文章利用几何凸函数的性质推广了一类重要的和式不等式，得到了一些新的结论。
In this paper, We availed the property of geometic convex function generalized a kind of important sum inequality and obtained some new conclusions.
本文中，利用目标函数或约束条件的几何性质，提供了某些多元函数极值或最值问题的几何解法。
In the paper, it provides the geometrical solution to extreme value of many variables function by geometric properties of objective function or constraint condition.
利用第二类契贝谢夫多项式的性质得到了关于正余弦函数的一组有趣的恒等式。
With the use of the properties of the second Chebyshev polynomial, a group of interesting identity of sine and cosine function is obtained.
最后，利用灰度函数的性质，给出套管缺陷分类的新方法，并对其进行分类和使用寿命预测分析。
Finally, the casing defects are classified by using the properties of grayscale function, and the lifetime of casing is forecasted.
摘要利用由三角级数和幂级数复合构成的函数项级数的有关性质，得到了一类变系数非齐次调和方程边值问题的级数解。
In this paper by using the property of Fourier series a compound series consisting of trigonometric series and power series is established.
利用多晶材料织构取向分布函数（ODF）对单晶性质进行加权平均可有效预估其宏观磁性各向异性。
The magnetic anisotropy of polycrystalline materials can be predicted by averaging the properties of monocrystals weighted by using orientation distribution function (ODF).
利用密码哈希函数的良好性质和DLP的困难性问题，构造了一个可验证可关联的环签名方案。
Making use of the good properties of cryptography Hash functions and the difficulties of DLP, a verifiable and linkable ring signature scheme is constructed.
利用演化规则的函数形式，给出了一些演化规则的演化性质。
By means of the function forms of the rules, evolution properties of some of the rules are described.
利用级数的正交性质，其中任一级数中的每项系数都可表达为另一级数的各项系数的线性函数。
Due to orthogonality property, the coefficient in each term of either series can be expressed in a linear function of the coefficients of the other series.
这个方法是根据周期函数的傅里叶级数的性质和利用数学的抽象性质，直接推导出另外三种形式的傅里叶变换。
According the basic properties of Fourier series of period function and using of the abstract nature of mathematics, the method directly derives other 3 kinds of Fourier transform.
由单强度测量来恢复相位问题，也有过讨论，可以利用解析函数特有性质或应用取样定理来实现相位恢复。
The phase retrieval problem from single intensity measurement was also discussed in terms of the properties of analytical function or under consideration of sampling theorem.
该文利用支持向量回归算法中结构风险函数的性质以及KT条件，提出一种回归中的异常值检测方法。
A method of outlier detection in re-gression is proposed making use of the character of structure risk function and KT condition in support vector regression in this paper.
文章利用其中间点的居中性及严格单调函数必存在反函数的性质，探讨了几种两相异正数平均的导出。
In this paper, of which the middle between the points and there exists strictly monotonic function of the inverse function of the nature of some average of two different positive export.
它在二维三次卷积插值法的基础上利用三次样条插值法的插值函数具有三阶连续导数的性质而得来的。
It is acquired from that it makes use of that the interpolation function of cubic spline interpolation has a continuous third derivative on the base of two-dementional cubic convolution interpolation.
利用球矢量波函数的定义及性质，提取出场的径向分量，将初级场分解为相对于径向的TE波和TM波，避免了复杂的矢量微分运算。
Using the definition and character of vector function, the field is separated to TM wave and TE wave relative tor without complex vector-differential operation.
利用集收敛、函数收敛建立了集值映射收敛的概念及其性质，并依此讨论了平衡问题解的收敛性。
By using set convergence and function convergence, we establish the convergence for set-valued mappings and present the convergence results for the perturbed equilibrium problems.
利用谱相关函数的这些性质可以识别出噪声中的调制信号。
These characteristics of spectral correlation can be used to classify modulated signals, even when the signals are buried in noise.
首先利用非对称的LINEX损失函数对双指数分布族刻度参数进行了经验贝叶斯估计，并讨论了该估计的性质，给出了收敛速度。
First, we obtain the empirical Bayesian estimator of the scale parameter for the double exponential distribution based on LINEX loss function and the convergence rate of the estimate.
针对所给出的有交易费的资产模型，引入了资产折算函数，并利用辅助鞅和凸函数对偶方法，讨论了该模型下折算资产优化的性质。
In this paper, constructs the asset conversion function for given asset model with the transaction costs and discusses some properties of asset conversion by using Martingale and dual approaches.
利用“图型序列的母函数”所给出的图型序列生成函数的性质，本文导出一些重要特殊图的生成函数。
The generating function of some special graphs is deduced by making use of the properties concerned in the generating function of graphical sequences.
在第三章中，我们利用格林函数方法研究了非对称的双量子点分子的谱性质和电子输运性质。
In chapter three, we study the spectral properties and electronic transport properties of asymmetrical double-dot molecule using causal Green's function approach.
利用矩阵的迹的性质和发生函数方法，给出了稳定性分析中一个矩阵的所有特征值。
In this paper, using the property of trace of matrix and the method of generating function, we obtain all the eigenvalues of a matrix which appears in stability analysis.
利用特殊函数的性质，较详细地分析了F分布密度函数之性质，指出了第二个参数的变化对密度曲线的影响。
This paper uses the properties of special functions, analyses properties of F distributed density function in detail, points out the effects of change of the second parameter on density curve.
利用解析方法研究了平方剩余数的若干性质，并给出了平方剩余数对于两个常用数论函数的几个均值公式。
By using the analytic method some properties of the square residues are studied, and several (interesting) mean value formulas are given.
本文导出了对数凸函数的又一性质，并利用该性质很方便地推导了一类不等式。
By using the q-exponential function and q-logarithm function, the analytical solution of the equation is derived.
本文从连续图像出发，将二阶偏微分算子应用于影像函数，利用多重网格算子能得到近似影像的性质，得出一种多分辨影像分解的方法，经过图像重建过程得到融合影像。
Using the so-called approximation of image property by a multi-grid operator, we can derive a method of multi-resolution decomposition of the image, thus the fusion image is formed by reconstructing.
给出了分段线性函数族的定义和有关的运算性质，利用这些性质得到直接求解变分问题的一种新的数值方法。
The definition of the Segmental Linear Functions and some operational properties are given. By means of the properties, a new numerical method for direct solving variational problems is obtained.
介绍了奇异函数的特点，利用奇异函数建立了一种新的高层结构竖向构件分析模型，给出了基本柔度矩阵方程，并讨论了方程的基本性质和意义。
By use of singularity functions, a new analyzing model of vertical member in structural analysis of high rise buildings was established, and the matrix equation was also presented.
定义了区间值函数的RS积分，并利用它来定义模糊值函数的RS积分，给出了这种积分的一些性质。
RS integral of interval valued functions and Fuzzy valued functions are defined. Some properties of this kind of integral are obtained.
根据ID3算法中信息增益计算原理的特点，利用上凸函数的性质提出一种新的改进的ID3算法，减少了信息增益的计算量，进而提高ID3算法中信息增益的计算效率。
According to the character of expected information, the article proposed a new ID3 algorithm of decision trees to reduce the complexity of computing expected information by the convex function.
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