查询词典 approximation theory

For the given endpoint interpolation conditions, a new approximation method of multidegree reduction is presented. Using Chebyshev polynomial approximation theory, the nearly best uniform approximation under the interpolation conditions of endpoints can be obtained.

对于给定的首末端点的各阶插值条件，给出了一种新的一次降多阶逼近算法，应用Chebyshev多项式逼近理论达到了满足端点插值条件下的近似最佳一致逼近。

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

This dissertation explores the Value Price Theory of Adam Smith, the Price Theory of David Ricardo, the Labor Value Theory of Karl-Marx, the Price Theory of the production expenditure of J. Say, the Marginal Utility theory of Eugen Von Bohn-Bawerk and the Equilibrium Price Theory of Maxieer. Meanwhile it researches the modem market price theory and modern enterprise price practice. Using Marxism and modern market price theory synthetically to analyze passenger price formation mechanism of Civil Aviation of China overall, systematically and deeply on theory.

本文全面分析了亚当·斯密的价值价格理论、大卫·李嘉图的价值价格理论、马克思的劳动价值论、萨伊的生产费用价格论、庞巴维克的边际效用论和马歇尔的均衡价格论，分析了现代市场价格理论以及企业定价实践研究的成果，综合运用马克思主义及现代市场价格理论，对中国民航客运价格形成机制进行了全面、深入、系统的理论分析。

As to the first research topic, we present a 'Noble Brand Positioning Four Master Phases Theory': Brand Space Theory, Brand Capital Theory, Brand Value Theory and Brand Circle Theory in advance. Following based on the Principal Component Analysis of statistical theory, we implemented the quantitative research in the 'Noble Brand Positioning Four Master Phases Theory'. We used the most famous fast food brand 'McDonald' s' as the sample space. The simulation test result shows that the Overall Index Explanatory Power is 83% under the Cronbath' s a is 0.88 through the quantitative verification. This result gives a strong support in defining the Noble Four Niche Phases Theory as the important strategic factor in establishing brand positioning index. After completing the quantitative research, the Principal Weight of each Sub-Niche is positive. This also implies that the Noble Brand Positioning Four master Phases Theory represents positive affection to brand positioning index. We also created the following Sub-Niches those are rarely mentioned in the past literatures. The Sub-Niches are:'Endless Running Strategy, Business Environment Strategy, Physical Capital Strategy, Brand Logo, Brand Music, Business Life Strategy, Personnel Capital Strategy, Life Cycle Strategy, Trust Mask Strategy, Re-Positioning Strategy, Word-Power Strategy, Globalization Strategy, Network Revolution Strategy and Green Brand Strategy'. The quantitative verification model can classify the responses of the sampling space into groups. After that, we used the quantitative verification process to classify the Target Consumer. And through the Principal Component Analysis, the group that owns the biggest average value consists of the Master Target Consumers for the business. This result would become the best suggestion for the business to adjust its strategies and to upgrade the productivity efficiency and create higher profit. As to the second research topic, we focused on finding the best corresponding characteristics attributes of the Brand Music for the Brand Log.

针对第一个研究主题，本文首先提出了一种创新性的品牌定位利基理论（A New Brand Positioning Niche Phase Theory）；品牌空间论，品牌资本论，品牌价值论与品牌循环论，接着本文以统计理论的主成份分析方法针对本文所提的创新性的品牌定位利基理论进行量化研究，本文以快餐业中知名品牌麦当劳作为样本空间，由量化验证的结果显示在信度分析Cronbatch's α为0.88之下其总指标解释力（Overall Index Explanatory Power）为83％，验证本文所提的创新性的品牌定位利基理论是构建品牌定位的重要策略因素，同时经由量化分析结果每项主成分权重值皆为正值更验证了本文所提的企业创新性的品牌定位利基理论与品牌定位指标呈现正相关：同时本文所提出次利基：'永续经营策略、企业环境策略、实体资本策略、企业生命策略、品牌标志策略、品牌音乐策略、人际资本策略、生命周期策略、信任标志策略、重新定位策略、文字威力策略、放眼全球策略、网络革命策略与绿色品牌策略'更是其它文献所未提及的：本文量化验证模式更可将样本空间中的responses分类群组，然后量化验证以界定目标市场，经由分析结果显示，其中具最大主成份百分位序均值者所属群组，即为企业中的主力消费群，提供企业决策者参考，进而调整其企业策略，而为企业提升生产效率创造更大的利润。

Applying the Euler method to the equation and particularly using the interpolation technique on variable delay, the Euler approximation is obtained. The discrete Euler approximation is extended to the continuous Euler approximation. It is proved that the Euler numerical solutions will converge strongly to the true solution under the local Lipschitz condition.

对方程应用欧拉方法，特别地对变延迟部分运用插值技巧进行数值离散后，将离散的欧拉格式延拓为连续的欧拉格式，从而得到欧拉格式在局部Lipschitz条件下强收敛到解析解。

The moving least squares approximation makes only require least squares approximation with regard to functional value on all nodes. It makes no require for the residual of derivative approximation.

移动最小二乘近似只要求近似函数在各节点处的误差的平方和最小，对近似函数导数的误差没有任何约束。

After introducing the primary approximation approaches for curve and surface offset, we give an optimal approximation approach for offsetting curve based on shifting control points, which relies on approximating the normal by Legendre polynomial approximation.

在全面介绍了等距曲线曲面逼近的主要方法以后，作者首先利用Legendre多项式得到基曲线法矢曲线的最佳平方逼近，由此给出了基于控制顶点偏移的等距曲线最优逼近的算法，它在算法效果和效率上都远优于其他同类算法。

This paper firstly established a general mathematical model for the approximation to gradient and suggested two optimization principles of the approximation model,and then developed two optimal algorithms to reach minimum anisotropy or minimum approximation error while...

提出了通用梯度近似算法的数学模型和两种优化准则，进而推导出两种梯度近似的优化算法。

The main work of the thesis consists of summarizing the characteristics of the approximation methods,compiling the programs of approximation methods,and getting availability of every approximation method according to examples.

本文的主要工作是总结各种近似方法的特点，编写各近似方法的程序，通过算例总结出各种近似方法的适用性。

It can adjust time interval in light of approximation effect, and the current segment's approximation error is not influenced by other segments'. This method can improve approximation precision of reach set and makes the verification applicable in practical systems.

该方法可根据近似误差自动调节近似时所用的时间间隔，每段的近似误差不受其它段的影响，达到提高近似精度和减少计算量的目的，从而进一步降低验证方法实现的难度。

The statistical analysis of this large set of mutations has led us to propose a diagnostic strategy that should help with the molecular work-up of optic neuropathies.

这一大系列基因突变的统计学分析引导我们提出一个诊断策略，可以帮助我们对视神经病变进行分子学的诊断检查。

The results show that the pipe grouting changes the mechanical parameters of surrounding rocks to achieve the security of engineering objectives by reinforcing surrounding rocks and bolcking the water.

研究表明：小导管注浆一方面改变了围岩的力学参数，另一方面利用浆液的固结特性可以实现堵水和加固围岩的工程目标，使隧道在开挖过程中的安全得到保障。