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In Bayesian analysis, the Markov Chain Monte Carlo (MCMC) algorithm is an efficient and simple method to compute posteriors. However, the chain may appear to converge while the posterior is improper, which will leads to incorrect statistical inferences. In this paper, we focus on the necessary and sufficient conditions for which improper hierarchical priors can yield proper posteriors in a multivariate linear model. In addition, we carry out a simulation study to illustrate the theoretical results, in which the Gibbs sampling and Metropolis-Hasting sampling are employed to generate the posteriors.     

Forcing operators on MTL‐algebras

We study the forcing operators on MTL‐algebras, an algebraic notion inspired by the Kripke semantics of the monoidal t ‐norm based logic (MTL). At logical level, they provide the notion of the forcing value of an MTL‐formula. We characterize the forcing operators in terms of some MTL‐algebras morphisms. From this result we derive the equality of the forcing value and the truth value of an MTL‐formula (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

多目标最优化恰当有效解的稳定性

主要研究当两种类型的参数扰动时,多目标最优化问题中恰当有效解的稳定性.在点集映射的连续性意义下,分析讨论这种稳定性问题并分别给出引起扰动的两参数u,v所对应的点集映射Q1(u)和Q2(v),同时严格证明了在两个闭凸锥U,V上Q1(u)和Q2(v)的连续性定理.最后,通过附注对其进行补充和改进.     

A reduced‐order extrapolated natural boundary element method based on POD for the 2D hyperbolic equation in unbounded domain

In this article, we primarily focuses to study the order‐reduction for the classical natural boundary element (NBE) method for the two‐dimensional (2D) hyperbolic equation in unbounded domain. To this end, we first build a semi‐discretized format about time for the hyperbolic equation and discuss the existence, stability, and convergence of the time semi‐discretized solutions. We then establish the classical fully discretized NBE format from the time semi‐discretized one and analyze the existence, stability, and convergence of the classical NBE solutions. Next, using proper orthogonal decomposition method, we build a reduced‐order extrapolated NBE (ROENBE) format containing very few unknowns but having adequately high accuracy, and we also discuss the existence, stability, and convergence of the ROENBE solutions. Finally, we use some numerical examples to show that the ROENBE method is far superior to the classical NBE one. It shows that the ROENBE method is reliable and effective for solving the 2D hyperbolic equation with the unbounded domain.     

Structure preserving model order reduction of shallow water equations

In this paper, we present two different approaches for constructing reduced‐order models (ROMs) for the two‐dimensional shallow water equation (SWE). The first one is based on the noncanonical Hamiltonian/Poisson form of the SWE. After integration in time by the fully implicit average vector field method, ROMs are constructed with proper orthogonal decomposition(POD)/discrete empirical interpolation method that preserves the Hamiltonian structure. In the second approach, the SWE as a partial differential equation with quadratic nonlinearity is integrated in time by the linearly implicit Kahan's method, and ROMs are constructed with the tensorial POD that preserves the linear‐quadratic structure of the SWE. We show that in both approaches, the invariants of the SWE such as the energy, enstrophy, mass and circulation are preserved over a long period of time, leading to stable solutions. We conclude by demonstrating the accuracy and the computational efficiency of the reduced solutions by a numerical test problem.     

基于Lorenz映射的混沌系统分支变换预报规律研究

尽管Lorenz系统具有混沌和非周期性质, 但其分支变换是可预报的.本文以强迫Lorenz系统为数学模型, 基于Lorenz映射, 研究了混沌系统分支变换的预报规律, 将原有关于分支开始变换条件和新分支持续时间的两条一般规律扩展到了3条, 并首次分析了系统当前状态达到变换条件所需时间的预报规律, 从而为预报混沌系统非周期演变提供了另一途径.结果表明: 映射尖点位置为分支变换的临界值, 当变量z超过相应临界值时, 系统在当前分支的运动即将结束, 下一循环将跳跃到另一分支运动; 系统在同一分支循环的次数随极值z_max单调减小, z_max 越小, 达到变换条件需循环的次数越多; 系统在新分支持续的时间是先前分支最大极值z_M 的单调增加函数, z_M越大, 持续时间增加的幅度也越大.此外, 外强迫影响着混沌系统分支变换的预报规律, 其不但使正负分支的变换条件出现差异, 且与新分支持续时间的增加速率和达到变换条件所需时间的递减速率密切相关. 关键词： Lorenz映射 分支变换 外强迫 预报规律     

Complete Cohomology for Extriangulated Categories

Let (C,E,s) be an extriangulated category with a proper class ξ of E-triangles.We study complete cohomology of objects in (C,E,s) by applying ξ-projective resolutions and ξ-injective coresolutions constructed in (C,E,s).Vanishing of complete cohomology detects objects with finite ξ-projective dimension and finite ξ-injective dimension.As a consequence,we obtain some criteria for the validity of the Wakamatsu tilting conjecture and give a necessary and sufficient condition for a virtually Gorenstein algebra to be Gorenstein.Moreover,we give a general technique for computing complete cohomology of objects with finite ξ-Gprojective dimension.As an application,the relations between ξ-projective dimension and ξ-Gprojective dimension for objects in (C,E,s) are given.     

关于RC-正则环（英文）

我们利用related单位正则无刻画了正则环的比较结构，进而把文[2]定理中的related单位元推广到了related单位正则无，并给出了RC－正则环的一个局部特征．     

The Necessary Maximality Principle for c. c. c. forcing is equiconsistent with a weakly compact cardinal

The Necessary Maximality Principle for c. c. c. forcing with real parameters is equiconsistent with the existence of a weakly compact cardinal. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uncertainties in measured and modelled asymmetry parameters of mineral dust aerosols

The error caused by the uncertainty in the refractive index in the determination of the asymmetry parameter g is studied for a variety of mineral dust aerosol samples at two different optical wavelengths. Lorenz–Mie computations for spherical model particles are compared with results based on laboratory-measured phase functions in conjunction with a commonly used extrapolation method. The difference between the g-value based on measurements and the g-value based on Lorenz–Mie simulations is generally on the same order of magnitude as the error caused by the uncertainty in the refractive index m. For larger effective radii the error in g related to the use of spherical model particles is even larger than that related to the uncertainty in m. This indicates that the use of spherical model particles can be among the major error sources in the determination of the asymmetry parameter of dust aerosols.