无穷

In the condition weaker than the condition, the corresponding functional of the equation is first proved satisfying the condition.

在比条件更弱的条件下，先证明方程相应的泛函满足条件，再应用山路引理得到了该问题无穷多解的存在性。

This paper is the continuance of that of Lewalle (2001). Lewalle has made use of Gaussian wavelet to obtain the N-S equations with flexion as fundamental quantity in the infinite domain. In that work, Lapalace operator has been degraded to one-order operator. Moreover the resulted N-S equations take the form of diffusion equations with local bilinear mutual interaction kernel.

本文是Lewalle工作的继续，Lewalle利用高斯子波，得到了以弯曲度为基本量的无穷域中N-S方程，此时Lapalace算子降低为一阶导数，并且N-S方程变形为具有局部化双线性相互作用的扩散方程的形式。

In the case ofreflectionlessness,after determining the gauge transformation,expressions of multi-soliton solutions of the L-L equation with an easy plane are obtained explicitly bysolving the linear algebraic equations with the aid of the well-known Binet-Canchyformula.

由于要克服因Jost解在参数趋于无穷时不独立于L-L方程的解的困难，必须引进规范变换，这是不涉及微分方程的Riemann问题方法无法解决的。

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

This approach could also be used to generalise the water flows to longer, or even endless, animations.

这种方法也可以用于概括水流较长，或甚至无穷，动画。

In a proper condition,U* is a generalized solution of the differential equation system.

不同于[1-2]用有限维空间去逼近无穷维空间，本文空间是不变的。2。

In this paper, we show a formula for the arciform area enclosed with a parabola and a straight line by means of two kinds of clever separation and the knowledges of elements mathematics such as the sum formula of infinite decreasing geometric sequence .

文章运用两种巧妙的分割和利用无穷递缩等比数列求和公式等初等数学知识，求出了抛物线与相交直线围成的弓形面积计算公式。

We define the sum of the infinite geometric series...

我们把无穷几何级数的和定义为。。。

Yesterday morning in the speech of 3 hours, he is run from capital speak of a technology innovation, from play philosophy is taught to children a little, the language is vivid and humorous, gesticulation commutation is boundless, appear passion and loosen, those who make the audience below the stage deep experience character of Tang Jun place " be an upright person to work again first, now and then make beautiful " play philosophy.

在昨天上午三个小时的演讲中，他从资本运作谈到技术创新、从处事哲学聊到子女教育，语言生动幽默，手势变换无穷，显得激情而又放松，让台下观众深刻体会到唐骏所言的"先做人再做事，偶然作作秀"的处事哲学。

His performance fully displayed the infinite glamor of Chinese dance.

他的表演充分展示了中华舞蹈的无穷魅力。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。