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Chapter two proposes the unified form of Hojman"s conservation law and Lutzky"s conservation law. Firstly, the author introduces the general Lie group of transformations that the variations of both the time and the generalized coordinates are considered, derives the determining equation of Lie symmetry for the system, presents a new conservation law, which contains the Hojman"s and the Lutzky"s conservation law as two special cases, and obtains a condition to exclude trivial Hojmans conserved quantities.

第二章，Hojman定理和Lutzky定理的统一形式：首先，引入一般意义下的Lie变换群(即位型变量q_s和时间变量t同时变换)，给出系统的Lie对称性确定方程，提出一个新的守恒律，Hojman定理与Lutzky定理则分别是这个新守恒律在两个特殊情况下的推论，导出一个可排除平凡Hojman守恒量的定理，并分别讨论了Birkhoff系统和非完整系统的Lie对称性和Hojman守恒量，最后，讨论了Hamilton系统的梅对称性与Lie对称性的关系，给出了由梅对称性求Hojman守恒量的方法。

In order to solve the problem,We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential manifold. The travel time are expressed as polynomials of the horizontal offset between the two points, and the single-square-root operator in frequency-wavenumber domain are expressed as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddle-point method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量(地面点到地下相点的水平距离)的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

In order to solve the problem, We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddlepoint method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量（地面点到地下相点的水平距离）的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

Vi.上床,分层 apple-pie bed be brought to bed confined to one's bed die in one's bed feather bed flock bed get up on the wrong side of the bed get out of bed on the wrong side go to bed go to bed in one's boots keep one's bed keep to one's bed leave one's bed lie on the bed one has made lie in the bed one has made lie on a bed of thorns make one's make one's bed bed and lie on it make one's own bed make one's own bed and lie on it make the bed make a bed narrow bed narrow cell narrow house narrow home put to bed put to bed with a shovel stretch on the Procrustean bed

发生性关系；付印喝得大醉早睡早起因病躺在床上因病躺在床上病愈起床自作自受自作自受如坐针毡；坐立不安自作自受自作自受自作自受自作自受整理床铺整理床铺坟墓坟墓坟墓坟墓使睡；将扣紧准备印刷；准备编排直至印刷为止埋葬，下葬；扶送回家上床按照同一标准判断；强求一致 24 As you make your bed， so you must lie on it。

Furthermore, in order to overcome the disadvantage of GMC, i.e., it can only apply to the processes with relative order of 1, based on Lie derivative, we propose to let the r th derivative of the process output follow the given reference trajectory, to get the control law expression through solving an optimization problem.

针对GMC方法只适于相对阶r为1的简单过程的缺点，采用Lie导数的概念，令过程输出的r阶导数的轨迹为事先设定的标称轨迹，通过解优化问题得到控制律表达式，把GMC方法推广至相对阶r大于1的复杂多输入多输出过程，从而提出了一种广义一般模型控制方法。

Lie's theory is used to extract the analytic solutions of nonlinearsystems in this thesis for the first time.The basic form of Lie group is ex-pounded through Lie series and Lie transformation.

本文首次将Lie群理论用于求解非线性系统的解析解，通过引用Lie级数和Lie变换，阐明了Lie群的基本形式。

Lie to anyone else under the sun, but don't lie to me.

大白天对其他人说谎可以，对我说谎可不行。

Some properties, such as primeness, semiprimeness and nondegeneracy are introduced. The primeness and semiprimeness are lifted from a Lie color algebra to its algebras of quotients.

在此基础上，本文提出了Lie color代数的商代数和弱商代数的概念，定义了Lie color代数的一些性质如素性、半素性和非退化性等，并将素性和半素性推广到Lie color代数的商代数中。

Among them 5 right room getting idiopathic room speed 4 melt target ordered and lie to flow out an alternate department, one lie and flow out dish and dissociate the side; 7 left room getting idiopathic room speed 5 melt some target on left ventricle underpart of the interval, 1 left ventricle flow out dish, 1 nearly apex of the heart department fail to bring out the tachycardia steadily, can bring out behind the skill, but the room nature tachycardia of recidivation while following up a case by regular visits to February, do and melt to achieve success moreover.

其中5例右室特发性室速中4例消融靶点位于流出道间隔部，1例位于流出道游离侧；7例左室特发性室速中5例消融靶点于左心室间隔中下部，1例左心室流出道，1例近心尖部未能稳定诱发心动过速，术后不能诱发，但随访二月时再发室性心动过速，再次行消融取得成功。

To live a lie would bring us pain: To live a life of lie would make us painful.

lie 表示&躺下&之意时，它的过去式、过去分词和现在分词分别是：lay， lain 和 lying 。

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。