Optimal tristance anticodes in certain graphs

For z₁,z₂,z₃∈Zⁿ, the tristance d₃(z₁,z₂,z₃) is a generalization of the L₁-distance on Zⁿ to a quantity that reflects the relative dispersion of three points rather than two. A tristance anticodeA_d of diameter d is a subset of Zⁿ with the property that d₃(z₁,z₂,z₃)?d for all z₁,z₂,z₃∈A_d. An anticode is optimal if it has the largest possible cardinality for its diameter d. We determine the cardinality and completely classify the optimal tristance anticodes in Z² for all diameters d?1. We then generalize this result to two related distance models: a different distance structure on Z² where d(z₁,z₂)=1 if z₁,z₂ are adjacent either horizontally, vertically, or diagonally, and the distance structure obtained when Z² is replaced by the hexagonal lattice A₂. We also investigate optimal tristance anticodes in Z³ and optimal quadristance anticodes in Z², and provide bounds on their cardinality. We conclude with a brief discussion of the applications of our results to multi-dimensional interleaving schemes and to connectivity loci in the game of Go.     

Absolutely indecomposable symmetric matrices

Let A be a symmetric matrix of size n×n with entries in some (commutative) field K. We study the possibility of decomposing A into two blocks by conjugation by an orthogonal matrix T∈Mat_n(K). We say that A is absolutely indecomposable if it is indecomposable over every extension of the base field. If K is formally real then every symmetric matrix A diagonalizes orthogonally over the real closure of K. Assume that K is a not formally real and of level s. We prove that in Mat_n(K) there exist symmetric, absolutely indecomposable matrices iff n is congruent to 0, 1 or −1 modulo 2s.     

New ligands for the Fe(III)‐mediated reverse atom transfer radical polymerization of methyl methacrylate

A series of (di)picolinic acids and their derivates are investigated as novel complexing tridentate or bidentate ligands in the iron‐mediated reverse atom transfer radical polymerization of methyl methacrylate in N,N‐dimethylformamide at 100 °C with 2,2′‐azobisisobutyrontrile as an initiator. The polymerization rates and polydispersity indices (1.32–1.8) of the resulting polymers are dependent on the structures of the ligands employed. Different iron complexes may be involved in iron‐mediated reverse atom transfer radical polymerization, depending on the type of acid used. ¹H NMR spectroscopy has been used to study the structure of the resulting polymers. Chain‐extension reactions have been performed to further confirm the living nature of this catalytic system. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2912–2921, 2006     

Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.     

A novel and efficient synthesis of porphine

meso-Tetra(n-hexyloxycarbonyl)porphyrin was found to be converted into porphine, the mother compound of porphyrins, in a 77% yield when heated in aqueous sulfuric acid at 180 °C over 30 min under an inert atmosphere. The observation demonstrates that the substituted porphyrin serves as a novel and useful precursor for porphine.     

Synthesis of coumarins by Pt-catalyzed hydroarylation of propiolic acids with phenols

Synthesis of coumarins from phenols and propiolic acids was examined by using a Pt catalyst such as PtCl₂/AgOTf, K₂PtCl₄/AgOTf, and K₂PtCl₄/AgOAc. Propiolic acid reacted even with less reactive phenols in trifluoroacetic acid to give coumarins and dihydrocoumarins. In the case of substituted propiolic acids, phenylpropiolic acid and 2-octynoic acid, the reactions proceeded selectively to afford coumarins in good to high yields.     

Proton conductivity of phosphoric acid derivative of fullerene

The proton conductive property of methano [60] fullerene diphosphoric acid has been investigated under various humidity conditions at the temperature range between 15 and 45 °C. It shows proton conductivity as high as 10⁻² S cm⁻¹ at 25 °C under relative humidity of 95%. Thermal analyses including TG–DTA and thermal desorption mass spectroscopy (TDS) confirm that the compound is thermally stable up to 200 °C. Proton conduction of the compound depends very much on humidity or water content. The logarithmic conductivity at 25 °C is increased linearly with increasing relative humidity. The activation energy (E_a) estimated from the slope of log(σT) vs. 1/T is decreased from 1.08 to 0.52 eV, as the relative humidity is increased from 40% to 75%. The humidity dependence of conductivity is discussed in the light of the observed hydration isotherm.     

Intramolecular photocycloaddition of β-stilbazoles tethered by silyl chains

Intramolecular (2+2) photocycloaddition of β-stilbazoles tethered by silyl chains took place with high efficiency. Complexation with dicarboxylic acid or catechol further enhanced both the efficiency and stereoselectivity.     

Asymmetric synthesis of phosphonic acid analogues for acylcarnitine

Phosphonic acid analogues of acylcarnitine were prepared in an optically active form expecting CPT I inhibitory activities. The synthetic methodology was based on catalytic asymmetric dihydroxylation of β,γ-unsaturated phosphonates and subsequent regioselective amination via the cyclic sulfates.     

均苯三甲酸铕及铕镧配合物的合成及荧光性质

以均苯三甲酸为配体,水热条件下合成了均苯三甲酸铕及铕镧系列发光配合物La_xEu_1-x(BTC)·nH₂O(x=0,0.1,0.3,0.5,0.7,0.9),通过元素分析及化学滴定法测定了配合物的组成。用红外光谱对其进行了表征,确定了该系列配合物的组成为La_xEu_1-x(BTC)·nH₂O。研究了系列配合物的荧光性质,荧光光谱表明:该类配合物均能发出强的铕离子的特征荧光,并且镧元素的掺入能增强铕配合物的发光强度,但发射峰的位置基本上没有变化;其中⁵D₀→⁷F₁和⁵D₀→⁷F₂的跃迁发射较强,且均劈裂为两个峰(587,593nm)和(611,618nm),这是由于铕离子所处的配位环境引起的。