解域

According to algebraic number theory,all solutions of Pocklington equation in a ring of integers of a quadratic imaginary field are determined,which implies that the equation has only several solutions in the ring.

利用代数数论的理论与方法，决定了一个重要的不定方程在一个特殊的虚二次域整数环中的解，从而指出这个方程在比整数环更大的环中也仅有有限个解。

It is shown that the leading term of interior asymptotic solutions is exactly the solution of Kirchhoff plate theory.

结果表明，内域解渐近级数的首项正是熟知的Kirchhoff板理论解。

Starting from two-line soliton solution of an integrable2+1-dimensional system in bilinear form,one can find a dromion solution that is localized in all directions for a suitable potential.

从2+1维双线性形式的非局域BussinesqNLBQ方程和KP方程的隐线孤子解出发，可以找到与某种势所相应的各方向都指数衰减的dromion解。

Based on this thought, in this thesis, the alternation theorem is first extended to the Chebyshev approximation problems with inequality constraints, and then two algorithms are devised for designing linear phase FIR filters with inequality constraints in Chebyshev sense according to the extended theorem.

L.J.Karam和McClellan在文献[20]中把交错点组定理扩展到复数域，并提出了求解复系数FIR滤波器的复Remez算法，但由于此扩展定理只是一个充分条件，所以此算法不能保证得到最优解。在文献[23]中，他们对复Remez算法进行了完善，使其收敛到最优解。

Special solutions for the ring circular domain with crack surfaces acted on uniform compressive force, linear compressive force and linear shearing force are deduced in polar coordinate employed the eigenfunction expansion technique in the Hamiltonian system of elastic mechanics. Combined with the general solution for the above problems, the analytical solutions for crack tip fields with surfaces acted on the above three kinds of loads are obtained. These solutions offer theoretical basis to construct analytical elements for plastic analysis of crack.

从弹性力学哈密顿体系理论出发，利用平面弹性力学极坐标系下的本征向量展开求解，推导了环形圆形域裂纹边作用有均布压力、线性压力和均布剪切力情况下的特解，从而得到了裂纹表面作用有以上三种荷载情况下的裂纹尖端场的解析解，为进一步构造进行弹塑性裂纹分析的奇异解析元奠定了理论基础。

Experimental results show the recognition rate of the method is 95%for a known expresser and 72% for a novel expresser. Aiming at the shortcomings of optical flow technique,two improved optical flow algorithms are presented.One way is to introduce forward and backword constraint eqution and Hessian matrix of optical flow equation is computed.The well- posedness of each point of local neighbourhood is examined and the weight of Lucas-Kanade's method is defined as the reciprocal of the conditioning number of its Hessian Matrix.

3针对传统光流法的缺点，分别提出了两种不同的改进方法：其一为引入前向-后向光流方程，计算其Hessian矩阵，把Hessian矩阵条件数的倒数作为Lucas-Kanade光流法的加权阵，可有效消除局部邻域中不可靠约束点，同时提高基本约束方程解的稳定性；其二为针对传统光流法只适用于刚体运动的特点，在扩展约束光流方程的基础上引入了div-curl样条函数作为扩展光流约束方程的附加约束条件，给出了一阶和二阶div-curl样条约束下光流的数值解。

Firstly, we combine the theories of monotone operator and maximal monotone operator's Yosida approaching with domain method to prove the solution's existence of single input-output equation in R n in the similar economical backgrounds in present articles and then gain the solution's continuity by exterior approaching method,at last we give the responding economical meaning about the solution's existence and continuity.

就R n空间中消耗为单调单值型的投入产出方程，在现有文献类似的经济背景之下，利用单调算子的理论以及极大单调算子的Yosida逼近结合邻域逼近法给出了投入产出方程的解的存在性的证明，然后利用外部逼近法结合方程截断技巧证明了投入产出方程的解的连续性，最后给出了相对应于存在性和连续性的经济解释。

In this paper, we discuss the evolution of the off waist incident Gaussian beam in the nonlocal nonlinear media by use of the (1+1) dimensional strongly nonlocal model.

从 1 +1维强非局域模型出发，讨论了偏离束腰入射的高斯光束在非局域非线性介质中的传输特性，得到了精确的解析解。

Cultured giant seaperch was three-piece filleted to prepare meat paste of the ordinary muscle. Changes in gel strength of the meat paste heated at 30-80℃ for 20-120min were investigated. The gel strength increased strikingly and reached a maximum at around 50℃, which then decreased at 60℃. This indicated that suwari, a setting phenomenon occurred at 50℃ and modori, a disintegration phenomenon occurred at 60℃.

本研究以省产养殖活金目鲈为材料，经三片切取普通肉制备肉糊，将此肉糊於30-80℃处理20-120min时，发现在50℃以下低温域加热处理，随时间之延长英凝胶强度有逐渐上升趋势，而在60℃以上高温域加热处理时，则见明显下降趋势，显示金自鲈肉糊之低温凝胶现象(suwari； setting)发生於50℃，而高温解胶现象(modori； disintegration)则发生於60℃。

A new algorithm of the regularizing image restoration based on wavelet transform in the frequency is presented and the advantages of the Fourier transform and wavelet transform are, respectively, adopted in this algorithm.

将图像复原正则解的小波变换在频域中执行，提出了一种基于频域的小波变换图像复原正则化方法，这种方法同时利用了傅立叶变换和小波变换各自的优点。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失