Spatial heterogeneity and population risk analysis of cotton bollworm, Helicoverpa armigera, in ChinaKey words spatial characteristics, spatial pattern, semivariance, population management, geostatistics, Helicoverpa armigera, population regulation

In this study, semivariance was used to quantitatively measure the spatial heterogeneity for the egg population of cotton bollworm during a growing season. The typical characteristic parameters of theoretical semivariance models against lag distances were applied to measure components of spatial heterogeneity： trend, range, spatial dependence, and the strength of spatial dependence. Then, kriging interpolation was used to evaluate the population risk of cotton bollworm exceeding economic thresholds. From early June through early September, the population densities were sampled 10 times in the study field. Results showed that the spatial patterns were related to population density. For its low-density population, the spatially heterogeneous trends were usually of spherical shapes; but for highdensity ones, the trends shifted to Gaussian shapes. The spatial dependence appeared at varied distances ranging from 52 meters to 936 meters, and the spatial dependence was in the range of 0.39-288.60, which changed with population densities. While having high heterogeneity, the strength of spatial dependence became much stronger. Results of population risk analysis showed that there was a high risk during its early stages, especially in mid-June. In August, population risk was so low that it did not need to be controlled.

Preliminary Study on Spatial Variability and Distribution of Soil Available Microelements in Pinggu County, Beijing, China

The objectives of this study were to explore the spatial distribution of soil available microelements and to provide a firm foundation for scientifically formulated fertilizer. 1 076 soil samples were collected from Pinggu County of Beijing, China, and the contents of available Cu, Zn, Fe, and Mn in topsoil （0-20 cm） and subsoil （20-40 cm） were analyzed respectively. Descriptive statistics and geostatistics were used to analyze the data. The mean values of topsoil available Cu, Zn, Fe, and Mn were 1.96, 2.51, 17.32, and 10.91 mg kg^-1, respectively, which were at medium or at slightly above medium level. The topsoil content of the soil available microelements was more than that of subsoil. The result of semivariance analysis showed that the topsoil available Fe and Mn were spatially correlated at a larger distance of 21.6 and 45.3 km, and the available Cu and Zn were at a shorter distance of 3.1 and 2.9 km, respectively. The subsoil spatial correlation distances were obviously different from the topsoil, which were in the order of available Mn 〉 Cu 〉 Zn = Fe. The Kriging method was applied to calculate the unobserved points and was used to generate the contour map. The results showed that the structural factors, such as topology, soil types, and soil properties, were the main factors influencing the spatial distribution of topsoil available Fe and Mn. Topsoil available Cu and Zn contents were mainly affected by land use, and their contents in orchard and in vegetable land were greatly higher than in field. The spatial distribution of subsoil microelements was similar to that of the topsoil, which exhibited vertical distribution patterns. Fertilizer and pesticide application resulted in the higher contents of available Cu and Zn in Pinggu County. The higher content of available Zn is potentially harmful to soil environmental quality, which should be inspected.

On Maximal Regularity and Semivariation of α-Times Resolvent Families

Let and A be the generator of an -times resolvent family on a Banach space X. It is shown that the fractional Cauchy problem has maximal regularity on if and only if is of bounded semivariation on .

Geostatistical modelling and mapping of nematode-based soil ecological quality indices in a polluted nature reserve

Nematodes are indicators of soil quality and soil health.Knowledge of the relationships between nematode-based soil quality indices and environmental properties is beneficial for assessing environmental threats on soil biota.This study evaluated the spatial distribution of nematode-based soil quality indices in a 23-ha heavy metal-polluted nature reserve using geostatistical methods.We expected that a selection of abiotic soil properties(pH and moisture,clay,organic matter,cadmium(Cd),and zinc(Zn)contents)could explain a significant portion of the spatial variation of the indices and that regression kriging could more accurately model their spatial distribution than ordinary kriging.A stratified simple random sampling scheme was used to select 80 locations where soil samples were taken to extract nematodes and derive the indices.The area had a distinct gradient in soil properties with Cd and Zn content ranging from 0.07 to 68.9 and 5.3 to 1329 mg kg^(-1),respectively.Linear regression models were fitted to describe the relationships between the indices and soil properties.By also modelling the spatial correlation structure of regression residuals using spherical semivariograms,regression kriging was used to produce maps of the indices.The regression models explained between 21% and 44% of the total original variance in the indices.Soil pH was a significant explanatory variable in almost all cases,while heavy metal conent had a remarkably low effect.In some cases,the regression residuals had spatial structure.Independent validation indicated that in all cases,regression kriging performed slightly better because of having lower values of the root mean square prediction error and a mean prediction error closer to zero than ordinary kriging.This study showed the importance of soil properties in explaining the spatial distribution of biological soil quality indices in ecological risk assessment.

Spatially Adaptive Image Restoration Using Fuzzy Punctual Kriging

We present a general formulation based on punctual kriging and fuzzy concepts for image restoration in spatial domain. Gray-level images degraded with Gaussian white noise have been considered. Based on the pixel local neighborhood, fuzzy logic has been employed intelligently to avoid unnecessary estimation of a pixel. The intensity estimation of the selected pixels is then carried out by employing punctual kriging in conjunction with the method of Lagrange multipliers and estimates of local semi-variances. Application of such a hybrid technique performing both selection and intensity estimation of a pixel demonstrates substantial improvement in the image quality as compared to the adaptive Wiener filter and existing fuzzykriging approaches. It has been found that these filters achieve noise reduction without loss of structural detail information, as indicated by their higher structure similarity indices, peak signal to noise ratios and the new variogram based quality measures.