STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequcncies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields(NSMC)on Cayley trees are studied.In the proof,a new technique for the study of strong liinit theorems of Markov chains is extended to the case of Markov chain fields.The asymptotic equiparti- tion properties with almost everywhere(a.e.)convergence for NSMC on Cayley trees are obtained.     

Activity evaluation of carbon paste electrodes loaded with pt nanoparticles prepared in different radiolytic conditions

Three Pt-based catalysts prepared in different radiolytic conditions and supported on graphite powder were packed into a carbon paste electrode configuration. They were compared to each other, to the commercial (Pt) deposited on activated carbon powder (Johnson Matthey) and to pure Vulcan XC-72 for their respective abilities toward the hydrogen evolution reaction (HER). The Tafel parameters were determined for all these electrodes. From the I–V curves and their quantitative treatment, the following order of activity emerged unambiguously and reads: (PtCO)₂ (fcc structure) > (PtCO)₁ (Chini cluster) > (Pt)_neat > (Pt)_JM (Johnson Matthey) ≫ (Vulcan XC-72). As expected, all the Pt-loaded electrodes were more efficient than Vulcan XC-72. The classification appears to be linked with the mean nanoparticle size, and for comparable sizes, with the surface morphology of the materials. The results and the stability of the electrodes suggest that the small particle sizes and the good dispersity on the carbon support were maintained during the HER.     

Methods in carbon K-edge NEXAFS: Experiment and analysis

Near-edge X-ray absorption spectroscopy (NEXAFS) is widely used to probe the chemistry and structure of surface layers. Moreover, using ultra-high brilliance polarised synchrotron light sources, it is possible to determine the molecular alignment of ultra-thin surface films. However, the quantitative analysis of NEXAFS data is complicated by many experimental factors and, historically, the essential methods of calibration, normalisation and artefact removal are presented in the literature in a somewhat fragmented manner, thus hindering their integrated implementation as well as their further development. This paper outlines a unified, systematic approach to the collection and quantitative analysis of NEXAFS data with a particular focus upon carbon K-edge spectra. As a consequence, we show that current methods neglect several important aspects of the data analysis process, which we address with a combination of novel and adapted techniques. We discuss multiple approaches in solving the issues commonly encountered in the analysis of NEXAFS data, revealing the inherent assumptions of each approach and providing guidelines for assessing their appropriateness in a broad range of experimental situations.     

How much sweetness is there in the universe?

We continue investigations of forcing notions with strong ccc properties introducing new methods of building sweet forcing notions. We also show that quotients of topologically sweet forcing notions over Cohen reals are topologically sweet while the quotients over random reals do not have to be such. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calorimetric study of Diepoxide Chain-Extended Poly(Ethylene Terephthalate)

A series of chain-extended PET samples were obtained by the use of different amounts of a diepoxide as chain extender, which was prepared for this purpose. These samples exhibited different intrinsic viscosities and degrees of branching or cross-linking. The effects of this differentiation on the thermal properties were studied by differential scanning calorimetry. The thermal parameters studied were the glass transition temperature (T_g), the cold-crystallization temperature (T_cc), the melting temperature (T_m), the enthalpy (ΔH_m) and the degree of crystallinity. The data revealed that, the higher the quantity of chain extender or the chain extension time, the higher T_gand T_cc, but the lower T_mand ΔH_m, i.e. the more amorphous the chain-extended samples, as also shown by density measurements. This revised version was published online in July 2006 with corrections to the Cover Date.     

Asymptotic behavior of energy band associated with a negative energy level

The mathematical foundation of the tight binding approximation is given. If ₀ is a negative energy level of a real potentialq, then there exists an energy band for a one-dimensional chain with period 2T of the same atoms which lies near ₀. We study this band whenT tends to infinity.On leave of absence from the Department of Physics, Leningrad State University, Leningrad, USSR.     

On concepts of directional differentiability

Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of Gâteaux, Fréchet, and Hadamard are singled out from the general framework of -directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equivalent. The chain rule for directional derivatives of a composite mapping is discussed.     

Random walks generated by affine mappings

This article is concerned with Markov chains on ^m constructed by randomly choosing an affine map at each stage, and then making the transition from the current point to its image under this map. The distribution of the random affine map can depend on the current point (i.e., state of the chain). Sufficient conditions are given under which this chain is ergodic.     

新的酰胺型开链冠醚的合成与性质

Simon在70年代开发了一类酰胺型开链冠醚,能选择性配位碱土金属离子并可作为中性载体制备离子选择性电极.由于酰胺型开链冠醚易于制备,因此受到人们广泛地重视.Vgtle等提出的“末端基”概念为开链冠醚的合成、设计起了重要的指导作用.前文报道2-甲氧基-1-氨甲基萘与三甘醇二碘化物在无水碳酸钠存在下于乙腈中反应得到双手臂的套索冠醚与碘化钠的配合物.X射线衍射晶体结构分析表明萘环上的甲氧基中的氧原子参加了与钠离子的配位,生成了扭曲的六边形双锥结构配合物.因此2-甲氧基-1-氨基萘可以作为开链冠醚的“末端基”.开链冠醚的合成路线是: