模糊有界变差函数全变差的积分表示与距离导数

定义和讨论了模糊数值函数的距离导数,给出了模糊有界变差函数全变差的积分表示.发现模糊绝对连续函数是几乎处处距离可导的,距离导数的积分等于其原函数的总变差,从而给出了模糊有界变差函数全变差的积分表示.     

A local hermitian RBF meshless numerical method for the solution of multi‐zone problems

The local Hermitian interpolation (LHI) method is a strong‐form meshless numerical technique in which the solution domain is covered by a series of small and heavily overlapping radial basis function (RBF) interpolation systems. Aside from its meshless nature and the ability to work on very large scattered datasets, the main strength of the LHI method lies in the formation of local interpolations, which themselves satisfy both boundary and governing PDE operators, leading to an accurate and stable reconstruction of partial derivatives without the need for artificial upwinding or adaptive stencil selection. In this work, an extension is proposed to the LHI formulation which allows the accurate capture of solution profiles across discontinuities in governing equation parameters. Continuity of solution value and mass flux is enforced between otherwise disconnected interpolation systems, at the location of the discontinuity. In contrast to other local meshless methods, due to the robustness of the Hermite RBF formulation, it is possible to impose both matching conditions simultaneously at the interface nodes. The procedure is demonstrated for 1D and 3D convection–diffusion problems, both steady and unsteady, with discontinuities in various PDE properties. The analytical solution profiles for these problems, which experience discontinuities in their first derivatives, are replicated to a high degree of accuracy. The technique has been developed as a tool for solving flow and transport problems around geological layers, as experienced in groundwater flow problems. The accuracy of the captured solution profiles, in scenarios where the local convective velocities exceed those typically encountered in such Darcy flow problems, suggests that the technique is indeed suitable for modeling discontinuities in porous media properties. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1201–1230, 2011     

Belief functions combination without the assumption of independence of the information sources

This paper considers the problem of combining belief functions obtained from not necessarily independent sources of information. It introduces two combination rules for the situation in which no assumption is made about the dependence of the information sources. These two rules are based on cautious combinations of plausibility and commonality functions, respectively. The paper studies the properties of these rules and their connection with Dempster’s rules of conditioning and combination and the minimum rule of possibility theory.     

严格反馈非线性系统中参数收敛的系统化方法

研究严格反馈非线性系统中参数的收敛性.在适当的持续激励条件下,通过构造一个显式、全局的强Lyapunov函数,给出了系统参数估计收敛于真值的充分条件,且闭环信号全局一致有界,跟踪误差渐近收敛于零.仿真算例验证了设计方案的可行性和有效性.     

带有p-Laplacian算子的高阶微分方程组边值问题多个正解的存在性

利用五个泛函的不动点定理,证明了带有p-Laplacian算子的高阶微分方程组边值问题多组正解的存在性.其中n≥2,Φ_p(s)=|s|~(p~(-2))s,p>1.     

用样条逼近Sobolev函数类W_p~1(R)的逼近误差

作者研究了定义在全实轴上的Sobolev函数类W_p~1(R)的逼近问题.以一次样条函数作为逼近工具,给出了p=1和p=∞时的逼近误差.     

基于区间AHP与粗糙集的决策系统的排序

针对决策系统中属性值以区间数形式给出的多指标决策问题,根据区间层次分析法(IAHP)与粗糙集的特点,提出了一种合理的排序方法.在保持分类能力不变的前提下,利用粗糙集理论中的知识约简方法,删除其中不相关或不重要的知识,结合区间层次分析法计算权重进行有效的排序.最后,给出算例说明了该方法的可行性和有效性.     

A new approach to the exact and approximate anharmonic vibrational partition function of diatomic and polyatomic molecules utilizing Morse and Rosen–Morse oscillators

Exact closed forms of the equilibrium partition functions in terms Jacobi elliptic functions are derived for a particle in a box and Rosen–Morse (Poschl–Teller) oscillator (perfect for modeling bending vibrational modes). An exact form of the equilibrium partition function of Morse oscillator is reported. Three other approximate forms of Morse partition function are presented. Having an exact closed‐form for the vibrational partition function can be very helpful in evaluating thermodynamic state functions, e.g., entropy, internal energy, enthalpy, and heat capacity. Moreover, the herein presented closed forms of the vibrational partition function can be used for obtaining spectroscopic and dynamical information through evaluating the two‐ and four‐point dipole moment time correlation functions in anharmonic media. Finally, a closed exact form of the rotational partition function of a particle on a ring in terms of the first kind of complete elliptic integral is derived. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Kronecker product and a new matrix form of Lagrangian equations with multipliers for constrained multibody systems

The automatic derivation of motion equations is an important problem of multibody system dynamics. Firstly, an overview of the matrix calculus related to Kronecker product of two matrices is presented. A new matrix form of Lagrangian equations with multipliers for constrained multibody systems is then developed to demonstrate the usefulness of Kronecker product of two matrices in the study of dynamics of multibody systems. Finally, the equations of motion of mechanisms are derived using the proposed matrix form of Lagrangian equations as application examples.     

基于层次分析法的隧道综合地质预报优化

隧道综合地质预报是解决隧道施工期地质问题、降低施工风险的一项重要技术手段。鉴于目前综合预报多为简单的数量上的综合,为更加有效地利用综合预报技术,首先归纳地质分析辨识常见不良地质体的方法,通过地质分析法初步判定隧道掌子面前方可能存在的地质异常,并结合层次分析法的基本思路,将影响预报手段的指标量化,即赋予预报方法权重,建立二级综合评价指标体系,研究不同预报方法对特定工程地质条件的适用性,以选择几种最优预报方法。主要研究结论如下:利用地质分析法定性、层次分析法定量的方法优选预报手段,减少了综合超前地质预报中物探手段选择的随意性,并据此建立综合预报体系。最后将该体系应用于紫荆山隧道F2断层的预报中,成功预报了ZK221+960处地下暗河,避免了施工事故的发生,取得了一定的经济效益,证明了通过层次分析法来优化综合预报方法的可行性。