半线性的

A L∞bound estimate is provided on the solutions of a semi-linear parabolic system by the theory of phase transitions.The existence of solutions of corresponding hyperbolic system of conservation laws is studied by viscosity methods and compensated compactness framework.

讨论来源于物理相变理论的一类半线性抛物型方程组解的一致L∞估计，该结果是利用粘性法和补偿列紧框架研究相应的双曲型守恒律解的存在性的重要内容。

The analytic expressions for the displacement components and stresses at any point of an infinite micropolar orthotropic elastic medium with an overlying elastic half space as a result of moving inclined load of arbitrary orientation were obtained.

在无限大微极正交各向异性弹性介质上覆盖弹性介质的弹性半空间的任意点上，作用着任意方向倾斜的移动荷载，给出了位移分量和应力的解析表达式·假设倾斜荷载是法向荷载和切向荷载的线性组合·利用Fourier变换采用特征值方法，并利用数值技术反演了Fourier变换·给出了铝环氧树脂复合材料的数值结果图形

Moreover, the semiopen mapping theorem, the semiclosed graph theorem and the semibounded inverse theorem are established under some conditions of weaker t-norms.

对MengerPN空间上的线性算子引入β-半有界，β-半开及β-半闭等概念，讨论了它们间的关系，并在较弱的t-模条件下建立了半开射定理，半闭图定理和半有界逆定理。

Both LDPC codes and OFDM technology are studied in this paper. The working and the results obtained are summarized as follow:1. The definition of LDPC codes and its coding/decoding ideas are systematically summarized, a general algorithm of changing any parity-check matrix to lower triangular form, which is suitable for quick encoding, is given out, along with a girth checking algorithm. Absolutely random LDPC codes construction is improved, a new half random construction of LDPC codes with linear time coding and no 4-cycles is brought out.

系统地阐述了低密度校验码的定义及编译码原理，提出了一种将任何校验矩阵变换成适于快速编码的近似下三角形式的通用算法及一种围长检测算法，对完全随机的校验矩阵构造法进行了改进，提出了一类消除4环且可近似线性编码的校验矩阵半随机构造法，仿真表明，在高编码效率情况下，改进后的半随机构造法，其性能稍优于完全随机构造法，并可以线性时间编码，因此更适合实际应用。

Under some conditions we obtain the existence of nontrivial solution by analyzing the best Sobolev embedding constant and by use of the minimax theorems without conditions.

通过使用没有条件的极小极大定理，以及对最佳Sobolev嵌入常数的详细分析，得到了一些具临界Sobolev指数的半线性椭圆系统的真正非平凡解的存在性，并讨论了解的一些性质。

Firstly, the eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is considered. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, we prove the existence of a nontrivial solution for a class of nonlinear elliptic with critical potentialand indefinite weights in R~2. Secondly, we prove the existence of nontrivial solutions for a class of subcritical and critical elliptic systems with indefinite part in R~2 byusing a generalized linking theorem, Trudinger-Moser inequality and concentration-compactness principle.5. The existence of at least three weak solutions for discrete boundary value problem is established by using a three critical point theorem introduced by Ricceri.

首先，讨论了R~2中一类带不定权且含临界位势的二阶椭圆型方程的特征值问题，并借此特征值问题的第一特征值性质，利用山路引理及Trudinger-Moser不等式，证明了R~2中一类带不定权且含临界位势的非线性椭圆型方程非平凡解的存在性；其次，利用广义环绕定理，Trudinger-Moser不等式及集中列紧原理，得到了R~2上一类具有强不定部分的半线性椭圆型方程组在非线性项分别为次临界增长和临界增长情形下非平凡解的存在性。

By introducing the general notion of nonwandering operator semigroup T and utilizing a basic result in normed linear space,the nonwandering property of T=e~ is investigated with the constructive method.

通过给出一般算子半群T的非游荡性概念，利用赋范空间的一个基本结果和直接的构造法证明了具有变系数的线性发展方程的强连续解半群T=etA在适当的条件下是非游荡的；另外，通过对C-半群T概念的引进，定义了一个无界算子半群etA，进一步证明了这二者关于非游荡性的联系；最后给出了一个无界算子半群etP关于非游荡性理论的刻画，其中P是微分多项式。

According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation, one new semi-implicit integration scheme also is designed. By adopting a kind of revised time-explicitdifference scheme to these linear terms still included in spectral model governing equations, this defect of spectral model only partly used in semi-implicit integrating scheme, can be overcome to some degree.

以简谐振动方程中线性项时间差分格式对其计算稳定性影响为理论依据，本文设计了一种新谱模式半隐式时间积分方案，此方案通过对一般谱模式求解框架中那些隐含的线性项采用了一种显式修正的差分格式，可有效克服其国际谱模式半隐式时间求积方案实质上只是部分应用了半隐式差分格式的问题。

A nonlinear semi-discrete model of investment dynamic system is set,and the existence and unique of solution for semi-discrete system are discussed.

建立了投资动力系统的一个非线性半离散模型，并讨论了半离散系统解的存在唯一性，给出了线性半离散系统稳定的一些充分条件。

The relationships between the eigenvalues of Jacobi iteration matrix and the block AOR iteration matrix make a very important role in our analysis. Then we prove some sufficient conditions for the semiconvergence of the block AOR method.

利用块AOR迭代矩阵和相应的块Jacobi迭代矩阵的特征值之间所存在的关系，我们证明了求解奇异p-循环线性方程组的块AOR迭代法半收敛的一些充分件。

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