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For an edge-localized particle source, using the complementarity relation of the solution, wellbehaved generalized Fourier expansion of the solution can be obtained.

对粒子源处在边界附近的情形，通过解的互补性关系，可以获得品质好的广义傅里叶展开。

Based on the Betti-Rayleigh dynamic reciprocal theorem, the reciprocal property of the Green function is demonstrated; and the analytical solution of soil vibration subjected to moving loads is deduced. By means of double Fourier integral transform, the problem is firstly transformed into wave number-frequency domain, which makes it very convenient to derive the solution and furthermore to analyze the frequency characteristics of soil vibration.

基于Betti-Rayleigh动力互易定理，论证了地基土Green函数的互易性，推导了移动荷载引起的地基土振动解析解，进而推证出移动常力荷载和移动简谐荷载作用下地基于表面振动在波数－频率域内和空间－时间域内的解析表达式，并采用Matlab对其进行数值计算。

According the connection between the solution of linear fractional differential equation and nonlinear fractional differential equation, the expression of the solution of the nonlinear fractional differential equation is formed.

在一定的条件下，建立了非线性分数阶微分方程在边值条件下有解存在。

First of all, the method of Fredholm alternative is used to obtain the approximate solution of the first order for the bifurcating periodic solutions of a nonlinear system with delayed velocity feedback. The bifurcation direction and the stability of the bifurcating periodic solution are also determined.

首先，用Fredholm择一方法分析了一具有时滞速度反馈的非线性振动系统的Hopf分叉，得到了局部分叉周期解的近似表达式，确定了分叉解的分叉方向及稳定性。

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To get calculation process of analytical solution for predicting the shape of ground arch in bearing soil by studying the theoretical solution for Calculating the shape of ground arch in free soil and Considering the effect of load.

并在此基础上给出了土体中不利于作用荷载的区域，在此区域内作用荷载将会引起隧道周边及荷载作用位置处的塑性区范围显著增加。

Use of analytical solution for predicting the ground settlement induced by tunneling in free soil and Plasticity Yield Criterion get the calculation process of analytical solution for predicting the plastic zone induced by tunneling in free soil.

利用预测自由地层中隧道开挖引起土体沉降的解析解，引入理想塑性屈服准则，得到了自由地层中隧道开挖产生塑性区范围的解析解的计算过程。

The existence and uniqueness of solution for FROE is proven,and its analytical solution is given.

证明了分数阶Relaxation-Oscillation方程解的存在惟一性，并利用格林函数给出了它的解析解。

Using developed optimal model for Ring-Pull Can size design,the optimal solution of cylindric can size design and the suboptimal solution of frustum of a cone on cylinder as well as CCB-1A can size design are botained.

建立了易拉罐尺寸设计的优化模型，得到了正圆柱形罐尺寸设计的最优解和上部为正圆台下部为正圆柱形罐以及CCB-1A型罐尺寸设计的次优解。

Result It was found in the results that the better pretreatment time for onion root-tip was 3.0 h and its better dyeing solution was basic fuchsin dyeing solution. On this basis, it was found that the chromosome number of tested onion was 2n=2x=16 through chromosome karyotype analysis on the root-tip cells of onion.

结果］结果发现，洋葱根尖的较好的预处理时间为3.0 h，较好的染液为碱性品红染液；在此基础上，通过洋葱根尖细胞染色体核型分析，发现试验所用洋葱的染色体数为2n=2x=16。

The studies on the developing of new media are very important to the increasing of the area density of HDD and to the implementation of hybrid recoding technology.

光磁混合记录方法，是一种可以突破超顺磁极限的限制，并进一步提高硬盘记录密度和读写速率的一种新型超高密度信息存储方式。

In io, mTOR inhibition promotes T cell anergy under conditions that would normally induce priming.

体内研究中，在正常可激发免疫反应的条件下，抑制mTOR可促使T细胞无能。