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By using the method of the gauge transformation,this paper obtains the gauge transformation of Eigenvalue problems of energy dependent potentials and the Backlund transformation.

用规范变换的方法,导出了位势依赖于能量的特征值问题的规范变换及相应的贝克隆变换。

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。

Unlike Gauss curvature, the mean curvature depends on the embedding, for instance, a

不象高斯曲率,平均曲率依赖于嵌入,例如,一个

Advances in Inorganic Geochemistry have often been dependant on introduction of new technology.

无机地球化学研究的进展通常依赖于新的技术开发。

But first of all, regional cooperation is influenced by region's geopolitics, especially the Sino-Indian relations.

而地区合作首先依赖于这个地区的地缘政治,尤其是中印关系。

We get addicted to it, so dependent on its moving pictures that it begins to dominate our lives.

我们得到上瘾,所以依赖于它的移动图片,它开始主宰我们的生活。

Little girls are made of sugar and spice and, according to a study published in the journal Cell, a fierce determination to maintain their girlishness. Because it seems that a single gene keeps their ovaries from turning into testes.

香香甜甜、温柔可爱是女孩子们的天性,而《细胞》杂志上刊登的一篇研究表明使这种女性特征得以维系依赖于一种顶级基因测定——一种单基因抑制着女孩子们的卵巢变成睾丸。

The degree of a woman's sexual pleasure depends on the distance of the clitoral glans from the vaginal opening.

妇女的性愉悦的程度依赖于阴蒂头到阴道口的距离。

Purified GO could oxidize both glycolate and glyoxylate, and both activities highly depended on FMN. The activity of glyoxylate oxidation was weaker than that of glycolate. During purification or storage of purified GO, the ratio of glycolate to glyoxylate oxidation was progressively enhanced.

纯化的菜心叶片乙醇酸氧化酶对乙醇酸和乙醛酸均有氧化活性,且两者都强烈依赖于FMN,但对乙醛酸的氧化能力相对较弱;在酶的纯化及纯化酶的贮存过程中其两催化活性的比值均呈逐渐升高的趋势。

The capability of monoamine to the secretion of gonadotropin depends on the serum level of estrogen.

单胺类递质对促性腺激素分泌的影响依赖于体内的雌激素水平。

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年美国个人破产法的一个改动使得破产登记急速下降,而后引起了信用卡大规模的亏损。

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