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Furthermor, we consider their nondiferentiable situation, we define nonsmooth univex functions for Lipschitz functions by using Clarke generalized directional derivative and study nonsmooth multiobjective fractional programming with the new convexity. We establish generalized Karush-Kuhn-Tucker necessary and sufficient optimality condition and prove weak, strong and strict converse duality theorems for nonsmooth multiobjective fractional programming problems containing univex functions.

而且，本文利用Clarke广义方向导数针对Lipschitz函数在原来一致凸函数概念的基础上定义了不可微的一致凸函数，并利用这类新凸性，我们研究了非光滑多目标分式规划，获得了广义Karush-Kuhn-Tucher最优性条件；弱对偶定理、强对偶定理和严格逆对偶定理。

In chapter 3, we study pricing of geometric average Asian capped calls, pricing of geometric average Asian option with transaction cost, pricing of the two kinds of exotic option in Fractional Brownian motion environment, pricing of capped calls with transaction cost in fractional Brownian motion environment.

在本文的第三章，研究了几何平均亚式上限型买权的定价，有交易成本的几何平均亚式期权的定价，分数次布朗运动环境中两种奇异期权的定价，以及分数次布朗运动环境中有交易成本的上限型买权的定价。

In photoelastic stress analysis, the accuracy of analysis can be improved by using fractional isochromatic fringes, so it is very important to study the approach for producing fractional fringes.

在光弹应力分析中，利用分数级条纹可以提高分析精度，于是，产生分数级条纹的方法研究就变得非常重要。

Using this method, the controller design for performance and robustness can be designed separately, which has the potential to overcome the conflict between performance and robustness in the traditional feedback framework. Third, to make the vehicle meet the performance index in full flight envelop, a H∞ gain-scheduled controller based on Linear Varying Parameter system are designed. A LPV plant with a linear fractional dependent variable can be represented by upper LFT (Linear Fractional Transformation) interconnection.

通过把非线性系统简化为了线性变参数系统，再有通过线性分式变换将LPV系统转化为一个线性定常系统和不确定性组成的LFT互联形式，使之转换成为一个经典鲁棒控制问题，然后通过求解一组线性矩阵不等式得到变增益H_∞控制器。

In the third chapter, based on the second chapter, we will study the boundedness of fractional intergral operator and maximal fractional operator with rough kernal on the weighted Herz-Morrey space.

在第三章中，我们研究了加权齐次Herz-Morrey空间MK_~(ω_1，ω_2)上另一类算子带粗糙核的分数次极大算子和分数次积分算子的有界性问题。

Fractional spline wavelets can obtain more information of image due to its fractional order of approximation when decomposing the image.

遥感图像融合作为一门新兴的技术，已被广泛应用于地形测绘和地图更新、国土资源调查、洪水监测、地质等领域。

School of Information Engineering,Zhengzhou University,Zhengzhou 450052,ChinaA novel chirp-typed watermarking scheme which uses the properties of index additivity and orthonormality of fractional Fourier transform to embed watermark in the different fractional Fourier domain is presented.

提出了一种新的分数阶Fourier域Chirp类数字水印方案，该方案利用分数阶Fourier变换基函数的正交性和旋转相加性，在不同的分数阶Fourier域嵌入Chirp水印，并利用分数阶Fourier域Chirp信号的聚集性进行盲检测。

In this method,the image is transformed two times with anamorphic fractional Fourier transform and modulated two times by random phase function in the original image plane and the fractional domain separately.

对要加密的图像分别进行两次变形分数傅里叶变换和两次随机相位函数调制，使加密图像的密钥由原来两重增加到六重。

Meanwhile, this paper systematically summarized the present fractional-order control theory results distributed mostly in such aspects as continuous and discrete time domain analysis, approximated numerical analysis, common frequency domain analysis, plane locus method based on variable transposition, etc, and became an effective foundation of forming a complete control and system theory for fractional-order control systems.

同时，论文对当前国内外已有的分数阶控制理论成果进行了较为系统的整理，主要集中在连续和离散时间域分析、近似数值分析、一般复频域分析、基于变量变换的平面根轨迹分析等方面，具有综述性质，是建立一套完整的分数系统控制理论与系统理论的有效基石。

First of all, modeling image by fractional-order derivative and negative Sobolev space, this paper presents a fractional-order multi-scale variation PDE model, and the proposes the adaptive parameter selection method and obtains the field and scale adaptively algorithm for SAR image denoising.

首先利用分数阶导数以及负指数Sobolev 空间对图像进行建模，建立了分数阶多尺度变分PDE 模型，然后给出了模型参数自适应选择方法，并在此基础上提出了区域、尺度自适应的SAR 图像去噪算法。

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。