双线性的

It consists of the next three aspects: firstly, we study Murthys' open problem whether the augmented matrix is a Q0-matrix for an arbitary square matrix A , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the Graves algorithm can be used to solve linear complementarity problem with bisymmetry Po-matrices; Secondly, we study Murthys' conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix, we also study Pang's conjecture , obtain two conditions when R0-matrices and Q-matrices are equivelent and some properties about E0 ∩ Q-matrices; Lastly, we give a counterexample to prove Danao's conjecture that if A is a Po-matrix, A ∈ E' A ∈ P1* is false, point out some mistakes of Murthys in [20] , obtain when n = 2 or 3, A ∈ E' A ∈ P1*, i.e.

本文分为三个部分，主要研究了线性互补问题的几个相关的公开问题以及猜想：(1)研究了Murthy等在[2]中提出的公开问题，即对任意的矩阵A，其扩充矩阵是否为Q_0-矩阵，给出了肯定的回答，得到充分矩阵的扩充矩阵是充分矩阵，并讨论了Graves算法，证明了若A是双对称的P_0-矩阵时，LCP可由Graves算法给出；(2)研究了Murthy等在[6]中提出关于半正定矩阵的猜想，给出了半正定矩阵的一些充分条件，并研究了Pang~-猜想，得到了只R_0-矩阵与Q-矩阵的二个等价条件，以及E_0∩Q-矩阵的一些性质；(3)研究了Danao在[25]中提出的Danao猜想，即，若A为P_0-矩阵，则，我们给出了反例证明了此猜想当n≥4时不成立，指出了Murthy等在[20]中的一些错误，得到n=2，3时，即[25]中定理3.2中A∈P_0的条件可以去掉。

On this basis, sectionalized linearization of bilinear hysteretic structural characteristics and bilinear hysteretic filtering of structural system are put forward.

在此基础上，又提出了双线形滞后体系的随机分段线性化法和双线形滞后体系的随机分段线性滤波器。

We used NCAR/NCEPT anew analyze data and the method of bilinearity insert to fix on profile distribution of several physical field in the air on observation point and the stream field of 700hPa. We primary discussed the possible mechanism to influence aerosol size distribution.The atmospheric condition of 1000hPa~700hPa level had great influence on aerosol size distribution, and influence on coarse particle mainly below 850hPa level. The horizontal wind velocity of 925hPa level is a primary gene which contributed to coarse particles in the air. Vorticity profile especially below 700hPa level is a key gene to influence diffuse and convergence of local aerosol. The air vertical motion velocity greatly influenced aggregation and remove of aerosol particles. The vertical distribution of air temperature mainly influenced vertical transportation of aerosol.

利用NCAR／NCEP逐日再分析资料，通过双线性插值方法，确定观测点上大气中几个物理量的廓线分布；及700hPa的流场，初步探讨了影响大气中气溶胶粒子谱分布的可能机制： 1000hPa～700hPa的大气状况对气溶胶粒子谱分布影响显著，对粗粒子气溶胶的影响显著的主要集中在850hPa以下；925hPa的水平风速是影响大气中粗粒子气溶胶的一个主要因子；涡度廓线(尤其是700hPa左右及以下的涡度廓线)是影响局地气溶胶的扩散的一个关键因子；大气的垂直运动速度对气溶胶的聚合及移出影响较大；大气温度的垂直分布主要影响气溶胶垂直输送。

We first show some properties of such operators and give an explit description about the image of a linear bounded operator on a linear normed space. Then based on these results, we show the mean ergordic theorem on a C*-bial-gebra and get a sufficient and necessary condition for a linear functional to be Haar measure. Finally we discuss the sufficent conditions for the existence of Haar measure on C*-bialgebras.

本文首先通过考察这样算子的性质和刻画赋范线性空间中连续线性算子的像集的性质，证明了C*－双代数中的一个平均遮历定理，得到了C*－双代数中的线性泛函是 Haar 测度的充分必要条件；利用遍历定理和这个充分必要条件探讨了C*－双代数中 Haar 浏度存在的一些充分条件。

It is shown that an exponentially bounded integrated bisemigroups can be considered as the integration of a strongly continuous bisemigroup of bounded linear operators in some subspace of a Banach space with stronger norm topology,and also as the restriction of a strongly continuous bisemigroup of bounded linear operators in a bigger space with weaker norm topology.

