二阶非线性微分方程解的振动性和渐近性

讨论了二阶非线性常微分方程(α(t)(?)(x)x′)′+q(t)f(x)=r(t)的解的振动性和渐近性.获得了有关该方程的五个新的定理.     

Some remarks on the physical models concerning two different approaches to inference in statistical process control

Summary For technological applications it can be useful to identify some simple physical mechanisms, which, on the basis of the available knowledge of the production process, may suggest the most appropriate approach to statistical control of the random quantities of interest. For this purpose the notion of rupture point is introduced firstly. A rupture point is characterized bym randomly arising out of control states, assumed to be mutually exclusive and stochastically independent. Shewhart's control charts seem to represent the natural statistical tool for controlling a rupture point; however it is shown that they are fully justified only when the hazard rates attached to the causes of failure are constant. Otherwise, typically in the presence of time increasing hazard rates, Shewhart's control charts should be completed by a preventive intervention rule (preventive maintenance). In the second place, the notion of dynamic instability point is introduced, which is specifically characterized by assuming that the random quantity of interest is ruled by a stochastic differential equation with constant coefficients. By discretization, developed according to a possibly new approach, it is shown that the former model reduces to an equation error model, which is among the simplest used in adaptive control, and thus particularly easy to deal with in regard to parameter estimation and the definition of the optimum control rule.     

变质量任意阶非线性非完整系统的相对论性广义Mac-Millan型方程

提出了变质量系统的相对论性万有D’Alembert原理,构造了相对论性广义动能函数,建立了变质量任意阶非线性非完整系统在准坐标下和广义坐标下的相对论性广义Mar-Millan型方程,并得到厂相应的型方程     

悬置线交指型带通滤波器设计

介绍了悬置线交指型带通滤波器的设计原理和方法,利用计算机辅助设计工具进行数值计算,给出了悬置线的电路板尺寸参数,并应用仿真软件对该悬置线交指型带通滤波器进行仿真和优化设计, 通过仿真得到了该滤波器的响应曲线,与实验结果吻合的较好。     

梯玛“求子”仪式中的符号化空间——以剪纸“天门”为中心

梯玛仪式“玩菩萨”中的剪纸、绘画使用了大量的形象性符号,包括剪纸天门、天梯、天钱、纸人纸伞、穿衣儿粑粑、神案等,考察其在堂中各自的位置、数量、用色及形式,从艺术形态学和美术人类学的角度出发,结合梯玛自己的解释和在仪式中的具体作用,同时与其他民族民间同类剪纸做比较,对“玩菩萨”仪式中的图像符号做深入的分析。并以“求子”一节为例,分析符号组成空间,符号在特定的空间情境中产生意义,阐明民间神圣符号在组成仪式空间情境中的作用,研究剪纸、绘画等符号在空间情境中意义的转换,体现出民间艺术、民间思维中象征性的特点。     

BAYESIAN SUBSET SELECTION AND MODEL AVERAGING USING A CENTRED AND DISPERSED PRIOR FOR THE ERROR VARIANCE

This article proposes a new data‐based prior distribution for the error variance in a Gaussian linear regression model, when the model is used for Bayesian variable selection and model averaging. For a given subset of variables in the model, this prior has a mode that is an unbiased estimator of the error variance but is suitably dispersed to make it uninformative relative to the marginal likelihood. The advantage of this empirical Bayes prior for the error variance is that it is centred and dispersed sensibly and avoids the arbitrary specification of hyperparameters. The performance of the new prior is compared to that of a prior proposed previously in the literature using several simulated examples and two loss functions. For each example our paper also reports results for the model that orthogonalizes the predictor variables before performing subset selection. A real example is also investigated. The empirical results suggest that for both the simulated and real data, the performance of the estimators based on the prior proposed in our article compares favourably with that of a prior used previously in the literature.     

一类非线性波动方程的新精确解

利用李群对称方法,通过构造变换不变量,将一类1 1维非线性波动方程化为常微分方程,得到了这一类非线性波动方程的一些新的显式精确解,包括孤子解、三角函数解和椭圆函数周期解。     

HEAVY-TAILED-DISTRIBUTED THRESHOLD STOCHASTIC VOLATILITY MODELS IN FINANCIAL TIME SERIES

To capture mean and variance asymmetries and time‐varying volatility in financial time series, we generalize the threshold stochastic volatility (THSV) model and incorporate a heavy‐tailed error distribution. Unlike existing stochastic volatility models, this model simultaneously accounts for uncertainty in the unobserved threshold value and in the time‐delay parameter. Self‐exciting and exogenous threshold variables are considered to investigate the impact of a number of market news variables on volatility changes. Adopting a Bayesian approach, we use Markov chain Monte Carlo methods to estimate all unknown parameters and latent variables. A simulation experiment demonstrates good estimation performance for reasonable sample sizes. In a study of two international financial market indices, we consider two variants of the generalized THSV model, with US market news as the threshold variable. Finally, we compare models using Bayesian forecasting in a value‐at‐risk (VaR) study. The results show that our proposed model can generate more accurate VaR forecasts than can standard models.     

洋桔梗叶盘高频率不定芽诱导的初步研究

采用正交设计法研究了细胞分裂素ZT,生长素NAA,培养基pH值和光照强度对洋桔梗叶盘不定芽诱导的影响.结果表明,实验的4个因子对洋桔梗叶盘不定芽都具有极显著的诱导作用,最佳培养基和培养条件为:MS ZT 0.5 mg/L NAA 0.01 mg/L,培养基pH值为6.3,光照强度为3000 lx.该处理中每叶盘再生不定芽数平均达9.41个.     

关于丢番图方程x2+by=cz

设s,t满足gcd(s,t)=1,s>t的正整数,a=2st,b=s~2-t~2,c=s~2+t~2。证明了:若c为素数幂且满足下列条件之一:(1)b有因子b_1≡±5(mod8),(2)b≡-1(mod8),(3)5|c。则不定方程x~2+b~y=c~z仅有一组正整数解(x,y,z)=a,2,2。