等价方程

In 1906, da Rios, a student of Leivi-Civita, wrote a masters thesis modeling the motion of a vortex in a viscous fluid by the motion of a curve propagating in R~3, in the direction of its binormal with a speed equal to its curvature.

很久以后，1971年Hasimoto证明了这个系统和非线性Schrodinger方程 q_t=iq_(ss 1/2|q|~2q是等价的。

It has been showed that the quantum PCII can be still valid for the general case Jacobi J 1, which is different from quantum Noether theorem. The equivalence between quantum canonical equation and PCII is deflved at the quantum level. The comparisons of these results in quantum level with those in classical theories are discussed in detail. The relationship of canonical transformation with quantum PCII is obtained.

结果表明，当变换的Jacobi行列式不为1时，量子PC积分不变量仍然存在，从而把PC积分不变量推广到了最一般情形；在量子水平上，证明了量子正则方程与该积分不变量之间的等价性；比较了经典与量子PC积分不变量以及PC积分不变量与Noether定理；给出正则变换与量子PC积分不变量间的关系。

We establish the equivalent integral equations to these problems, and prove that the defined operator is completely continuous.

建立了与这些问题等价的算子方程，并证明了所定义的算子是全连续的。

In the first part, convex duality method linearizes convex wealth equation, and the introduction of Lagrange multiplier converts original problem to an unconstrained static optimum problem. At last, we obtain another equivalent optimum problem with convex control domain.

文章前一部分运用凸对偶的方法先将财富方程线性化，Lagrange乘子的引入使最优问题等价与一个无约束的静态最优问题，最后转化为一个凸控制域的最优问题。

Chapter 2 is devoted to the effects of cross correlation between additive and multiplicative noises in a single-mode laser.

从泛函的途径建立了与具有相关加法和乘法噪声的单模激光场方程随机等价同时描述光强和位相的一个普遍的二维模型。

Therefore, the existence of periodic solutions for the Hamiltonian system and its equivalent differential delay equation is established.

从而建立哈密顿系统以及与之等价的时滞微分方程的周期解的存在性定理。

Scatchard analysis showed that one type of binding sites was formed in the imprinted polymer in the studied concentration range. The dissociation constant and the apparent maximum number of the binding sites were calculated to be 0.80 mmol/L and 52.68 μmol/g, respectively, and the maximum template selective site was 21.26 μmol/g.

Scatchard方程研究表明，在研究的浓度范围内在聚合物中形成了一类等价的结合位点，结合位点对模板分子的平衡离解常数为0.80 mmol/L，最大表观结合量为52.68 μmol/g，最大特异性吸附量为21.26 μmol/g。

Scatchard analysis demonstrates that one equal class of binding sites was formed in the imprinted polymer in the studied concentration range. The dissociation constant and the apparent maximum number of the binding sites are 1.94 mmol/L and 92.33 μmol/g, respectively.

Scatchard方程研究表明，在研究的浓度范围内聚合物中形成了一类等价的结合位点，其对模板分子的平衡离解常数K=1.94 mmol/L，最大表观结合量Cpmax=92.33 μmol/g。

The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry Beginning at the introductory level with curves in Euclidean space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book:transformation groups, the geometry of differential equations,geometric structures, the equivalence problem the geometry of elliptic operators, G-structures and contact geometry.

这本书是结构，以便读者可以选择部分文本阅读，还带了一个完整的画面，有些地区的微分几何开始入门级和曲线的部分，在欧氏空间变得更有挑战性，终于到达了高级的主题，形成了最大的一部分书：变换团体、几何的微分方程、几何结构、等价问题的几何形状，G-structures椭圆算子和接触几何。

These rules describe the equational semantics of FOPL and are the basis of type checking and program proof system creating.

第四章主要讨论了FOPL类型系统的附类型规则、纯洁性规则和表达式等价规则，从而给出了FOPL的方程语义的描述。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。