On the divergence of certain Hermite-Fejér interpolation

Summary In his paper [1]P. Turán discovers the interesting behaviour of Hermite-Fejér interpolation (based on the ebyev roots) not describing the derivative values at exceptional nodes {_n} _n=1 . Answering to his question we construct such exceptional node-sequence for which the mentioned process is bounded for bounded functions whenever –1<x<1 but does not converge for a suitable continuous function at any point of the whole interval [–1, 1].     

Characteristics of excited-state intermediates of TiO2–Y-Zeolite and MCM41 encapsulating photosensitive molecules: design of new photocatalysts

Some photosensitive molecules, such as p-N,N′-dimethylaminobenzoic acid (DMABA), Nile Red, heteropolytungstic acid (H₃PW₁₂O₄₀, HPA) and metalloporphyrins, have been entrapped onto nano-scale pores or channels of TiO₂-modified Y-Zeolite (TiO₂-Y-Zeolite) and MCM41 (TiO₂-MCM41) and their excited-state intermediates have been characterized in terms of the excited-state dynamics by using laser spectroscopic techniques. Through these studies, it has been found that the photo-induced electrons are generated from the intramolecular charge transfer (ICT) state of DMABA, Nile Red or metalloporphyrin (MnTPP(Cl)), followed by transferring to the TiO₂-Y-Zeolite or TiO₂-MCM41 more efficiently as compared to the bulk TiO₂, NaY-Zeolite or MCM41. The efficient photoinduced interfacial electron transfer causes the rapid formation of radicals of those photosensitive molecules (a few tens ps). It has been also found that these photophysical properties can be applied to develop the new photocatalyst as observed by the efficient photocatalytic activities of the DMABA or Nile Red-entrapped TiO₂-Y-Zeolites for the photoreduction of an azo-dye such as Methyl Orange in water. On the other hand, in case of HPA-entrapped TiO₂-Y-zeolite, the electron generated from the excited-state TiO₂ is transferred to HPA, followed by formation of the reduction product, heteropoly blue (HPB) which is also generated by UV irradiation of HPA. This electron transfer is analogous to the Z-scheme mechanism of plant photosynthetic systems showing two photon reactions. Because of this photoelectron transfer mechanism, the HPA-entrapped TiO₂-Y-zeolite has demonstrated the synergistic enhancement of the photocatalytic decomposition of Methyl Orange and hydrogen generation from photolysis of water.     

MCM-41分子筛负载钼钴系催化剂的噻吩HDS研究

通过氧吸附量、噻吩吸附热及反应速率常数的测定，研究了MoO3/MCM-41、MoO3-CoO(NiO)/MCM-41系列催化剂，发现，对于MoO3/MCM-41催化剂，当MoO3的质量分数（以MCM－41为底数，即MCM－41＝1g时，MoO3含量为0．15g，下同）从15％增加到20％时，其噻吩的加氢硫（HDS）活性增大，至25％时活性下降，所对应的氧吸附量（mL/g催化剂）也是先增大后减少，并且两者有很好的线性对应关系，而且噻吩吸附热则基本保持不变，采用不同的MoO3-CoO(NiO)浸渍顺序制备的MoO3-CoO(NiO)/MCM-41催化剂中，先浸渍CoO(NiO）再浸渍MoO3的催化剂，其噻吩HDS活性明显优于对其它浸渍顺序制备的催化剂，同时催化剂的氧吸附量和噻吩吸附热也最大。     

A gas-phase electron diffraction study of the molecular structure of tetravinylsilane

The molecular structure of tetravinylsilane has been studied by gas-phase electron diffraction. The radial distribution curve suggests the absence of conformers having vinyl double bonds staggered with respect to the SiC₄ skeleton. Of the eclipsed or approximately-eclipsed conformers, the one with S₄ symmetry gives the best fit with experiment, although a small admixture of a C₁ conformation cannot be ruled out. Least-squares refinement gave the following values for the independent structural parameters (lengths, r_a basis; angles, r_α basis): C-H = 1.118 ± 0.003 Å, CC = 1.355 ± 0.002 Å, Si-C = 1.855 ±0.002 Å, ∠SiCC = 124.0 ± 0.3°, ∠SiCH = 118.4 ± 1.0°, torsion angles CSiCC are 17.5 ± 0.6° from the eclipsed conformation. During the refinement the vibrational amplitudes u and perpendicular amplitude corrections K were held constant at calculated values. The CC bond length provides evidence of interaction between the vinyl π-bonds and the vacant d-orbitals of silicon.     

