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.     

On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z_2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H(5)≥25=5~2, where H(5)is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.     

Synthesis and absolute configuration of cordiaquinone K, antifungal and larvicidal meroterpenoid isolated from the Panamanian plant, Cordia curassavica

Total synthesis of cordiaquinone K, a new antifungal and larvicidal meroterpenoid, is reported. The absolute configuration of cordiaquinone K was confirmed by the synthesis.     

Local chain‐configuration dependence of the mechanisms of the chemical reaction of poly(vinyl chloride). IX. Novel results on stereoselectivity of chlorination reaction

A poly(vinyl chloride) (PVC) sample was chlorinated in solution in the presence of 2,2′‐azobisisobutyronitrile and by the fluid‐bed method. The aim was to evaluate the scope of the stereoselectivity of the chlorination reaction. The quantitative microstructural analysis of the residual PVC with a degree of chlorination was followed by ¹³C NMR spectroscopy. From the evolution of the content of isotactic (mm), heterotactic (mr), and syndiotactic (rr) triads and of mmmm, mmmr, and rmmr isotactic pentads in the unchlorinated parts of the polymer, it was unambiguously inferred that the chlorination reaction proceeds by a stereoselective mechanism in that the mr heterotactic triads are the most reactive structures followed by the isotactic triad at mmmr and rmmr pentads. This conclusion was confirmed on the basis of the Fourier transform infrared results. The results provide valuable information regarding the effect of tacticity and related local conformations in the chemical reactions of PVC. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 508–519, 2003     

Infinite classes of anti‐mitre and 5‐sparse Steiner triple systems

In this paper, we present three constructions for anti‐mitre Steiner triple systems and a construction for 5‐sparse ones. The first construction for anti‐mitre STSs settles two of the four unsettled admissible residue classes modulo 18 and the second construction covers such a class modulo 36. The third construction generates many infinite classes of anti‐mitre STSs in the remaining possible orders. As a consequence of these three constructions we can construct anti‐mitre systems for at least 13/14 of the admissible orders. For 5‐sparse STS(υ), we give a construction for υ ≡ 1, 19 (mod 54) and υ ≠ 109. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 237–250, 2006     

5,6—二亚甲基双环[2.2.1]庚—2—醇及其衍生物的旋光与构型

从（－）－（１Ｓ，２Ｒ，４Ｓ）－５，６－二亚甲基双环［２．２．１］庚－２－醇（Ｉ）和（－）－（１Ｓ，２Ｓ，４Ｓ）－５，６－二亚甲基双环［２．２．１］庚－２－醇（Ⅱ）出发，合成了它们的醚类和取代苯甲酸酯类光学纯的衍生物。通过［α］Ｄ测定和构型分析，发现它们是含有３个手性碳（Ｃ１，Ｃ２和Ｃ４）的桥环化合物，其旋光性与构型的关系均符合可极化度多级圆球不对称性模型。     

Quantum-Chemical Investigation of Intermediates in the Addition of Phenylsulfenium Cation to Substituted Acetylenes

The reaction paths for the transformations of substituted acetylenes (X—CC—Y; X, Y = H, Me, Ph, CN) in reaction with phenylsulfenium cation were studied by quantum-chemical methods. It was shown that the reactions take place with the formation of acyclic and cyclic cationic intermediates. The factor that determines the structure and characteristics of these cations is the induction and polarizing action of the substituents in the acetylenes and to a lesser degree their electron-donor characteristics. The resonance effect of the phenyl substituent has a predominantly levelling action on the distribution of charges.     

X-Ray Investigation of Chiral β-Hydroxyketone Derived From (+)-Isomenthone

X-ray analysis was carried out to study the molecular structure of β-hydroxyketone, which is one of the minor products of selective aldol condensation of (−)-menthone with 4-carbomethoxybenzaldehyde. The cyclohexanone ring of the compound has a practically undistorted chair conformation with an axial orientation of the 1-methyl group and the bulkiest 2-[1′-hydroxy-1′ -(4-carbomethoxyphenyl)]methyl substituent and the equatorial orientation of the isopropyl group in the 4 position. The stereochemical configuration was found to be (1R,2R,4 R, 1′ S), supporting that the compound belongs to the group of (+)-isomenthones; i.e., the starting (-)-menthone undergoes (to a certain extent) epimerization under the reaction conditions used. In crystal, there is intermolecular hydrogen bonding >C=O...HO- (the -O...H- bond length is 2.15 Å). The molecular conformation in hydroxyketone crystals differs from the one which prevails in solutions (according to previous NMR data) and which is characterized by an inverted cyclohexanone ring and intramolecular hydrogen bonding >C=O...HO.Original Russian Text Copyright © 2004 by S. V. Shishkina, T. G. Drushlyak, L. A. Kutulya, N. S. Pivnenko, and O. V. Shishkin__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 933–940, September–October, 2004.     

Tensor products of coherent configurations

A Cartesian decomposition of a coherent configuration ✗ is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of ✗ comes from a certain Cartesian decomposition. It is proved that if the coherent configuration ✗ is thick, then there is a unique maximal Cartesian decomposition of ✗; i.e., there is exactly one internal tensor decomposition of ✗ into indecomposable components. In particular, this implies an analog of the Krull–Schmidt theorem for the thick coherent configurations. A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.     

Fermionic solution of the Andrews-Baxter-Forrester model. II. Proof of Melzer's polynomial identities

We compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter, and Forrester, we prove polynomial identities for finitizations of the Virasoro characters as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers-Ramanujan-type identities for the unitary minimal Virasoro characters conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer's identities and application of Bailey's lemma.Dedicated to the memory of Piet Kasteleyn.