The Characterization Problem for Isotropic Covariance Functions

Isotropic covariance functions are successfully used to model spatial continuity in a multitude of scientific disciplines. Nevertheless, a satisfactory characterization of the class of permissible isotropic covariance models has been missing. The intention of this note is to review, complete, and extend the existing literature on the problem. As it turns out, a famous conjecture of Schoenberg (1938) holds true: any measurable, isotropic covariance function on ^d (d 2) admits a decomposition as the sum of a pure nugget effect and a continuous covariance function. Moreover, any measurable, isotropic covariance function defined on a ball in ^d can be extended to an isotropic covariance function defined on the entire space ^d .     

Global Secular Dynamics in the Planar Three-Body Problem

We use the global construction which was made in [6, 7] of the secular systems of the planar three-body problem, with regularized double inner collisions. These normal forms describe the slow deformations of the Keplerian ellipses which each of the bodies would describe if it underwent the universal attraction of only one fictitious other body. They are parametrized by the masses and the semi-major axes of the bodies and are completely integrable on a fixed transversally Cantor set of the parameter space. We study this global integrable dynamics reduced by the symmetry of rotation and determine its bifurcation diagram when the semi-major axes ratio is small enough. In particular it is shown that there are some new secular hyperbolic or elliptic singularities, some of which do not belong to the subset of aligned ellipses. The bifurcation diagram may be used to prove the existence of some new families of 2-, 3- or 4-frequency quasiperiodic motions in the planar three-body problem [7], as well as some drift orbits in the planar n-body problem [8].     

Stereological and Other Methods Applied to Rock Joint Size Estimation—Does Crofton''s Theorem Apply?

A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.     

受迫Liénard方程周期解的存在性

对于受迫Liénard方程,利用Sobolev空间范数,给出了周期解的估计,进而利用变分原理、Schauder不动点定理,证明了周期解的存在性。     

水电站进水口高边坡稳定性三维极限分析

某水电站进水口边坡为一典型的顺向坡，岩层发育有数层软弱夹层，施丁开挖时坡脚岩层将被大范围切断，由此产生施工期和蓄水后进水口边坡的稳定问题，并给工程安全带来威胁。采用边坡稳定三维极限(上限)分析方法，对进水口边坡在施工期和运行期的三维抗滑稳定性进行了分析研究。分析表明，进水口边坡在施工期和运行期的稳定性较差，需采取进一步的加固措施。研究结果为工程建设提供了有价值的参考依据。     

核旋分量仪的倾斜对地磁观测值的影响

１９９５年９月后文安台绝对磁测Ｚ分量有一明显下降，经落实这是由地磁分量仪的倾斜引起的，本文主要根据这一变化，分析计算了仪器倾斜可能给观测资料带来的误差，并利用向量合成定理计算了仪器向南，北不同方向倾斜使观测值增大或减小的数值，以此对该台资料进行改正，取得了较好的效果，但应指出，若出２ｎＴ的观测误差范围内，则仪器倾斜必须小于半格。     

开采沉陷中的抽样定理及其应用

根据数字处理中的数学原理，提出了开采沉陷中的抽样定理。以此为基础，导出了地表移动观测站的合理点间距ｒ·其值为Ｈ（５ｔ），获得了以离散的地表移动观测值或预计值，恢复其连续性的地表移动变形值的计算公式。并以计算实例，给出了其计算方法。     

利用热成风适应原理对暖性西南低涡生成机制的再分析

本文采用σ-p混合坐标系,根据非绝热和地形影响下的热成风适应原理,探讨了暖性西南低涡生成的机制。分析表明:正的非热成风涡度是低涡生成的一个重要指标;对流层中低层的暖平流中心,地面的可感加热,低层的暖空气与场面气压p~*的负变压中心配合,或与它的负平流中心相配合,将产生正的非热成风涡度;场面气压的梯度(?)p~*,高低压中心的空间分布(?)~2p~*,场面气压的变压(?)p~*/(?)t和平流(-(?)_h·(?)p_*)等都与垂直运动直接有关。地形还影响热成风适应特征尺度(或变形半径)L~o。在一般条件下,地形和潜热的作用使L_o比不考虑两者作用时的L_o变小,易使L>L_o条件满足,更有利于流场向温度场适应。     

Piezomagnetic fields produced by dislocation sources

Tectonomagnetic modeling based on the linear piezomagnetic effect is reviewed with special attention to dislocation models. Stacey's scheme was the prototype for such modeling, as proposed in his first seismomagnetic calculations in 1964. The linear piezomagnetic law is presented, in which the stress-induced magnetization is expressed as a linear combination of stress components. The Gauss law for magnetic field and the Cauchy-Navier equation for static elastic equilibrium are combined through linear piezomagnetism and the Hooke law to yield the basic equation for piezomagnetic potential. A representation theorem for its solution is given by surface integrals of the displacement and its normal derivative over the strained body.A Green's function method is developed to compute the piezomagnetic field produced by a dislocation surface in an elastic half-space. Volterra's formula for piezomagnetic potential is derived by modifying Stacey's scheme for tectonomagnetic modeling. The Green's functions for the problem are called elementary piezomagnetic potentials, which are defined as potentials produced by elementary dislocations. Special consideration is required to construct the elementary piezomagnetic potentials, because the stress field around a point dislocation has a singularity of orderr ^–3. The integral representing elementary piezomagnetic potentials is not uniformly convergent. Owing to inappropriate convergency, the Green's functions obtained in an earlier study led to a puzzling outcome. Revised Green's functions give consistent results with those obtained so far by numerical integrations. Generally the piezomagnetic field produced by dislocation sources is weak in the case of a homogeneous earth model. Two enhancement effects for piezomagnetic signals are suggested: one due to inhomogeneous magnetization and the other via bore-hole observations.     

Note on the Symmetric Stability of Quasi－Homogeneous and Incompressible Rotating Ocean

The general property of zonally symmetric stability of quasi-homogeneous and incompressible rotating ocean can be determined by a nondimensional parameter Rs which is similar to the Richardson number in Howard’s paper. The results indicate that the rotating effect leads to stabilize the basic flows and the horizontal shear effect leads to destabilize the basic flows. In addition, the most unstable growth rate is obtained and the semicircle and semiellipse theorem about the distributions of the unstable phase velocity are given in this paper.