有序聚类投影寻踪模型在郑州市房地产风险评价中的应用

针对目前房地产风险评价标准的片面性,选择5个特征指标作为房地产风险指标体系,并提出应用投影寻踪算法对郑州市2002年到2012年的房地产风险行分类.分析结果表明:方法能克服传统方法和既定标准法的片面性问题,避免了高维空间聚类和人为确定权重问题,为房地产风险的评价提供一种科学准确的新方法.     

中国海洋产业结构时空分异研究

利用偏离-份额分析法,从海洋三次产业和海洋产业部门两个层次对中国沿海地区海洋产业结构时间和空间分异特征进行定量研究.结果表明:中国沿海地区海洋产业结构存在明显的时空分异特征;上海、天津、山东、浙江、广东5省市偏离总量、份额分量、结构分量和竞争力分量都较其他省市优势明显,对全国海洋经济发展的贡献较大;优势海洋产业部门主要分布在山东、广东、浙江、上海4省市.     

滩海地区运移聚集的精细数值模拟和分析

对滩海地区三层油资源运移聚集进行高精度精细平行数值模拟,提出数学模型和精细平行算子分裂隐式迭代格式,设计了并行计算程序,提出了并行计算的信息传递和交替方向网格剖分方法. 并对不同的CPU组合进行并行计算和分析,对滩海地区数值模拟结果和实际情况吻合.对模型问题进行数值分析,得到最佳阶误差估计,成功地解决了这一困难问题．     

Hammerstein型方程的Galerkin—Newton方法

1 引言 关于Hammerstein型方程的数值逼近方法,许多作者做了工作,例如[1]、[2]、[3]、[4]等,他们把无限维空间中的 Hammerstein型方程转化为有限维空间中的非线性 Hammer-stein型方程,在此基础上,[1]、[2]又用Newton型迭代方法对有限维空间中的非线性方程做了进一步地讨论.[5]中把Newton迭代方法与投影方法结合在一起,考虑了Hilbert空间中具有紧性的非线性算子的不动点问题的数值解法.本文把Galerkin有限维逼近方法与Newton迭代方法紧密结合,把无限维Banach空间中一类具有单调型算子的非线性Ham-merstein型方程的求解问题在迭代过程中化为有限维空间中的线性代数方程组求解.并证明了迭代序列超线性收敛于原方程的解,最后举例说明了这一方法的应用.     

海水入侵及防治工程的后效预测

提出了海水入侵及防治工程的后效预测的数学模型,处理三维问题的分裂迎风交替方向格式。对山东省莱州湾地区海水入侵进行数值模拟比较,结果与实测结果完全吻合。对工程的后效预测合理。     

我国劳动力老化对劳动生产率的影响研究

人口老龄化对经济的直接影响体现为劳动力老化对劳动生产率的影响.本文在基于标准C-D生产函数的计量经济模型框架下,采用省级面板数据和固定效应估计方法,深入探究全国以及不同区域劳动力老化对劳动生产率的影响.实证结果显示,我国劳动力老化对劳动生产率有显著的消极影响,且沿海地区劳动力老化对劳动生产率的消极影响比非沿海地区更强烈.要缓解劳动力力老化对劳动生产率的消极影响,可以从以下三个方面入手:首先,稳定低生育水平,适当放宽人口政策;其次,大力发展教育事业,特别是对老年劳动力的教育和培训;第三,合理引导人口流动,实现地区间劳动力年龄结构的优势互补.     

银行项目信贷风险决策分析

利用实物期权的方法对银行项目信贷的期权特性进行了讨论,对项目的收益与风险进行了更为准确的数理分析.为使结论更加准确可靠,并对具体的实例进行了剖析,说明了衍生产品在银行的项目信贷过程中也可以很好地理论指导实践,使银行能够更好地对贷前风险进行有效控制.     

一致风险度量和锥优化分析

一致风险理论的公理系统为风险分析建立了坚实的基础,然而它背后的数学却和凸优化理论思想密切相关,特别是对偶理论. 本文在有限维空间中,利用锥优化的对偶定理给出了一致风险度量的一般表达式的简单证明. 分析了可接受集的概念在一致风险度量中的中心作用,根据锥优化的对偶关系,探索了常用风险度量的性质. 尽管可接受集的大小能够表达风险控制的强弱,但是我们不知道如何定量地表示. 本文提出用相对熵控制风险度量松紧度的方法和意义. 另外,根据一致风险度量的灵活的结构,给出了无套利条件的一种放松,这一结果可用于不完全市场中的期权定价问题.     

基于LBFGS的求解最小闭包球的光滑化方法

考虑在n维空间中求m个球的最小闭包球(the Smallest Enclosing Ball,SEB)问题.首先将SEB问题转化为一个含有函数max(0,z)的等价无约束非光滑凸优化问题,然后利用光滑化技巧和有限内存BFGS方法来求解高维空间中的SEB问题,并分析了方法的收敛性.数值实验结果表明文中给出的算法是有效的.     

有限维逼近无限维总极值的水平值估计方法

变分计算、最优控制、微分对策等常常要求考虑无限维空间中的总极值问题,但实际计算中只能得出有限维空间中的解.本文用有限维逼近无限维的方法来讨论函数空间中的总体最优化问题.用水平值估计和变侧度方法来求得有限维逼近总体最优化问题.对于有约束问题,用不连续精确罚函数法将其转化为无约束问题求解.     

