弱解

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。

An inhomogeneous Benjamin-Davis-Ono-Burgers equation including topographic forcing and turbulent dissipation is derived in terms of the quasi-geostrophic vorticity equation, an approximate analytic solution of the BDO-Burgers equation with a small dissipation is obtained, the time variations of mass and energy of the algebraic solitary waves are discussed, and finally, the forced BDO-Burgers equation is integrated numerically and the numerical solutions are given for a given basic flow with a weak shear and a localized topographic forcing.

利用包括地形外源和湍流耗散的准地转涡度方程导出了包含强迫项和湍流耗散项的非齐次强迫BDO-Burgers方程，求出了小耗散存在情况下BDO-Burgers方程的近似解析解，讨论了代数孤立波的质量和能量的守恒关系，最后，对给定的弱切变基本气流和局地地形强迫，数值积分强迫BDO-Burgers方程，求得了不同参数下的数值解。

In the second chapter, modefied Taylor\'s expansion method is studied for solving Fredholm-Volterra integral equations, several illustative examples are given to show the efficiency of the proposed method. More over, by simple algebra, the modified Taylor\'s expansion can also be used to solve integral equations with weakly singular kernel, and the corresponding accuracy is dramatically promoted.

第二章重点讨论了应用Taylor展开方法解Fredholm-Volterra积分方程，通过数值例子，表明了该方法的简单有效性，特别应用于具有弱奇异核积分方程获得了更高精度的解。

Meanwhile, we proved the unboundedness of solutions of Lienard equations with weaker damping terms when the rotation number is irrational. We still obtained the unboundedness of solutions of Lienard equations with asymmetric nonlinearities at resonance.

另外，还通过应用Birkhoff遍历定理证明了当旋转数为无理数时，弱阻尼的Lienard方程无界解的存在性；同时，证明了共振条件下具有不对称非线性项的Lienard方程无界解的存在性。

Recently, some characterizations of solutions of VVI and its weak sharp minima under strong monotonicity have been proved.

近年来，得到了广泛的研究，其解的性质得到了刻画，其解的弱尖极小已经在强单调条件下得到了证明。

According to the graph of adsorption speed, a conclusion can be drawn that formic acid and acetic acid are fixed on the resin with multimolecular adsorption while propanoic acid and pentanoic acid are carried by monomolecular adsorption.

通过其吸附速度、吸附等温线的研究，得出甲酸和乙酸在该树脂上以单分子吸附为主，丙酸和成酸以多分子吸附为主，而且吸附的强弱与羧酸的解离有关，解离越强吸附越弱，反之，吸附越强。

We obtain the closedness and semicontinuity of cone efficient solution sets and cone weakly efficient solution sets for multiobjective programming problem under constraint cone perturbations.

得到了约束锥扰动多目标规划问题的锥有效解集和锥弱有效解集的闭性和半连续性。

The notes of essential solution and essential components of solution set for vector optimization are introduced in order to research the stability of weak efficient solution of general vector optimization including the infinite dimensional problems.

对向量优化引入本质解和解集的本质连通区的概念，研究一般向量优化问题弱有效解集的稳定性。

Uniqueness of the global weakly strong solution and global strong solution for the probem were obtained.

得到上述初边值问题的整体弱强解和整体强解的存在、唯一性。

Flash pyrolysis and agglomeration of slightly caking and noncaking coals were studied.

对弱粘煤和不粘煤的快速加氢热解及在快速热解情况下发生的团聚现象进行了研究。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。