自动综合算子分析及算法库的建立

在分析自动综合过程和自动综合系统构成的基础上，指出了自动综合算子库对自动综合的必要性，并以现有的各种综合算子划分为参考，对自动综合算子进行了重新划分，提出了算子库中的算法集合，以此来建立自动综合算子库。     

复杂系统模糊模式识别动态规划模型研究

将模糊识别集合算子和非结构决策分析方法引入模糊动态规划中,推导出了两种求解复杂系统多目标多阶段决策问题的方法:级别特征值最小法和阶段模糊识别递推法。这两种方法具有不同的递推方程,可以应用于不同的情况,从而形成了模糊模式识别动态规划模型。此模型可以有效地获取和集成决策者的经验知识和偏好。此模型已应用到实践中,并取得良好效果。     

Estimating groundwater recharge rates in the southeastern Holstein region, northern Germany

In the southeastern Holstein region, located to the east of the metropolitan zone of Hamburg, northern Germany, a groundwater investigation program was conducted from 1984 to 2000 by the State Agency for Nature and Environment (Landesamt für Natur und Umwelt, LANU) of Schleswig-Holstein, Germany, with the aim of providing long-term, ecologically acceptable groundwater management plans for the region. The focal point of the investigation comprised the determination of groundwater recharge rates. The investigation method was based on the transfer of available lysimeter results from other regions to comparable regions within the area studied. With the help of lysimeter equations, potential amounts of percolation water were calculated. The groundwater recharge rate was then determined after subtraction of the surface runoff which was calculated for the entire area. All computations were performed with a spreadsheet program. Groundwater recharge rates were calculated for two areas. One consisted of roughly determining groundwater recharge rates for the total region (1,392 km²) of southeastern Holstein. The overall goal of these investigations was to identify potential areas of water exploitation. Areas in which groundwater recharge rates are high and groundwater outflow is low are particularly suited to water exploitation, since inflow rates into deeper aquifers are high. These areas are located on the flanks of the Elbe and Stecknitz River valleys. Subsurface groundwater runoff to these lowlands would be reduced through groundwater withdrawal. However, the resulting decline in shallow groundwater tables would be so small that it would have no detrimental ecological effects. Groundwater recharge rates were also calculated for a 110-km² area in the outskirts of Hamburg (Grosshansdorf model area) which is intensively developed for water supply. These investigations showed that the amount of groundwater recharge is already being withdrawn to a large extent. Approximately 65% of the recharge rate is currently withdrawn by the waterworks in this area, thus making further increases in exploitation rates unjustifiable from an ecological point of view. Electronic Publication     

用切贝谢夫配点法消除地球自振常微分方程组在地心处的奇异性

用切贝谢夫配点法求解地球自振常微分方程组，无需进一步改化即可消除这组方程在地心处的奇异性，并能获得高精度的结果     

不同方案求解非线性化学动力学方程组的比较

在一个简化的气相化学模式的基础上，比较了Ｈｙｂｒｉｄ、ＱＳＳＡ、Ｓｋｌａｒｅｗ三种计算方案求解非线性化学动力学方程组的差异，并引入误差分配和线性组合两种质量守恒技术，分析它们对模拟结果的影响．研究结果表明：不同方案对有机烃类浓度的计算几乎没有影响，但对其它气态物浓度有一定的影响．用ＱＳＳＡ和Ｓｌａｒｅｗ方案预测的结果更为相近，而采用Ｈｙｂｒｉｄ方案得到的气态物浓度的平衡时间略为提前．从计算效率来看，ＱＳＳＡ方案优于其它两种方案，两种质量守恒技术均能改善模拟结果．     

第一类算子方程的吉洪诺夫正则解的收敛性和渐近阶估计

本文对于第一类算子方程当右端近似给定和当算子与右端皆近似分别给定时,讨论如何确定正则参数。并给出吉洪诺夫正则解的收敛性和渐近阶估计。     

Groebner-basis solution of the three-dimensional resection problem (P4P)

