A COMMENT ON THE PROOF OF FERMAT'S LAST THEOREM

I.IntroductionItiswell-knownthatFermat'sLastTheoremll'2'31:"TheequationX" yn=Z"(l.1)hasnosolutioninpositiveintegersx,.1',:whicharealldifferentfrom0foranarbitrarynumbern>2"isahardmathematicalproblem,proposedbyFrenchmathematicianPierredeFermatinabout1637.Sincethenmorethan300yearspast,manyfamousmathematicianshavemadegreatcontributionsintheresearchesanddevelopmentsinthenumbertheoryofalgebraaswellasothermathematicalbranchestolookouttheproofoftheproblematthemoment,buttilefinalproofhasonlybeenobt…     

The Influence of Moduli Slope of a Linearly Graded Matrix on the Bulk Moduli of Some Particle- and Fiber-Reinforced Composites

The stored energy functional of a homogeneous isotropic elastic body is invariant with respect to translation and rotation of a reference configuration. One can use Noether's Theorem to derive the conservation laws corresponding to these invariant transformations. These conservation laws provide an alternative way of formulating the system of equations governing equilibrium of a homogeneous isotropic body. The resulting system is mathematically identical to the system of equilibrium equations and constitutive relations, generally, of another material. This implies that each solution of the system of equilibrium equations gives rise to another solution, which describes the reciprocal deformation and solves the system of equilibrium equations of another material. In this paper we derive conservation laws and prove the theorem on conjugate solutions for two models of elastic homogeneous isotropic bodies – the model of a simple material and the model of a material with couple stress (Cosserat continuum). This revised version was published online in August 2006 with corrections to the Cover Date.     

利用REDUCE语言识别结构系统的支承刚度

本文提出一种识别结构系统支承刚度的新方法，该方法以传递矩阵法为基础，利用ＲＥＤＵＣＥ计算机代数语言推导以刚度参数为未知数的非线性方程组，进而解此方程组识别结构系统的支承刚度。模态试验及计算实例验证了该方法的有效性和正确性。     

双参数地基板振动的中值定理

本文提出并证明了双参数地其板振动的中值定理。Ｇｐ＝０，Ｇｐ＝ｋ＝０就分别得到Ｗｉｎｋｌｅｒ地基板和一般弹性薄板振动的中值定理。如果ω＝０，ω＝Ｇｐ＝０，ωＧｐ＝ｋ＝０就分别得到双参数地基板，Ｗｉｎｋｌｅｒ地基板和一般弹性薄板的中值定理。     

宁夏山区建设中的岩土工程问题

近年来 ,随着工业和旅游业的发展 ,在宁夏 ,特别是宁南低山黄土丘陵区及银川西侧的贺兰山区 ,一些不适于建筑的山坡、谷地 ,也成为建筑场地 ,随着也带来一系列与环境保护、岩土工程有密切关系的问题 ,如不慎重对待 ,妥善解决 ,必将产生十分严重的后果 ,阻碍山区建设的进一步发展。     

三峡库区白衣庵滑坡地质研究

白衣庵滑坡是一个由古滑坡、老滑坡和新滑坡组成的滑坡群,是川、峡二江在奉节东西贯通形成统一的长江后,三叠系巴东组(T2b)地层在江水强烈下切侵蚀事件的持续作用下导致江岸斜坡逐渐卸荷、倾倒、崩塌和表层滑坡等多期作用形成的古崩滑体。     

微分几何与向后差分相结合的多柔体系统动力学数值方法

将处理微分－代数混合方程的微分几何方法与向后差分相结合，建立了一种新的求解多柔体系统的力学方程的数值方法，通过典型算例验证了方法的正确性和有效性。     

编队飞行星座的地球扁率摄动和大气阻力摄动分析

在前一篇文章推导的运动学模型的基础上,推导了J2项摄动下编队构型在x,y,z三个方向上随时间变化的解析式,详细分析了J2项摄动对三个方向上相对距离的影响。并研究了大气阻力摄动对各轨道参数的影响,给出了几条有益的结论。     

Analytical Solutions for Partitioned Diffusion in Laminates: I. Initial Value Problem with Steady Cauchy Conditions

Studies of the transport of contaminants and nutrients in industrial and environmental systems are complicated by the heterogeneous nature of the supporting porous or permeable media, and by the numerical problems associated with high Peclet number advection and sharp interface models. In order to provide independent theoretical checks of numerical transport theories, this set of papers presents analytical solutions to diffusive transport equations in simplified (one-dimensional) laminate systems subject to partitioning interactions. Here, in Part I, a standard separation of variables technique is used to develop analytical eigenfunction expansions of the concentration solution in an N-laminate system subject to steady Cauchy (third-type) nonhomogeneous boundary conditions. Both Cartesian and radial (axisymmetric) coordinate systems are considered. The solutions are developed for two different interface partitioning formulations, allowing the partitioning processes to be described by instantaneous equilibration mechanisms, or in terms of gradual equilibration mediated by mass transfer coefficients. Worked examples are presented and limitations of the approach discussed.     

