双线性

We first got the PML equations by making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Grding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experiments which show that this method is feasible to a certain extent.

首先通过复化极径得到PML方程，然后在关于吸收参数的假设下，证明了PML问题变分形式中的半双线性形式满足Grding不等式，进而证明了PML问题解的存在惟一性，并给出了数值实验。实验结果表明，该方法有一定的可行性。

We first got the PML equationsby making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Garding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experimentswhich show that this method is feasible to a certain extent.

首先通过复化极径得到PML方程，然后在关于吸收参数的假设下，证明了PML问题变分形式中的半双线性形式满足Garding不等式，进而证明了PML问题解的存在惟一性，并给出了数值实验。实验结果表明，该方法有一定的可行性。

We have the "Tomb Raider 2" image to illustrate: in Figure III, a 3D accelerator card as a result of the closure of the "bilinear interpolation" function, in the figures behind the wood on the left there is a clear " mosaic "phenomenon.

我们还是采用《古墓丽影2》的图像来说明：在图三中，由于关闭了3D加速卡上的"双线性插补"功能，在人物身后左边的木桩上出现了明显的"马赛克"现象。

In th is paper, w e p ropo se a cert ificateless ring signature scheme, based on the bilinear pairings, w h ich p rovides uncondit ional anonym ity, and p rove th is scheme is existent ially un fo rgeable under adap t ive cho se2message at tack s, in the random o raclemodel, assum ing that the computat ionalD iffie2Hellman p roblem is hard to so lve.

摘 要 在这篇文章里，我们用双线性对构造了一种无证书的环签名方案，并证明它是无条件匿名的，且在随机预言模型中，计算性D iffie2Hellman 问题是难解的，我们方案在适应性选择消息攻击下是存在性不可伪造的，它的安全性比在基于身份的公钥密码体制下高。

In the second part,we studyboth the bilinear and the biquadratic coupling in the magnetic metallic multilayerswith the Anderson s-d mixing model.

在第二部份中我们使用Anderson s-d混合模型研究了磁性金属多层膜中的双线性和双二次耦合。

Ourresults show that only when the s-d mixing is strong enough,can the bilinear orthe biquadratic coupling show an oscillatory behavior in the experimental range ofthe spacer thickness.

我们的结果表明，只有在s-d混合作用足够强的时候双线性和双二次耦合强度才会在实验观测的中间非磁金属夹层厚度的范围内表现为中间夹层厚度的振荡函数。

A comparative study of the bilinear, biquadratic quadrilateral element and quadratic triangular element for solving incompressible viscous flows was presented. These elements make use of the Galerkin/Least squares stabilized finite element formulation, in which the pressures and velocities are interpolated with the equal orders.

本文比较了用于求解不可压缩粘性流的四边形双线性、双二次单元及三角形二次单元的性能，这些单元采用GLS稳定化有限元格式，而压力和速度采用等阶数插值。

We also find that the temperature dependence of those interlayercouplingsare considerably enhanced with the decrease of the Hubbard interaction.

我们还发现当Hubbard互作用减弱时，双线性和双二次耦合强度随温度升高的衰减会显著增强。

Simulation results show that the proposed approach exhibited better performance than the standard linear interpolation, particularly in the edge regions.

在仿真实验中，应用该方法能够得到比传统的双线性和双三次插值方法更优的结果，特别是在边缘区域。

Plentiful and substantial achievements have been made, which motivate a lot of methods to obtain the exact solutions of solitary wave equations, such as: the homogeneous balance method, the hyperbolic function method, the power series method, besides the traditional methods, such as: the inverse scatting method, the bilinear Hirota method, and the Backlund transformation method etc.

求解孤立波方程精确解的方法除了传统的反散射方法、Hirota双线性方法、Backlünd变换方法外，近年来又涌现了很多新方法，如齐次平衡法、双曲正切法，级数展开法等。

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