高斯投影与横墨卡托投影等价性证明

为探寻球面高斯与横墨卡托投影间的内在联系,将墨卡托投影中的圆柱旋转90°,与某一子午线相切,并根据球面三角形定理得到横墨卡托投影的一般表达式;考虑到高斯投影实数型级数展开式不易于进行公式变换,推导出球面高斯投影复变函数表示式;根据复变函数及常用初等函数的定义,从高斯投影复变函数表示出发,经过一系列数学分析过程,给出球面高斯投影与横轴墨卡托投影等价性的严格证明。     

21世纪重庆最大连续5d降水的预估分析

 利用用于IPCC第四次评估报告的全球气候模式产品,验证其对重庆地区最大连续5 d降水（R5d）的模拟能力的基础上,对模拟能力较好的模式进行组合,预估温室气体排放高（A2）、中（A1B)、低（B1）3种情景下未来21世纪重庆地区R5d的变化。与目前（1980-1999年）气候相比,不同情景下21世纪重庆地区R5d均可能增加,尤其是21世纪后期相比21世纪前、中期增加更为显著。     

基于局部投影和边缘检测的自动分层模型

笔者将局部投影算法和边缘检测运用于测井曲线的自动分层。首先将测井时间序列进行相空间重构,在高维相空间中用局部投影算法来分离测井信号中的由非地层因素引起的噪声;再由边缘检测确定出隶属度高的数据点,根据损失函数确定出可能的分界点集,最后用最优分割法实现自动分层。通过对测井时间序列的处理,得到较满意的结果。     

一个地图投影直角坐标变网格差分模式的设计

设计了一个以均匀网格差分模式为基础的变网格差分模式，如证明：如前者满足一定条件并具有质量和能量守恒性质，以及与连续情况一致的动，位能之间的转换关系，则变网格模式也同样具有，而且，把前者改变为后者增加的运算量很小，也非常方便。     

地震特征拾取及其在解释应用中的新进展

本文通过对瞬时振幅、瞬时相应、瞬时频率的应用研究的回顾，进一步论述了对这三种瞬时特征在地震记录分析中，如何利用模式识别技术和引用最新的ＰＰ方法即投影寻踪方法，同时介绍了倾角和方位角在三维 震资料解释中的应用，文中给出了每一种特征的应用实例。     

数学在我国地图学发展中所起的作用

本文系统地论述了我国地图学各个时期数学所起的作用,指出了我国历史上“制图六体”和“计里画方”的数学意义,探讨了数学在地图投影、制图综合和制图专家系统中的推动作用。     

一种用于小体积偏置探测器锥束CT系统的反投影滤波重建算法

在传统的CT系统中,系统的硬件成本和计算量都是非常巨大的.本文深入分析了一种利用偏移放置的面阵探测器的锥束CT系统,在这种系统中X射线束仅仅覆盖被扫描物体的一半体积,投影数据在探测器方向上是截断的,探测器尺寸和投影数据量都减少为传统CT系统的一半.在这种扫描方式下,现有的重建方法是首先利用重排算法获得180度范围内的平行束投影数据,然后再利用滤波反投影(FBP)算法重建出物体的三维图像.但是重排算法不可避免地会引入误差,降低重建图像的空间分辨率.本文提出了一种反投影滤波(BPF)形式的直接反投影重建方法,该方法不需要对投影数据重排,直接反投影滤波重建出最终的图像.因此,该算法在数学上更简洁,计算速度更快,能够更多地保留重建图像的高频信息.最后,数值模拟实验结果验证了该系统和重建算法能够获得高质量的CT图像.     

Basalt magma genesis and fractionation in collision- and extension-related provinces: A comparison between eastern, central and western Anatolia

Experimental studies of synthetic and natural basalt systems suggest that conditions of magma genesis and fractionation depend fundamentally on mantle temperatures and lithospheric stress fields. In general, compressional settings are more conducive to polybaric fractionation than extensional settings and in this regard, the Anatolian magmatic province offers a natural laboratory for comparing near-coeval basalt eruptions as a function of regional tectonics — compressional (collision-related) régimes dominating in eastern Anatolia and extensional tectonics characterizing a western province related to Aegean Sea opening. Projection of Plio-Quaternary basalt normative compositions from the Western Anatolia Extensional Province (WAEP), the Central Anatolian ‘Ova’ Province (CAOP), and Eastern Anatolia Compressional Province (EACP) are projected onto Ol–Ne–Cpx and Pl–Cpx–Ol planes in the simplified basalt system (Ne–Cpx–Ol–Qz), each showing distinctive liquid lines of descent. WAEP basalts are mostly constrained by low-pressure (< 0.5 GPa) cotectics while CAOP and EACP compositions conform to moderate and/or high-pressure (0.8–3.0 GPa) cotectics. Overall, a quasi-linear shift from moderate and/or high-pressure to low-pressure equilibria matches the westward transgression from compressional east Anatolia to the extensional west Anatolian–Aegean region. Comparison of their respective primary (mantle-equilibrated) magmas–simulated by normalizing their compositions to MgO = 15 wt.% (Mg-15)–with parameterized anhydrous and H₂O-undersaturated experimental melts suggests they segregated from spinel- to garnet-lherzolite mantle facies at pressures between c. 2 and 3 GPa (c. 70–100 km depth) under H₂O-undersaturated conditions. Interpolated potential temperatures (T_p) and lithospheric stretching factors (β) range as follows: (1) eastern Anatolian basalts associated with the Arabian foreland show T_p varying between 1250 and 1400 °C (except for the Karacalidag alkali basalts, south of the Bitlis–Zagros fracture zone, for which T_p ranges up to 1450 °C), for β values of 1.2–1.8. T_p values for central Anatolia (e.g. Sivas) range between 1300 and 1375 °C (except for Karapinar, Egrikuyu and Hasandag, which show < 1150 °C), and β values of 1.3–1.4. For western Anatolian basalts, T_p range mostly between 1250 and 1330 °C, except for a single value for Canakkale of 1400 °C and Kula sample showing T_p < 1200 °C, and β values of 1.3–2.0. Variation of these conditions is as great or greater than that between provinces, although there are clearly significant constraints on the inferred polybaric to low-pressure isobaric fractionation régimes. Covariation of total FeO, TiO₂, La/Yb, Ce/Sm, Zr/Y and Zr/Nb reflects small but significant differences in bulk composition and ambient melt fraction while the covariance of Ce/Sm and Sm/Yb is consistent with the segregation of primitive melts at the spinel- to garnet-lherzolite transition.     

参心大地坐标系中的几何量算问题

通过对目前国内外几种典型GIS软件的几何量算模型比较研究，提出距离、面积、周长等在不同条件下适用的几何量算模型。试验分析证明，弦线法与等积投影法对于大范围内距离与面积的量算效果理想，其量算精度与区域大小、纬度有关。     

赤平投影图的数学解析

先对赤平投影成图原理进行分析,在此基础上对投影图作了数学解析,得出构图要素(线、面)在投影图上的等量关系和组合规律,使得用计算机语言来精确表达成为可能,以便于编程求解线与面问题。另外,文中还对其计算机语言表达的相关问题进行了探索,提出了在实现编程求解过程中值得注意的一些问题。