Fermat猜想的两个等价命题

对每个奇素数p,我们提出了关于p的两个命题:(I)不存在正整数m和n,使代数曲线f(y)=y~3-(2m+1)y-2n的三个零点同时为p方有理整数;(I)不存在正整数m,使不定方程x~2+3y~2=4(2m+1)具有三组正整数解x_i,y_i(i=1,2,3),满足x_1=x_2+x_3,x_1~2+x_2~2+x_3~2=6(2m+1)。本文旨在证明(I)及(I)都与关于素数p的Fermat猜想等价。     

Pore characterization of organic-rich Lower Cambrian shales in Qiannan Depression of Guizhou Province,Southwestern China

Nine organic-rich shale samples of Lower Cambrian black shales were collected from a recently drilled well in the Qiannan Depression, Guizhou Province where they are widely distributed with shallower burial depth than in Sichuan Basin, and their geochemistry and pore characterization were investigated. The results show that the Lower Cambrian shales in Qiannan Depression are organic rich with TOC content ranging from 2.81% to 12.9%, thermally overmature with equivalent vitrinite reflectance values in the range of 2.92–3.25%, and clay contents are high and range from 32.4% to 53.2%. The samples have a total helium porosity ranging from 2.46% to 4.13% and total surface area in the range of 9.08–37.19 m²/g. The estimated porosity in organic matters (defined as the ratio of organic pores to the volume of total organic matters) based on the plot of TOC vs helium porosity is about 10% for the Lower Cambrian shales in Qiannan Depression and is far lower than that of the Lower Silurian shales (36%) in and around Sichan Basin. This indicates that either the organic pores in the Lower Cambrian shale samples have been more severely compacted than or they did not develop organic pores as abundantly as the Lower Silurian shales. Our studies also reveal that the micropore volumes determined by Dubinin–Radushkevich (DR) equation is usually overestimated and this overestimation is closely related to the non-micropore surface area of shales (i.e. the surface area of meso- and macro-pores). However, the modified BET equation can remove this overestimation and be conveniently used to evaluate the micropore volumes/surface area and the non-micropore surface areas of micropore-rich shales.     

Ronge-Kutta法在计算复杂构造区域地震波旅行时中的应用

采用Ronge-Kutta射线追踪法对地震勘探中几个典型地质模型的地震波射线路径和旅行时计算的实例和效果进行分析。将Ronge-Kutta射线追踪模拟的结果与程函方程计算的时距曲线结果进行对比,验证了Ronge-Kutta射线追踪法的易实现性和程函方程有限差分旅行时算法的强稳定性,表明Ronge-Kutta射线追踪法在复杂构造区域进行地震射线路径和旅行时计算时能得到较好的模拟效果。     

基于Landsat TM影像不同地表温度反演算法的比较

地表温度是反映地表环境的一个重要参数,精确获取地表温度的方法对研究城市热岛效应、进行生态环境监测评价是必不可少的。利用遥感手段进行地表温度的反演是一种较新颖的方法,相对成熟的反演算法主要有单通道算法、辐射传输方程法及单窗算法。本文以山东省威海市Landsat TM数据为例,分别利用辐射传输方程法和单窗算法进行地表温度反演,通过遥感目视解译的方法提取研究区各类典型地物对应的地表温度,进行统计分析,结果表明,两者反演得到的地表温度具有一致的变化趋势,其中单窗算法中不同典型地物的地表温度整体标准差较小,如建设用地为0.530,起伏波动小,算法精度略优于辐射传输方程法。     

热带风压场平衡特征及其对GRAPES系统中同化预报的影响研究I:平衡特征分析

本文基于GRAPES全球模式的短期预报误差样本,利用赤道波动正规模态研究了热带风、压场平衡特征,并根据这些特征分析了线性平衡方程(LBE)在该区域应用时存在的问题。结果表明:(1)赤道波动能成功解释热带短期预报误差样本的大部分分量,对流层中层为60%~80%,对流层顶和平流层低层为80%以上。(2)在可解释的误差方差中,赤道罗斯贝波(ER)占比仅为30%~55%,其他赤道波动的作用不可忽视。(3)在ER模态基础上引入其他赤道波动会大幅削弱原有风、压场平衡约束,重力惯性波与Kelvin波的作用最为显著。此时,对流层中层位势高度h与u风、v风间的约束接近于零,而平流层低层h-u的平衡特征由Kelvin波主导。(4)LBE主要表达了ER模态下的风、压场平衡特征,与实际情形相比高估了热带风、压场的耦合程度,进一步的改进中需削弱这一虚假平衡,使得热带风、压场分析变得更加独立。     

