观测向量的变换对广义线性模型参数估计的影响

本文一般地考察了观测向量Ｙ用线性变换ＦＹ代替对广义线性模型Ｙ＝Ｘβ＋ε的系数估计的影响，得到了由变换引起的方差增量公式，并由此得到了一个可估子空间，当且仅当其中元素的估计优良性不因观测向量的变化而改变，这一结果推广了文献［１］的结果．     

沪深300股指期货价格发现能力研究

利用沪深300指数及其期货当月主力合约的5分钟高频数据,本文采用Granger因果检验、向量自回归模型、Johansen协整检验及向量误差修正模型,系统分析不同价格趋势下沪深300股指期货的价格发现能力。研究表明:第一,在上涨趋势中期货收益率单方面引起现货收益率变化,现货收益率不是引导期货收益变化的原因;但是,在下跌趋势中现货收益率与期货收益率具有相互引导的Granger因果关系。第二,无论在上涨阶段还是下跌阶段,期货市场都在价格发现能力方面处于主导地位。第三,期货价格与现货价格存在长期均衡关系,当二者短期内偏离均衡时,期货价格引导现货价格向均衡方向调整。     

Earthquake曲线切向量上的范数

本文研究了定义在earthquake曲线切向量上的范数，首先证明了一条earthquake曲线ht上初始切向量的范数等价于earthquake测度σ的Thurston范数．其次证明了当t→∞时，ht的切向量Vt的范数增长渐近等于O(||→||The^Ct||σ||Th)，其中C是正的万有常数，||σ||Th是σ的Thurston范数，而O所代表的常数是渐近万有的，也即当t||σ||Th充分大时它是万有的．此外，附带证明了定义在Zygmund有界函数上的两种交比范数是等价的．     

线性变换对带约束奇异线性模型的条件G—M估计的影响

考虑带约束奇异线性模型Y=Xβ＋ε，Lβ＝0，E（ε）＝0，cov（ε）＝σ~2V，其中V为非负定矩阵，X为任意秩．文章研究了观察向量Y的线性变换对回归系数条件可估函数Sβ的G－M估计的影响，并将条件可估子空间μ（X'L'）划分成Ω＋Ω_＋Ω_2.当μ（S'）Ω时，Sβ的条件G-M估计在模型变化后其优良性不变；当μ（S'）Ω_1时，模型变化后Sβ仍可估，但Sβ的条件G－M估计的方差要变大；当μ（S'）Ω_2时，Sβ不可估．     

二路平衡动态布隆过滤器

针对动态布隆过滤器所表示的集合中由于元素的增加而导致的存储空间增加问题,提出了二路平衡动态布隆过滤器结构及相应的集合元素插入算法.新过滤器按向量组的方式扩充存储空间,新元素的插入是在向量组中查找插入位置,使得组向量中新置为1的位置增加最少.实验结果表明,当向量组中的向量数为2时,新方法比动态布隆过滤器节省5%的存储空间.     

几类图张量乘积的同构因子分解

对任意给定的正整数ｔ，当ｔ能整除图Ｇ的边数时．Ｇ就可分解成ｔ个同构的生成子图，则称Ｇ为可分图．本文证明了路、圈的张量乘积，以及可分图与路、圈的张量乘积仍然是可分图．此外，文中讨论了完全图张量积乘的同构因子分解．     

向量对策理想-Nash平衡点的存在性

本文采用向量优化问题中理想解的概念,定义向量对策理想-Nash平衡点,并证明这一平衡点的存在性．这一结果一方面体现了向量对策Pareto-Nash平衡点和弱Pareto-Nash平衡点的存在性,同时,还给出了特殊的Pareto-Nash平衡点的存在性．     

基于约束总体最小二乘方法的近似消逝理想算法

提出了基于约束总体最小二乘方法的近似消逝理想算法.给定经验点集Xε,该算法输出序理想(O)和多项式集合(g).当(O)中单项的个数等于经验点集Xε的基数时,(g)即为Xε的近似消逝理想基.该算法充分考虑赋值向量的扰动之间的内在联系,因此在关注向量的数值相关性方面,算法优于目前其它同类算法.     

需求随价格变化的具有折扣的易变质物品的库存模型

本文研究了在需求随价格变化及物品易变质的条件下，当供应商给予数量折扣时的库存问题。证明了当供应商给予数量折扣时，零售商的需求量是增大的，并给出了供应商给予数量折扣时零售商的订货量和订货周期的计算方法。对物品变质率和需求价格敏感系数对零售商的订货量、订货周期、出售价格和单位时间利润的影响进行了数值分析，并给出了数值算例。     

复数的模及其性质

复数的模及其性质于鸣（武汉中学）［基本概念］设复数ｚ＝ａ＋ｂｉ（ａ、ｂ∈Ｒ），则定义ｚ的模为，记为．复数的模的几何意义是，复数ｚ在复平面内对应的点Ｚ到原点的距离，即向量ＯＺ的长度．显然．当且仅当ｚ＝０时，特别地，当ｚ为实数时，设ｚ＝ａ，则，与实数绝对...     

