可积条件

From the perspective of the variational discussion of Lagrange\'s contributions to the principles and analyzation of mechanics,the interaction between the calculus of variations and mechanics,especially the variational principles is made clear.

结合拉格朗日微积分代数化方案和18世纪可积性条件的研究，探讨了拉格朗日关于变分法基础研究的数学背景及相关工作；通过对《分析力学》中静力学约束平衡问题的细致考察，系统探讨了变分法中乘子法则的力学渊源、提出过程及意义。

Under the constraints between potentials and eigenfunctions, the Lax systems are nonlinearized to be finite dimensional completely integrable systems in Liouville sense.

在位势与特征函数之间的约束条件下，Lax系统被非线性化成为有限维Liouville完全可积系统。

We study the relations among MS, QMDS, RBVS, AMDS, GBVS and NBVS. Finally. we improve some classic results in Fourier analysis such as uniform convergence, L~1 convergence, L~p-integrability, strong approximation of continuous functions et al., by applying this new condition.

我们研究了MS，QMDS，RBVS，AMDS，GBVS和NBVS等不同数列之间的关系，在此基础上，我们给出了NBV条件在研究三角级数的一致收敛性、L~1收敛性、L~p可积性、连续函数的强逼近等Fourier分析经典问题上的应用，对一些经典的结论作了推广。

The main tool is the notion of theLipschitz condition with positive nondecreasing integrable function L-average along thepieces one-parameter subgroup which includes the classical Lipschitz condition as well as theγ-condition as special cases.

我们在研究中引入沿着任意段单参数子群的关于取正值非减可积函数L-平均的Lipschitz条件。从而把李群上的Kantorovich定理及Smale理论放在统一的形式下进行研究。

The main tool is the notion of the Lipschitz condition with positive non-decreasing integrable function L-average along the piecewise geodesic which includes theclassical Lipschitz condition as well as theγ-condition as special cases.

同时，我们在研究中引入了沿着分段测地线的关于取正值非减可积函数L-平均的Lipschitz条件的概念，从而把流形上的Kantorovich定理及Smale理论统一起来研究。

Then we study theaffine Toda field theory and its integrable boundary condition.

然后研究了affine Toda场论及ZMS模型的可积边界条件。

We first introduced a new concept called transitive resolvable idempotent symmetric quasigroup, proved that the necessary condition for the existence of TRISQ is also sufficient, then presented a tripling construction for LKTS by using TRISQ instead of TKTS, thus removed the condition "there exists a TKTS" in Denniston''s tripling construction for LKTS; We also improved J. Lei''s product construction for LKTS by removing the condition "there exists a TKTS".

我们首先引入了可迁可分解幂等对称拟群的新概念，证明了TRISQ存在的必要条件也是充分的，然后给出了用TRISQ取代可迁Kirkamns三元系的LKTS的三倍构造法，这样就去掉了在Denniston的关于LKTS的3倍构造中的条件"存在一个TKTS"；我们用TRISQ取代TKTS改进了雷建国的关于LKTS的一个积构造方法，从而去掉了该构造方法中的条件"存在一个TKTS"。

The adaptive compensation term of the optimal approximation error and a new robust term are adopted to minify the influence of modeling error and parameter estimation error.

该方案通过引入最优逼近误差的自适应补偿项和新的鲁棒项，削减建模误差和参数估计误差的影响，从而在稳定性分析中取消了要求逼近误差平方可积或逼近误差的上确界已知的条件。

An integrable model with non-period boundary condition is constructed by use of factorized L operator.

用因式化的L算子构造了一类在非周期边界条件下的可积模型。

A sufficient condition is presented for the existence of square integrable and joint continuity of its self-intersection local time.

给出了其自相交局部时平方可积和联合连续的一个充分条件，并通过对广义α-stable过程自相交局部时的H？

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。