Chaotic phenomenon and the maximum predictable time scale of observation series of urban hourly water consumption

The chaotic characteristics and maximum predictable time scale of the observation series of hourly water consumption in Hangzhou were investigated using the advanced algorithm presented here is based on the conventional Wolf's algorithm for the largest Lyapunov exponent. For comparison, the largest Lyapunov exponents of water consumption series with one-hour and 24-hour intervals were calculated respectively. The results indicated that chaotic characteristics obviously exist in the hourly water consumption system; and that observation series with 24-hour interval have longer maximum predictable scale than hourly series. These findings could have significant practical application for better prediction of urban hourly water consumption.     

具临界Sobolev指标的奇异椭圆方程在RN上解的存在性

文章克服了无界域上嵌入Hr1(RN)→L2*(RN)的非紧性困难及μ≠0时解的奇性问题,运用没有(PS)c条件的山路引理证明了一类具有临界Sobolev和Hardy指标的椭圆型方程的非平凡解的存在性问题.     

二维正方晶格Ising模型的重整化群计算

用实空间重整化群方法计算二维正方晶格Ising模型，给出临界温度及临界指数。     

Some nonlinear parameters of PP intervals of pulse main peaks

The PP intervals of pulse main peaks from healthy and unhealthy people(arrhythmia) have different nonlinear char-acteristics. In this paper,the extraction of PP intervals of pulse main peaks is achieved by picking up P peaks of pulse wave with wavelet transform. Furthermore,several nonlinear parameters(correlative dimensions,maximum Lyapunov exponents,com-plexity and approximate entropy) of the PP intervals of pulse main peaks extracted from normal and unhealthy pulse signals are calculated,with the results showing that these nonlinear parameters calculated from the main wave interval signals are helpful for analyzing human's health state and diagnosing heart diseases.     

带第一特征值具临界指数的半线性椭圆方程非平凡古典解存在的必要条件等

指出一类带第一特征值λ1的具临界指数的半线性椭圆方程-Δu=λ1u |u|^2^*-2u零边值问题，正、负强解的不存在性及非平凡古典解存在的必要条件．     

贾鲁河水质的变化规律研究

通过对贾鲁河水质化学需氧量(COD)、生化需氧量(BOD)、氨氮、电导率、pH值以及高锰酸盐指数6个参数的的监测和研究,总结了贾鲁河水质近三年的变化规律,为贾鲁河水污染的治理提供了依据.     

e^π与π^e谁大？

本文首先用确界原理给出实指数乘幂的定义,然后指出eπ与πe的含义,最后用导数研究函数单调性的方法,确定出实数eπ＞πe。     

下喷自吸环流反应器内局部混沌特性(英文)

应用确定性混沌分析技术,初步研究了下喷自吸环流反应器内气－液两相流动的时序压力波动的局部混沌特性．结果发现,在本文实验条件下,该反应器内局部最大李雅普诺夫指数值均大于零,并且呈现出与局部分形维数类似的分布规律．这些结果表明,该反应器内的流动行为呈现混沌特性,可以应用诸如局部最大李雅普诺夫指数和局部分形维数等局部非线性特征参数从更深层上揭示多相反应器内的流动特性,例如流区过渡及流动结构等．     

河西地区1960年至2008年潜在蒸发量的时空变化分析

利用FAO Penman-Monteith模型计算出潜在蒸发量,运用数理统计理论和GIS空间分析技术,对河西地区潜在蒸发的时空特征进行了分析,结合Morlet小波分析和Hurst指数预测潜在蒸发变化趋势。结果表明:①河西地区潜在蒸发总体呈波动下降趋势,20世纪60年代～90年代,潜在蒸发为稳定下降期,约2.76mm/年,其中70年代减少率最大,约11.3mm/年;夏季潜在蒸发变化速率最大,约-2.07mm/年,其次为春季和秋季,冬季最小;②河西地区潜在蒸发自西北向东南呈递减趋势,靠近祁连山地区最小;潜在蒸发主要集中在春季和夏季,分别占年潜在蒸发30%和40%,秋季次之,冬季最小;③影响河西地区潜在蒸发的主要因素为风速,而影响春季潜在蒸发的主要因素是气温;④河西地区潜在蒸发存在12年左右的主振荡周期,年潜在蒸发表现出比较强的持续性,即未来趋势与近12年变化趋势的一致,潜在蒸发呈上升趋势。     

Nonlinear dynamic analysis of the whole vehicle on bumpy road

Through the research into the characteristics of 7-DoF high dimensional nonlinear dynamics of a vehicle on bumpy road, the periodic movement and chaotic behavior of the vehicle were found.The methods of nonlinear frequency response analysis, global bifurcation, frequency chart and Poincaré maps were used simultaneously to derive strange super chaotic attractor.According to Lyapunov exponents calculated by Gram-Schmidt method, the unstable region was compartmentalized and the super chaotic characteristic of the nonlinear system was verified.Numerical results by 4-order Runge-Kutta method presented the multiform dynamic behavior of the system.