Comparison theorems forL-monosplines of minimal norm

Summary LetLM _N be the set of allL-monosplines withN free knots, prescribed by a pair (x;E) of pointsx = {x _i } ₁ ⁿ ,a <x ₁ < ... <x _n <b and an incidence matrixE = (e _ij ) _i=1 ⁿ , _r-1 ^j=0 with Denote byLM _N ^O the subset ofLM _N consisting of theL-monosplines withN simple knots (n=N). We prove that theL-monosplines of minimalL _p-norms inLM _N belong toLM _N ^O .The results are reformulated as comparison theorems for quadrature formulae.     

Continued fractions associated with the Newton-Padé table

Summary We discuss first the block structure of the Newton-Padé table (or, rational interpolation table) corresponding to the double sequence of rational interpolants for the data{(z _k, h(z_k)} _k =0. (The (m, n)-entry of this table is the rational function of type (m,n) solving the linearized rational interpolation problem on the firstm+n+1 data.) We then construct continued fractions that are associated with either a diagonal or two adjacent diagonals of this Newton-Padé table in such a way that the convergents of the continued fractions are equal to the distinct entries on this diagonal or this pair of diagonals, respectively. The resulting continued fractions are generalizations of Thiele fractions and of Magnus'sP-fractions. A discussion of an some new results on related algorithms of Werner and Graves-Morris and Hopkins are also given.Dedicated to the memory of Helmut Werner (1931–1985)     

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.     

A proof of Freud's conjecture for exponential weights

LetW (x) be a function nonnegative inR, positive on a set of positive measure, and such that all power moments ofW ²(x) are finite. Let {p _n (W ²;x)} ₀ denote the sequence of orthonormal polynomials with respect to the weightW ²(x), and let {A _n } ₁ and {B _n } ₁ denote the coefficients in the recurrence relation

晶化温度对中孔分子筛（M41S）结构转变的影响

在低表面活性剂浓度及低表面活性剂与氧化硅比的条件下，研究了十六烷基三甲基溴化铵－硅酸钠体系中晶化温度对中孔分子筛Ｍ４１Ｓ材料结构转变的影响。结果有，晶化温度提高至１３５℃改变了原六方晶相ＭＣＭ－４１的结构，晶化温度提高到１５０℃后，中孔结构六方ＭＣＭ－４１晶格转变为变不稳定的层状相，     

Mesoporous micelle templated silica with incorporated C<Subscript>8</Subscript> and C<Subscript>18</Subscript> phase

Mesoporous silica material of MCM-41 type was synthesized by co-condensation of highly concentrated octyltriethoxysilane (OTEOS), octadecyltriethoxysilane (ODTEOS) and tetraethoxysilane (TEOS). The obtained hybrid materials were characterized using XRD, TG-DSC and low temperature adsorption/desorption of nitrogen. It was shown that the applied method of synthesis allows to obtain silica of MCM-41 type with a high degree of hydrocarbon saturation.     

纯硅MCM-41中孔分子筛合成因素的研究Ⅰ.Na~+、K~+阳离子对合成的影响

本文采用表面活性剂十六烷基三甲基溴化铵（Ｃ１６ＴＡＢｒ，以下为１６３１），在（Ｎａ，Ｋ）ＯＨＳｉＯ２Ｃ１６ＴＡＢｒＨ２Ｏ体系中分别利用室温、水热及干粉法进行了纯硅ＭＣＭ４１中孔分子筛的合成，考察了阳离子Ｎａ＋、Ｋ＋对ＭＣＭ４１合成及稳定性的影响。通过ＸＲＤ对结晶度的测定，发现ＮａＭＣＭ４１的晶化速率明显高于ＫＭＣＭ４１，而热稳定性和水热稳定性较差，且ａ０值小于后者。同时发现，就合成方法而言，室温法得到的产物具有很高的结晶度，利用水热法合成的样品的热稳定性明显较高，而干法得到的分子筛产品具有优良的水热稳定性。     

中孔MCM—41分子筛在微孔沸石ZSM—5上附晶生长的研究

首次在微孔沸石ＺＳＭ５表面进行了ＭＣＭ４１分子筛的附晶生长，并首次提出中孔材料ＭＣＭ４１分子筛静电组配理论的新形式（ＸＳ＋Ｉ）；同时利用ＸＲＤ、ＴＥＭ、ＢＥＴ等测试手段表征了合成样品，并讨论了微孔沸石表面附晶生长中孔分子筛ＭＣＭ４１的合成化学，考察了Ｆ离子效应、ｐＨ值及表面活性剂ＣＴＡＢ（十六烷基三甲基溴化铵）的影响。     

Interconnection between the Structures and Sorption Characteristics of Mesophase Materials of MCM-41 Type Containing Alkylpyridines

Under the conditions studied for the synthesis of mesophase materials with alkylpyridinium halides an increase in the density of packing of these molecules in the encapsulated micelles was observed with an increase in the length of the alkyl radicals. The difference in the density of packing of these surface active reagents (SAR) depended to a considerable extent on the perfection of the hexagonal structure and the characteristic absorption properties of the mesophase materials of MCM-41 type.     

基于MCM-41分子筛表面的镱离子印迹聚合物的制备及其性能

运用离子印迹技术,以3-氯丙基三乙氧基硅烷为锚定剂,将功能单体直链聚乙烯亚胺(PEI)接枝在MCM-41分子筛表面,选择镱离子作为模板离子,以环氧氯丙烷交联制备出基于MCM-41表面的镱离子印迹聚合物Yb(Ⅲ)-IIP-PEI/MCM-41,并以同样的方法制备非离子印迹聚合物(NIP-PEI/MCM-41)。 利用傅里叶变换红外光谱仪和扫描电子显微镜等技术手段对Yb³⁺印迹聚合物进行表征,采用静态吸附法确定了Yb(Ⅲ)-IIP-PEI/MCM-41对Yb³⁺的最佳吸附条件及选择性吸附性能。 结果表明,Yb(Ⅲ)-IIP-PEI/MCM-41和NIP-PEI/MCM-41的最大吸附量分别为229.93和99.27 mg/g;印迹材料对Yb³⁺的吸附符合Langmuir模型;吸附平衡在40 min的时候基本可以达到,可以利用准二级动力学模型来描述其吸附过程;Yb(Ⅲ)-IIP-PEI/MCM-41对Yb³⁺具有较强的选择性,同时也具有很好的重复使用性能。 成功地将MCM-41和离子印迹聚合物的优点结合起来,制备出一种对稀土Yb离子既有高吸附量又有高选择性的吸附材料,为进一步将其应用在处理实际废水,分离回收低浓度稀土废水中的稀土元素等方面打下了基础。