可积函数

We use B-spline smoothing technique to smooth the characteristic function without changing the integral quantity and get a differentiable weight function.

我们用B样条磨光技术在不改变积分值的前提下磨光特征函数，用可微的权重函数代替特征函数，提高了采样的质量。

The penalty function is adopted to impose the essential boundary condition, the tensor product weight function with a rectangular influence domain is chosen, and the finite element background cell is considered as the integration unit.

将无网格再生核质点法用于刚塑性可压缩材料轧制过程的模拟，采用罚函数满足本质边界条件，选用矩形影响域的张量积核函数，利用有限元网格作为积分单元，对求解域内和边界上采用不同的高斯积分方案。

The definition of Wavelet Analysis is that shifting the mother wavelet e.g. which has limited energy, such as shifting for, then proceeding dimensions, we obtained wavelet basis function ,, which make the inside product to the function to analysis With the Fourier transformation to the and, then the equivalent frequency spectrum of wavelet transformation can be expressed as where 、 are the transformations of 、 respectively and i is an imaginary number unit.

小波变换的含义是：把一具有有限能量的母小波，如进行移位后，再进行尺度的伸缩得到小波基函数为然后与待分析的函数作内积，即对和作Fourier变换后，可得到小波变换的等效频域表示为：其中、分别是、的Fourier变换，i为虚数单位。

The integrand in the variational principle is rewritten in symmetrical form for duality variables.

变分原理被积函数可导向对于对偶变量为对称的形式。

Firstly, this paper definited pseudometric d for n -foldproduct of σ-algebra A of subsets of a given set X , and definited indicator function ; secondly, gave the concept of differentiable of set function at S° and concept of partial derivative at S° with respect to the ith argument Si through indicator function, and defound the weak efficient solution of and optimality necessary condition; Finally, obtained three weak duality results and strong duality results under generalized convexity conditions.

首先，对已知集X的子集的σ-代数A的n-折积A^n，定义了伪度量d，给出了相应的特征函数〈h，Is〉；其次，通过特征函数给出了集函数在S 可微的定义及集函数在S 关于第i个变量Si的偏导数定义；给出了多目标规划问题的弱有效解概念及的最优性必要条件；最后，分别在目标函数和约束函数的3种较弱凸性条件下，研究n-集函数多目标规划问题的对偶问题，获得了3个弱对偶结果和强对偶结果。

Use samiliar reciprocal transformation on Lax pairs of DGH equation, we obtain a new integrable system through introducing appropriate potential function.

把类似的倒数变换应用到DGH方程的Lax对中，通过引入恰当的势函数得到了一组新的可积系统。

From teaching experience of long term,in a new way,author put forward to a brand new succinct comment and certification of Riemann Integral.

在传统的定积分教学中，往往采用达布上和、下和方法来证明函数可积性，过程繁琐，难于理解。

Secondly, the existence of chaos in a special class of discrete-time neural network models with sinusoidal activation function in the sense of Devaney with some parameters of the systems entering some regions are rigorously presented by means of anti-integrable limit method. Whats more, period-doubling bifurcation and saddle-node bifurcation in the neuron model are studied.

其次，利用反向可积极限方法证明了一类周期输入输出函数的离散神经网络模型在参数达到一定范围时产生Devaney意义下的混沌，并讨论了其一维情形的神经元模型出现倍周期分支和鞍-结点分支的情况。

Which have right or left limit everywhere are Riemannian integrable.

b上几乎处处存在右极限的抽象函数是黎曼可积的。

The wavelet function corresponding to a certain scale can be regarded as the transfer function of a band-pass filter according to the definition of CWT, thus, sampling the signal and the wavelet function respectively, the wavelet coefficients at this scale can be obtained by convolving the two time series.

根据CWT的定义，可将某一尺度下的小波函数看作一带通滤波器的传递函数，于是对信号和小波函数分别进行采样后，再利用快速傅里叶变换实现两个序列的线性卷积，便能求出相应尺度下的小波系数。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。