Strong Convergence of Spherical Harmonic Expansions on H1(Sd-1)

Let $\sigma_k^\delta$ denote the Cesaro means of order $\delta > -1$ of the spherical harmonic expansions on the unit sphere $S^{d-1}$, and let $E_j(f, H^1)$ denote the best approximation of $f$ in the Hardy space $H^1(S^{d-1})$ by spherical polynomials of degree at most $j$. It is known that $\lambda:= (d-2)/2$ is the critical index for the summability of the Cesaro means on $H^1(S^{d-1})$. The main result of this paper states that, for $ f\in H^1(S^{d-1})$, $$\sum_{j=0}^N \f 1{j+1} \|\sigma_j^\lambda (f) -f\|_{H^1}\approx \sum_{j=0}^N \f 1{j+1} E_j(f, H^1),$$ where “$\approx$” means that the ratio of both sides lies between two positive constants independent of $f$ and $N$.     

气相色谱法测定眼药水中琥珀酸钠的含量

用气相色谱法测定眼药水中琥珀酸钠的含量。样品减压蒸干后,经酸化使琥珀酸钠变成琥珀酸,加入丙二酸进行衍生化反应,形成琥珀酸丁二酯和丙二酸丁二酯,以DEGS玻璃填充柱为色谱柱,用FID检测,进行气相色谱分析,结果令人满意。     

DNA-modified electrodes (VII)

Two kinds of DNA-modified electrodes were prepared by covalent and adsorptive immobilization of DNA onto self-assembled monolayers of 2, 2’-dithiodiethanol on gold electrodes and characterized by cyclic voltammetry, X-ray photoelectron spectroscopy and scanning tunneling microscopy. The results suggest that the methods are satisfactory for the immobilization of DNA on electrodes. Project supported by the National Natural Science Foundation of China (Grant Nos. 39370213; 39770220; 29773034), State Key Laboratory for Physical Chemistry of Solid Surfaces (Xiamen University), and Natural Science Foundation of Hubei Province (Grant NO. 96J037).     

A new macrolide and glycosides from the stem of Sargentodoxa cuneata

A new macrolide glycoside,cuneataside F was isolated from the n-butanol extract of the stem of Sargentodoxa cuneata. The structure was elucidated on the basis of extensive 1D and 2D NMR as well as HRESI-MS spectroscopic analysis.     

Fractal sets determined by dilation-stable processes

Let be a dilation-stable process on . We determine a Hausdorff measure function (a) such that the fractal set X[0,1]={X(t):0t1} has positive finite -measure. We also investigate the packing measure of X[0,1].     

The reaction of terminal alkynes with PhI(OAc)2: a convenient procedure for the preparation of α-acyloxy ketones

Treatment of terminal alkynes with PhI(OAc)₂ in different acids at 70 °C provided the corresponding α-acyloxy ketones in good to excellent yields. A plausible mechanism has been proposed based on the experimental results.     

An application of Furuta inequality and its best possibility

This paper shows the best possibility for outer exponents of some inequalities under some conditions, and a counter example is obtained.     

Nonlinear inversion of strong scatterer of elastic wave for two parameters in half-space

The inversion of strong scatterer embedded in the half-space is an important problem in engineering and a very difficult nonlinear problem in mathematics, for which the Born iterative method is of no effect. In this paper the moment method is used in the discretization procedure. A numerical approach is presented by employing the regularization technique and DBI (distorted Born iterative) method. The simulation results show that the approach presented is efficient. Project supported by the Research Fund for the Doctoral Program of Higher Education (RFDP: 98048705).     

Study on asymmetric syntheses of steroids: XIII. Synthesis of two new (±)-3-oxa-A-nor steroids 1a and 1b

This paper deals with the synthesis of two new (±)-3-oxa-A-nor steroids 1a and 1 b. The conjugated addition of 5′-methylfurandithane anion 8b to the CD-ring synthon 9 in HMPA-THF afforded 9, 10-seco-3-oxa-A-nor steroid 22. The intramolecular cyclization of 22 in acidic medium gave 23, which underwent hydrolytic desulfurization at elevated temperature in acidic medium to give 1b. The desulfurization of 23 over Raney nickel gave 1a.