北京市水资源利用建模分析研究

以北京市为例,分别应用无偏灰色GM(1,1)模型和非线性模型对北京市2001年-2010年的用水量进行了建模,利用最优化方法,计算了上述两种模型的最优组合模型,通过三种模型分别计算了北京市2001年-2010年的水资源利用量,并与北京市2001年-2010年的实际用水量进行了对比,采用精度检验方法,分别对无偏灰色模型,非线性模型和组合模型进行了精度检验,计算结果表明,加权组合模型是三种模型中精度最高的模型,通过组合模型计算得出的用水量值与实际水资源利用量相比误差最小,由此得出,可以利用组合模型对北京市未来的水资源利用量进行预测,预测结果可为其他相关研究提供参考.     

短纤维复合材料的本征应变边界积分方程计算模型

提出了短纤维复合材料的本征应变边界积分方程计算模型,并采用新发展的边界点法进行了求解．模型依据Eshelby等效夹杂物的概念并借助Eshelby张量,采用迭代方法来计算基体中各种性能短纤维的本征应变,其中所需的Eshelby张量不难通过解析或数值方法获得．由于未知量只出现在边界上,与已有的有限元和边界元模型相比,提出的计算模型可极大地减小异质体问题的求解规模,提高计算效率．通过数值算例计算了代表性体积单元上各种短纤维复合材料的整体弹性性能,验证了计算模型和求解方法的正确性和有效性．     

Markov调制L′evy模型定价的Fourier-Cos方法

对一般的Markov调制L′evy模型,利用Fourier Cosine级数展开原理得到欧式期权价格的计算方法。进一步,为了改进期权定价的Fourier Cosine级数展开方法的计算精度, Fourier Cosine级数展开的对象进行了修正,获得了欧式期权价格的修正Fourier Cosine级数展开计算方法。此外,还将获得的方法应用于Markov调制Black-Scholes模型, Markov调制Merton跳扩散模型和Markov调制CGMY L′evy模型期权定价的计算。具体的数值计算说明：修正Fourier Cosine级数展开方法应与Fourier Cosine级数展开方法相比,收敛速度要慢一些,但准确性却有很大的提高。特别是对Markov调制纯跳模型,效果更为显著。     

双重孔隙渗流作用井眼围岩损伤力学模型研究

考虑双重介质建立了井眼围岩力学模型,考虑井眼围岩岩体为孔隙、裂缝双重介质,将围岩区域分为破坏区、损伤区和弹性区,建立双重介质渗流作用下的井壁围岩不同区域的损伤力学计算模型和井眼损伤区域的计算方法,计算结果表明理论计算模型与有限元模拟结果吻合较好.     

油藏油水两相流低阶模型算法

目前,油藏数值模拟主要采用的方法如有限元方法、有限容积法等在油藏数值计算时均需要较长的计算时间,很大程度上限制了油藏注采的实时预测与快速动态模拟.该文以一种高效的数据处理方法(最佳正交分解(POD)方法)为基础,对油藏油、水两相流抽取特征函数,并对油藏两相流模型进行Galerkin投影得到新的低阶计算模型.数值计算表明,POD方法所得到的特征向量能量具有最优的特征,能以较少的特征向量捕捉到数学模型中较大的“能量”,因此能最大限度地描述油藏的特征(压力、饱和度),对油藏偏微分方程模型起到较好的降阶作用.结论表明,低阶模型的计算结果与隐压显饱(IMPES)所得计算结果吻合较好,且能节省更多的计算时间,因此能较好地在油藏注采数值模拟中进行历史拟合与仿真计算.     

度量尾部风险的剩余熵模型

本文研究了尾部风险的度量问题.首先从信息熵的角度给出累积剩余熵模型和其计算方法,并将该模型与标准差、VaR等常见尾部风险度量方法比较.结果证明该模型计算简单;不需要假设先验分布形式,而只依赖经验数据.     

随机波动率的美式期权定价

本文利用随机波动率状态有限Markov链,通过有限差分方法计算美式期权的价值.这种方法既避免了建立复杂的随机波动率模型,又较大程度地改进了常数波动率的计算结果,获得与真实结果比较接近数值解,推广了二项式概率树模型.     

Markov调制Lévy模型定价的Fourier-Cos方法

对一般的Markov调制Lévy模型,利用Fourier Cosine级数展开原理得到欧式期权价格的计算方法.进一步,为了改进期权定价的Fourier Cosine级数展开方法的计算精度,Fourier Cosine级数展开的对象进行了修正,获得了欧式期权价格的修正Fourier Cosine级数展开计算方法.此外,还将获得的方法应用于Markov调制Black-Scholes模型,Markov调制Merton跳扩散模型和Markov调制CGMY Lévy模型期权定价的计算.具体的数值计算说明:修正Fourier Cosine级数展开方法应与Fourier Cosine级数展开方法相比,收敛速度要慢一些,但准确性却有很大的提高.特别是对Markov调制纯跳模型,效果更为显著.     

基于DNA链置换与荧光标记的0-1规划问题的计算模型

DNA链置换技术和荧光标记是近年生物计算领域的新兴的方法,并且因为它们都有着操作简单的优势而成为DNA计算的常用方法.DNA自组装算法是以DNA分子作为数据存储和运算的一种新型计算模式.为了提高算法的特异性和检测的灵敏度,在自组装算法的基础上,首次将DNA链置换技术和荧光标记结合引入到自组装模型中,提出了一个解决0-1规划问题的DNA计算新模型.与以往DNA计算模型相比,该模型提高了运算的可靠性和准确性,而且可以逐步缩小解空间,降低运算的复杂度,同时也使检测的方法更加灵活,易于引入到其他自组装算法模型中.     