编队飞行星座相对运动的运动学描述与编队构型设计

分别以纬度幅角和平近点角、平纬度幅角及偏近点角为变量,推导了几种简单的编队飞行星座相对运动的运动学模型,这些模型和动力学模型(Hill方程)相一致,但更便于应用。并在此基础上,给出了当编队构型为空间圆形和星下点圆形时进行编队构型设计的一种运动学方法,该方法直接给出了星座中各星的轨道根数的计算方法,实例证明该方法简单实用。     

Effective Relative Permeabilities and Capillary Pressure for One-Dimensional Heterogeneous Media

The paper presents an analytical construction of effective two-phase parameters for one-dimensional heterogeneous porous media, and studies their properties. We base the computation of effective parameters on analytical solutions for steady-state saturation distributions. Special care has to be taken with respect to saturation and pressure discontinuities at the interface between different rocks. The ensuing effective relative permeabilities and effective capillary pressure will be functions of rate, flow direction, fluid viscosities, and spatial scale of the heterogeneities.The applicability of the effective parameters in dynamic displacement situations is studied by comparing fine-gridded simulations in heterogeneous media with simulations in their homogeneous (effective) counterparts. Performance is quite satisfactory, even with strong fronts present. Also, we report computations studying the applicability of capillary limit parameters outside the strict limit.     

预应力锚索抗滑桩设计中确定锚索预应力值的一种方法

在现有预应力锚索抗滑桩设计中确定锚索预应力值的各种方法的基础上 ,考虑了预应力锚索抗滑桩在工作期间承受滑坡推力的变化 ,提出将锚索、桩及桩锚固段周围岩土作为一个整体根据长期作用荷载来进行锚索预应力值计算的方法 ,对于短期作用的最危险荷载则在锚索与桩的承载力设计中予以考虑。算例分析表明 ,该方法能使锚索桩长期处于较为有利的受力状态 ,从而提高了其安全余量     

含万向铰偏斜旋转轴的组合共振及其稳定性分析

基于欧拉方程推导出了含万向铰偏斜旋转轴的横向振动模型,利用多尺度方法对该模型进行求解,得出了该偏斜系统可能出现的多种共振模式,进而对含万向铰偏斜轴系横向振动和型组合共振、差型组合共振进行稳定性分析,并对该类偏斜系统横向振动和型组合共振响应进行数值计算与仿真,检验所得稳定性理论分析结果。研究表明:对于和型组合共振而言,其稳定性边界与输入扭矩T0、支撑轴承安装位置l、轴承刚度Kx2和Ky2等因素有关;当轴承安装位置距万向铰中心较近或者轴承弹簧刚度系数较小时,系统在频率(ω10+ω20)/2附近产生和型组合共振的区域减小,即能够抑制系统和型组合共振的产生。该研究可为偏斜轴系振动与噪声抑制提供理论支持。     

地震作用下主-从结构的被动优化控制研究

提出了一种利用主－从结构间的相互作用来减少在地震作用下结构响应的控制方法。该方法通过优化设计主－从结构间的被动耗能单元,最大限度地耗散结构的相对振动能量能减小主、从结构的整体振动水平,或最大限度地吸收主结构的相对振动能量以减小主结构的振动。文章首先导出了在平稳白噪声激励下被动耗能单元优化刚度和阻尼的一般表达式,并分析了不同结构参数对控制效果的影响,比较了在不同的平稳过滤白噪声激励下主－从结构相对位     

三维编织复合材料剪切性能分析

根据三维四向编织复合材料的结构特点，提出了刚度合成法预测编织复合材料剪切弹性模量，比较了整体编织试件和裁剪所得试件理论剪切性能差别，分析了三维编织T300／QY9512复合材料的剪切性能随试件沿宽度和厚度两个方向内部单胞数目的变化规律。结果表明，三维编织复合材料剪切弹性模量是与试件尺寸相关的，只有当试件尺寸较大、沿宽度和厚度两个方向内部单胞数目较多时，试件尺寸的影响可以忽略。当沿宽度方向单胞数目较大时，整体编织试件和裁剪所得试件的剪切模量相近。本文还得到了在复合材料板的纤维体积含量不变的情况下，剪切模量随编织角的变化规律。