Packing two disks into a polygonal environment

We consider the following problem. Given a polygon P, possibly with holes, and having n vertices, compute a pair of equal radius disks that do not intersect each other, are contained in P, and whose radius is maximized. Our main result is a simple randomized algorithm whose expected running time, on any input, is O(nlogn). This is optimal in the algebraic decision tree model of computation.     

Some Further Properties of the Accelerated Kerr-Schild Metrics

We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions.     

An Efficient Method for the Synthesis of 3-Cyano-6-hydroxy-2(1H)-pyridinones under Microwave Irradiation and Solvent-free Conditions

Summary. Three component condensation of alkylacetoacetates, primary amines, and alkyl cyanoacetates catalyzed by solid supports under microwave irradiation gave N-alkyl 3-cyano-6-hydroxy-2(1H)-pyridinones with high yields. Upon carrying out the reaction under the same condition on acidic alumina, zeolite HY, silica gel, and montmorillonite K-10, the best yields were achieved by silica gel. Corresponding author. E-mail: balalaie@yahoo.com Received August 28, 2002; accepted September 3, 2002     

S3上阿诺德弦猜想中的变分方法

本文使用变分方法证明了三维标准切触球的标准勒让德扭结，至少存在一个弦连结适应于标准切触结构的任何选定切触形式，这部分证明了著名的阿诺德弦猜想。     

An Improved Synthesis of Retinoic Acid from β-Ionone

A convenient and large-scale preparation of retinoic acid 1 from β-ionone in five steps with 38% overall yield is described.The key steps are the epoxidization of 2 with a new methylated agent and the condensation 4 with tetraethyl methylenediphophonate in one-pot procedure to prepare 6.     

Silane photoabsorption spectra mear the Si 2p thresholds：the geometry of Si 2p excited SiH4

Based on the multiple-scattering self-consistent-field method, we have studied the photoabsorption spectra near the Si 2p thresholds of silane. According to our calculations, the clear assignments of the inner-shell photoabsorption spectra are provided. In comparison with the high-resolution experimental spectra, the geometric structure of the Si 2p-excited SiH_{4}^{**} is recommended to be of a C_{2v} symmetry. More specifically, the Si 2p-excited SiH_{4}^{**} have two bond lengths of 2.50 a.u. and another two bond lengths of 2.77 a.u., and the corresponding two bond angles are 104.0° and 112.5° respectively.     

Synthesis and crystal structure of the octahedral cluster complex [Th(DMSO)8Cl][Re6Se7Cl7]

A cluster complex of the composition [Th(DMSO)₈Cl][Re₆Se₇Cl₇] has been obtained by interaction of ThCl₄ solution in DMSO with a water solution of K₃[Re₆Se₇Cl₇] and KCl. The compound crystallizes in the rhombic space group Pbcm with unit cell parameters a = 12.262(2) Å, b = 19.653(6) Å, c = 23.603(6) Å, V = 5688(2) ų, Z = 4, d _calc = 3.282 g/cm³. The structure is built from centrosymmetric cluster anions [Re₆Se₇Cl₇]^3? and complex cations [Th(DMSO)₈Cl]³⁺ possessing mirror-plane symmetry, half of the DMSO ligands being doubly disordered.     

Diameter graphs of polygons and the proof of a conjecture of Graham

We show that for an n-gon with unit diameter to have maximum area, its diameter graph must contain a cycle, and we derive an isodiametric theorem for such n-gons in terms of the length of the cycle. We then apply this theorem to prove Graham's 1975 conjecture that the diameter graph of a maximal 2m-gon (m?3) must be a cycle of length 2m−1 with one additional edge attached to it.     

A New Pathway to Synthesize Cyclomercurated Ferrocenylimines Containing Heterocyclic Ring

The cyclomercurated ferrocenylimines containing heterocyclic ring were prepared by the condensation of cyclomercuration of acylferrocene with the appropriate heterocyclic amine.This procedure provides an efficient method for the synthesis of cyclomerucurated ferrocenylimines containing heterocyclic ring which are difficultly synthesized by the conventional method.The reaction mechanism is proposed.     

2,3-二硫甲基-6,7-二硫十六烷基四硫代富瓦烯的合成

Langmuir-Blodgett(简称LB)法作为分子水平的成膜技术,能制备纳米级几乎无缺陷的单分子层或多分子层膜,在微电子学,分子器件,磁性有序材料,生物膜等方面有广泛的应用前景。目前,四硫富瓦烯类衍生物作为导电LB膜材料的研究,引起人们极大的兴