零函数

Theorem 1 constructs a set of universal measure zero using continuous extension; Theorem 2 verifies absolutely continuous function being of good property under some condition; Theorem 3 reveals some relation between real function and meager.

定理1 主要运用了连续延拓构造了一个泛测度零集；定理2 证明绝对连续函数在一定条件下具有良好的性质；定理3 揭示了实函数与第一纲集的某种关系。

Besides, through the method of concatenation, the upper bound of algebraic immunity and the form of the annihilators of any generalized boolean function were also determined.

此外，还通过级联函数的方法确定了任意广义布尔函数的代数免疫的上界和零化子的形式。

In Section 3.1, some basic properties of almost automorphic functions and functions with 0 mean value are investigated.

sect；3.1主要研究了概自守函数和具有零平均值的函数的一些基本性质。

By use of the series representation of the Bessel function of the first kind and zero order, the approximate expression of the wave structure function under all conditions of atmospheric turbulence is derived.

由第一类零阶贝塞尔函数的级数展开推导出波结构函数在任意湍流条件下的近似表达式。

We will prove that the only compact dual Toeplitz operator is the zero operator, and that a densely defined dual Toeplitz operator with square integrable symbol is bounded if and only if its symbol is essentially bounded.

首先，我们证明了只有零算子是紧的对偶Toeplitz算子，同时给出了以平方可积函数为符号稠定义的对偶Toeplitz算子有界当且仅当它的符号函数是本性有界的。

They difined and kept the moving interface as zero level of Level Set function.

他们把运动界面定义成Level Set函数的零等值面，然后始终保持它是零等值面。

The design of output feedback H(subscript ∞) controllers is discussed for nonlinear discrete singular systems. First of all, by means of generalized Lyapunov function and linear matrix inequalities, zero solution E-asymptotically stable is studied for the system, a sufficient condition is given such that the system is zero solution E-asymptotically stable and a H(subscript ∞) norm constraint. And the output feedback H(subscript ∞) controller is designed to guarantee the performance of the resulting closed-loop system.

主要对非线性离散广义系统的输出反馈H控制器的设计问题进行讨论，首先利用广义Lyapunov函数和线性矩阵不等式，对系统的零解E-渐近稳定性问题进行分析，在此条件基础上给出系统零解E-渐近稳定且具有H范数约束的充分条件，然后设计系统的输出反馈H控制器，使得闭环系统具有同样的性能。

A configuration that transition points are reflection symmetric about the midpoint with phase offset in one period is proposed. The intensity of the zero order becomes the function of the phases and can be eliminated.

采用周期内位相突变点镜向对称，前后半周期位相相差结构设计的反对称型达曼光栅，可使其零级衍射光斑强度仅是位相的函数，因此可消除零级谱点。

Using the autocorrelation function, the principal of homodyne method is explored. The relationship between delay time induced by delay fiber and characteristics of additive frequency-domain fluctuation affixed on homodyne beat noise photoelectric-current spectrum are intensively analyzed.

一、利用自相关函数研究了零拍法测量激光线宽的原理，重点考察了零拍光电流谱线上所附加的频域周期性波动，确定了该波动的频域周期与光纤延时线所产生的时延成反比。

By employing the Jordan-Wigner transformation and a modified mean field method, we are able to determine its ground-state quantum phase diagram approximately. The chapter IV is the main part of this Thesis. It contains the main innovations in our work. We propose and study in detail a S=1 Ising chain with the interplay of single-ion anisotropy and dimerization. The main results and innovations are the following: We show that the total number of the zero-component of spins at each site is a conserved quantity. This quantity, which may intuitively called as hole's quantum number, is hidden in the system. We show further that the hole's number in the ground-state is zero; By using the Jordan-Wigner transformation, we map this model onto a series of subsystems described by the spin 1/2 dimerized transverse Ising model. We solve the subsystems exactly, by presenting the exact wave functions and spectra;We show that this system exhibits a series of quantum phase transitions by varying the dimerization strength. We determine the quantum critical points exactly. We also show that the criticality is the same as that of the uniform S = 1/2 transverse Ising chain.

第四章是本文的重点及主要创新内容，我们具体研究了自旋为1的在横向单离子晶格场中的一维二聚化Ising链，我们得到的主要结果和创新之处是：(1)证明了这一模型具有一种隐藏的对称性，即自旋第三分量为零的格点数目是一个守恒量，并证明基态出现在空穴数目为零的子空间中；(2)利用Jordan-Wigner 变换将此模型变换到一系列自旋为1/2的横磁场中的二聚化Ising 模型，并给出了相应严格的波函数及能谱；(3)我们发现系统的基态随着二聚化强度的变化将呈现出一系列量子相变，我们得到了量子临界点的精确位置，并证明其临界性质与自旋为1/2的横磁场中的均匀Ising 链中的临界行为属于同一普适类。

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。