Nonlinear viscoelasticity of polymer melts in different types of flow

The nonlinear viscoelastic properties of a fairly large class of polymeric fluids can be described with the factorable single integral constitutive equation. For this class of fluids, a connection between the rheological behaviour in different flow geometries can be defined if the strain tensor (or the damping function) is expressed as a function of the invariants of a tensor which describes the macroscopic strain, such as the Finger tensor. A number of these expressions, proposed in the literature, are tested on the basis of the measuring data for a low-density polyethylene melt. In the factorable BKZ constitutive equation the strain-energy function must be expressed as a function of the invariants of the Finger tensor. The paper demonstrates that the strain-energy function can be calculated from the simple shear and simple elongation strain measures, if it is assumed to be of the shape proposed by Valanis and Landel. The measuring data for the LDPE melt indicate that the Valanis-Landel hypothesis concerning the shape of the strainenergy function is probably not valid for polymer melts.     

Notes on Convection in a Porous Medium: (i) an Effctive Rayleigh Number for an Anisotropic Layer, (ii) the Malkus Hypothesis and Wavenumber Selection

Studies of convection in a layer of a saturated anisotropic porous medium uniformly heated from below are reviewed. Emphasis is placed on the usefulness of an effective Rayleigh number, defined (for certain boundary conditions) as the square harmonic-mean square root of horizontally-based and vertically-based Rayleigh numbers. The status of the Malkus hypothesis, together with its relationship with observed cell size, is also discussed. A possible explanation is provided for the observed phenomenon that in a porous medium the cell size decreases as the amplitude of convection increases, whereas in a clear fluid the cell size increases.     

概率假设密度滤波的物理空间意义

为了深入理解概率假设密度滤波,本文在Ozgur Erdinc对随机集的物理空间假设的基础上,采用Bayes公式和全概率公式对概率假设密度滤波的迭代过程进行了推导.为有效改善概率假设密度滤波的目标漏检问题提供了理论基础.     

带势估计的概率假设密度滤波的物理空间意义

为了便于人们深入理解带势估计的概率假设密度滤波,本文在Ozgur Erdin对随机集做的物理空间假设的基础上,采用Bayes公式和全概率公式对带势估计的概率假设密度滤波的迭代过程进行了推导.推导过程详细明了,推导结果与文献一致.这为带势估计的概率假设密度滤波在目标跟踪中的应用及性能改进提供了理论基础.     

状态转移下的利率预期与误差学习假说

采用线性回归和状态转移模型讨论利率预期的"误差学习假说"和不同期限利率预测误差之间的关联性,并考虑带有风险溢价时预测误差的作用.分析发现,1年期限的"误差学习假说"在银行间国债市场中是成立的,不同期限的利率预期对预测误差的反应呈现一定的独立性,不同的状态中预测误差和风险溢价对利率预期的影响是不同的,考虑风险溢价有助于提升对利率预期变动的解释.     

完全随机缺失数据下配对试验的Bayes分析

采用Bayes分析方法,对完全随机缺失下配对试验设计数据进行统计分析,给出了参数的Bayes后验概率密度函数及参数的置信区间计算表达式,并对基于Bayes分析的假设检验功效进行了模拟.从模拟结果看,Bayes分析检验功效一致性地高于缺失数据配对删除的t检验方法,特别,在缺失数据相对较多或配对数据相关系数较低时,其表现出更大优势.     

外商直接投资与环境库兹涅茨曲线——基于中国城市数据的空间计量分析

大多数关于环境库兹涅茨曲线的实证研究隐含地假定地区间环境质量彼此独立,这种对空间相关性的忽视可能导致实证结果的偏误。本文利用2007年中国275个地级及以上城市的数据,对纳入FDI和空间相关性的环境库兹涅茨扩展模型进行了实证检验。研究结果发现:环境库兹涅茨倒U型曲线是否存在很大程度上取决于污染指标以及估计方法的选取;FDI并不一定导致城市环境的恶化;空间相关是影响城市环境质量的重要因素,一个城市的污染物排放受到邻近城市的影响。     

Empirical likelihood hypothesis test on mean with inequality constraints

Hypothesis test on the population mean with various inequality constraints is studied in this paper.The empirical likelihood method is applied to construct test statistics.Limiting distributions of the empirical likelihood ratio test statistics are proven to be a weighted mixture of chi-square distributions.Numerical results are presented to show the validity of the proposed method.     

Assessing Markov property in multistate transition models with applications to credit risk modeling

Multistate transition models are increasingly used in credit risk applications as they allow us to quantify the evolution of the process among different states. If the process is Markov, analysis and prediction are substantially simpler, so analysts would like to use these models if they are applicable. In this paper, we develop a procedure for assessing the Markov hypothesis and discuss different ways of implementing the test procedure. One issue when sample size is large is that the statistical test procedures will detect even small deviations from the Markov model when these differences are not of practical interest. To address this problem, we propose an approach to formulate and test the null hypothesis of “weak non‐Markov.” The situation where the transition probabilities are heterogeneous is also examined, and approaches to accommodate this case are indicated. Simulation studies are used extensively to study the properties of the procedures, and two applications are to illustrate the results.     

An abundance of invariant polynomials satisfying the Riemann hypothesis

In 1999, Iwan Duursma defined the zeta function for a linear code as a generating function of its Hamming weight enumerator. It can also be defined for other homogeneous polynomials not corresponding to existing codes. If the homogeneous polynomial is invariant under the MacWilliams transform, then its zeta function satisfies a functional equation and we can formulate an analogue of the Riemann hypothesis. As far as existing codes are concerned, the Riemann hypothesis is believed to be closely related to the extremal property.In this article, we show there are abundant polynomials invariant by the MacWilliams transform which satisfy the Riemann hypothesis. The proof is carried out by explicit construction of such polynomials. To prove the Riemann hypothesis for a certain class of invariant polynomials, we establish an analogue of the Eneström-Kakeya theorem.