Combining the least correlation design, wavelet packet transform and correlation coefficient test to reduce the size of calibration set for NIR quantitative analysis in multi-component systems

The paper focuses on solving a common and important problem of NIR quantitative analysis in multi-component systems: how to significantly reduce the size of the calibration set while not impairing the predictive precision. To cope with the problem orthogonal discrete wavelet packet transform (WPT), the least correlation design and correlation coefficient test (r-test) have been combined together. As three examples, a two-component carbon tetrachloride system with 21 calibration samples, a two-component aqueous system with 21 calibration samples, and a two-component aqueous system with 41 calibration samples have been treated with the proposed strategy, respectively. In comparison with some previous methods based on much more calibration samples, the results out of the strategy showed that the predictive ability was not obviously decreased for the first system while being clearly strengthened for the second one, and the predictive precision out of the third one was even satisfactory enough for most cases of quantitative analysis. In addition, all important factors and parameters related to our strategy are discussed in detail.     

不确定的时间范围下含期权的最优投资决策

不同于以往研究的含期权的最优投资消费决策,研究了不确定的时间范围下含期权的最优投资决策,运用动态规划原理和随机分析的方法,解决对应的最优控制问题,最优策略可通过对应的HJB方程得到,并显式地得到了HARA效用下的最优投资策略及最优财富过程.     

一类非线性中立型脉冲时滞微分方程解的渐近性

该文研究具有正负系数的非线性中立型脉冲时滞微分方程获得了该方程的每一个解当t→∞时趋于一个常数的充分条件.     

Some Exponential Inequalities for Positively Associated Random Variables and Rates of Convergence of the Strong Law of Large Numbers

We present some exponential inequalities for positively associated unbounded random variables. By these inequalities, we obtain the rate of convergence n ^−1/2 β _n log ^3/2 n in which β _n can be particularly taken as (log log n)^1/σ with any σ>2 for the case of geometrically decreasing covariances, which is faster than the corresponding one n ^−1/2(log log n)^1/2log ² n obtained by Xing, Yang, and Liu in J. Inequal. Appl., doi: (2008) for the case mentioned above, and derive the convergence rate n ^−1/2 β _n log ^1/2 n for the above β _n under the given covariance function, which improves the relevant one n ^−1/2(log log n)^1/2log n obtained by Yang and Chen in Sci. China, Ser. A 49(1), 78–85 (2006) for associated uniformly bounded random variables. In addition, some moment inequalities are given to prove the main results, which extend and improve some known results.     

二阶脉冲时滞微分方程的振动性

具有固定脉冲时刻的二阶时滞微分方程的解的振动性条件被建立,结果改进和推广了已有文献的相应结果.     

带强迫项的n阶脉冲微分方程的振动性与渐近性

给出引理,解决了一类带强迫项的n阶脉冲微分方程的非振动解与其各阶导数的符号关系,得到其振动性与渐近性的判别准则,并举例说明准则的有效性.     

Complex dynamics in physical pendulum equation with suspension axis vibrations

The physical pendulum equation with suspension axis vibrations is investigated. By using Melnikov＇s method, we prove the conditions for the existence of chaos under periodic perturbations. By using second-order averaging method and Melinikov＇s method, we give the conditions for the existence of chaos in an averaged system under quasi-periodic perturbations for Ω = nω ＋ εv, n = 1 - 4, where ν is not rational to ω. We are not able to prove the existence of chaos for n = 5 - 15, but show the chaotic behavior for n = 5 by numerical simulation. By numerical simulation we check on our theoretical analysis and further exhibit the complex dynamical behavior, including the bifurcation and reverse bifurcation from period-one to period-two orbits; the onset of chaos, the entire chaotic region without periodic windows, chaotic regions with complex periodic windows or with complex quasi-periodic windows; chaotic behaviors suddenly disappearing, or converting to period-one orbit which means that the system can be stabilized to periodic motion by adjusting bifurcation parameters α, δ, f0 and Ω; and the onset of invariant torus or quasi-periodic behaviors, the entire invariant torus region or quasi-periodic region without periodic window, quasi-periodic behaviors or invariant torus behaviors suddenly disappearing or converting to periodic orbit; and the jumping behaviors which including from period- one orbit to anther period-one orbit, from quasi-periodic set to another quasi-periodic set; and the interleaving occurrence of chaotic behaviors and invariant torus behaviors or quasi-periodic behaviors; and the interior crisis; and the symmetry breaking of period-one orbit; and the different nice chaotic attractors. However, we haven＇t find the cascades of period-doubling bifurcations under the quasi-periodic perturbations and show the differences of dynamical behaviors and technics of research between the periodic perturbations and quasi-periodic perturbations.     

Bifurcations of resonant solutions and chaos in physical pendulum equation with suspension axis vibrations

This paper is a continuation of ＂Complex Dynamics in Physical Pendulum Equation with Suspension Axis Vibrations＂[1].In this paper,we investigate the existence and the bifurcations of resonant solution for ω0：ω：Ω ≈ 1：1：n,1：2：n,1：3：n,2：1：n and 3：1：n by using second-order averaging method,give a criterion for the existence of resonant solution for ω0：ω：Ω ≈ 1：m：n by using Melnikov＇s method and verify the theoretical analysis by numerical simulations.By numerical simulation,we expose some other interesting dynamical behaviors including the entire invariant torus region,the cascade of invariant torus behaviors,the entire chaos region without periodic windows,chaotic region with complex periodic windows,the entire period-one orbits region;the jumping behaviors including invariant torus behaviors converting to period-one orbits,from chaos to invariant torus behaviors or from invariant torus behaviors to chaos,from period-one to chaos,from invariant torus behaviors to another invariant torus behaviors;the interior crisis;and the different nice invariant torus attractors and chaotic attractors.The numerical results show the difference of dynamical behaviors for the physical pendulum equation with suspension axis vibrations between the cases under the three frequencies resonant condition and under the periodic/quasi-periodic perturbations.It exhibits many invariant torus behaviors under the resonant conditions.We find a lot of chaotic behaviors which are different from those under the periodic/quasi-periodic perturbations.However,we did not find the cascades of period-doubling bifurcation.     

SUPER-GEOMETRIC CONVERGENCE OF A SPECTRAL ELEMENT METHOD FOR EIGENVALUE PROBLEMS WITH JUMP COEFFICIENTS

We propose and analyze a C^0 spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise constant coefficients case and verified by numerical tests. Furthermore, the asymptotical equivalence between a Gauss-Lobatto collocation method and a spectral Galerkin method is established for a simplified model.     

基于两类型灾害事件考虑的赈灾物资储备

赈灾物资的储备,既要符合物资的科学储存规律、又要满足物资储备的经济规律.在建立赈灾物资储备一般模型后,按照重复灾害事件和未遂灾害事件两类灾害事件的理论之说,对模型进行修改完善,分别构建未遂灾害事件的赈灾物资储备模型以及重复灾害事件的赈灾物资储备模型.通过实例分析,验证了所建模型的合理性和可行性.