查询词典 fractional

In recent years, systems which based on fractional differential and integral fractional, have been researched extensively, involving fractional circuit, fractional digital signal processing, fractional dynamics control systems and fractional-Chaos and super-chaos, Chaos Control and fractional chaos synchronization, and security communications. And a lot of theoretical and practical results are obtained.

故而近年来基于分数阶微分和积分的分数阶系统已在动力学系统中得以较为广泛的研究，其中涉及分数阶电路、分数阶数字信号处理、分数阶动力学控制系统以及分数阶混沌和超混沌、分数阶混沌控制与混沌同步、保密通信等多个领域，取得了不少的理论和实际结果。

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。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

this paper proposes a design method which can improve the performance of fractional order differential filter obviously under the premise of not increasing the structure complexity of the filter.this scheme which bases on mutually compensatory characters of typical differentiator and uses interpolated method to improve performance of iir digital fractional differential filter.the improved frequency response of fractional differential filter is more close to ideal fractional differential filter,it indicates the validity of proposed method.

摘 要：提出一种在不增加分数阶微分滤波器复杂度的前提下，能有效提高分数阶微分滤波器性能的方法。该方法利用几种基于典型微分算子的分数阶微分滤波器之间的互补性，通过相互内插结合的方式，用于提高iir分数阶数字滤波器的性能。改进后的分数阶微分滤波器频率响应更接近理想分数阶微分滤波器，表明所提方法的有效性。

Then using classical fractional differential G-L definition deduces fractional order differential difference function and constructs an approximate fractional order differential Tiansi module.

然后由经典的分数阶微分定义出发，推导出了分数阶差分方程，构建了近似的分数阶Tiansi微分模板。

The design method of fractional Controller for angle stability loop and mass center control loop of GREP was studied.The fractional PI~λD~μController and integral PID Controller were designed respectively for some type GREP.The simulation results show that the fractional PI~λD~μController designed by this method has its own features compared with PID Controller.

研究了滑翔增程炮弹角稳定回路和高度控制回路的分数阶控制器设计方法，并对某滑翔增程炮弹算例分别进行了分数阶控制器和整数阶PID控制器设计，仿真结果表明该设计方法设计的分数阶控制器较PID控制器有其自身的特点。

According the connection between the solution of linear fractional differential equation and nonlinear fractional differential equation, the expression of the solution of the nonlinear fractional differential equation is formed.

在一定的条件下，建立了非线性分数阶微分方程在边值条件下有解存在。

In Chapter 3, considering fractional relaxation equation, we make use of directlythe Grunwald-Letnikov definition to discrete fractional derivative, obtain a numericalmethod of fractional relaxation equation,and give the proof of consistency ,conver-gency and stability.

第三章对于一个推广到分数阶的松驰方程，直接利用Gru¨nwald-Letnikov分数阶导数定义进行离散，得到分数阶松驰方程一个数值方法，并给出了相容性，收敛性和稳定性的证明。

Based on the principle of fractional graphics generated from overlapping function system, the realization method of algorithmetic fractional graphics and the influence upon fractional graphics by adjusting parameter have been dealt with.

介绍分形几何生成计算机图形的基本方法，在阐述迭代函数系统IFS方法生成分形图形原理的基础上，讨论分形图形算法的实现方法、参数C对分形图形的影响及分形理论在纺织品花形设计中的应用。

You can't choose a fractional number, deal fractional damage, gain fractional life, and so on.

你不能选择分数，造成有小数点的伤害，或获得小数点的生命等等。

As of Tuesday, Google's results were still censored in China.

截至周二，谷歌的搜索结果仍受中国审查。

In order to make the positive action increase and negative one decrease, the sub-forces of the social factors must be adjusted to form a centripetal force.

在这一过程中，人的主体性发挥是社会有机体健康发展的灵魂。