A survey of numerical methods for stochastic differential equations

The development of numerical methods for stochastic differential equations has intensified over the past decade. The earliest methods were usually heuristic adaptations of deterministic methods, but were found to have limited accuracy regardless of the order of the original scheme. A stochastic counterpart of the Taylor formula now provides a framework for the systematic investigation of numerical methods for stochastic differential equations. It suggests numerical schemes, which involve multiple stochastic integrals, of higher order of convergence. We shall survey the literature on these and on the earlier schemes in this paper. Our discussion will focus on diffusion processes, but we shall also indicate the extensions needed to handle processes with jump components. In particular, we shall classify the schemes according to strong or weak convergence criteria, depending on whether the approximation of the sample paths or of the probability distribution is of main interest.     

Frictional heat generation and seismic radiation in a foam rubber model of earthquakes

Results from a study of stick-slip particle motion at the interface between two stressed foam rubber blocks indicate that normal vibrations and interface separation are an important part of the stick-slip process in foam rubber. The dimension of the dynamic slip pulse is small compared to the dimension of the model (approximately 10 cm vs. 200 cm) consistent with the abrupt-locking slip pulse model ofBrune (1970, 1976), andHeaton (1990). A comparison of frictional heat generation between stable-sliding and stick-slip foam rubber models indicates a linear relation between the temperature increase on the fault surface (for a given distance of slip) and the driving shear force for the stable-sliding model, while for the stick-slip model there is essentially no variation in frictional heat generation with an increase in shear stress. We performed experiments to investigate the ratio of normal motion to shear motion at different levels of normal stress in the stick-slip foam rubber model. Preliminary result indicate that the normal component of the particle motion increases more rapidly with increasing normal stress than the shear component. The phenomenon of interface separation and normal vibrations may thus explain some of the most frustrating problems in earthquake mechanics, e.g., the heat flow paradox, the long-term weakness of major active faults, and anomalousP-wave radiation.     

淮南市区浅层地下水求参公式的建立

根据淮南市区浅层地下水埋深浅，滞后效应小等特点，推导出一套实用的水文参数计算公式，包括：降水入渗补给地下水系数ａ，蒸发极限深度Ｌ，蒸发系数Ｃ，以及浅层地下水的给水度ｕ的计算公式。     

关于部分变元的非常稳定性

本文利用极限方程的方法研究微分方程关于部分变元的多种非常稳定性,讨论了给定方程与其积限方程的非常稳定性的关系。     

铀矿层真实厚度的确定和最佳测井点距

本文讨论了最佳测井点距的选择原理,其最佳值大致为8-12.5cm.并从原理上分析了矿层解释厚度增大的主要原因:根据离散测量值所作的分层解释结果必然导致矿层解释厚度的增大.大量的模型测量结果完全证实了理论分析的正确性,并且还提出了合适的解决办法.     

Development of the instantaneous unit hydrograph using stochastic differential equations

Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement.     

黄原酯棉富集分离—全差示光度法测定痕量银

在5—35％HClO_4介质中,0.1g黄原酯棉可定量吸附500μg Ag,灰化解脱后Ag回收率在99％以上。Ag-金试剂-OP络合物的显色条件是:pH为4.5—6.5,最大吸收波长505nm,摩尔吸光系数1.0×10~5,络合物组成是Ag:金试剂=1:4,Ag量在0—10μg/25ml范围内符合比尔定律。采用全差示分光光度法测定地质样品中的Ag,操作简单快速、灵敏度高、选择性好、测定范围宽.     

反演地层电阻率的单调同伦法

本文从电法测井的数学模型出发,给出了一种反演地层参数的单调同伦法,把非线性方程组的求解转化成常微分方程初值问题的数值求解,从而给出一种大范围收敛的反演方法.最后的数值结果表明,本文给出的算法是十分有效的.     

RAP－10型桩基检测仪放大器频率补偿

本文叙述了ＲＡＰ－１０仪中一种新型的差动放大器。进行了理论分析、模拟计算和实验。结果表明：这种新型的差动放大电路与通用的差动放大电路相比，具有宽带频率补偿作用。是一种宽带差动放大器。关键词