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Furthermore, the first-order optimality condition and its equivalent reformulations for generalized semi-infinite max-min programming with a non-compact set are presented using the lower-Hadamard directional derivative and subdifferential.2. Chapter 3 studies the gradient-type methods for unconstrained optimization problems. Section 1 proposes a new class of three-term memory gradient methods. The global convergence property of the method is established. Furthermore, in order to improve the convergence property of the method, a new class of memory gradient projection methods is presented with the property that the whole sequence of iterates converges to a solution to the problem under the conditions such as pseudo-convexity and continuous differentiability of objective function. In section 2, two new classes of methods, called gradient-type method with perturbations and hybrid projection method with perturbations, are proposed. In these methods, non-monotone line search technique is employed, which makes them easily executed in computer.

第3章研究了无约束优化问题的梯度型算法，第1节提出了一类新的三项记忆梯度算法，讨论了算法的全局收敛性，进一步提出了一类新的具有更好收敛性质的记忆梯度投影算法，并证明了该算法在函数伪凸的情况下具有整体收敛性，第2节在非单调步长搜索下提出了带扰动项的梯度型算法及其混合投影算法，这两类算法的一个重要特征就是步长采用线搜索确定而不象许多文献中那样要求步长趋于零，这样更容易在计算机上实现，在较弱的条件下证明了这些算法的全局收敛性，数值算例表明了算法的有效性。

And then the approach is extended to continuous random variable. The optimal rule of general group decision-making is drawn by the new approach, which turns out to be a generalized weighted majority rule. The weight allocated to a decision-maker should be equal to the information quantity he provides.

鉴于Boltzmann—Shannon熵难以直接用来度量群体决策中信息的变动情况，我们提出了一种对离散随机变量的新的信息度量方法，证明了该信息函数仍然满足等状态时信息量最小这一性质；随后将其推广到了连续随机变量。

In this paper, the new bargaining set for continuous convex games is proved to be coincided with the core, thus the main results of [1] and [2] may be generalized to a great extent.

在这篇短文里，我们证明，对于连续凸对策，这种新的谈判集与核心重合。这就大大推广了文献[1]和[2]的主要结果。

The grids can be densified locally where the flow is complicated for the sharp change of water depth.(5) 2-D hydrodynamic equations in the generalized curvilinear coordinates have been derived with the contravariant velocities as main variables. The new equations keep the original styles and physical meanings. Based on the water depth correction method, the 2-D flow numerical model has been established and validated by the measured data.

推导了广义曲线坐标系下以逆变流速张量作为主变量的二维水动力方程，新方程保持原有结构形式及物理含义，采用水位校正法建立了二维水流数学模型，经实测资料验证后的模型，模拟并分析了分流角度、宽深比等因素变化对分汊流平面二维水流结构的影响。

Generalized Pulse-Spectrum Technique is a kind of widely applied and effective methods for solving inverse problems of geophysical prospecting. But it is still imperfect in the aspects of convergence domain, ability of anti-noise, computaional cost, choice of regularized parameter, and so on.

广义脉冲谱方法是求解地球物理反问题的应用广泛而有效的一类方法，但在收敛范围、抗噪能力、计算量、以及正则参数选取等方面仍存在较大不足。

In the third chapter, we study the approximation and weighted approximation for a kind of generalized Baskakov operators of two-variable. Using different weight functions, we discuss the convergence on weighted space of polynomials and rate of convergence with Jacobi weight for this kind of two-dimensional product-type operators, which extends the results of one-dimensional operators.

第三章研究一类二元广义Baskakov算子的逼近及其加权逼近，主要针对于不同的权函数讨论了这类乘积型的二元算子及其导数在多项式权空间上的收敛性和加Jacobi权的收敛阶，把一元的结果推广到多元的情形。

In chapter 2, we point out that some condition of a convergence theorem of generalized fuzzy integral in [8] (Theorem 1) is not valid by a counterexample.

通过一个反例，指出了文[8]给出的一个广义模糊积分序列的收敛定理(即定理1)中，有的条件不合理。

Stability and convergence of the model are proven by means of the weak convergence theorem of generalized function and the convolved integration theory.

由广义函数弱收敛定理和卷积理论，证明所提出的非局部连续模型具备收敛性和稳定性。

A new definition and a new iterative scheme are introduced and the result that the iterative sequence is strongly convergent to common zero point s of maximal monotone operators Ai(i=1,2,…,m) is obtained by using the techniques of Lyapunov functional and generalized projection operator,etc.

将引进一个新定义、给出一种新迭代算法，并利用Lyapunov泛函与广义投影算子等技巧，证明迭代序列强收敛于Ai的公共零点，i=1，2，…，m。

If the Landweber method and pre-iteration method were convergent, the residue sequence would be monotone decreasing. By analyzing the convergence, the fact is demonstrated that for the severe ill-conditioned matrix of sensitivity coefficient, because of the limitation of the precision of the computer, the residue sequence is not monotone decreasing; thereby the reconstruction images diverge from the true distribution of the conductivity. So the generalized inverse method with threshold is established and the selection way of the regularization parameter is presented, by which the better images are reconstructed.

Landweber法和预迭代法收敛，则其残差序列单调递减，通过对它们的收敛性进行分析，证实对于病态性严重的灵敏度系数矩阵，由于受计算精度的限制，迭代过程中的残差序列不再单调递减，从而导致重建图象偏离实际电导率分布，因此作者建立了带阈值的广义逆算法，提出了规则化参数选择方法，获得了较好的图象重建质量。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。