查询词典 Lenard

With the help of nonlinearization approach, the Lenard spectral problem related to the DNLS hierarchy is turned into a completely integrable Hamiltonian system with a Lie-Poisson structure on the Poisson manifold

通过非线性化方法，证明了与DNLS孤子族相联系的Lenard特征值问题在具有Lie-Poisson结构的Poisson流形C~N×R~N上是完全可积的Hamilton系统。

It thus became possible to study the cathode rays, and also the fluorescence they caused, outside the discharge tube and Lenard concluded from the experiments that he then did that the cathode rays were propagated through the air for distances of the order of a decimetre and that they travel in a vacuum for several metres without being weakened.

但是后来，1892年他在波恩大学做赫兹的助手时，赫兹让他观察了他的新发现，赫兹将一片盖上铝箔的含铀玻璃片放入放电管，当用阴极射线轰击铝箔时，铝箔下面发出了亮光。

A 2×2 matrix differential Lenard operator is extended to a 3×3 oneand the soliton hierarchy with their Lax pairs are deduced easily.

并使孤立子方程谱问题的伴随表示与Lenard算子对有机的连系在一起。

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。

It was this sacrifice that made Virginia think that she stole Lenard's life.

就是这样子的牺牲令Virginia感觉自己绑架了Lenard的生命。

Based on a 2×2 eigenvalue problem, a 3×3 Lenard pair of operators and a new 1+1 dimensional soliton hierarchy are presented.

本文立足于一个2×2谱问题，获得了3×3 Lenard算子对，并由此导出一类非平凡的(1+1)维孤子方程族。

By choosing the special values of parameters in the hierarchy, the hierarchies of the general TD, TD, the general C-KdV and C-KdV can be obtained. In order to investigate the Hamiltonian structure of this soliton hierarchy, a new Lenard gradient sequence {Gj} and its corresponding 2×2 Lenard pair of operators are introduced.

对该方程族中的参数取不同的值，可得到广义TD族，TD族，广义C-KdV族和C-KdV族；为研究其Hamilton结构，通过定义新的Lenard递推序列{G_j}得到了该等谱方程族的2×2 Lenard算子对

The study underscores the need for common sense to be exercised by psychiatrists and patients alike, said Lenard Adler, MD, in a telephone interview seeking outside commentary. Dr. Alder is the director of the Adult ADHD Program at New York University Medical Center in New York, where he is also an associate professor of psychiatry and neurology.

Lenard Alder医师在电话访谈中表示，精神科医师及患者都必须具备必要的共识，但是这项需求在本试验中被低估了；Alder是纽约大学医学中心成人ADHD计画的主持人，也是该校的精神科与神经科副教授。

Used with permission. Steven R. Lenard

PDF （Steven Lenard提供，授权使用

Chapter 5 and 6 are concentrated on the fundamental problem how to con-struct finite-dimensional and infinite-dimensional Liouville integrable Hamiltonsystem.Starting from two isospectral problems,Tu's scheme is applied to gen-erate the corresponding CKdV hierarohy and coupled Burgers hievachy,andthey are shown to be Liouville integrable Hamilton systems.Two spectral prob-lems,which contain three and four potentials respectively,are also studied byTu's scheme.Two new Liouville integrable Hamilton hierarchy are estab-lished.A new general approach using Lenard's gradient sequence is presentedto obtain Lax integrable hierarchy and their zero curvature representation,andsome examples are given.The nonlinearization procedure is applied to theeigenvalue problem of coupled Burgerrs hierarchy.It is shown that underBargmann constraint,the spatial part of the Lax pairs is nonlimearized to be afinite-dimensional Liouville completeiy integrable Hamilton system.

第五、六章研究如何从一个谱问题出发构造可积发展方程族及其零曲率表示、Hamilton结构和判断Liouville可积性：通过对二类具有2个位势的等谱问题直接研究，利用屠格式生成了耦合KdV族和耦合Burgers族，并证明它们均为Liouville可积的广义Hamilton方程族；而通过分别具有3个和4个位势的等谱问题，遵循屠格式构造了二族新的Liouville可积的广义Hamilton方程族；给出了利用Lenard梯度递推序列产生发展方程族及其零曲率表示的一种方法，作为应用，讨论了CKdV族，BPT族及耦合Burgers族的产生及其零曲率表示；应用非线性化技巧，证明了在Bargmann约束下，耦合Burgers族的Lax组可被线性化为Liou-ville完全可积的Hamilton系统。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。