheets were prepared through the microwave irradiation and sonication of synthesized expandable graphite. The nanocomposites were fabricated via the in situ polymerization of the monomer at the presence of graphite nanosheets. The as-synthesized graphite nanosheets and PANI/graphite nanocomposite materials were characterized with Fourier transform infrared spectroscopy, scanning electron microscopy, transmission electron microscopy, and thermogravimetric analysis (TGA). The conductivity of the PANI/graphite nanocomposites was dramatically increased over that of pure PANI. TGA indicated that the incorporation of graphite greatly improved the thermal stability of PANI. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1972–1978, 2004     

A Note on Geometric Structures of Linear Ordered Orthogonal Arrays and (T,M,S)-Nets of Low Strength

The equivalent geometrical configurations of linear ordered orthogonal arrays are determined when their strengths are 3 and 4. Existence of such geometrical configurations is investigated. They are also useful in the study of (T, M, S)-nets.     

Crystal structure and magnetic ordering of RNi Si compounds

The element distributions and the magnetic ordering behaviour of compounds RNi₁₀Si₂ (R = Tb, Dy, Ho, Er, Tm) have been studied by neutron powder diffraction down to temperatures of 1.6 K. The compounds crystallize in an ordered variant of the ThMn₁₂ structure type in the tetragonal space group P4/nmm. An ordered 1:1 distribution of Ni and Si on sites 4d and 4e, respectively, corresponds to a modulation vector [0, 0, 1] with respect to the space group I4/mmm of the ThMn₁₂ structure. TbNi₁₀Si₂ orders antiferromagnetically below T _N = 4.5 K with a magnetic propagation vector of [0, 0, 1/2]. The magnetic Tb moments, 8.97(2) /Tb atom at 1.6 K, are aligned along the c-axis. The Ni sites in TbNi₁₀Si₂ do not carry any ordered magnetic moments. The compounds with R = Dy, Ho, Er, and Tm are paramagnetic down to 1.6 K and 3.0 K, respectively. Received 10 July 2002 / Received in final form 12 September 2002 Published online 29 October 2002     

金钢石的制备研究

本文研究了两种不同质异构体石墨—金刚石的转化条件，以及在实验室现有条件下，利用石墨材料制备金刚石颗粒的具体方法和试验结果。     

Interpolation of positive operators

We study problems of interpolation of positive linear operators in couples of ordered Banach spaces. From this viewpoint, we study couples of noncommutative spaces L ₁, L _∞ associated with weights and traces on von Neumann algebras.     

Searching for extensible Korobov rules

Extensible lattice sequences have been proposed and studied in [F.J. Hickernell, H.S. Hong, Computing multivariate normal probabilities using rank-1 lattice sequences, in: G.H. Golub, S.H. Lui, F.T. Luk, R.J. Plemmons (Eds.), Proceedings of the Workshop on Scientific Computing (Hong Kong), Singapore, Springer, Berlin, 1997, pp. 209–215; F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C. Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138; F.J. Hickernell, H.Niederreiter, The existence of good extensible rank-1 lattices, J. Complexity 19 (2003) 286–300]. For the special case of extensible Korobov sequences, parameters can be found in [F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C.Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138]. The searches made to obtain these parameters were based on quality measures that look at several projections of the lattice. Because it is often the case in practice that low-dimensional projections are very important, it is of interest to find parameters for these sequences based on measures that look more closely at these projections. In this paper, we prove the existence of “good” extensible Korobov rules with respect to a quality measure that considers two-dimensional projections. We also report results of experiments made on different problems where the newly obtained parameters compare favorably with those given in [F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C. Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138].