线性

In the fourth chapter, firstly it introduces the Boolean functions algebraic expressions of the 2-value clock-controlled stop-and-go generator and Gunther generator. It reveals the balanced property of the two kinds of Boolean functions, and studies the Walsh cycle spectrum and the autocorrelation function. It also obtains the coincidence rate of their output sequences with affine sum of some bits of input sequences, and analyzes their ability of resisting the best affine approximation cryptanalysis and differential cryptanalysis. Secondly, we properly present a new definition of the Best Affine Approximation, namely BAA on the Boolean vector functions, followed by the spectral characteristic of such defined BAA attacks through using the decomposition formula of the union distribution for random variables. A lower bound of such BAA attacks is proposed. Finally, we also study the spectral characteristic of the second kind of nonlinearity of Boolean vector functions, followed by a higher bound of such nonlinearity. Furthermore, the limited relationship between the second kind of nonlinearity of Boolean vector functions and the linear structure of the linear combination of every component is analyzed.

在第四章中，首先给出了2值密钥流"停走生成器"和"衮特生成器"中实际存在的布尔函数的代数表示，揭示了这两类布尔函数的平衡性，随后研究了它们的Walsh循环谱和自相关函数等，得到了它们的输出序列与输入序列中的某些bit的仿射项的符合率，分析了它们抵抗最佳仿射逼近攻击和差分攻击的能力；其次，我们合理地给出了布尔向量函数最佳仿射逼近的新定义，利用布尔随机变量联合分布的分解式考察了相应的谱特征，并给出了布尔向量函数与其最佳仿射逼近的符合率的一个下界；最后，我们还考察了布尔向量函数第二类非线性度的谱特征，给出了布尔向量函数第二类非线性度的一个上界，并揭示了布尔向量函数第二类非线性度与其各个分量的线性和的线性结构之间存在的制约关系。

It enlarges the range of quasi-linear Born approximation, and makes the prestack depth migration method based on quasi-linear Born approximation to be able to adapt strong lateral velocity variation.

在散射波场计算中，使用了一个更稳定的散射波场计算公式，扩大了拟线性Born近似的应用范围，使基于拟线性Born近似的叠前深度偏移方法能够适应更强的横向速度变化。

In this dissertation, we mainly discuss the resonance theorems for families of linear and nonlinear operators, and the theory of bounded linear operator space in F~* spaces.

本文主要研究F~*空间上的线性、非线性算子族的共鸣定理和有界线性算子空间理论。

In Chapter Three, we use the method of interpolation spline of differential operater to come up with the reproducing kernel in H01 with respect to bounded linear operator in H10. Then we use the reproducing kernel to develop the expression of the best approximating of bounded linear operator in H10 and prove its convergence.

第三章中，对于H_0~1中的有界线性算子，用微分算子插值样条函数的方法给出了H_0~1空间中的再生核，利用此再生核给出了H_0~1上的有界线性算子的最佳逼近的表达形式，并证明了其收敛性。

Let A" denote the commutant of a bounded linear operator S on H and R denote the collection of all operators in A" which are compact and upper triangular operators with diagonal sequence being zeros. In this paper, we show that if A"= CI + R, the K_0-group of A" is isomorphic to the integer group.

本文指出若H上的有界线性算子S的换位代数A′=CI+R，其中C是复数域，I是H上的单位算子，R是所有与S可交换的对角线为0的紧上三角有界线性算子的集合，则K_0A′

The reference domain is assumed to be a bounded open set of R~N with boundary Γ of class C~2. We investigate in this paper the null controllability for the semilinear parabolic equations in non-cylindrical domains. The fixed point method is used in the proof.

本文讨论了定义在上述非柱形区域中的半线性抛物方程零能控性，我们使用的方法主要是通过同胚映射将非柱形区域中的抛物方程转化为柱形区域中的抛物方程，再利用不动点方法得到半线性抛物方程的有关结果。

The reaction mechanism between nickel ion and butynediols in the electroless plating process was analyzed. The results show that the change of BOZ concentration is a quasi first-order reaction, the change of the nickel ion concentration is related to the BOZ density, and this change belongs to a higher order reaction. The reaction rate equation was determined as dC/dt=-8.585×10^(-4)+1.188×10^(-4)t-4.64×10^(-6)t^2+5.8×10^(-8)t^3-2.3×10^(-11)t^4. The activation energy of this process decreases as temperature increases, and it decreases with the BOZ concentration as 64-423 mg/L, it increases with the BOZ concentration as 123~240 mg/L. The S value is positively correlated to temperature, when the temperature is 80℃, the reaction rate and S value are the largest; while when the temperature is above 80℃ and BOZ concentration is over 160 mg/L, S value and the reaction rate decrease gradually.

结果表明，镀液中BOZ浓度的变化是准一级反应，镍离子的浓度变化与BOZ的浓度有关，属多级反应，其反应速率方程为dC/dt=-8.585×10^(-4)+1.188×10^(-4)t-4.64×10^(-6)t^2+5.8×10^(-8)t^3-2.3×10^(-11)t^4，反应体系的活化能E随温度的升高而减少，随BOZ浓度的变化而变化：当BOZ浓度在64~123mg/L时，E线性减少；在123~240mg/L时E线性增加。S随温度的升高而增加，当温度达到80℃时S值最大，反应速度最大；当温度超过80℃，BOZ浓度大于160mg/L时，蝎的值逐渐减少，反应速度降低。

ABSTRACT In this thesis, using the methods of ODE and calculus of variations, we prove the existence of radial and non-radial solutions of some classes of quasilinear elliptic equations.

本文主要是用ODE方法和极小变分方法证明拟线性椭圆型方程径向解和非径向解的存在性，用先验估计方法证明拟线性抛物型方程整体解的不存在性，得到了一些关于拟线性方程的新结果。

Using a decomposition in canonical form, a multi-sensor distributed optimal fusion reduced-order filter for each state component is proposed based on the component fusion algorithm weighted by scalars in the linear minimum variance sense for descriptor discrete stochastic linear systems with multiple sensors. It requires in parallel the calculating of a series of scalar weights.

对带多个传感器广义离散随机线性系统，利用典范型分解，基于线性最小方差各分量按标量加权融合算法，给出了多传感器分布式最优分量融合降阶滤波器，它要求并行计算一系列标量权重。

The proposal of the canonical representation makes this problem settled theoretically.

而且分片线性函数的复合函数和反函数仍为分片线性函数，这一许多其它函数族不具备的封闭性在电路分析中非常有用。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。