Angstrom公式参数对ET0的影响及FAO建议值适用性评价

作为计算太阳总辐射(R_s)的主要公式,Angstrom公式参数(a、b)的合理取值是计算参照腾发量(ET₀)的重要前提。针对FAO所提出的a、b建议值(a=0.25、b=0.5)在中国无辐射观测资料地区被大量使用,而其合理性尚未得到系统评价的情况,基于中国104个地面站的观测数据,在逐月时间尺度上,讨论了a、b变化对ET₀的影响,分析了a、b的地区分布规律,评价了FAO建议值所导致的ET₀计算误差,进而阐明了该建议值在中国7个区域的适用性。提出了无辐射资料情况下a、b的地区综合取值方法。主要研究结论是:①参数a、b偏差对ET₀的计算有重要影响,在中国无资料地区采用FAO建议值将导致较大的太阳总辐射(R_s)和ET₀计算误差。②大多数站点,a的率定值较FAO建议值明显偏小,而b的率定值明显偏大。新疆地区和华南地区a、b率定值分布比较集中,而在其它区域比较分散。③FAO建议参数值在东北、西北和新疆3个区域计算ET₀的适用性较好,而在西南和华南两个区域的适用性很差,计算的ET₀偏高较大。④提出的地区综合取值方法,能使R_s和ET₀的计算精度较FAO建议值显著提高。     

Numerical estimation of effective diffusion coefficients for charged porous materials based on micro-scale analyses

In order to describe diffusive transport of solutes through a porous material, estimation of effective diffusion coefficients is required. It has been shown theoretically that in the case of uncharged porous materials the effective diffusion coefficient of solutes is a function of the pore morphology of the material and can be described by the tortuosity (tensor) (Bear, 1988 [1]). Given detailed information of the pore geometry at the micro-scale the tortuosity of different materials can be accurately estimated using homogenization procedures. However, many engineering materials (e.g., clays and shales) are characterized by electrical surface charges on particles of the porous material which strongly affect the (diffusive) transport properties of ions. For these type of materials, estimation of effective diffusion coefficients have been mostly based on phenomenological equations with no link to underlying micro-scale properties of these charged materials although a few recent studies have used alternative methods to obtain the diffusion parameters (Jougnot et al., 2009; Pivonka et al., 2009; Revil and Linde, 2006 2, 3 and 4). In this paper we employ a recently proposed up-scaled Poisson–Nernst–Planck type of equation (PNP) and its micro-scale counterpart to estimate effective ion diffusion coefficients in thin charged membranes. We investigate a variety of different pore geometries together with different surface charges on particles. Here, we show that independent of the charges on particles, a (generalized) tortuosity factor can be identified as function of the pore morphology only using the new PNP model. On the other hand, all electro-static interactions of ions and charges on particles can consistently be captured by the ratio of average concentration to effective intrinsic concentration in the macroscopic PNP equations. Using this formulation allows to consistently take into account electrochemical interactions of ions and charges on particles and so excludes any ambiguity generally encountered in phenomenological equations.     

利用自然γ能谱测井资料确定粘土矿物的含量及其应用

根据粘土矿物含量的图版计算方法,计算了实际井段的粘土矿物含量,分析了高岭石、伊利石和蒙脱石与U、Th、K含量的相关关系,由此分析得到粘土矿物含量与放射性元素含量的多元线性关系,建立了粘土矿物含量计算的回归方程。通过对不同井段以及同一井段不同地层数据建立的回归方程分析,给出了具有代表性的线性回归方程模型。根据一个实际井段粘土矿物的计算,获得粘土矿物含量随深度的变化,其粘土矿物含量计算结果与原测井解释相吻合,同时与岩心分析误差在10%左右。     

水源涵养功能概念的生态和水文视角辨析

水源涵养是评价陆地生态系统服务功能的重要指标,然而学界对水源涵养功能概念和计算方法仍存在诸多争论。这一方面说明水源涵养功能评估具有重要的现实意义,同时也说明其概念的复杂性和模糊性,亟需从生态学和水文学的基本理论出发,厘清水源涵养功能概念的内涵和评估方法,促进科学决策和有效管理。研究水源涵养功能时,生态学家更关注陆地生态系统的蓄水能力（Smax）,而水文学家更关注流域的产流量（Q）,两者均具有合理性,但各有侧重,若不分别辨析,极易造成概念混淆。理论和数据分析表明,蓄水能力和产流量虽然联系紧密,但概念完全不同。陆地生态系统的Smax决定了流域对降水的分配：即蒸散发（绿水）和Q（蓝水）,Smax和Q在降水量一定的情况下往往存在此消彼长的关系。研究发现生态系统的根区蓄水能力（SRmax）是联系绿水和蓝水的核心要素,是水源涵养功能评估的关键变量。大尺度根区蓄水能力主要由气候决定,可借鉴工程水文中设计水库的累积曲线法,根据生态系统用水的生存策略通过气候反演。最后,本文提出3点建议：(1)在实践中分别评估生态系统的绿水和蓝水涵养功能;(2)进一步全面考虑冰川积雪、地下水等多要素的水源涵养功能;(3)...     

LNAPL在二维含水介质中运移规律的研究

为研究LNAPL （轻质非水相液体）污染物在均匀含水介质中的运移规律,本文建立微元模型推导出LNAPL在均匀含水介质中的对流--弥散方程。针对不同的介质模型,对二维对流--弥散方程运用差分法进行数值模拟,求其数值解。分析LNAPL污染物的运移特征,得出在均匀介质和非均匀层状介质中运移规律： LNAPL污染物在含水介质中的运移规律遵循对流--弥散方程,介质的弥散系数是影响LNAPL污染物运移的主要因素。