Existence and structure of solutions for a class of optimal control systems with discounting arising in economic dynamics

We study the existence and a turnpike property of solutions of a discrete-time control system with discounting and with a compact metric space of states. In our recent work for this discrete-time optimal control system without discounting we establish the turnpike property and show that it is stable under perturbations of an objective function. In the present paper we show that this turnpike property together with its stability also hold for the system with discounting.     

Equilibrium price as a coincidence point of two mappings

The existence of an equilibrium price vector in a nonlinear market model is analyzed. In the model, the demand and supply functions are obtained by maximizing the producer utility and profit, respectively. Sufficient conditions for the existence of an equilibrium price vector and its stability with respect to small perturbations in the model are given. The results are consequences of theorems on the existence and stability of coincidence points in the theory of α-covering mappings.     

Global stabilization in nonlinear discrete systems with time-delay

A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved.     

Convergence of an Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems

The anisotropic perfectly matched layer (APML) defines a continuous vector field outside a rectangle domain and performs the complex coordinate stretching along the vector field. Inspired by [Z. Chen et al., Inverse Probl. Imag., 7, (2013):663--678] and based on the idea of the shortest distance, we propose a new approach to construct the vector field which still allows us to prove the exponential decay of the stretched Green function without the constraint on the thickness of the PML layer. Moreover, by using the reflection argument, we prove the stability of the PML problem in the PML layer and the convergence of the PML method. Numerical experiments are also included.     

Turnpike property and convergence rate for an investment and consumption model

Mathematics and Financial Economics - We discuss the turnpike property for optimal investment and consumption problems. We find there exists a threshold value that determines the turnpike property...     

二层决策问题的灵敏度分析(2)

二层决策系统包含着两个最优化决策问题,其中上层决策问题的目标值是由下层决策的解所隐含地确定的.本文研究了二层决策问题的另一方面的灵敏度分析问题,讨论了上层决策者的价值系数发生变化而二层决策问题的最优解不变所产生的灵敏度分析问题.为了确定二层决策问题价值系数发生变化的范围,首先我们给出了灵敏度分析的基本方法,结合“k th-best”算法我们又给出了灵敏度分析的操作步骤.在所确定的变化范围内,价值系数的变化,不会引起二层决策问题的全局最优解的变化,从而为决策者提供了相对稳定的决策方案.最后我们给出了数值实例,它表明本文所给出的灵敏度分析的方法是正确的.     

Structure of approximate solutions for discrete-time control systems arising in economic dynamics

In this work we study the structure of approximate solutions of an autonomous discrete-time control system with a compact metric space of states X which is a subset of a finite-dimensional Euclidean space. This control system is described by a nonempty closed set Ω⊂X×X which determines a class of admissible trajectories (programs) and by a bounded upper semicontinuous function v:Ω→R¹ which determines an optimality criterion. We are interested in turnpike properties of the approximate solutions which are independent of the length of the interval, for all sufficiently large intervals. Usually, in economic dynamics, the turnpike properties have been studied for systems such that all their good programs converge to a turnpike which was an interior point of Ω. In this paper we establish turnpike results for a large class of control systems for which the turnpike is not necessarily an interior point of Ω.     

一类变价格的物资库存优化模型

本文提出一类变价格的物资库存优化模型，对模型作了近似处理并求解，从而确定最佳订购次数．     

Neighborhood Turnpike Theorem for Continuous-Time Optimization Models

A neighborhood turnpike theorem is proved for continuous-time, infinite-horizon optimization models with positive discounting. Our approach is a primal one and no differentiability assumption is made. The basic hypothesis is a condition of uniform concavity at the point defining the undiscounted steady state. The main novelty here is that we formulate the theorem by taking the undiscounted steady state as the turnpike.     

On the Dynamics of Knowledge-Based Economic Growth

A geometric approach to characterize the solutions of higher-dimensional dynamic optimization problems is applied to a model of knowledge-based economic growth. The characterization reveals a variety of growth patterns, ranging from sustained growth to stagnation. Growth processes exhibit a turnpike property, reaching as rapidly as possible the path along which human and physical capital are equally productive at the margin and evolving along it thereafter. Some growth processes display overshooting behavior and some are sensitive to threshold capital stocks. This work has been supported by the Paul Ivanier Center of Robotics and Production Management, Ben Gurion University of the Negev, Beer Sheva, Israel.