Heat “polynomials” for a singular differential operator on (0, ∞)

We generalize the theory of the heat polynomials introduced by P. V. Rosenbloom and D. V. Widder for a more general class of singular differential operator on (0, ). The heat polynomials associated with the Bessel operator and studied by D. T. Haimo appear as a particular case in this paper. In the special cases of second derivative and Bessel operators the heat polynomials are in fact polynomials inx andt, however, this property does not hold in general.Communicated by Tom. H. Koornwinder.     

~(13)C-NMR研究溶液法丁苯共聚物的微观序列

本文利用~(13)C-NMR,对“准”稳态下以n-BuLi-THF引发的丁苯共聚物的序列结构进行了研究。获得了THF与n-BuLi在不同比例下产物的数均嵌段长度、混合单体嵌段长度和交替结构的变化情况。     

Solutions rationnelles de certaines équations fonctionnelles

Dans cet article, nous démontrons essentiellement les deux résultats suivants, qui montrent que les solutions séries formelles à coefficients dans de certaines équations fonctionnelles sont rationnelles. Soient tout d'abords un entier naturel non nul, eta _i ,b _i ,(i = 1, , s), 2s nombres complexes, lesa _i étant non nuls. On définit l'ensembleA comme étant l'intersection des parties de , contenant l'origine et stables par toutes les applicationsg _i (x) = a _i x + b _i . On a alors le résultat suivant: Théorème 1.Soient f, R ₁, ,R _s s + 1 fractions rationnelles de (x), régulières à l'origine, et a_i, b_i (i = 1,, s), 2s éléments de . On suppose que les a_i sont non nuls et de module strictement inférieur à un pour tout i = 1,, s. Soit y(x) un élément de [[x]], vérifiant l'équation fonctionnelle

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

氢谱在甾醇类化合物定量和纯度分析中的应用

用^1HNMR谱可定量确定繁茂膜海绵(Hymeniacidon perleve)中分离得到的结构类似的甾醇类化合物的含量，这种方法是对鉴定分析组成复杂而性质很相近的天然甾醇化合物的新思路。     

Alginate Properties and Heavy Metal Biosorption by Marine Algae

The physical properties of the alginate component in four different brown seaweeds (Sargassumfluitans, Ascophyllum nodosum, Fucus vesiculo-sus, andLaminaria japonica) were characterized using potentiometric titration,¹³C-nuclear magnetic resonance (NMR), chemical analysis, and viscosity measurements. The heavy metal binding capacities of the corresponding seaweeds were directly proportional to their respective total carboxyl group content, and related to the electronegativity of the elements investigated (Ca, Zn, Cd, Cu, and Pb). The uronic acid composition or sequence of the alginate component did not affect the metal uptake properties of the biosorbents studied here. However, the alginate leaching owing to its solubilization by Na ions was observed to decrease with increasing intrinsic viscosity of the extracted alginate, related to its molecular weight, and with increasing apparent acidic dissociation constant, related to the alginate density inside the biomass.     

Pulsed field gradient NMR on polybutylcyanoacrylate nanocapsules

The applicability of pulsed field gradient nuclear magnetic resonance spectroscopy to nanocapsule systems is demonstrated on dispersed poly-n-butylcyanoacrylate nanocapsules as a model system. Spectroscopic data are presented that allow for the structural characterization of the inner cavities, the observation of Brownian motion of the capsules and the detection of rapid molecular exchange through the capsule walls. An analytical formula is proposed that yields equilibrium populations and average residence times of a given tracer molecule, thus leading to crucial information regarding the permeability of the capsule walls. Based on these analytical methods, two varieties of nanocapsules are compared that derive from two different preparation procedures. It is found that thinner capsule walls obtained under acidic conditions of the organic phase during interfacial polymerization lead to correspondingly higher exchange rates of benzene as a tracer molecule.     

Synthesis of Gels in the System Na2O-ZrO2-SiO2

Gels have been synthesized in the SiO₂-Na₂O-ZrO₂ system and calcined at various temperatures up to 700°C. They have been studied by infrared absorption spectroscopy. The position of the asymmetric stretching frequency of the SiO₄ unit is used as a tracer of the homogeneity. It is shown that sodium increases the solubility of zirconium in the silica matrix as already observed in fused glasses.