无约束最优化的一个算法

无约束最优化是最优化的重要组成部分，一方面它可以用来直接解一些实际问题，另一方面它又是解决其它一些数学问题的工具。本文给出求解无约束最优化的一个算法，该算法简便，且具有二次终结性。证明了算法的全局收敛性，数值结果表明有较快的收敛速度。     

应力奇异问题自适应有限元分析初探

讨论了应力奇异问题的ｈ型自适应分析非收敛性和伪收敛性，并从理论上进行了分析。从工程应用出发，在保证一定计算粘度的前题下，提出了一种避免自适应分析失败的方法。算例验证了其适用性。     

BP网络的改进及模拟退火神经网络在地学中应用

本文针对ＢＰ神经网络收敛速度慢的缺点，提出了改进方案。还引进了模拟退火理论，将模拟退火算法与ＢＰ神经网络计算方法结合，并通过对正弦函数岩性识别及跨孔地震层析成象的试验，证明模拟退火ＢＰ算法是有效的、大范围收敛的。而且，具有良好的收敛速度和很高的精确度。     

非线性最优化问题的一个算法及其收敛性

讨论了具有广泛应用的线性等式、线性不等式及非负约束的非线性最优化问题。以极方向的特殊组合加上修正向量为搜索方向，给出一个具有超线性收敛速度的算法。较以往的算法有明显的优点，具有较好的稳定性和实用性。     

圆内解析函数在闭圆上连续的条件

研究解析函数的边界性质。通过将Ｐｌｅｓｓｎｅｒ定理的可积条件加强为连续，得到了国内解析函数在闭圆上实部连续导致虚部连续的充分必要条件。     

LONG VALID TIME ENERGY PERFECT CONSERVATIVE FIDELITY SPECTRAL SCHEMES OF BAROTROPIC PRIMITIVE EQUATIONS*

In accordance with a new compensation principle of discrete computations,the traditional meteorological global (pseudo-) spectral schemes of barotropic primitive equation (s) are transformed into perfect energy conservative fidelity schemes,thus resolving the problems of both nonlinear computational instability and incomplete energy conservation,and raising the computational efficiency of the traditional schemes.As the numerical tests of the new schemes demonstrate,in solving the problem of energy conservation in operational computations,the new schemes can eliminate the (nonlinear) computational instability and,to some extent even the (nonlinear) computational diverging as found in the traditional schemes,Further contrasts between new and traditional schemes also indicate that,in discrete operational computations,the new scheme in the case of nondivergence is capable of prolonging the valid in-tegral time of the corresponding traditional scheme,and eliminating certain kind of systematical computational "climate drift",meanwhile increasing its computational accuracy and reducing its amount of computation.The working principle of this paper is also applicable to the problem concerning baroclinic primitive equations.     

球壳形磁性层磁异常正反演方法

为了适应卫星磁测资料解释的需要,作者在磁性界面和磁性层磁异常正反演方法研究的基础上,首次提出了球壳形磁性层磁异常正反演理论和方法。 作者首先阐述了垂直磁化球壳型磁性层模型,导出了场垂直分量Z_(λο)的球谐系数正演公式。然后,给出了磁性层上,下层面埋深变化值与磁化强度变化值的球谐系数反演公式。进而导出了迭代反演收敛条件。本文的磁化强度反演方法不同于目前国内外已有的方法,其反演对象是磁化强度变化值△J_(λθ),磁化强度平均值J是必须给定的定解条件。这种反演方法能给出尽可能满足人们解释要求的解,克服了前人反演方法总存在负值的困难。 为了增加球壳形磁性层反演方法的实用性,作者还在类似平面频率城反演方法所作假设的前提下,把这种利用球谐分析理论在全球面导出的方法,严格地推广应用于局部区域。这也是球谐分析理论在局部区域应用的一个实例,在理沦上具有一定的意义。     

Sustainable transpression: An examination of strain and kinematics in deforming zones with migrating boundaries

Most orogenic belts owe their development to oblique convergence and commonly have many orogen-parallel transpressional high-strain zones. To constrain the tectonic history of orogenic belts by structural and fabric analysis of rocks, it is desirable to understand quantitatively the relationship between the boundary conditions and the resulting strain distribution and kinematics in these zones. Most current models for transpression assume homogeneous deformation confined by boundaries that are fixed to material planes. This creates a strain compatibility problem at the margins of the active deforming zone and also requires that the strain rate normal to the zone boundaries increase to implausibly high values soon after the onset of oblique convergence (transpressional motion). The latter contradicts with the observation that transpressional motion can be sustained throughout an orogeny. The assumption that zone boundaries are fixed to material planes is unrealistic. The outstanding problems of current transpressional models are resolved in this paper by allowing the zone boundaries to migrate through the rock material. The consequence of zone boundary migration for the strain field and kinematics within a transpressional high-strain zone is investigated mathematically. The implications of the modeling for fabric interpretation are discussed. The modeling makes general predictions consistent with observed planar and linear fabric patterns in natural transpressional high-strain zones. It predicts that foliations in transpressional high-strain zones are subparallel to the zone boundaries regardless of variation in the imposed boundary conditions. Lineations cluster along the great circle girdle subparallel to the average foliation. The spread of the lineations may vary from point maxima to complete girdles.     

2004年云南秋季强降水位涡诊断分析

利用NCEP格点资料和常规观测资料对2004年云南秋季强降水进行位涡诊断分析，结果表明，干湿位涡均能较好地反映天气系统的演变特征，干位涡能很好地反映滇黔辐合强弱和地面冷空气的移动路径。湿位涡则能反映暖湿气流活动特征。强降水发生期间，中高层强干湿位涡向低层传送，低层负湿位涡向上伸展。对流层中高层的干湿位涡强中心向低层传送方向和强度变化与强降水雨带移动方向及雨强变化一致。此次强降水对流层中层的强干位涡源位于川东，表明该过程与9月2—6日川东大暴雨有关。