中阶

Theorem 7 Let G be a group, if every subgroup of G of prime order is contained in Z_∞,2 ∈π, every cyclic subgroup of G of order 4 is π-supplemented in G,then G will be nilpotent.

定理7设G是群，G的素数阶子群包含在Z_∞中，2∈π，如果G的每个4阶循环子群在G中π-可补，则G为幂零群。

Within this context, four specific areas are addressed:(1) By means of finite integration technique, a new kind of the first order partial difference equation is derived from the original disperse transmission line equation of the uniform waveguide's. As it is the kind of one dimension Dirichlet's boundary problem, it is convenient for us to solve this equation from the leapfrog scheme. Because computation is carried out in one dimension, both high calculation efficiency and precision have been obtained in this method. Meanwhile, this method provide us a different selection to simulate the transient response of waveguide with non-simplical, for examples cylinder and elliptic waveguide, and avoid solving the second order equation, or using finite difference time domain to simulate a three dimension problem, sometimes the latter precision is not satisfied with the need, or low efficiency.

在这一研究内容下，主要研究四个方面的问题：(1)在完成金属波导传输线方程时域形式的基础之上，应用有限积分技术，把波导特征模式的色散传输线方程，化简为一组新的一阶偏微分方程组，该边值问题属一维Dirichlet边值问题，从而便于用蛙跳格式求解，由于是在一维中计算，该方法具有很高计算效率和精度，从而避免了以往为得到金属波导中特征模的时域响应特性，须要求解二阶方程，或用时域有限差分方法求解三维问题的方法，对于后者来说，计算有时是不准确的，或是很耗时的例如计算诸如圆波导、椭圆波导等其它复杂形状的波导。

It is a non-symmetirc fractional derivative, with two-side fractional derivatives and skewness parameter,which results in the complicated disposal of the discrete form.

分数阶微分方程是指方程中含有非整数阶的导数，它非常有效地描述各种各样物质的记忆和遗传性质，在工程、物理、金融、水文等领域中发挥了越来越重要的作用。

By Fourier transform, the authors propose a new method to calculate non integer order differential and integral on the basis of the integer order differential and integral in frequency space domain in this paper.

该文以傅氏域中整数阶微积分计算方法为基础，将该方法推广到傅氏域中非整数阶微积分的计算。经过模型计算、精度分析及地震信号处理中的若干运用，表明了该方法的有效性及可靠性。

It is pointed out at first time that two popular methods of investigating intermittency——-bin-wise integral and strip integral are inequivalent when the translational invariance of semi-inclusive density functions is destroyed, and the anomalous scaling of these two quantities may originate from different dynamics.

我们在研究中首次指出，研究间歇现象的实验中目前流行的两种统计阶乘矩方法：关联函数Bin-Wise和Strip积分方法并不等价，它们所得到的阶乘矩的不同标度行为可能反映了不同的物理起源。

A comparative study of pollen floras between two cores: Core 17940 from the northern slope of the South China Sea and a core from the Toushe Basin in central Taiwan Province, reveals that there were three different vegetation types around the two areas during 15-40kaBP. The first type is characterized with the subtropical evergreen broadleaved forest during MIS2 (20-15kaBP). The second is the Pinus/Alnus-dominated woody plant communitites, corresponding to an interstadial summer monsoon dominated warm and humid climate and higher sea/lake level. The third is the Artemisia/Poaceae-dominated herb communities, corresponding to a stadial winter monsoon dominated warm and dry climate and lower sea/lake level.

根据南海北部17940孔和台湾中部头社孔孢粉序列对比结果，首次提出了华南地区15-40kaBP期间的三个具代表性植物群：1以青栲类为主的亚热带常绿阔叶林为第1植物群，该植物群在MIS2阶段(20-15kaBP)，为南海北部周边地区和台湾中部头社盆地周围地带性植被；2以松属或桤木属为主的木本植物为第2植物群，对应于间冰阶，夏季风盛行，降水充沛，气候暖湿，高海面；3以蒿属或以禾草为主的草本植物为第3植物群，对应于冰阶，冬季风盛行，降水少，气候暖干，低海面。

In chapter 4, the prime reasons for the ill-posed inversion are analyzed at first and then the remedy method is described. The basic formula of stochastic inversion method tor impedance with broarband constraint of well log is deduced from basic level.

第二章首先将信号分析中的MA过程的定阶问题引入到地震子波的提取中，发展了利用地震记录的高阶累积量矩阵的特征值的变化估计地震子波的有效长度的方法。

This paper extracted and analysed 11Math-Mophological Features such as Area, Perimeter, X-Length, Y-Length, Shape-Parameter, Lobation, Sphericity, Circularity, Roundness, Eccentricity and HoleNumber. Based on 40 species of insects which belonging to 8 Orders, 25 Families. And then ranks the accountability of 11 features each in insect identification while assessing their implication to insect taxonomy on levels of Order, Superfamily, Family and Species. More than those, also describes the kinship among the insects of various categories within the same level from the perspective of mathematical morphology through cluster analyses.

论文对隶属于8个目25科的40种昆虫利用计算机视觉技术进行了自动鉴别研究，从昆虫图像中提取和分析了这些昆虫的面积、周长、横轴长、纵轴长、形状参数、叶状性、球状性、圆形性、似圆度、偏心率、亮斑数等11项数学形态特征，并分别探讨了在目、总科、科及种分类阶元上这些数学特征在昆虫分类中的应用可能性和可靠性，利用聚类分析从数学形态学角度对所涉及到的同阶元昆虫类群的亲缘关系做了描述。

But most of these papers only considered the nonsingular case...

本章主要内容包括：在§1.1中，我们考虑了如下奇异四阶微分边值问题到目前为止，有关四阶微分边值问题已有不少文献，但大多数文献中作者只讨论了非线性项是非奇异的情形，很少有文献讨论奇异的情形。

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

本研究在探讨数值积分程式之平行化，所使用的演算法为林聪悟与林佳慧[1997]一书所提出的「Romberg树自动布点数值积分」架构，此一数值积分方法能以适应被积函数值变化情形方式自动安排积分点来进行数值求积计算，在提高阶数以获得更高精度积分值的过程中，此一方法只须再计算新增加积分点的函数值，搭配先前已计算过的函数值的重覆运用即可获得更精确的数值积分估计值，如此将能减少升阶过程中函数求值计算的次数，有效率地完成单重积分的数值计算。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。