Probing the Brønsted Acidity of the External Surface of Faujasite-Type Zeolites

We outline two methodologies to selectively characterize the Brønsted acidity of the external surface of FAU-type zeolites by IR and NMR spectroscopy of adsorbed basic probe molecules. The challenge and goal are to develop reliable and quantitative IR and NMR methodologies to investigate the accessibility of acidic sites in the large pore FAU-type zeolite Y and its mesoporous derivatives often referred to as ultra-stable Y (USY). The accessibility of their Brønsted acid sites to probe molecules (n-alkylamines, n-alkylpyridines, n-alkylphosphine- and phenylphosphine-oxides) of different molecular sizes is quantitatively monitored either by IR or ³¹P NMR spectroscopy. It is now possible, for the first time to quantitatively discriminate between the Brønsted acidity located in the microporosity and on the external surface of large pore zeolites. For instance, the number of external acid sites on a Y (LZY-64) zeolite represents 2 % of its total acid sites while that of a USY (CBV760) represents 4 % while the latter has a much lower framework Si/Al ratio.     

Fractal differential equations on the Sierpinski gasket

Let denote the symmetric Laplacian on the Sierpinski gasket SG defined by Kigami [11] as a renormalized limit of graph Laplacians on the sequence of pregaskets G_m whose limit is SG. We study the analogs of some of the classical partial differential equations with playing the role of the usual Laplacian. For harmonic functions, biharmonic functions, and Dirichlet eigenfunctions of , we give efficient algorithms to compute the solutions exactly, we display the results of implementing these algorithms, and we prove various properties of the solutions that are suggested by the data. Completing the work of Fukushima and Shima [8] who computed the Dirichlet eigenvalues and their multiplicities, we show how to construct a basis (but not orthonormal) for the eigenspaces, so that we have the analog of Fourier sine series on the unit interval. We also show that certain eigenfunctions have the property that they are a nonzero constant along certain lines contained in SG. For the analogs of the heat and wave equation, we give algorithms for approximating the solution, and display the results of implementing these algorithms. We give strong evidence that the analog of finite propagation for the wave equation does not hold because of inconsistent scaling behavior in space and time.Research supported in part by the National Science Foundation, Grant DMS-9623250.Research supported by the National Science Foundation through the Research Experiences for Undergraduates (REU) Program.     

Potential theory of hyperfinite Dirichlet forms

In this paper, we are going to study the capacity theory and exceptionality of hyperfinite Dirichlet forms. We shall introduce positive measures of hyperfinite energy integrals and associated theory. Fukushima's decomposition theorem will be established on the basis of discussing hyperfinite additive functionals and hyperfinite measures. We shall study the properties of internal multiplicative functionals, subordinate semigroups and subprocesses. Moreover, we shall discuss transformation of hyperfinite Dirichlet forms.Research was supported by the National Natural Science Foundation of P.R. China, No. 18901004. The support from the position of Wissenschaftliche Hilfskraft of Ruhr-University Bochum under Prof. Sergio Albeverio is also acknowledged.     

系列Mo-Cu(Ag,Au)-Se簇合物的95Mo和31P NMR研究

报道了含硬币金属和四硒代钼酸盐的异金属硒簇合物的⁹⁵Mo NMR研究结果和含膦配体Mo(W)-Cu(Ag,Au)-Se配合物的³¹P NMR谱学性能。发现不同硬币金属对⁹⁵Mo核的化学屏蔽效应顺序为Au > Cu > Ag;对系列Mo-Cu-Se化合物的⁹⁵Mo NMR研究结果表明:⁹⁵Mo NMR的化学位移和线宽不仅与配位的Cu原子数目有关,而且对结构的变化特别敏感;[MoSe₄]^2-离子的相对四个方向被Cu⁺配位后,其Mo核的屏蔽基本饱和;外围配体对⁹⁵Mo NMR数据影响甚微。同时还用动态⁹⁵Mo NMR谱技术跟踪配体的取代反应和从MoCu₄到MoCu₁₀核的簇骼转变过程。此外,还讨论了这些化合物在不同构型之间,同一构型不同金属中心和不同配体基团的³¹P NMR化学位移的变化特征。     

Studies of silicophosphate derivatives by 31P-->29Si CP MAS NMR

We show that it is possible to efficiently transfer magnetization from ³¹P to ²⁹Si, using variable amplitude CP MAS experiment. This experiment is demonstrated by using Si₅O(PO₄)₆, the synthesis protocol of which is described. From the obtained results, we show that the experiment allows the spectral edition of ²⁹Si spectra from ³¹P→²⁹Si CP, enabling the studies of derivatives involving Si–O–P linkages, such as phosphosilicate glasses, microporous silicoaluminophosphates (SAPO) and bioactive phosphosilicates.     

On higher order Bessel potentials

The solutions of the equation in , where are investigated, Bessel potentials of higher order are defined, and recurrence relations between these solutions and these Bessel potentials are obtained. It is also proved that these solutions and the solutions of , under certain conditions, are identical. Received: 6 November 2002     

Transmission problems and spectral theory for singular integral operators on Lipschitz domains

We prove the well-posedness of the transmission problem for the Laplacian across a Lipschitz interface, with optimal non-tangential maximal function estimates, for data in Lebesgue and Hardy spaces on the boundary. As a corollary, we show that the spectral radius of the (adjoint) harmonic double layer potential K∗ in is less than , whenever is a bounded convex domain and 1<p?2.     

Capillary Coated with Layer-by-Layer Assembly of γ-Zirconium Phosphate/ Lysozyme Nanocomposite Film for Open Tubular Capillary Electrochromatography Chiral Separation

A new capillary coating of alternate 31n/xxlarge947.gif" alt="gamma" align="MIDDLE" BORDER="0">-zirconium phosphate lysozyme fabricated for open-tubular electrochromatography enantioseparation. The chiral compounds D, L-tryptophan tested were enantiomerically resolved. The influences brought by experimental parameters, such as organic modifier, temperature, applied voltage and pH of running buffer on the performance of the column, were investigated.     

Are the Elements Elementary? Nineteenth-Century Chemical and Spectroscopical Answers

We analyze the role and influence of a tradition of research linked to the concept of 31dee30v5t/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0">primary matter31dee30v5t/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> in nineteenth-century studies on the nature of the elements.The suggestion of William Prout (1785-1850) in 1816 that the atomic weights of pure chemical elements are whole numbers and multiples of the atomic weight of hydrogen, taken as unity, was met with serious confutations,which in turn prompted several attempts to save Prout31dee30v5t/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s hypothesis.We discuss these attempts in detail and the objections raised against them, for instance by Dmitry Ivanovich Mendeleev (1834-1907). We pay particular attention to the use of spectroscopy as a method for proving the existence of elementary forms of matter inside atoms. Leaders in this field of research were two English scientists, the astrophysicist Norman Lockyer (1836-1920) and the chemist William Crookes (1832- 1919). Both of their approaches involved the idea of primary matter. However, while Crookes31dee30v5t/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s approach proved to be incorrect, Lockyer31dee30v5t/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s ideas survived for several years and supported the discovery of the electron by J.J.Thomson (1856-1940).