特征函数

After it is proved that the fractal dimensions are stable characteristic parameters of images, and there is correlation between them in undeformed and deformed states, the fractal correlation function are found for displacement measurement, which the correlation parameters are Box Dimensions.

在确定了变形前后数字散斑图像的分形维数之间具有相关性，而且其分形维数是稳定的特征参数之后，以图像的盒维数为相关参数进行互相关运算而形成分形相关函数。即利用变形前后数字散斑图像的分形维数序列做为相关参数进行相关运算，实现位移测量。

Key words: geometry; fractal; characteristic angle sequence function; method of undetermined coefficient; square wave Koch-like curve

关键 词：几何学；分形；特征角序列函数；待定系数法；Koch类方波曲线

Those fuzz systems, their structural characters, the basic approximation properties and uniform convergent properties of them are compared by using the fuzzy basis functions.

利用模糊基本函数形式化描述模糊系统的方法，比较了它们的结构特征，以及由此导出的模糊推理系统的各种逼近性质。

Utility function is the basic tool and of vital importance in the research of Economics.

效用函数是刻画行为人特征的基本工具，在经济学研究中具有重要的地位。

The research is about the reuse of urban sewage for virescence irrigation, and the influence of sewage irrigation on eco-environment such as soil, plant, etc. is studied. Under the condition of field sewage irrigation, the transport and transformation and accumulation mechanism of heavy metals, nutrients and organic pollutants as vaporizable hydroxybenzene etc. in the soil-plant system are analyzed. The heavy metal pollution is evaluated by the comprehensive pollution index. The spatial variability of heavy metals in sewage irrigation area is further understood. The spatial variability of heavy metals and physical and chemical properties of soil are reflected in a more straight way by the theory model of variance function curve based on the geographical information system.

在城市污水回用于绿化灌溉对土壤、植物等生态环境的影响研究中分析了大田条件下污灌对土壤-植物体系中重金属、养分及挥发酚等有机污染物迁移转化及富集机理，对重金属污染进行了综合污染指数评价，进一步了解了污灌区重金属分布的空间异质性，基于地理信息系统提出了变异函数曲线的理论模型，更直观地反映出了重金属元素与土壤理化参数的空间变异特征。

To find some useful eigenvalue in time series by mining the distributing values of original series, and deduce a collection of candidate slide-window size, find the optimal slide window size by adapting to the series eigenvalue variable motion movement.

通过对时序特征值分布函数挖掘，发现时间序列中的有效特征点，进而确定一组合适的滑动窗口宽度；最后根据序列的变化情况来决定最优的滑动窗口宽度，对原数据维度进行简约。

The first conclusion infers the sufficient condition with the aid of thealgebra Riccati equation solution and the semi-group theory nature which the systemmay optimize;Next discussed when the system operator characteristic vector forms theRiesz base,causes control function concrete mathematical expression which its systemmay optimize;Finally summarized the system to be possible to optimize the researchnewest conclusion and the research forecast.

第一个结论借助代数Riccati方程的解及半群理论性质推导出系统可最优化；其次讨论了系统算子的特征向量形成Riesz基时，使其系统可最优化的控制函数的具体数学表达式；最后总结了系统可最优化研究的最新结论和研究展望。

Based on human cognize character ,the article put forward a Weightiness Amend Coefficient to denote the important extent of different character.

本文从人类认知学的角度出发，提出了一种对特征参数进行修正的重要性修正因子，并设计了模糊隶属度函数。

In this thesis, by the means of calefactive oxidation test of coal samples, the characteristics of different samples spontaneous combustion are analyzed; the infrared spectrum is assimilated to review the rule that coal function corps change in the process of coal low-temperature oxidation ; by the means of thermal analysis by differential scanning calorimeter, thermogravimeter, the kinetic function of coal low-temperature oxidation in spontaneous combustion process are analyzed , depend on the device, the mathematical model of coal spontaneous combustion is developed, the model are dealt with, Finally, the temperature field and the velocity field with velocity of the entry flow is got.

论文通过煤的低温氧化和自燃过程，实验研究了煤的低温氧化气体产物特征和变化规律，研究得出了煤的低温氧化过程中气体生成量与氧气消耗量与煤温之间的指数关系式；在煤的低温自热氧化过程中，对煤的官能团等化学结构的变化研究，揭示了煤炭低温自热氧化化学基团变化规律；采用非等温TG和DSC法研究了烟煤低温氧化动力学，得出了煤低温氧化分布活化能及煤低温氧化机理函数的变化规律；建立了煤低温氧化自热数学模型，并对该模型进行数值解算，可得煤样的温度场与速度场随入口风量变化情况。

Furthermore ,after analyzing the congregative characteristic of inner measure ,we obtain the relationship between belief function and inner measure .

其次，对内测度的集合特征作了分析后，给出了信任函数与内测度的关系。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。