查询词典 fractional integral

The content of this course is: analytic function (the definition of analytic function, elementary functions, etc.), conformal mapping (the definition if conformal mapping, fractional linear functions, elementary mappings, etc.), complex integration (Cauchy's integral formula, Cauchy's theorem, etc.), Series (Laurent Series, singularities, local property, etc.), residues and its applications (the Residues Theorem, integration by residues, the Argument Principle, the Maximum Principle, Schwarz's Lemma, etc.), analytic continuation and harmonic functions, etc.

本课程内容主要包括：解析函数(解析函数的定义、初等函数等)、共形映射(共形映射的定义、分式线性变换及初等映射等)、复积分(Cauchy 积分公式、 Cauchy 定理等)、级数(Laurent 级数、孤立奇点、局部映射等)、留数及其应用(留数定理、利用留数计算积分、幅角原理、最大模原理、 Schwarz 引理等)、解析开拓和调和函数等内容。

Firstly, we introduce the definition, properties and integral theory of fractional Brownian motion.

首先介绍了关于分数布朗运动的定义，性质。

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 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。

We give some equivalent characterizations of Bloch type functions in term of fractional derivative, via studying the relative of growth of the different order fractional derivatives of holomorphic function, including the form of supremum and limit, the form of integral and Carleson measure, which are the generalizations of some known results in the unit disc and in the unit ball.

我们从研究全纯函数分数次导数的增长性入手，利用分数次导数给出了它的一类刻画，包括上确界和极限形式的特征，积分形式的特征以及Carleson测度形式的特征，推广了单位圆盘和单位球上一些已有的结论。

It is difficult to compute directly the coefficients from the integral formula, since the integral function in the formula of the ideal digital fractional differentiator is a high-order oscillating function.

从理想数字分数微分器系数计算公式的特点考虑，利用变量代换把积分函数中的振荡因子转换成积分上限，避免高阶振荡函数积分计算，给出了计算分数微分器系数的递推公式。

Fractional Hilbert transform, a generalization of Hilbert transform from integral order to fractional order, extends the application fields.

基于广义Hilbert变换将传统的Hilbert变换由整数阶向分数阶的推广，其应用领域也得到了扩展。

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。

From the proof of the m-ain theorem it follows that we replace fractional integral〓in the definition of〓by equal operator I and obtain the boundedness of〓on〓(1＜p＜∞),so we generalize some of results in.

从主要结果的证明可知〓的定义中可用恒等算子取代〓而得到〓从〓到〓有界〓，从而推广了中的结论。

It was suggested that aging did not only influence diastolic filling period, but also influence STI. 3. With increasing age, whether at rest or during exercice, fractional shortening of minor semiaxis, mean velocity of circumferential fiber shortening, cardiac index and ejection fraction did not change, but immediately post pacing, PEP prolonged and PEP/ LVET increased in elderly group and did not change in young group. It was suggested that STI was sensitivity in detecting systolic function of LV. 4. There was a good correlation between aging and decreased compliance and diastolic function of left ventricle which was manifested by a reduction of early diastolic peak folw velocity, time-velocity integral of early diastole, 1/3 filling fraction (1/3FF)(r=-0.958,-0.875 and -0.937, P＜0.01～0.001) and a significant compansatory increase in peak flow velocity of atrial contraction, time-velocity integral of atrial contraction, the ratio between APFV and EPFV and the ratio of ATVI and Total TVI (r=0.958, 0.956, 0.966 and 0.986, P＜0.001) and the prolongation of Dec T and RFP with increasing age. It was particularly true for the subgroups above the age of 50 years.

静息状态下收缩时间间期与年龄无相关性，负荷后即刻，老年组射血前期延长(P＜0.05)，射血前期与射血期比值加大(P＜0.05)，青年组无变化，提示年龄因素亦影响STI，但由于静息状态下得到代偿，STI变化往往表现不明显。3、静息及负荷状态左室短轴缩短率、平均周径缩短率、心指数及射血分数均不随年龄增长而变化，而负荷后即刻老年组PEF延长，PEP/LVET加大，提示STI是检测左室收缩功能的敏感指标。4、随年龄增长，心房收缩期充盈峰值流速、流速积分、充盈分数及心房收缩期与舒张早期充盈峰值流速之比值显著增高(r＝0.958、0.956、0.986及0.966，P均＜0.001)，舒张早期充盈峰值流速及流速积分、1/3充盈分数(1/3FF)下降(r＝-0.958、-0.875及-0.937，P＜0.01～0.001)。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。