共轭性

The notion of the adjoint operator of amodule homomorph ism defined on a densely submodule of a comp lete random inner p roduct module is introduced and discussed, in particular the closedness of adjoint operators is p roved.

摘 要 对定义在完备随机内积模的稠子模上的模同态引入了共轭算子的概念并讨论其基本性质，尤其证明了共轭算子的闭性。

Our results are complementary to the earlier work by Law and co-workers. The photosensitivity is enhanced for the pigments with larger anilide ring.

首次考察了偶合基酰胺芳环共轭环扩大时光敏性的变化规律，发现酰胺芳环共轭环扩大时有所提高。

The factors such as conjugate framework withsmall conjugation energy, central asymmetry, long conjugate chain,introduction of electron donors-acceptors, strong electron-donating orelectron-withdrawing abilities, long distance between electron donors andelectron acceptors, good coplanarity and so on lead to high third-order optical nonlinearities.

离域能小的共轭骨架，非中心对称结构，长的共轭链，吸供取代基的引入，取代基强的供电子性或吸电子性，长的吸供电子取代基之间的距离，以及良好的共平面程度等因素有利于获得较大的三阶非线性光学性能。

As compared to the l max absorption of regioregular poly(3-alkylthiophene)s (RR-P3ATs), the red-shift about 120 nm for RR-P3ATVs resulted from the more coplanarity and the longer conjugation length due to the additional vinylene linkage introduced to the conjugated chains.

与立体规则性聚(3-烷基噻吩)(RR-P3ATs)比较， RR-P3ATVs 之 UV-vis 最大吸收波长约有120 nm 的红外移，显示共轭主链导入乙烯基后，有较佳的共平面性与较长的共轭长度。

Chapter 4,based on strong efficiency rather than efficiency or weak effi-ciency,discusses the similar problem to chapter 3.The concepts of strongsupremum and strong infimum for the set in finite-dimensionalEuclidean space are given,s-conjugate functions and s-subdifferentials theory is developed,by means of which,the duality problem ofmulitobjectivre programming for strong efficient solutions or called absoluteoptimal solutions is analysed,and a new duality theory-s-conjugateduality theory is proposed.

第四章，基于强有效性而不是有效性和弱有效性，给出了类似于第三章的结果，提出了有限维欧氏空间中集合的强上、下确界等概念，研究了点集映象的强共轭函数和强次微分问题，建立了点集映象的s-共轭函数及其s-次微分理论，并借助于这一理论，讨论了多目标规划关于绝对最优解或称强有效解的对偶性问题，建立了基于强有效性的s-共轭对偶理论。

The reconstruction problem is ill-posed, so two optimal criterions, the least module and the smoothness criterion base on Tikhonov regularization technique, are introduced into reconstruction algorithm. Many regularization parameters choice strategies are investigated, and the TPA(Two—Parameter Algorithm) strategy which is based on the Morozov discrepancy principles, is implemented in two regularization reconstruction algorithms.Numerical experiment results show that the nonnegative and smoothness constraint condition can overcome the difficulty of iteration semiconvergent, preconditioned technique can improve convergence rate and reconstruction accuracy, smoothness regularization criterion can meliorate ill-posed problem of reconstruction and enhance iteration stability, and the TPA is an effective strategy of regularization parameters choice.

数值试验表明：在共轭梯度法中引入非负约束和光滑约束改善了迭代的"半收敛"性，非负约束保证了解的非负性，光滑约束抑制了重建解的振荡现象，约束算法的重建精度与无约束算法相比大幅度提高；在约束共轭梯度重建算法中引入预优技术，可以加快算法的收敛速度，提高迭代的稳定性和重建精度；引入光滑准则的正则化技术可以有效改善图像重建问题的不适定性，加快迭代的收敛速度，提高迭代的稳定性和图像重建质量，计算正则参数的TPA算法在闪光照相图像重建中是有效的。

Then,we prove the convergence of the radial basis function for solving partial differential equations with projection methods .

本文讨论用MQ作为插值的径向基函数，对自共轭椭圆型方程进行插值，证明了插值系数的唯一性，并用投影法证明了用径向基函数解自共轭椭圆型方程的收敛性。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

And we get a criterion for the cyclic conjugacy separability of generalized free products.

第五章研究了群的共轭可分性，而且我们还得到了循环共轭可分性的一个判定定理。

The reconstruction problem is ill-posed, so two optimal criterions, the least module and the smoothness criterion base on Tikhonov regularization technique, are introduced into reconstruction algorithm. Many regularization parameters choice strategies are investigated, and the TPA(Two—Parameter Algorithm) strategy which is based on the Morozov discrepancy principles, is implemented in two regularization reconstruction algorithms.Numerical experiment results show that the nonnegative and smoothness constraint condition can overcome the difficulty of iteration semiconvergent, preconditioned technique can improve convergence rate and reconstruction accuracy, smoothness regularization criterion can meliorate ill-posed problem of reconstruction and enhance iteration stability, and the TPA is an effective strategy of regularization parameters choice.

数值试验表明：在共轭梯度法中引入非负约束和光滑约束改善了迭代的&半收敛&性，非负约束保证了解的非负性，光滑约束抑制了重建解的振荡现象，约束算法的重建精度与无约束算法相比大幅度提高；在约束共轭梯度重建算法中引入预优技术，可以加快算法的收敛速度，提高迭代的稳定性和重建精度；引入光滑准则的正则化技术可以有效改善图像重建问题的不适定性，加快迭代的收敛速度，提高迭代的稳定性和图像重建质量，计算正则参数的TPA算法在闪光照相图像重建中是有效的。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。