Minkowski空间中类光增长曲面的几何结构

在三维闵可夫斯基(Minkowski)空间中,以类光曲线做为初始曲线,在曲线上每一点指定增长方向和增长速度,提出类光增长曲面的概念.通过类光曲线的结构函数研究类光增长曲面的几何结构,同时探究由类光螺线作为初始曲线生成的类光增长曲面的结构表达式,并通过具体的实例描述类光增长曲面的生成过程.     

一种求解混合多目标规划问题的功效函数法

逻辑生长函数相对于龚珀兹生长函数具有拐点高和对称性的特点,采用逻辑生长函数形式的功效函数法求解混合多目标规划问题具有形式简单、计算量小、符合实际的优点。证明了用这种方法求出的最优解是有效解。讨论了满意值对有效解的影响。逻辑生长函数还可以应用于多维变量评价的功效系数法中。     

增长曲线模型回归系数线性估计的可容许性

本文讨论增长曲线模型回归系数线性估计的可容许性，给出了常见的三种形式不同的可容许性定义．我们在较特殊的齐次（或非齐次）线性估计类中，证明了这三种容许性的一致性，并且得到了其共同的可容许估计的充要条件．     

带有约束的增长曲线模型中回归系数线性估计的可容许性与泛容许性(英文)

本文研究了参数受约束的增长曲线模型中多元回归系数线性估计的可容许性和泛容许性.利用线性估计类中的八种最优标准和圣函数,得到了在三个等价了类中线性估计可容许以及回归系数线性估计泛容许的充要条件.本文的结论推广了覃红等人的工作.     

增长曲线模型参数的似然比检验

正态假设下增长曲线模型参数的极大似然估计已被广为研究。本文在两类更为广泛的分布族——椭球等高分布族中研究了增长曲线模型参数的极大似然估计问题;并讨论它们与正态假设下其估计的内在联系;导出了一般假设检验的似然比准则;对某些特殊而常见的检验问题,研究了其验检统计量的零分布不变性。     

龚帕兹曲线参数估计方法及应用研究

在现有文献研究的基础上,对龚帕兹曲线参数估计问题又作了进一步研究,给出了求解龚帕兹曲线参数的一种新方法.将最优化方法与回归方法结合在一起,利用最优化理论中的区间搜索和一维搜索得到一系列c值,利用回归方法可求得与其相对应的一系列a和b的值,当c取最优c*时,a和b便得到最优值a*和b*.经示例计算表明,这种求解龚帕兹曲线参数的方法在电力系统负荷预测中具有较高的预测精度.     

Richards模型参数估计及其模型应用

在非线性模型中,Richards模型是一个含有四参数的增长曲线模型,该模型对数据的拟合有较强的适应性,应用较为广泛.但其参数的估计较为复杂,给出简便易行的三种方法,实例应用表明拟合效果很好.     

中国金融发展与经济增长关系及同步性研究:兼对二者关系实证结果矛盾的解释

关于金融发展与经济增长的关系,不同学者的研究结果存在较大矛盾.采用格兰杰因果检验、协整、岭回归、成长曲线、聚类分析综合研究了二者之间的关系,发现银行贷款余额比率及广义货币发行量比率是经济增长的格兰杰原因,但经济增长不是广义货币发行量比率和银行贷款余额比率的格兰杰原因.工商业贷款余额不是经济增长的格兰杰原因,但经济发展对工商业贷款的增长有一定的贡献.广义货币发行量比率和银行贷款余额比率对经济增长都有显著的贡献,前者略大,工商业贷款比率对经济增长有负面影响.银行贷款余额的成长曲线和经济增长是同步的,但是广义货币发行量在改革开放初期滞后于经济增长,近几年又快于经济增长,二者并不同步,主要与中国实行的投资为主的经济发展路径及过度的货币发行量有关.作者认为有3个原因导致不同学者对金融发展与经济增长关系矛盾的结果,一是金融发展的度量方法存在困难;二是短期研究数据难以获得;三是研究方法本身存在的偏误问题.     

微信用户数发展趋势的理论分析与因素探讨

给出Logistic,Gompertz,Usher和Von Bertalanffy 4种增长曲线的拐点、最大加速点和最大减速点的表达式.利用R语言编写程序,结合拟牛顿算法与随机优化算法,对微信月活跃用户数(WMAUs)的发展趋势进行分析与拟合.结果表明,4条曲线的拟合值在最大加速点到最大减速点时间段内基本吻合,但在初期和后期有所差别.Logistic曲线在初期的预测值偏大,而后期偏小,偏差相对较大;Von Bertalanffy曲线的偏差最小,且在饱和值、拐点、最大加速点、最大减速点及拟合优度的估计值方面都优于另外3种曲线;Usher和Gompertz曲线居于Logistic与Von Bertalanffy曲线之间,对后期的预测值有些保守.最后,基于价值理念的观点分析了影响WMAUs变动的主要因素.     

