应用函数

The paper provides the theorem of the limit of combination of power and exponent function ,which gives us a new method to work out the limit of this kind of function.

给出了幂指函数极限定理，对求幂指函数极限的方法进行了讨论，并给出一些应用实例。

By introducing special stress functions, we find solutions of eighth order homogeneous linear equation set with complex functions method and approach of undetermined coefficients, deduce calculation formulas of bi-material elastic constants for two dissimilar orthotropic composite materials. The expressions of stress intensity factors near finite interface crack tip subjected to symmetric loadings are derived. A engineering application numerical example is given.

通过引入特殊的应力函数，采用复变函数方法和待定系数法求解了八阶齐次线性方程组，推出了两种相异正交异性复合材料板的双材料弹性常数的计算公式，得到了受对称载荷作用的界面裂纹尖端应力强度因子的计算公式，给出了一个工程应用算例。

The supper-resolution of the PR method is pointed out for the first time and the uniqueness of the retrieved complex image is proved with the help of linear independence of given discrete system response.

通过实际信号分析得出由图象强度定义的对比度函数更适合于聚焦参数的最优化求解，解析得到对比度函数的梯度，能够应用FFT进行高效计算。

Based on the analysis of some aspects, such as the approximative algorithm of FOC, the Tustin transform theory and its generating function formula's character, the convergence guarantee of binomial power function by Maclaurin expanding, and the consideration of the limitation of conventional methods, an improved method is proposed to compute the numerical evalution of FOC using PSE and Tustin transform and is further applied to solving the linear FOS.

以分数阶算子近似方法的分析研究为基础，基于Tustin变换理论及其用于分数阶算子的离散生成函数公式特点，利用二项式幂函数的Maclaurin展开能够保证收敛的特性，考虑常用算法的局限性，提出了一种改进的基于幂级数展开和Tustin变换的分数阶运算方法，并应用于线性分数阶系统的求解，给出了递推算法的详细推导。

By calculating the relative integrals of the function and the residues of a meromorphic function and taking their real part,thus this paper got the analogous result with primitive Poisson-Jensen′s formula in form,then applied the analogous result to a practical example,it illustrated correctly.

由计算有关函数的积分和亚纯函数的留数，并取它们的实部得到了形式上与原来的Poisson-Jensen公式类似的结果，通过将其应用到实例中，说明它是正确的。

The basic idea was to discrete the structure and find the load function according to the energy criterion of buckling and the principle of random displacement method. As the critical load is the minimum of the load function, a problem of frame buckling can be transformed into an optimization problem. Therefore, the critical load can be found through solving the optimization problem.

先将结构离散为一个有限自由度系统；然后根据有限自由度系统平衡稳定性的能量准则和随机位移法的基本原理，建立符合能量准则的载荷函数，该函数不为零的最小值即为临界载荷，由此将稳定问题转化为无约束的多维优化问题；最后应用遗传算法求出相应于最优解的目标函数值。

Second, taking risk taste coefficient into the model solve the problem of without risk taste in model. Third, it builds up a new model based on the thought of GA and mistiness mathematics as the fit function in GA.

第二，以遗传算法中的目标函数的方式建立了基金投资组合模型，以风险调整的收益的最大值作为遗传算法中的目标函数，应用遗传算法进行了求解。

The speciality to let several coefficients of S-M algorithm are analyzed;(2) We first propose the nonlinear and adaptive prediction model based on several closest neighbors and extend the method to multistep prediction;(3) We first exploit Empirical Mode Decomposition technology to predict hopping frequency codes, it is namely that a complex time series is decomposed as several Intrinsic Mode Functions easy to prediction, then predict these IMF respectively, at last reconstruct estimated values of the time series;(4) We exploit the above prediction model validate effect while there are omitted data in observed time series and propose the corresponding resolve.

1具体分析了S-M算法中几个参数设置的特点；(2)首次提出了基于邻近点的非线性自适应预测模型，同时将这种算法推广到多步预测；(3)首次采用经验模态分解技术预测跳频码，即将一个复杂难以预测的时间序列分解为几个相对容易预测的本征函数，然后分别预测这些本征函数，最后重构出时间序列的估计值；(4)应用基于邻近点的非线性自适应预测模型验证了观测时间序列存在数据缺损时的预测效果，并提出了相应的解决办法。

The preliminary chromatogram data were resolved with Mallat algorithm of wavelet analysis theory. This method that resetting the high frequency signals, reconstructing low frequency and then correcting the background signals in the original signal was to avoid the data skewness with negative digital points after background correction and achieve the baseline correction; according to the study and analysis of simulated data including curve background and real data of the needle-plate and free metal partials insulation defects, the method is effective; the best wavelet function of the background correction is Db5 and the best resolution times of the background correction is 8 for chromatogram data of SF_6 decomposition products, based on the calculation with different wavelet functions and resolution times.

在初步获取的气相色谱数据基础上，运用小波分析技术中的Mallat算法对色谱数据进行小波分解，采取将高频信号置零，重构低频背景信号，再用原始信号扣除背景信号的方法，并对背景信号进行纵向平移以避免扣除后出现负数据点造成色谱峰失真的题目及达到色谱图基线校正的目的；通过对含曲线背景信号的模拟色谱数据和针-板、自由金属微粒缺陷下的真实数据的计算研究表明，该方法的应用是有效的；并通过对不用小波函数和不同分解次数的背景扣除计算，确定了SF_6气体放电分解组分色谱背景扣除所选用的最佳小波函数为Db5小波和最佳分解次数为8次。

Are also given by constructing Lyapunov function. Finally, by applying the energy methods, Sobolev embedding theorems and bootstrap arguments, the global existence of nonnegative classical solutions to equations with homogeneous Neumann boundary value condition is proved when the space dimension is at most 5. Under certain conditions for the coefficients of the reaction functions, the convergence of the solutions is established for the system with large diffusion coefficients by constructing Lyapunov function.

的正平衡点全局渐近稳定的充分条件；最后，当空间维数不超过5时，应用能量估计、Sobolev嵌入定理和bootstrap技巧证明在齐次Neumann边值条件下非负古典解的整体存在性，并通过构造Lyapunov函数给出当反应函数的系数满足一定条件、扩散系数较大时该模型解的收敛性。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。