Application of solvent extraction and synchronous spectrofluorimetry to the determination of the formation constant for a 1:1 complex of carbazole withβ-cyclodextrin in water-dimethyl sulfoxide medium

Extraction of carbazole in heptane was performed at 25±1°C with an aqueous dimethyl sulfoxide (DMSO) medium containing -cyclodextrin (CD) at consecutive concentrations in the range of 0–10 mM. The fluorescence intensity of carbazole remaining in the heptane phase was measured by synchronous scanning fluorimetry. The apparent formation constant (K _f) for a 1:1 carbazole: CD inclusion complex in water-DMSO medium was determined by using a linear plot of the distribution ratio calculated from the fluorescence intensities vs. the -CD concentration. The values thus obtained ranged from 477 M^–1 in a 10% v/v DMSO medium to 12.1 M^–1 in a 60% v/v medium. Good linear relationships were observed between logK _f and the DMSO concentration ([DMSO]), and also between logK _f and the logarithm of the distribution coefficient (K _d) for carbazole. The formation constant in 100% water was estimated to be approximately 1.0×10³ M^–1 on the basis of the logK _f vs. [DMSO] and the logK _f vs. logK _d correlations.     

Some positive cotes numbers for the chebyshev weight function

We show that, for the Chebyshev weight function (1–x ²)^–1/2, the Cotes numbers for the quadrature rule with nodes at the zeros of the ultraspherical polynomialP _n ^/() are nonnegative if and only if –1/2<1.     

TiO2-CdS-MCM-41复合纳米材料的合成和表征

利用γ-巯丙基三甲氧基硅烷及表面预吸附水解技术在MCM-41介孔分子筛孔道内部以化学键合的形式依次引入了CdS和TiO2纳米粒子.紫外-可见吸收光谱结果表明,借助于巯基的络合能力,MCM-41能有效地从反胶束中萃取CdS纳米粒子.利用小角XRD谱图成功地跟踪观察到了MCM-41介孔分子筛随纳米粒子的引入而产生的孔径变化.     

Silver Selective Electrode Based on Hybrid Mesoporous Silica (MCM‐41) Modified Material

A silver selective electrode based on TEPQA‐MCM‐41 material was developed and used for the selective determination of Ag⁺ ion in various samples. The effect of various plasticizers i. e. dimethyl phthalate (DMP), Tris(ethylhexyl)phosphate (TEP), bis‐(2‐ethylhexyl)sebacate (BEHS), bis‐(2‐ethylhexyl)adipate (BEHA) was investigated. The electrode of the composition of 2 : 1 : 77 : 12 : 8 (w/w, %) of TEPQA‐MCM‐41 : NaTPB : Graphite powder : paraffin oil : DMP respectively, works satisfactorily in a wide concentration range of 1.3×10^?9 M–1.0×10^?1 M for Ag⁺ ion with a lower detection limit (LOD) of 1.0×10^?9 M and has Nernstian slope of 63.4 1 mV/decay. The electrode can be used in a pH range of 2.3 to 6.7 for a period of 3 months without any divergence in potential response. The selectivity coefficient calculated by fixed interference method indicates the high selectivity of the electrode towards Ag⁺ ion over other tested cations.     

Cr/MCM-41催化剂上的乙烯聚合行为

以纯硅ＭＣＭ４１为载体，负载Ｐｈｉｌｉｐｓ烯烃聚合催化剂活性组分Ｃｒ．ＸＲＤ及ＴＥＭ表征结果表明，所得到的Ｃｒ／ＭＣＭ４１催化剂具有良好的晶体结构和较理想的长程有序一维孔道．ＦＴＩＲ和Ｒａｍａｎ光谱表征结果表明，Ｃｒ／ＭＣＭ４１上不仅可发生乙烯聚合过程，而且形成的聚乙烯以结晶和无定形两种形态存在．乙烯聚合活性不仅与反应参数有关，而且与Ｃｒ的负载量密切相关．用于乙烯聚合后，Ｃｒ／ＭＣＭ４１催化剂仍保持其特征的晶体结构和一维孔道结构．     

Synthesis,Characterization and Catalysis of Ce‐MCM‐41

The cerium‐containing MCM‐41 (Ce‐MCM‐41) has been synthesized by direct hydrothermal method. The low‐angle XRD patterns revealed the typical five major peaks of MCM‐41 type hexagonal structures. The interplanar spacing d₁₀₀ = 38.4 Å was obtained that can be indexed on a hexagonal unit cell parameter with a_o = 44.3 Å which was larger than that of pure siliceous MCM‐41 (Si‐MCM‐41). Transmission electron micrograph shows the regular hexagonal array of uniform channel characteristics of MCM‐41. The BET surface area of Ce‐MCM‐41 was 840 m²/g, which is much reduced as compared to that of Si‐MCM‐41, with the pore size of 26.9 Å and mesopore volume of 0.78 cm³/g were measured by nitrogen adsorption‐desorption isotherm at 77 K. Along with the results, the synthesized Ce‐MCM‐41 exhibited a well‐ordered MCM‐41‐type mesoporous structure with the incorporation of cerium. Using Ce‐MCM‐41 as a support, the Rh (0.5 wt%) catalyst exhibited very high activity for the NO/CO reactions.