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Next, through a finite iteration of the solution sequence, an approximate solution of the optimal output-tracking control problem is obtained.

首先根据原系统最优输出跟踪控制问题构造了两个分别具有已知初始条件和终端条件的微分方程迭代序列，并证明它们一致收敛于原问题的最优解。

In the solution of the problems in algebraic equation, differential equation and integral equation, we usually resort the sotution of equation to the fixed point of mapping in metric space. The contraction mapping principle can be used to solve many problems of the existence and uniqueness of equation solution.

在代数方程、微分方程和积分方程的求解问题中，通常把所求的解归结为度量空间中映射的不动点，然后应用压缩映象原理来统一处理许多方程解的存在性和唯一性问题。

The interaction between concentrated CMC-Na solution and CB[6]could not induce the formation of gel bead.In concentrated CMC-Na solution,floccule was separated out from CMC-Na/CB[6]system and visible with naked eyes after placement.(4) CB[6]can complex with butyl ammonium hydrochloride to form stable pseudorotaxane(CB[6]/BA).

在CMC-Na/CB[6]配合体系中，CMC-Na与CB[6]聚集的纳米粒子形成较慢，需要经过放置才可以形成一些不太规整的球形纳米粒子；CMC-Na的浓溶液与CB[6]相互作用后，CB[6]对CMC-Na分子链的架桥作用要弱一些，在我们的实验条件下也没有象海藻酸钠浓溶液那样，形成球形凝胶粒子，将CMC-Na/CB[6]浓溶液配合体系在室温放置后，体系会出现许多絮状结构的聚集体。

Li2CO3 could greatly surpress the production of hydro fluoric acid in electrolyte solution even at elevated temperatures. With the increase of Li2CO3 ratio in electrolyte solution, the HF contents decreased.

使用6 Ah尖晶石锰酸锂铝塑膜电池，测试了含有添加剂Li2CO3的电解液的高温(55 ℃)循环性能，并与常规电解液进行了对比。

In order to know more about the microcosmic structure of the important biochemical model molecule formamide in aqueous solution, the Optimized Potentials for Liquid Simulations-All Atom model were used in the molecular dynamics simulation for the aqueous solution of FM in the whole concentration range. The radial distribution functions of the solutions were obtained. The interaction between water molecule and FM molecule was analyzed and calculated.

为了解重要的生化模型甲酰胺在水溶液中的微观结构，采用全原子力场在全浓度范围内对甲酰胺溶液进行了分子动力学模拟，得到了溶液的径向分布函数，分析计算了溶质和溶剂分子间的相互作用，对甲酰胺和水分子的氢键缔合情况进行了分析。

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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Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。