证明了Banach空间x上的指数有界积分双半群可以作为x的某个子空间上具有较强范数拓扑下的有界线性算子强连续双半群的积分，同时也可作为较大空间上具有较弱范数拓扑下的有界线性算子强连续双半群积分的限制。

In addition, the nonlinear processes such as cross-phase modulation, non-degenerate two-photon absorption, and stimulated Raman scattering must also be considered for double wavelengths propagating in waveguide.

在归纳分析了SOI对光信号处理的研究进展的基础上，进一步完善了超快脉冲在脊形硅波导中演变时所满足的线性和非线性传输方程，在此非线性方程中包括波导线性损耗、群速度色散和三阶色散等线性效应；同时也包含了自相位调制、简并双光子吸收、自由载流子吸收和自由载流子色散等非线性过程；当双光场在波导中传输时，脉冲之间的交叉相位调制、非简并双光子吸收和受激拉曼散射效应等非线性效应也被考虑。

The features of the design approach are that the coupling function between water utilization network and heat exchange network is considered;in the first stage,the step-by-step double-linear programming method is employed for the design of water utilization network targeting both minimum water consumption and minimum energy loss,realizing the minimum water consumpt.

其特点是：考虑了用水网络和换热网络之间的耦合作用，在设计的第一阶段即用水网络设计阶段，以同时的用水量最小和火用损最小为目标采用逐步双线性规划法来设计用水网络，实现整个过程的用水最小化并为第二阶段的换热网络设计提供最合理的冷流和热流股以确保能量的合理利用；对于设计的第二阶段的换热网络设计，可直接采用文献中的方法。

Through Hilbert transform, a signal's plane trace can be get. There are two frequencies in the tested signal, so the signal's plane trace may be looked as the track of the out pole's end when two poles rotate around parallel axles. Using the knowledge of motion synthesis in theory mechanics, a formula to describing the change of plane trace's step length and angle for two-frequency be get. So we may prolongate the tested signal's plane trace from the echo's initial arriving moment, and get a certain length of the signal's prolongation.

通过Hilbert变换可得到测试信号的平面迹线，测试信号中只含有两个频率成分，视为双频信号，双频信号的平面迹线相当于两连杆绕平行轴转动时外杆杆端迹线，利用理论力学中运动合成和瞬心知识，推导出双频信号平面迹线步长平方满足余弦线性复合函数，而迹线转角可视为线性变化，据此可对回波到来之前的测试信号平面迹线作延长，得到一定长度的信号延展段，信号延展段与实测段作差可得到一次、二次回波的第一个波峰值。

We study on the controllability of parabolic systems with a nonlinear term involving the state and the gradient ,the null controllability property of a 1-d parabolic equation involving a fractional power of the Laplace operator ,null controllability of some systems of two parabolic equations with one control force ,and exact controllability of the parabolic system with bilinear control.

我们研究了含有状态和梯度的非线性的项抛物系统的能控性，含有拉普拉斯算子的分数阶的1-d抛物方程的零能控性，带有一个强控制的两个抛物方程的一些系统的零能控性和具有双线性控制抛物系统的精确能控性。

The second part is the controllability of parabolic equation .We study on the controllability of parabolic systems with a nonlinear term involving the state and the gradient ,the null-controllability property of a 1-d parabolic equation involving a fractional power of the Laplace operator ,null controllability of some systems of two parabolic equations with one control force ,and exact controllability of the parabolic system with bilinear control .

第二部分写的是，抛物方程的能控性，我们研究了含有状态和梯度的非线性的项抛物系统的能控性，含有拉普拉斯算子的分数阶的1-d抛物方程的零能控性，带有一个强控制的两个抛物方程的一些系统的零能控性和具有双线性控制抛物系统的精确能控性。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

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。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新