A comment on the proof of Fermat's last theorem

In this paper, some conmments on the proof of Fermat’s last theorem are proposed.The main resuilt is thai the proof proposed by Wong Chiahe is only part of proof for fermat’s last theorem. That is to sqy,the proof is not all-full proof to Fermat’s last theorem.     

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…     

Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows

The lattice Boltzmann method (LBM) is coupled with the multiple-relaxation-time (MRT) collision model and the three-dimensional 19-discrete-velocity (D3Q19) model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high-order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investigated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity (ESS) method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This validation provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.     

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.     

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。