时空数据插值的杨赤中滤波法

时空数据插值是时空数据分析的一项基础性任务,其核心问题在于建模时空自相关结构。当时空数据非平稳、分布稀疏时,现有方法难以准确建模时空自相关结构,直接影响了插值的精度与可靠性。本文基于空间域复合变量理论,采用几何学与统计学相结合的策略对时空自相关结构进行建模,提出了一种基于杨赤中滤波的时空数据插值方法。该方法首先耦合杨赤中滤波与时空积和模型,建立定量描述时空自相关结构的时空基本变化函数;然后,基于时空基本变化函数,构建满足最优线性无偏估计准则的时空数据插值模型。采用模拟数据、2000—2009年我国大陆区域年平均气温与2014年5月—2015年4月北京市日均PM 2.5浓度时空数据集进行试验验证,结果表明:本文方法的时空插值精度明显优于当前的3种代表性时空插值方法,且不需要时空平稳性假设,可以更好地适应分布稀疏的时空数据集。

Effect of Copper and Zinc on Accumulation of Vitamin E in Wheat Embryo-derived Callus

[Objective] The aim was to study the effect of the content of copper and zinc on in medium the vitamin E accumulation in wheat embryo-dreived callus.[Method] The mathematical models were established to describe the growth kinetics and the vitamin E accumulation in wheat embryo callus cells.With the aim of getting the highest accumulation of the secondary metabolite Vitamin E,the optimal combination of copper and zinc in medium was confirmed by testing.[Result] The results showed that the production of vitamin E in B5 medium reached the highest value with 2.0 mg/mL ZnSO4·7H2O and 0.1 mg/mL CuSO4·5H2O.The fitting degrees of kinetic models of vitamin E accumulation and cell growth were 97.53% and 95.60%,respectively,which indicated good nonlinear relationships.[Conclusion] Both copper and zinc could affect the accumulation of vitamin E in wheat germ callus,and Copper showed more prominent effect than Zn.Synergism existed in low copper and zinc concentration,and the inhibitive effect enhanced with the increase of the concentrations.

Spatiotemporal interpolation of precipitation across Xinjiang, China using space-time CoKriging

In various environmental studies, geoscience variables not only have the characteristics of time and space, but also are influenced by other variables. Multivariate spatiotemporal variables can improve the accuracy of spatiotemporal estimation. Taking the monthly mean ground observation data of the period 1960–2013 precipitation in the Xinjiang Uygur Autonomous Region, China, the spatiotemporal distribution from January to December in 2013 was respectively estimated by space-time Kriging and space-time CoKriging. Modeling spatiotemporal direct variograms and a cross variogram was a key step in space-time CoKriging. Taking the monthly mean air relative humidity of the same site at the same time as the covariates, the spatiotemporal direct variograms and the spatiotemporal cross variogram of the monthly mean precipitation for the period 1960–2013 were modeled. The experimental results show that the space-time CoKriging reduces the mean square error by 31.46% compared with the space-time ordinary Kriging. The correlation coefficient between the estimated values and the observed values of the space-time CoKriging is 5.07% higher than the one of the space-time ordinary Kriging. Therefore, a space-time CoKriging interpolation with air humidity as a covariate improves the interpolation accuracy.

On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations

In the paper,we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly.By the approach the various loop algebras of the Lie algebra A_1are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained,respectively.A reduction of the later hierarchy is just right the famous Ablowitz-Ladik hierarchy.Finally,via two different enlarging Lie algebras of the Lie algebra A_1,we derive two resulting differential-difference integrable couplings of the Toda hierarchy,of course,they are all various discrete expanding integrable models of the Toda hierarchy.When the introduced spectral matrices are higher degrees,the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple.

Residual Cusum Test for Parameters Change in ARCH Errors Models with Deterministic Trend

This paper analyzes the problem of testing for parameters change in ARCH errors models with deterministic trend based on residual cusum test. It is shown that the asymptotically limiting distribution of the residual cusum test statistic is still the sup of a standard Brownian bridge under null hypothesis. In order to check this, we carry out a Monte Carlo simulation and examine the return of IBM data. The results from both simulation and real data analysis support our claim. We also can explain this phenomenon from a theoretical viewpoint that the variance in ARCH model in mainly determined by its parameters.