飞机辅助动力装置引气特性计算方法

作为飞机环控系统与主发动机起动的气源,以目前广泛应用的带负载压气机结构APU(Auxiliary Power Unit)为研究对象,进行引气特性计算模型与计算方法研究。首先介绍了APU结构与引气工作特点,然后分析了建模时喘振控制阀SCV(Surge Control Valve)控制方法与APU共同工作机理,最后采用部件法建立了该类型APU引气计算数学模型。以某型APU为对象进行数值仿真并与实际试车数据比较,计算误差小于3%,表明所采用的建模方法是正确的,所建立的模型能够满足工程需求。      

Methods for the Elimination of Unknowns from Systems of Linear Inequalities and Their Applications

We study methods for the elimination of an unknown or a group of unknowns from systems of linear inequalities. We justify these methods by using the Helly theorem. The methods considered are applied to the calculation of streams in networks with a generalized conservation law.     

Reachability sets of hybrid systems in the presence of successive switchings

The concept of reachability domains of hybrid systems is described together with the use of ellipsoidal methods for calculation of such domains in the case when there are successive switchings on several given hyperplanes or bands. An algorithm for calculation of the reachability sets for a hybrid system that uses ellipsoidal approximations is given for the cases in which the switching sets are planes or bands. The parametrization of nonconvex reachability domains is obtained as a union of intersections of the corresponding ellipsoidal estimates.     

复变函数中由调和函数求解析函数的方法

本文给出了由解析函数的实部或虚部求该解析函数的几个定理,再以例题说明其应用。这些方法及应用,解决了复变函数中这一问题的理论与计算,而且所给方法能广泛进行推广。     

L'intégration graphique des équations différentielles ordinaires

In the period which precedes the appearance of computers, needs in calculation of the scientists and engineers led to an important development of graphic methods of integration. To contribute to the study of this little known phenomenon, the article presents techniques and instruments used for the graphic integration of ordinary differential equations, and looks for their historic origins by going back to the beginning of calculus: processes of geometric calculation by the polygonal method or the method of radius of curvature, use of tractional motion for the conception of integraphs, reduction to graphic quadratures in finite or infinite number.     

Numerical calculation of the frequency of an oscillatory problem

A numerical technique for the calculation of the frequency of an oscillatory problems is shown. This new technique is useful to improve the numerical results obtained when this kind of problems are integrated with special codes, such as Bettis or SMF methods.     

1D gas dynamic modelling of mass conservation in engine duct systems with thermal contact discontinuities

A detailed analysis of mass non-conservation in the proximity of thermal contact discontinuities, when solving 1-D gas dynamic flow equations with finite difference numerical methods, is carried out in this paper. A wide spectrum of finite difference numerical methods has been applied to solve such conditions. Thermal contact discontinuities are very common in current diesel engines due to back-flow in the intake valves during the valve overlap period. Every method has been shown to be incapable of correctly solving the problem raised, displaying (or revealing) a different behavior. Taking as base line these analyses a study regarding mesh size reduction in ducts has been also performed. This solution becomes suitable since it leads to making mass conservation problems disappear. Nevertheless, most extended calculation structure in 1D gas dynamic models is not advised due to the increase of computational effort required. Thus, a new calculation structure for solving governing equations in ducts is suggested. This proposed calculation structure is based on independent time discretisation of every duct according to its CFL stability criterion. Its application to thermal contact discontinuities points out its advantages with regard to computational demand as the calculation time of every duct is adapted to its mesh size.     

粗糙面分形计算理论研究进展

为提出一种工程上适用可靠的粗糙面分形维数计算方法,在分形曲线的维数计算方法(码尺法,盒维法)基础上,先后提出了星积分形曲面的维数计算方法、三角形棱柱表面积法、投影覆盖法、立方体覆盖法、改进的立方体覆盖法、分形的增变量描述法等曲面分形维数理论.鉴于上述方法的共有缺陷——获取三维坐标的激光表面仪器的扫描尺度限制,研究者提出了粗糙面图像维数计算理论,包括二值化图像维数、灰度图像维数、RGB图像维数计算理论.最后,本文展望了分形维数计算理论领域内亟待解决的三大问题.     

蒙特卡罗计算点通量的二次碰撞概率方法和重要抽样方法

1.引言 应用蒙特卡罗方法计算点通量,在粒子输运问题中占有非常重要的地位。首先,是由于点通量的计算问题在实际问题中经常遇到;其次,是由于任何局部通量计算问题均可通过点通量的计算实现;最后,是由于用其他数值方法计算点通量存在一点困难,尤其是对于那些几何以及其他因素复杂的问题更是如此。     

An investigation of stresses in composite shells on the basis of methods of asymptotic synthesis due to various local actions

It is assumed that the shells are infinite or semi-infinitely long. The fundamental differential equations of twodimensional shell theory are employed in order to obtain a solution of the problem. Also, effective methods of an asymptotic synthesis (MAS) are suggested to avoid difficulties in calculations. For these methods various approximate equations are used, which are: Vlasov-Donnell's, of the semi-membrane theory, of the edge effect theory, the bending or planning states. Solutions of the local thermoelastic problem were obtained in the form of Fourier's series along the contour and in the form of Fourier's integral to the axis direction. Convenient expressions for stresses are obtained by using the MAS, which permits us to reduce the calculation to a calculation of the elementary functions and a very rapidly convergent series.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October 1995.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 6, pp. 783–791, November–December, 1995.     

New standards for the solution of geometric calculation problems by using computers

The availability of computers and of software for the geometric tasks of construction, measurement and calculation, as well as the availability of software for numerical and symbolic computation induce new methods for the solution of geometric calculation problems: computer-aided graphical, numerical and algebraic methods of solution. These computer-aided solutions are explained in relation to suitably chosen tools (Mathematica and Cabri Géomètre) and traditional examples.