ON VECTOR VALUED FUNCTION APPROXIMATION USING A PEAK NORM

A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems.

Normative values of pulmonary function testing in Chinese adults

Objectives To compare the difference in pulmonary function between Caucasians and Chinese and assess the best reference values of pulmonary function for Chinese adults.Methods Values for pulmonary function were predicted by tests on 4773 Chinese healthy subjects (male: 2560, female: 2213, aged 15-78 years) in six parts (north, northeast, northwest, east, southwest and south) of China. Prediction equations of the European Community for Steel and Coal (ECSC), other equations for overseas Chinese or for Caucasians were also selected. The regression coefficients of forced vital capacity (FVC), forced expiratory volume in one second (FEV 1), FEV 1/FVC, total lung capacity (TLC) and residual volume (RV) were summarized. Results ECSC predictions were closer to the Chinese ones than other selected equations. Comparison with ECSC predictions showed that on average the values for FVC, FEV 1 were 5.3% smaller in Chinese males and 3.3% smaller in Chinese females, with the maximal differences in south China and the minimal differences in North China. RV and TLC in Chinese were lower than in Caucasians (males 4.8%, 5.5%, respectively; females 8.7% and 6.0%, respectively). Conversion factors were given for adjusting ECSC equations to fit Chinese. Conclusions For predicting values of pulmonary function in Chinese, we suggest to use the equations reported here. Alternatively, ECSC regression equations may be used with appropriate conversion factors.

Optimal L_∞ Estimates for Galerkin Methods for Nonlinear Singular Two-point Boundary Value Problems

In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining full superconvergence uniformly at all nodal points, we introduce local mesh refinements. Then we extend these results to a class of nonlinear problems. Finally, we present some numerical results which confirm our theoretical conclusions.

Minimum Data Set for Assessing Soil Quality in Farmland of Northeast China

Soil quality assessment provides a tool for agriculture managers and policy makers to gain a better understanding of how various agricultural systems affect soil resources. Soil quality of Hailun County, a typical soybean （Glycine max L. Merill） growing area located in Northeast China, was evaluated using soil quality index （SQI） methods. Each SQI was computed using a minimum data set （MDS） selected using principal components analysis （PCA） as a data reduction technique. Eight MDS indicators were selected from 20 physical and chemical soil measurements. The MDS accounted for 74.9% of the total variance in the total data set （TDS）. The SQI values for 88 soil samples were evaluated with linear scoring techniques and various weight methods. The results showed that SQI values correlated well with soybean yield （r = 0.658＊＊） when indicators in MDS were weighted by the regression coefficient computed for each yield and index. Stepwise regression between yield and principal components （PCs） indicated that available boron （AvB）, available phosphorus （AvP）, available potassium （AvK）, available iron （AvFe） and texture were the main factors limiting soybean yield. The method used to select an MDS could not only appropriately assess soil quality but also be used as a powerful tool for soil nutrient diagnosis at the regional level.