一阶可变号非线性奇异初值问题

获得了一类一阶可变号非线性奇异初值问题的新结果。     

SECOND-ORDER ANALYSIS OF BIVARIATE POINT PATTERNS

Second-order methods of point pattern analysis have only recently received attention from geographers. This paper demonstrates the use of these methods in a spatial analysis of two interrelated categories of objects in a finite region. Two contrasting methods of analyzing the spatial structure of bivariate point data provide insight into the potential of second-order methods. The first is the conventional “within” group analysis that compares a spatial pattern of points to a Poisson random pattern. The second, a “between” groups analysis, allows a distribution-free investigation of locational interdependencies between two categories of points. The map pattern of a sample of commercial investments in Cincinnati illustrates the utility of this approach.     

关于正确处理对流－弥散方程和渗流方程中源汇项的若干问题

对流─弥散方程和渗流基本微分方程中的源汇项，分别是决定含水层中任一内点上水质量和溶质质量时变率的重要因素之一。而关于源汇项不适当的乃至是错误的表述，在文献中却不乏其见，其影响之大是显而易见的．本文深入分析了某些表述的不当或错误之处，给出了正确的处理与表述方法。     

Analytical calculations related to facies simulation

The paper presents calculations related to the volumes of different facies types. Asymptotic distributions are derived approximating the volumes of facies proportions. The number of bodies required to meet net-gross specifications are shown to follow an inverse gaussian distribution. The calculations typically are performed prior to simulations of reservoir facies and may add substantially to the understanding of the model. In particular, analytical results are useful when it comes to assessing parameters of complex simulation models. The theoretical distributions agree well with results based on marked point process simulations of a turbiditic reservoir.     

Stresses due to vertical subsurface loading for an inhomogeneous cross‐anisotropic half‐space

In this article, we present the solutions for the stresses induced by four different loads associated with an axially loaded pile in a continuously inhomogeneous cross‐anisotropic half‐space. The planes of cross‐anisotropy are parallel to the horizontal surface of the half‐space, and the Young's and shear moduli are assumed to vary exponentially with depth. The four loading types are: an embedded point load for an end‐bearing pile, uniform skin friction, linear variation of skin friction, and non‐linear parabolic variation of skin friction for a friction pile. The solutions for the stresses due to the pile load are expressed in terms of the Hankel integral and are obtained from the point load solutions of the same inhomogeneous cross‐anisotropic half‐space which were derived recently by the authors (Int. J. Rock Mech. Min. Sci. 2003; 40 (5):667–685). A numerical procedure is proposed to carry out the integral. For the special case of homogeneous isotropic and cross‐anisotropic half‐space, the stresses predicted by the numerical procedure agree well with the solutions of Geddes and Wang (Geotechnique 1966; 16 (3):231–255; Soils Found. 2003; 43 (5):41–52). An illustrative example is also given to investigate the effect of soil inhomogeneity, the type and degree of soil anisotropy, and the four different loading types on the vertical normal stress. The presented solutions are more realistic in simulating the actual stratum of loading problem in many areas of engineering practice. Copyright © 2004 John Wiley & Sons, Ltd.     

TPS测设道路填挖边线方法探讨

道路建设中,测设填挖线是经常遇到的问题,就此提出了TPS(全站仪)在任意控制点设站、测定辅助点和填挖点的放样方法。该方法的关键之处是,利用曲线要素推算各放样点的坐标,然后在道路施工现场附近选择一视野开阔的控制点安置TPS,一次性放样出全视野内的辅助点和填挖点,并连接填挖点组成填挖边线。为保证各阶削坡的精度,应注意保护各辅助点的平面位置,正确地削出最上阶平台,以控制以下各阶削坡。而以往的放样方法是抬竿法,需要在逐个横断面多次设站,用定向、量距、抬高的方法放样填挖点。这种方法的缺点是:效率低下,作业难度大,累计误差大。显然,用TPS一次设站,放样若干横断面填挖点的方法,提高了施工效率,降低了作业难度,且提高了放样点的精度。