Finitely additive integration and local integration with respect to upper integrals

Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the q_l-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as q_l-integrable f with q(|f|) < ∞, and of q_l-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most finitely additive integration theories.     

Canonical correlation analysis based on information theory

In this article, we propose a new canonical correlation method based on information theory. This method examines potential nonlinear relationships between p×1 vector Y-set and q×1 vector X-set. It finds canonical coefficient vectors a and b by maximizing a more general measure, the mutual information, between a^TX and b^TY. We use a permutation test to determine the pairs of the new canonical correlation variates, which requires no specific distributions for X and Y as long as one can estimate the densities of a^TX and b^TY nonparametrically. Examples illustrating the new method are presented.     

炉液倾动重心近似计算的数学分析

为给转炉设计提供依据,需要计算炉液倾动的重心.利用数学方法将实际问题进行简化,通过分析炉液倾动过程中变量间的相互关系,来确定每个倾动角度对应情况下的液面位置.利用数学中三重积分的有关应用,进一步得出转炉在每个倾动角度为α∈(0,π2)时的重心计算方法及相关结论,在理论上为工程计算重心的方法提供参考.     

Local polynomial fitting under association

We consider the estimation of multivariate regression functions r(x₁,…,x_d) and their partial derivatives up to a total order p1 using high-order local polynomial fitting. The processes {Y_i,X_i} are assumed to be (jointly) associated. Joint asymptotic normality is established for the estimates of the regression function r and all its partial derivatives up to the total order p. Expressions for the bias and variance/covariance matrix (of the asymptotic distribution) are given.     

The influence of temperature gradients on the kinetic boundary layer problem for a condensing droplet

We extend an earlier method for solving kinetic boundary layer problems to the case of particles moving in aspatially inhomogeneous background. The method is developed for a gas mixture containing a supersaturated vapor and a light carrier gas from which a small droplet condenses. The release of heat of condensation causes a temperature difference between droplet and gas in the quasistationary state; the kinetic equation describing the vapor is the stationary Klein-Kramers equation for Brownian particles diffusing in a temperature gradient. By means of an expansion in Burnett functions, this equation is transformed into a set of coupled algebrodifferential equations. By numerical integration we construct fundamental solutions of this equation that are subsequently combined linearly to fulfill appropriate mesoscopic boundary conditions for particles leaving the droplet surface. In view of the intrinsic numerical instability of the system of equations, a novel procedure is developed to remove the admixture of fast growing solutions to the solutions of interest. The procedure is tested for a few model problems and then applied to a slightly simplified condensation problem with parameters corresponding to the condensation of mercury in a background of neon. The effects of thermal gradients and thermodiffusion on the growth rate of the droplet are small (of the order of 1%), but well outside of the margin of error of the method.     

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

The thermodynamic stability of⁴He_4–13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.     

有效需求与通货紧缩的统计关系研究

本文通过对有效需求一物价指数统计模型的研究 ,估计出了有效需求方程 ,并且通过对模型的估计结果分析得出如下结论 :物价指数对有效需求的影响是显著的 :通货紧缩、物价指数持续走低是有效需求不足的主要原因 ,治理通货紧缩应该是解决我国有效需求不足的主要任务。     

Solution of the hyperbolic mild‐slope equation using the finite volume method

A finite volume solver for the 2D depth‐integrated harmonic hyperbolic formulation of the mild‐slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov‐type second‐order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild‐slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality‐free. Copyright © 2003 John Wiley & Sons, Ltd.     

Clustering Effect on the Statistical Estimation Accuracy of Distribution Density

The paper is devoted to statistical nonparametric estimation of multivariate distribution density. The influence of data pre-clustering on the estimation accuracy of multimodal density is analyzed by means of the Monte Carlo method. It is shown that the soft clustering is more advantageous than the hard one. While a moderate increase in the number of clusters also increases the calculation time, it considerably reduces the estimation error.