测度

In this paper we finded several explicit and similarity solution to the so-callednonlinear Fokker-Planck equationsut =xx +xfor ∈ S with initial datum u(x, 0)=δ, where the physical constants m ≥ 1 and n ≥ 0and δ is Dirac measure.

本文讨论对流扩散方程：的相似源型解。由于方程具有对流项且初始值为Dirac测度，特别当m＞1时方程在{u＝0}处退化，给求解造成实质的困难。

Directed HD distance is taken as the similarity measuring of template matching and effectively it can reduce the matching calculation amount; the immune genetic algorithm has powerful robust and parallel searching.

部分HD距离作为模板匹配的相似性测度，可有效减少匹配计算量；免疫遗传算法具有较强的鲁棒性和强大的并行搜索能力。

Firstly, we investigate the Dirichlet problems comparison principle on a bounded subset for this fully nonlinear intergro-differential equation, at the same time we must assume the measure in the intergro-differential item is absolute continuous.

首先研究这类完全非线性积分微分方程在有界区域上Dirichlet问题的比较原理，此时须假设积分项所涉及的测度是绝对连续的。

On this newconcept, we succeed to prove the uniqueness of Cauchy Problem of the aboveequation by the methods of using the Hausdorff measure of the set of the discontinuous points of BV solution and Kruzkov technique etc.

基于此概念，通过对BV函数的间断点集合Hausdorff测度的仔细分析，以及利用Kruzkov技巧等我们证明了上述方程BV解的存在唯一性。

The effective prediction space concept is established, On the base of these, this paper deduces two representations' evaluating equation, one evaluates the prediction error and the other evaluates the prediction error in limited space. First, the error transfer characteristic among subsystems at different space locations is analyzed, and the direct transfer characteristic from discrete standard measure space to the workpiece measure space under measured in measure system is proven. Second, the error reconstruction condition and method of mapping from discrete standard measurement system to continuous standard measurespace are analyzed.

分析了不同空间位置子系统间的误差传递特性，证明了在测量系统中离散标准量值空间向被测量工件量值空间的直接传递性；分析了离散标准量系统向连续量值空间映射的误差重构条件和方法；基于测量样本的有限距离的平稳性，证明了预报模型对动态测量误差的有限收敛性和预报误差的可测度性，进而证明了以离散标准量值系统对被测工件预报修正的可行性和合理性。

It is pointed that reasonable ecological sings for land-use should contain the producer, consumer and disintegrator.

认为生态脆弱矿区土地利用调控标志应该是包含土壤、植物、动物的综合体在内的一系列可测度值。

At the same time, the practical implementation of evolutionary algorithm is given in order that evolutionary algorithm is introduced into vector quantizer. In the fourth section the asymptotic theory of vector quantization is studied. Then the partial distortion theorem that when codebook size is large enough, each region of the partition makes an equal contribution to the distortion for an optimal quantizer, which is the key part of vector quantizer is obtained. Finally, the competitive learning algorithm based on the partial distortion theorem is proposed, which introduces the subdistortion of each region into the distortion measure to assure that the subdistortion of each region approximately equals to each other.

第四章详细研究矢量量化的渐近理论，然后得出了矢量量化器设计的核心部分——部分失真定理，当码本尺寸足够大且输出矢量的渐近概率密度与输入矢量的概率密度的幂成比例时，最优量化器划分的各个区域对该量化器的平均误差产生相同的影响，最后提出基于部分失真定理的竞争学习算法，它通过在误差测度中，引入与各区域相关的子误差以保证各区域的子误差近似相等，该算法实现较为简单，在一定程度上确保全局最优。

It introduces normal families, including equicontinuity, Arzela's theorem, Montel's and Marty's theorems, Zalcman's lemma; univalent functions, including Koebe's and de Branges' theorems; quasiconformal mappings, including conformal length, extremal length, geometric, analytic and metric definitions, quasiconformal extension, distortion theorem, quasicircle; iteration of rational functions, including fixed points, the Fatou and Julia sets, periodic points, Siegel disks, the Hausdorff measure and dimension, etc.

具体为：正规族，包括等度连续性、Arzela定理、Montel和Marty正规定则、Zalcman引理；单叶函数，包括Koebe定理和de Branges定理；拟共形映照，包括共形模、极值长度、几何、分析和距离定义、拟共形延拓、偏差定理，拟圆周等；有理函数的迭代，包括不动点、Fatou集和Julia集、周期点、Siegel盘、Hausdorff测度和维数，等等。在教学内容上充分体现综合性、前沿性。

By defining ε-hedging strategy, applying duality principle of linear programming and martingale measure theory, we present a kind of calculation method for the seller's arbitrage price and the buyer's arbitrage price of capital asset in finite security market.

在定义ε-套期保值策略的基础上，采用线性规划对偶原理和鞅测度理论，给出了有限证券市场资本资产的卖方套利价格和买方套利价格的计算方法。

Calculation of some nonlinear index of EEG based on phase space reconstruction is important for study of brain.

在脑电序列相空间重构的基础上计算非线性测度是研究大脑功能和状态的重要方法。

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。