The three-dimensional (3-D) resection problem is usually solved by first obtaining the distances connecting the unknown point P{X,Y,Z} to the known points P_i{X_i,Y_i,Z_i}i=1,2,3 through the solution of the three nonlinear Grunert equations and then using the obtained distances to determine the position {X,Y,Z} and the 3-D orientation parameters {,, }. Starting from the work of the German J. A. Grunert (1841), the Grunert equations have been solved in several substitutional steps and the desire as evidenced by several publications has been to reduce these number of steps. Similarly, the 3-D ranging step for position determination which follows the distance determination step involves the solution of three nonlinear ranging (`Bogenschnitt') equations solved in several substitution steps. It is illustrated how the algebraic technique of Groebner basis solves explicitly the nonlinear Grunert distance equations and the nonlinear 3-D ranging (`Bogenschnitt') equations in a single step once the equations have been converted into algebraic (polynomial) form. In particular, the algebraic tool of the Groebner basis provides symbolic solutions to the problem of 3-D resection. The various forward and backward substitution steps inherent in the classical closed-form solutions of the problem are avoided. Similar to the Gauss elimination technique in linear systems of equations, the Groebner basis eliminates several variables in a multivariate system of nonlinear equations in such a manner that the end product normally consists of a univariate polynomial whose roots can be determined by existing programs e.g. by using the roots command in Matlab.Acknowledgments.The first author wishes to acknowledge the support of JSPS (Japan Society of Promotion of Science) for the financial support that enabled the completion of the write-up of the paper at Kyoto University, Japan. The author is further grateful for the warm welcome and the good working atmosphere provided by his hosts Professors S. Takemoto and Y. Fukuda of the Department of Geophysics, Graduate School of Science, Kyoto University, Japan.     

Ground water contaminant transport by nondivergence-free, unsteady and nonstationary velocity fields

Pore flow velocity is assumed to be a nondivergence-free, unsteady, and nonstationary random function of space and time for ground water contaminant transport in a heterogeneous medium. The laboratory-scale stochastic contaminant transport equation is up scaled to field scale by taking the ensemble average of the equation by using the cumulant expansion method. A new velocity correction, which is a function of mean pore flow velocity divergence, is obtained due to strict second order cumulant expansion (without omitting any term after the expansion). The field scale transport equations under the divergence-free pore flow velocity field assumption are also derived by simplifying the nondivergence-free field scale equation. The significance of the new velocity correction term is investigated on a two dimensional transport problem driven by a density dependent flow.     

起伏地表条件下地震波场数值模拟有限积分变换有限差分方法

针对起伏地表条件下的地震波数值模拟问题,提出将起伏的地表映射到一个规则的长方形网格坐标系中,并在此基础上推导出变换域中的波动方程。根据导出来的波动方程应用有限余弦变换有限差分方法进行地震波场的数值模拟,以解决起伏地表条件下的数值模拟。     

The solution of the Korn–Lichtenstein equations of conformal mapping: the direct generation of ellipsoidal Gauß–Krüger conformal coordinates or the Transverse Mercator Projection

The differential equations which generate a general conformal mapping of a two-dimensional Riemann manifold found by Korn and Lichtenstein are reviewed. The Korn–Lichtenstein equations subject to the integrability conditions of type vectorial Laplace–Beltrami equations are solved for the geometry of an ellipsoid of revolution (International Reference Ellipsoid), specifically in the function space of bivariate polynomials in terms of surface normal ellipsoidal longitude and ellipsoidal latitude. The related coefficient constraints are collected in two corollaries. We present the constraints to the general solution of the Korn–Lichtenstein equations which directly generates Gau?–Krüger conformal coordinates as well as the Universal Transverse Mercator Projection (UTM) avoiding any intermediate isometric coordinate representation. Namely, the equidistant mapping of a meridian of reference generates the constraints in question. Finally, the detailed computation of the solution is given in terms of bivariate polynomials up to degree five with coefficients listed in closed form. Received: 3 June 1997 / Accepted: 17 November 1997