查询词典 degenerate set

In this paper we define distribution cosine functions covering the degenerate case. We also consider the degenerate distribution function generated by a multi valued operator A, its relation to the integrated cosine function and the wellposedness of the degenerate abstract Cauchy problem.

引 言分布半群的概念最早由 L ions在 6 0年代引入，近年来，其他类型的分布半群相继被定义和讨论[1— 4]，由于研究退化线性方程的需要，多值算子对应的 Cauchy问题也开始受到人们关注，在 [2 ，4]中有退化情形的分布半群的定义及研究。

For an abitrary set X, appropriate order relations on WCL (the set of all weak closure operators), WIN (the set of all weak interior operators), WOU (the set of all weak exterior operators), WB (the set of all weak boundary operators), WD (the set of all weak derived operators), WD*(the set of all weak difference derived operators), WR (the set of all weak remote neighborhood system operators) and WN (the set of all weak neighborhood system operators) can be defined respectively, which make WCL, WIN, WOU, WB, WD, WD*, WR and WN to be complete lattices that are ismorphic to CS(X,CS is the set of all closure systems on X.

证明了可以在WCL(X上的弱闭包算子的全体)、 WIN(X上的弱内部算子的全体)、 WOU (X上的弱外部算子的全体)、 WB (X上的弱边界算子的全体)、WD、 WD*(X上的弱差导算子的全体)、 WR(X上的弱远域系算子的全体)和WN(X上的弱邻域系算子的全体)上定义适当的序关系，使它们成为与CS(X，〖JX-*5[JX*5]同构的完备格其中CS(X是给定集合X上的闭包系统的全体。

The 4 nucleotides of DNA sequences can be further encoded with two - bit digits in which t he first bit is the base bit to encode purines and pyrimidines and the second bit is the functional group bit to encode the keto group and amino group. According to the degree of degeneracy of genetic codes and the two dimension distribution of molecular weights and isoelectricpoints of amino acids , a set of classification graph(Venn' s diagram) of amino acids can be obtained. It is suggested that the amino acids of high degenerate group are mostly small and simple, and constitute the transmembranic structure or the structural domains of protein molecules. So amino acids of high degenerate group might appear in the early evolution stage.

根据氨基酸遗传密码子的简并程度并以分子量及等电点作为氨基酸的化学特性坐标，作出其二维集合MP分类图，根据氨基酸的分类分析，可以认为：高简并度氨基酸多数是脂烃类和羟脂烃类的氨基酸，分子量比较小，分子结构比较简单，大部分为疏水性，主要组成跨膜结构或蛋白质的结构域，可能是出现较早的氨基酸；而低简并度的氨基酸，分子结构比较复杂，分子量比较大，多数是和蛋白质功能有密切联系的基团，可能是进化出现较晚的结构。

The ultrastructural changes during the development of sieve element companion cell complex (SE/CC complex) in Populus deltoides were investigated using electronic microscopy. The result showed that SE and CC tome from the same secondary phloem mother cell. The development of sieve element went through three stages, i. e. immature, mature, and degenerate stage. In immature stages the sieve element presented radial expansion, cell wall thickening, and production of sieve plastid and P-protein. The cytoplasma selectivly autolysed in mature stage. At the same time, karyoplasm was dispersed, and nuclear envelope was not clear, or karyoplasm was disorgnized, and nuclear envelope was clear. The karyopalsm finally turned into P-protein. In degenerate stage, the cytoplasm completely disappeared, and the function was lost.

利用电镜技术研究美洲黑杨次生韧皮部筛管和伴胞发育过程中细胞超微结构的动态变化，观察到筛管和伴胞由同一个次生韧皮部衍生细胞分裂分化形成筛管约发育历经未成熟期、成熟期和衰退期的变化未成熟期筛管分子表现为细胞的径向扩展、壁的增厚、筛管质体和P-蛋白质的产生；成熟期筛管分子细胞组分发生选择性自溶，细胞核核质弥散状，核膜不清晰，或核膜清晰而核物质降解，最后细胞核完全解体转化为P-蛋白质类的物质；衰退期筛管分子细胞质完全解体消失，失去功能。

But in the complete degenerate case,the thermo-electric voltage decreases to zero,and in the complete non-degenerate case it isindependent of the statistical properties.

但是在粒子完全兼并的条件下，热电压趋于零；并且在完全非兼并条件下，热电压与统计参数g无关。

As we all know, it is equivalent to the null controllability of a cascade system governedby two linear degenerate parabolic equations. Next, we study the null controllability of acascade system governed by a semilinear degenerate parabolic equation and a semilinear heatequation.

众所周知，这等价于两个线性退化抛物方程构成的耦合系统在单个控制作用下的零能控问题；接下来我们又考虑了一类半线性退化抛物方程与半线性热方程构成的耦合系统的零能控问题。

If the systems satisfy linearly degenerate or weakly linearly degenerate, the classical solutions to Cauchy problem for quasilinear hyperbolic system will exist as the initial data with compact support is small enough.

本章第一节，我们主要推导了波的分解公式，提出了弱线性退化、适配性条件和正规化坐标系的概念，并且给出了在正规化坐标系下一些关系式。

The results show that the emission probability behaviors in the non-degenerate two-photon mazer differ from those in the degenerate two-photon mazer,since two cavity modes are allowed in the mazer so that there are two freedoms changing the potentials that the atoms experience as they transit the cavity.

发现由于在微脉塞中存在两种腔场模式，导致有两个自由度来改变原子在经过腔场时所受到的势场，因此非简并双光子微脉塞的发射几率的行为不同于简并双光子情况下的发射几率。

By using the non-degenerate TPA absorption process between both of pulses, a novel project if explored for compressing and shaping the self-compression pulse induced by FCA, in which shaping of self-compression can be optimized by adjusting the initial delay time and control pulse energy. In addition, the operations of ultrafast all-optical modulation and logic NOR gate are achieved by utilizing the non-degenerate TPA effect.

应用脉冲之间的非简并双光子吸收过程，探索出了对受自由载流子吸收作用而形成的自压缩脉冲进行压缩整形的新方案，通过调节脉冲之间的初始时延和控制脉冲的能量，可以优化自压缩脉冲的质量；另外，应用此效应，也实现了超快脉冲对连续光场的全光调制和超快逻辑非门的操作，在光调制过程中，发现了色散和初始啁啾都将改变所形成的调制暗脉冲的调制深度。

The Pappus theorem and Pascal theorem are the important theorems of three points colinearity of degenerate and non degenerate two stage curves respectively.

常见资料如文献 [1～ 3]等均介绍了著名的Pappus定理和Pascal定理，这两个定理分别是退化和非退化二阶曲线中关于三点共线的重要定理，应用广泛。

A carrier gas such as nitrogen is directed through line 20 and valve 22 to connect with line 26 and mix with the gas sample.

如氮气之类的载体通过管线20和阀22引入，与管线26相通，与气体样品混合。

But for the most part, knaves and parasites had the command of his fortune

然而支配他的家产的大多是恶棍和寄生虫。