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Based on a temperature anomaly time series from 16 international exchange stations in Xinjiang from 1957 to 2012, the multi-scale characteristics of temperature variability were analysed using the ensemble empirical mode decomposition (EEMD) method. Regional differences in variation trends and change-points were also preliminarily discussed. The results indicated that in the past 50+ years, the overall temperature in Xinjiang has exhibited a significant nonlinear upward trend, and its changes have clearly exhibited an inter-annual scale (quasi-3 and quasi-6-year) and inter-decadal scale (quasi-10 and quasi-30-year). The variance contribution rates of each component demonstrated that the inter-annual change had a strong influence on the overall temperature change in Xinjiang, and the reconstructed inter-annual variation trend could describe the fluctuation state of the original temperature anomaly during the study period. The reconstructed inter-decadal variability revealed that the climate mode in Xinjiang had a significant transformation before and after 1995, namely the temperature anomaly shift from a negative phase to a positive one. Furthermore, there were regional differences in the nonlinear changes and change-points of temperature. At the same time, the results also suggested that the EEMD method can effectively reveal variations in long-term temperature sequences at different time scales and can be used for the complex diagnosis of nonlinear and non-stationary signal changes.

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In terms of the chaos theory, the phase-spacereconstruction method has been employed to describe the multi-dimensional phase space for the time series of air pollution index (API) during the past 10 years in Lanzhou, northwest China. The mutual information and Cao method were used to determine the reconstruction parameters, and the characteristic quantities including the Lyapunov exponent and the correlation dimension were calculated respectively. As a result, the correlation dimensions were fractioned, and the maximum Lyapunov exponent (k 1 ) [ 0. It shows that these presented the obvious chaotic characteristics that resulted from the evolution of non-linear chaotic dynamic system in the time series of air pollution index over the past 10 years. In the meanwhile, three or even four main dynamic variables were discussed here that could effectively interpret the changes of air pollution index time series and their causes. Some reasonable preventive countermeasures were thus put forward. These findings might provide a scientific basis for probing further into the regional complexity and evolution of the time series of air pollution index.

Based on the observed data from 51 meteorological stations during the period from 1958 to 2012 in Xinjiang, China, we investigated the complexity of temperature dynamics from the temporal and spatial perspectives by using a comprehensive approach including the correlation dimension (CD), classical statistics, and geostatistics. The main conclusions are as follows (1) The integer CD values indicate that the temperature dynamics are a complex and chaotic system, which is sensitive to the initial conditions. (2) The complexity of temperature dynamics decreases along with the increase of temporal scale. To describe the temperature dynamics, at least 3 independent variables are needed at daily scale, whereas at least 2 independent variables are needed at monthly, seasonal, and annual scales. (3) The spatial patterns of CD values at different temporal scales indicate that the complex temperature dynamics are derived from the complex landform.

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Abstract.A variational problem related to the Ginzburg-Landau model of superconductivity with normal impurity inclusion is considered. A standing feature of this problem is the vortex-pinning effect (i.e., the zeros of solutions are attracted to the region occupied by the normal impurities) as some parameters are sufficiently small. Asymptotic behaviors of the solutions of this problem as these parameters tend to zero is studied, and the vortex-pinning effect is proved.