查询词典 fractional derivative

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。

The characteristic of fractional order differential equation iscontaining the non-integer order derivative. It can effectively describe the memory andtransmissibility of many kinds of material, and plays an increasingly important role inengineering, physics, finance, hydrology and other fields.

分数阶微分方程的特点是含有非整数阶导数，能非常有效的描述各种各样的物质的记忆和遗传性质，在工程，物理，金融，水文等领域发挥越来越重要的作用。

The method can beused to solve the integro-differential equation included fractional integral orfractional derivative in a long history and the difficulty of storing all history data isovercome and the error can be controlled.Two numerical examples are presented.

利用该方法可对包含分数积分和微分的积分-微分方程进行较长时间的数值模拟，克服了存储全部历史数据的困难，并能对计算误差进行控制。

This method was applied to preprocess the 2-D seismic data of Shengli oilfield, showing that the fractional order derivative profile can effectively describe the unconformity and reflect the lateral changes of actual interface.

对胜利油田某区块实际二维地震资料进行了试处理，结果表明分数阶导数剖面能很好地描述不整合面，反映实际界面的横向变化。

According to the fractional derivative model of viscoelastic damper and force-deformation-slip relation of friction element,a precise finite element model of FVD is constructed,and the method for forming element stiffness matrix and control force vector of FVD is deduced.

针对粘弹性材料的分数导数模型和摩擦单元的力-位移-滑移量的矩阵关系式，建立了FVD精确的有限元模型，推导了FVD单元刚度矩阵和控制力向量计算公式和求解方法；根据钢筋混凝土框架结构的非线性特性，建立了设置FVD非线性钢筋混凝土框架结构地震反应时程分析的控制方法。

Comparing with classical viscoelastic models, fractional derivative models describe not only the constitutive of viscoelastic material and the related mechanics properties accurately in wide range, but also need less model parameters.

分数导数模型与其他经典模型相比不但能够精确地描述粘弹性材料的本构关系及其力学特性，而且确定模型所需实验参数少、能够在较宽的频率范围内描述材料的力学行为。

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。

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。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。