微分中值问题中辅助函数的构造程式

给出解决微分中值问题时，所需辅助函数的构造程式，并通过实例加以详细解释．所给程式具有一定的可操作性，可帮助学生掌握同类问题解决方案中的规律性．     

一个Grüs型积分不等式的单参数推广

利用Cauchy中值定理给出Pachpatte B G建立的一个Grüss型积分不等式的单参数推广.     

Percentile residual life orders

In this paper we study a family of stochastic orders of random variables defined via the comparison of their percentile residual life functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are also studied. Finally, some applications in reliability theory and finance are described. Copyright © 2010 John Wiley & Sons, Ltd.     

Could one single dichotomous noise cause resonant activation for exit time over potential barrier？

This paper studies the mean first passage time （or exit time, or escape time） over the non-fluctuating potential harrier for a system driven only by a dichotomous noise. It finds that the dichotomous noise can make the particles escape over the potential barrier, in some circumstances; but in other circumstances, it can not. In the case that the particles escape over the potential harrier, a resonant activation phenomenon for the mean first passage time over the potential barrier is obtained.     

Analytic equation of state for solids with multi-exponential potential based on analytic mean field potential approach and applied to the epsilon phase of solid oxygen

The thermodynamic properties of the ε phase of solid oxygen are studied by using the analytic mean field approach （AMFP）. Analytic expressions for the Helmholtz free energy, internal energy and equation of state of solid oxygen have been derived based on the multi-exponential potential. The formulism for the case of double-exponential （DE） model is applied to the ε phase of solid oxygen. Its four potential parameters are determined through fitting the experimental compression data of the ε phase of solid oxygen. Numerical results of the pressure dependence of the volume calculated by using the AMFP are in good agreement with the original experimental data. This suggests that the AMFP is a useful approach to study the thermodynamic properties of the ε phase of solid oxygen. Furthermore, we predict the variation of the volume, lattice parameters and intermolecular distances with pressure, and some thermodynamic quantities versus volume, at several higher temperatures.     

Seasonal variability of cloud optical depth over northwestern China derived from CERES/MODIS satellite measurements

The seasonal variability of cloud optical depth over northwestern China derived from Clouds and the Earth＇s Radiant Energy System （CERES） Single Scanner Footprint （SSF） Aqua Moderate Resolution Imaging Spectroradiometer （MODIS） Edition IB data from July 2002 to June 2004 is presented. The regions of interest are those with Asia monsoon influence, the Tianshan and Qilian Mountains, and the Taklimakan Desert. The results show that the instantaneous measurements presented here are much higher than the previous results derived from International Satellite Cloud Climatology Project （ISCCP） D2 monthly mean data. Generally the measurements of cloud optical depth are the highest in summer and the lowest in winter, however, Taklimakan Desert has the lowest measurements in autumn. The regional variation is quite significant over northwestern China.     

VARIATIONAL PROPERTIES OF THE INTEGRATED MEAN CURVATURES OF TUBES IN SYMMETRIC SPACES

61. IntroductionLet P be a submanifold of an n-dimensional riemannian manifold AI. Expressions fOrthe kth integrated mean curvatures, M^P(t), (i. e. the integral of tho kth mcan curvature,k = 0, 1,' l n -- l), of a tubular hypersurface P of radius t about P, in terms of theRiemann curvature tensor of P. are calculated when AI is Euclidean or a rank one symmetricspace[5'13"1. Moreover, when P is a closed convex hypersurface of thc n-dimensional spaceof constant curvature A', Santal6 has…     

Simple bounds for closed queueing networks

Consider a closed Jackson type network in which each queue has a single exponential server. Assume that N customers are moving among k queues. We establish simple closed form bounds on the network throughput (both lower and upper), which are sharper than those that are currently available. Numerical evaluation indicates that the improvements are significant.     

Integrated squared error of kernel-type estimator of distribution function

Let X ₁ ,...,X _n be a random sample drawn from distribution function F(x) with density function f(x) and suppose we want to estimate X(x). It is already shown that kernel estimator of F(x) is better than usual empirical distribution function in the sense of mean integrated squared error. In this paper we derive integrated squared error of kernel estimator and compare the error with that of the empirical distribution function. It is shown that the superiority of kernel estimators is not necessarily true in the sense of integrated squared error.