维数

From given controller rank number sets out, the L1 problem translate into of will infinite dimension is finite the linear programming problem of dimension.

从给定的控制器阶数出发，将无限维的l1新问题转化为有限维的线性规划新问题。

For the one-dimensional p-Laplacian with indefinite weights, four sequences of periodic and anti-periodic eigenvalues are given by introducing the rotation number function, and these eigenvalues are the endpoints of the preimage intervals of the rotation number function at nonnegative integers.

本文以带变号权函数和带变号势函数的一维p-Laplacian为基本模型，系统地阐述了特征值的旋转数方法、带正权Dirichlet特征值的最佳估计、特征值在正则和奇异渐近半线性方程的可解性中的应用、Fucik谱的旋转数方法以及Fucik谱在周期解的扭转性和多解性中的应用。

Three different numerical iterative algorithms are developed and the accuracy and stabilities of them are compared. Tension and compression instabilities are studied and effects of Conservative Smoothing Approach and artificial viscosity on stabilities are discussed. Based on Taylor series expansion, Modified SPH method is proposed. The discrete forms of the function and its first derivative estimations of the kernel function are deduced in both one and two dimensional space.

讨论了三种不同的数值迭代算法对计算精度和稳定性的影响；分析了不稳定性产生的根源，包括拉伸不稳定和压缩不稳定，探讨了保守光滑算法和人为粘性对稳定性的影响；在Taylor展开的基础上提出了一种修正的SPH方法，并推导一维和二维情形下函数的核估计和函数的一阶导数核估计的离散形式，结果表明，二维情形下MSPH方法可以很好的改善边界粒子的计算精度。

By means of estimates for three-dimensional discrete derivative Green's function , the theory of the interpolation operator of projection type and the technique of cancellation of elements, for several usual elements in the three-dimensional setting, including rectangular parallelepiped elements, tetrahedr.

借助三维离散导数Green函数的估计，投影型插值算子理论和单元合并技术，本文详细讨论了几种常用三维单元(包括长方体元，四面体元和三棱柱元)的有限元解梯度的最大模超逼近，均获得了高精度的超逼近结果。

A positive and negative projection method of object to be tested based on universal pattern display card includes using 3D texture to present rebuilt body data of object to be tested, calculating out directional vector array of ray outgoing point to detectors, storing said vector array into pattern display card to form directional vector texture, rotating directional vector texture and directional vector around rotary shaft to realize once of positive projection course on any projective angle, using 3D texture index technique to let virtual slab set position be not limited any more in negative projection course.

本发明属于投影探测与成像技术领域，其特点在于该方法含有以下步骤：把被测物体的重建体数据用三维纹理存储表示；预先计算射线出射点至平面探测器上个探测器之间的方向向量数组，并存储到通用图形显示卡中形成方向向量纹理；利用方向向量纹理与方向向量绕旋转轴旋转来实现任一投影角度的正投影过程的一次完成，无中间结果转存；在反投影过程中，利用三维纹理索引技术使虚拟切片组的放置位置不再受到限制。

It was found:(1) the stability of the clusters increased with the bond number in the clusters;(2) the clusters with three dimensional geometry are more stable than ones with two decisional geometry;(3) the ionic potential of the clusters in gas phase and on the surface of the silver bromide grains are all positive, and the electron affinity are all negative.

结果表明；气相中团簇的稳定性随团簇中键数的增加而升高，三维构型的稳定性大于二维构型的稳定性；气相中Ag〓团簇的电离能都大于零，电子亲和势都小于零；溴化银颗粒表面的Ag〓团簇的电离势也是大于零，电子亲和势也是小于零。

Using two new methods, this paper prores one pertubation theorem on the finite Hilbert space of 2×2 operator matrices, and gereralizes this theorem to the infinite Hilbert space of selfadjoint operators.

给出了有限维Hilbert空间中2×2算子矩阵的数值域扰动定理的两种证明方法，并且将该定理推广到无限维Hilbert空间上的自伴算子。

The results showed that the sphericity was approximately 0.42 μm,and the average surface roughnesses were 105.7,12.2,6.2 and 18.25 nm corresponding to the mode number in the range of 2~10,11~50,51~100,and 101~1000,respectively.

结果表明：其球度值为0.42μm；模数范围为2～10，11～50，51～100及101～1 000对应的表面粗糙度值平均为105.7，12.2，6.2，18.25nm；并得出了平均1维功率谱-模数关系曲线。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

The effect of the angel between vessels and bifurcation ratio were taken into account,and the local Nusselt number at three typical radial angels and the mean Nusselt number on a section in the branching vessel were obtained.

用有限元方法数值模拟了血管分支结构内血液流动的三维速度场和温度场，得到了分支血管壁面3个典型径向角度的局部努塞尔数和血管截面平均努塞尔数沿管长的变化曲线。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。