多维

Traditional cartography develops from two dimensional and static state to the multidimensional, dynamic, interaction and virtual reality.

地图学的研究方向也突破了二维静态的限制，向多维、动态、交互和虚拟的方向发展。

In the first charpter,response variable is generalized to q dimensions, we propose the concept of QMLE and quasi function in nonlinear models, then under mild conditions, we prove that there exists the solution_n with probability 1 for sufficiently large n, and obtain the strong consistency, some results of asymptotic normality, meanwhile consistent estimator of σ~2 for QMLE for heterosedastic nonlinear models is presented.

在第一章中，我们首先将响应变量由一维推广到了多维，得出了非线性模型的极大拟似然估计的定义和拟似然方程，然后在一定的条件下，证明了当样本量n充分大时，拟似然方程以概率1有解？？_n且收敛于参数的真值(即定理1.2)，并且给出了极大拟似然估计的渐近正态性(即定理1.3，1.4)，最后考虑了异方差非线性模型的离差参数σ~2的相合估计(即定理1.5)。

In this process, by making use of the theory of decomposability, a multi-dimension problem is changed into some one-dimension problems in order to reduce the time complexity.

在资源分配过程中，应用线性规划中分治法的思想，将排课这样一个多维的资源分配问题转化成几个一维的资源分配问题加以解决，从而降低了推理过程的时间复杂度。

By utilizing the basic theory of chaos and fractal,on the basis of reading a vast amount of literatureand summing up predecessors achievements,using the three methods of analysis,computation andexperiment,this paper research for the overlapping embedment topology distribution structure of thegeneralized M-J sets and chaos phenomenon in the multi-dimension determinate nonlinear system(such as the cardiac system of species of the different level of evolution,the two-dimensional nonlinearmap,etc).

本文利用混沌与分形的基本理论，在大量阅读文献，总结前人的成果的基础上，采用解析、计算和实验三种手段并用，主要研究了广义M-J集的嵌套拓扑分布结构和多维确定性非线性系统(如进化程度不同物种的心脏系统、二维非线性映射等)中的混沌现象，取得了以下方面的创新

Because the equation is a various coefficients second-order parabolical partial differential equation,explicit difference formats usually have high condition for stability. Implicit difference formats have good stability,but they must calculate a set of algebraic equations,which are too complex.

由于泥沙扩散方程是一个二维变系数的抛物型方程，对于多维的方程，显格式往往稳定性要求很高，而隐格式虽然稳定性较好，但它要解大型的代数方程组，工作量也非常大，为了克服这两种格式的不足，常用ADI法求解，但仍存在一些计算量偏大等不足之处，因此构造出更好的差分格式是有必要的。

Whether in its narrow or broad definition, stereology is essentially an interdisciplinary branch of science about 2D and 3D structures and images,especially the three-dimensional interpretation of flat images by criteria of geometric probability.

不同定义中有一点是共同的，即体视学是一门关于多维几何结构及图像的边缘和交叉科学分支，是不同学科中获得三维显微组织结构几何形态信息的基本工具。

The GKS stability theorem for one-dimensional model of hyperbolic initial and boundary value problem, Trefethen's explanation and extension based on the concept of group velocity are generalized firstly. Another possible high-frequency instability mechanism in numerical realization of MTF is pointed out based on his explanation and extension, namely, coupling effect of outgoing harmonic wave along one direction and node motion in the other directions can reverse the energy propagation in multi-dimensional discrete grids.

本文概述了—维双曲型偏微分方程组初边值问题数值稳定性的GKS定理及Trefethen基于群速度概念对这一定理的解释和推广；并应用Trefethen的解释和推广指出了MTF在数值实现中可能出现的另一种高频失稳机制，即在多维离散网格中，沿某一空间方向的外行简谐波，由于与其他空间方向节点运动的耦合效应可以使能量传播方向反向。

This book deals with integral representations of holomorphic functions of several complex variables, the multidimensional logarithmic residue, and the theory of multidimensional residues.

与多复变数的全纯函数的积分表示这本书优惠，对数的多维残留，残留的多层面理论。

It is essential for us to study the infinite dimensional manifoldssince there is a lot of progress to have b...

由多维流形和理论物理的发展，可知无限维流形是一个自然的研究对象。

Based on the results of the iterated logarithm law and the uniform modulus of continuity for Brownian motion, Orey and Taylor(1972) discussed the multifractal decomposition of one dimension white noise.

但有关多维白噪音的重分形分解问题，即多指标Wiener过程样本轨道的重分形分析性质至今仍未见有讨论，本文旨在讨论多指标Wiener过程样本轨道的重分形分析性质。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。