一种估计Logistic模型参数的方法及应用实例

分析了Logistic函数的解析性质,得到了曲线上三个关键点和三个不同的增长阶段,利用差分和最小二乘法,给出了Logistic模型的一种便于使用的参数估计方法．并通过实例,建立Logistic模型对我国城镇居民家庭平均每百户彩色电视机拥有量的增长变化趋势进行了分析和预测．     

Aitken插值在几何作图中的应用

本文利用 Aitken插值 ,介绍一种过已知三点的抛物线的几何作图法 .     

具有二重抛物线解的二次系统

本文给出了具有二重抛物线解的二次系统的一般形状，并与具有并重抛物线解的二次系统相比较，证明了具有二重抛物线解的二次系统也有存在极限环的可能的，而且也是唯一的，但是二重抛物线解却是不可能成为二次系统的分界线不的。     

Forecasting Using Growth Curves—An Adaptive Approach

Growth curves such as the logistic and Gompertz are widely used for forecasting market development. The approach proposed is specifically designed for forecasting, rather than fitting available data—the usual approach with non-linear least squares regression. Two innovations form the foundation for this approach. The growth curves are reformulated from a time basis to an observation basis. This ensures that the available observations and the forecasts form a monotonic series; this is not necessarily true for least squares extrapolations of growth curves. An extension of the Kalman filter, an approach already used with linear forecasting models, is applied to the estimation of the growth curve coefficients. This allows the coefficients the flexibility to change over time if the market environment changes. The extended Kalman filter also proves the information for the generation of confidence intervals about the forecasts. Alternative forecasting approaches, least squares and an adaptive Bass model, suggested by Bretschneider and Mahajan, are used to produce comparative forecasts for a number of different data sets. The approach using the extended Kalman filter is shown to be more robust and almost always more accurate than the alternatives.     

求解非线性方程的抛物线迭代法

利用x2=g(x)进行迭代,从而求出非线性方程f(x)=0的根x*,是继用x=g(x)的简单迭代法的延拓,讨论抛物线迭代法的具体方法和步骤,给出收敛性定理.     

Optimal and efficient designs for Gompertz regression models

Gompertz functions have been widely used in characterizing biological growth curves. In this paper we consider D-optimal designs for Gompertz regression models. For homoscedastic Gompertz regression models with two or three parameters, we prove that D-optimal designs are minimally supported. Considering that minimally supported designs might not be applicable in practice, alternative designs are proposed. Using the D-optimal designs as benchmark designs, these alternative designs are found to be efficient in general.     

FEATURES AND APPLICATIONS OF BERTALANFFY-RICHARDS‘ AND SCHNUTE'S GROWTH EQUATIONS

ABSTRACT. Based on various ranges of the parameter m (or b), the paper analyzes the features and the integral forms of the Schnute and the Bertalanffy-Richards growth equations as well as the two aspects of their special cases (such as Gompertz, logistic and monomolecular models). It is a first attempt to investigate all the corresponding relationships among parameters of the models derived from the Schnute and the Bertalanffy-Richards growth equations. All the models from the two are empirically fitted by different data sets for eucalypt plantations. Unlike earlier papers, the results of this paper show that either of the two growth equations can be considered as a model for estimating forest growth given a parameter range, and both can produce similar growth performances. Some other aspects of the two growth equations are discussed so that the two can be used correctly.     

From a cellular automaton model of tumor–immune interactions to its macroscopic dynamical equation: A drift–diffusion data analysis approach

Several models of tumor growth have been developed from various perspectives and for multiple scales. Due to the complexity of interactions, how the macroscopic dynamics formed by such interactions at the microscopic level is a difficult problem. In this paper, we focus on reconstructing a model from the output of an experimental model. This is carried out by the data analysis approach. We simulate the growth process of tumor with immune competition by using cellular automata technique adapted from previous studies. We employ an analysis of data given by the simulation output to derive an evolution equation of macroscopic dynamics of tumor growth. In a numerical example we show that the dynamics of tumor at stationary state can be described by an Ornstein–Uhlenbeck process. We show further how the result can be linked to the stochastic Gompertz model.     

Singular periodic waves of an integrable equation from short capillary-gravity waves

The effects of parabola singular curves in the integrable nonlinear wave equation are studied by using the bifurcation theory of dynamical system. We find new singular periodic waves for a nonlinear wave equation from short capillary-gravity waves. The new periodic waves possess weaker singularity than the periodic peakon. It is shown that the second derivatives of the new singular periodic wave solutions do not exist in countable number of points but the first derivatives exist. We show that there exist close connection between the new singular periodic waves and parabola singular curve in phase plane of traveling wave system for the first time.     

各阶欺骗概率相等的最优认证码

本文研究各阶欺骗概率相等的、一般阶的最优认证码的构造。利用有限域上高次抛物线、M-序列和线性校验办法分别构造了一类保密最优认证码和两类Cartesian最优认证码。