Remarks on integrable systems

The problem of integrability conditions for systems of differential equations is discussed. Darboux’s classical results on the integrability of linear non-autonomous systems with an incomplete set of particular solutions are generalized. Special attention is paid to linear Hamiltonian systems. The paper discusses the general problem of integrability of the systems of autonomous differential equations in an n-dimensional space, which admit the algebra of symmetry fields of dimension ? n. Using a method due to Liouville, this problem is reduced to investigating the integrability conditions for Hamiltonian systems with Hamiltonians linear in the momenta in phase space of dimension that is twice as large. In conclusion, the integrability of an autonomous system in three-dimensional space with two independent non-trivial symmetry fields is proved. It should be emphasized that no additional conditions are imposed on these fields.     

Local optimization of black-box functions with high or infinite-dimensional inputs: application to nuclear safety

Black-box optimization problems when the input space is a high-dimensional space or a function space appear in more and more applications. In this context, the methods available for finite-dimensional data do not apply. The aim is then to propose a general method for optimization involving dimension reduction techniques. Different dimension reduction basis are considered (including data-driven basis). The methodology is illustrated on simulated functional data. The choice of the different parameters, in particular the dimension of the approximation space, is discussed. The method is finally applied to a problem of nuclear safety.     

L~1空间带弱奇异核的第二类Fredholm积分方程解法探究

针对带有弱奇异核的第二类Fredholm积分方程数值解法问题,介绍了两种方法.一种方法是直接用L~1空间中的离散化方法求其数值解;另一种方法是将弱奇异核通过迭代变为连续核,再用L~1空间中的离散化方法求其数值解,且通过对具体算例作图分析,从而得出直接用L~1空间中离散化方法更好.     

Quadratic spline collocation for one-dimensional linear parabolic partial differential equations

New methods for solving general linear parabolic partial differential equations (PDEs) in one space dimension are developed. The methods combine quadratic-spline collocation for the space discretization and classical finite differences, such as Crank-Nicolson, for the time discretization. The main computational requirements of the most efficient method are the solution of one tridiagonal linear system at each time step, while the resulting errors at the gridpoints and midpoints of the space partition are fourth order. The stability and convergence properties of some of the new methods are analyzed for a model problem. Numerical results demonstrate the stability and accuracy of the methods. Adaptive mesh techniques are introduced in the space dimension, and the resulting method is applied to the American put option pricing problem, giving very competitive results.     

On the Problem of Instability in the Dimensions of Spline Spaces over T-Meshes with T-Cycles

The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a basic problem for the theories and applications of splines. However, the problem of determining the dimension of a spline space is difficult since it heavily depends on the geometric properties of the partition. In many cases, the dimension is unstable. In this paper, we study the instability in the dimensions of spline spaces over T-meshes by using the smoothing cofactor-conformality method. The modified dimension formulas of spline spaces over T-meshes with T-cycles are also presented. Moreover, some examples are given to illustrate the instability in the dimensions of the spline spaces over some special meshes.     

On some boundary element methods for the heat equation

Summary The object of this paper is to study some boundary element methods for the heat equation. Two approaches are considered. The first, based on the heat potential, has been studied numerically by previous authors. Here the convergence analysis in one space dimension is presented. In the second approach, the heat equation is first descretized in time and the resulting elliptic problem is put in the boundary formulation. A straight forward implicit method and Crank-Nicolson's method are thus studied. Again convergence in one space dimension is proved.     

Spreading–vanishing dichotomy in a diffusive logistic model with a free boundary, II

We study the diffusive logistic equation with a free boundary in higher space dimensions and heterogeneous environment. Such a model may be used to describe the spreading of a new or invasive species, with the free boundary representing the expanding front. For simplicity, we assume that the environment and the solution are radially symmetric. In the special case of one space dimension and homogeneous environment, this free boundary problem was investigated in Du and Lin (2010) [10]. We prove that the spreading-vanishing dichotomy established in Du and Lin (2010) [10] still holds in the more general and ecologically realistic setting considered here. Moreover, when spreading occurs, we obtain best possible upper and lower bounds for the spreading speed of the expanding front. When the environment is asymptotically homogeneous at infinity, these two bounds coincide. Our results indicate that the asymptotic spreading speed determined by this model does not depend on the spatial dimension.     

Remarks on a weighted energy estimate and its application to nonlinear wave equations in one space dimension

A weighted energy estimate with tangential derivatives on the light cone is applied for the Cauchy problem of semilinear wave equations with the null conditions in one space dimension. The well-posedness and lifespan of the solutions are considered based on the vector field method.     

Unconditionally Stable Splitting Methods for the Shallow Water Equations

The front-tracking method for hyperbolic conservation laws is combined with operator splitting to study the shallow water equations. Furthermore, the method includes adaptive grid refinement in multidimensions and shock tracking in one dimension. The front-tracking method is unconditionally stable, but for practical computations feasible CFL numbers are moderately above unity (typically between 1 and 5). The method resolves shocks sharply and is highly efficient. The numerical technique is applied to four test cases, the first being an expanding bore with rotational symmetry. The second problem addresses the question of describing the time development of two constant water levels separated by a dam that breaks instantaneously. The third problem compares the front-tracking method with an explicit analytic solution of water waves rotating over a parabolic bottom profile. Finally, we study flow over an obstacle in one dimension.     

On complexity of a choice problem of the vector subset with the maximum sum length

The choice problem of the vector subset with the maximum sum length is considered. In the case of fixed space dimension, this problem is polynomially solvable. The NP-completeness of the problem is proved if the space dimension is not fixed.