元函数

One of such distribution functions can be used to describe satisfactorily the three-dimensional quasi-stationary grain size distribution obtained from experimental measurement results for pure iron by serial sectioning, and those obtained from computer simulations by vertex method, surface evolver method, phase-field method, Monte Carlo method with Potts model.

采用纯Fe实验数据以及顶点法、基元演化法、相场模型和Monte Carlo法进行了验证，结果表明，函数族中峰值左偏的函数适合三维准稳态晶粒尺寸分布的定量表述。

In this paper, the results of [1,4] are generalized, and mean value theory are discussed further. In this basis, we talk over mean function and mean family of n variables in m dimensions.

本文推广了文[1，4]的结果，进一步深入讨论一维的平均族理论，并在此基础上讨论高维n元平均函数和n元平均族。

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。

To analyze the effects of heterogeneous material characteristics on rock failure,a micro-heterogeneous physical cellular automata model is introduced according to the cellular automata theory from a general power view.In this model,the neighbor is the Moore pattern and the Weibull distribution is adopted to simulate the rock heterogeneousness.

为了分析岩石材料的非均质性对其破坏演化的影响，根据元胞自动机理论，从能量的角度建立了一种能够从细观层次上对岩石破坏演化进行模拟的物理元胞自动机模型，模型引用的Weibull随机分布函数对材料的非均质性进行描述。

To perfect it,this paper,by using the basic knowledge in definite integral Newton—'Leibniz formula,offers an applied method of definite integral,partial quantity function infinitesimal calculus method,which is both theoretically reliable and easily applied.

一般教材都使用"微元法"给出被积函数，这一方法在理论上并非严格，为弥补该方法在理论上的不足之处，将定积分的应用方法总结为"部分量函数微积分法"。

We use a different transmission method where binary Golay complementary pairs are sent simultaneously on the inphase and quadrature parts of the subcarrier, and compare the performance with existing method. Using our method, the radar obtains a pair of Golay sequences from only one echo, which reduces the ambiguity function sidelobes when the reflected signals are partially received, and fully exploits the property of Golay pairs.

我们采用将二位元格雷互补对以复数组合，发射时以调变正交载波的方式同时传送，并且将一个时段同时传送格雷互补对之方式，与一个时段仅传送一个二位元格雷互补序列比较，可使雷达仅接收一个回波即可得到一对格雷互补序列，以降低回波部份接收时之混淆函数旁峰，使格雷互补对之特性充分发挥。

Kernel principal component analysis can compute principal components in high-dimensional feature space by means of integral operators and nonlinear kernel functions.It can effectively capture the nonlinear relationship in the process variables.

核主元分析方法通过集成算子与非线性核函数计算高维特性空间的主元成分，有效捕捉过程变量中的非线性关系。

Through the proposed measures, the reduction of model icon in the control flow is realized, and thus the correct transformation form model map description to simulation program is guaranteed.

3提出了模型函数的生成方法及其图元之间的归约规则，实现了控制流中模型图元的归约，保证了从图形化模型说明到仿真程序的正确转换。

From the minimum potential energy principle, the shape discrimination is transformed into the solution of minimum characteristic value.

将轧后板带离散为若干纵向条元，用三次样条插值函数和正弦函数构造挠度模式，根据最小势能原理，将板形判别——失稳判别——归结为最小特征值的求解。

A friend may be an ordinary, nonmember function, a member function of another previously defined class, or an entire class.

友元可以是普通的非成员函数，或前面定义的其他类的成员函数，或整个类。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。