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Under some excess convex assumptions on the boundary, we get a Hardy type inequality similar to that in Euclidean space.

进一步对区域作某种凸性假设后，得到了与Euclid空间中形式非常接近的Hardy型不等式。

It is shown that for an exchange ring R, the lattice of directed convex subgroups of K〓 is isomorphic to the lattice of all stably co-finite and semiprimitive ideals of R.

作为特殊情形立得Goodearl的结果[41，定理15.20]，作为直接应用，给出了exchange环秩函数存性的一个新刻画。

Matting were as granula convex peak exorbitance, fotographic and photoptic layer of PS gap is too large, resulting in a fine image so that the density of hihglights part of the net-point drop in the level of the gradient image is missing.

不净背颗粒较大，会变成颗粒凸峰过矮，胶片与PS版感平层的间隙过大，以致精粗影像难以还原，矮平局部网不背的稠度回升，图像阶调条理迷失。

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

At last, the extremal problems of some convex intuitionistic fuzzy mappings are discussed, which is the theoretical basis for the research on intuitionistic fuzzy optimization.

最后，讨论了一些凸直觉模糊映射的极值问题，为进一步研究直觉模糊优化问题提供了理论基础。

Under the G-differentiable ,using the alternative theorem of generalized subconvexlike map and other some conclusions in locally-convex Hausdorff topological spaces, the optimality conditions of vector extremum problems with set constraint are established.

在局部凸Hausdorff拓扑空间中，在G-可微的意义下，运用广义次似凸映射的择一定理和其他一些结论，建立了带集合约束的向量极值问题的最优性条件。

The purpose of this book is to provide an exposition of the theory of convex sets and functions in which applications to extremum problems play the central role.

这本书的目的是为了提供各类凸集和凸函数理论的介绍，它们在极值问题的应用中发挥核心作用。

However, because its feasible region is neither convex nor connected, this problem is intractable. Therefore, the nonlinear programming theory cannot be applied here directly.

然而该问题又是难解的，原因在于它的可行域既不是凸的又不是连通的，所以不能直接用现有的非线性规划理论来解决。

This grey method is an analysis one for small sample finite sequence, which can be used for judging the convergence rate of a convex-concave sequence, or an irregular curve sequence, or several irregular curve sequences, and for comparing one with another, and can be also employed in other field.

该灰色方法是一个有限序列小样本的分析方法，它不仅可以用于凸凹单个序列的收敛速度判断，也可以用于一般情况的单个序列的收敛速度判断，而且，它还可以用于多个序列的收敛速度判断和相互比较，以及在其它领域的数值分析。

In complete convex metric spaces , we use Ishikawa iterative process to approximate common fixed point of quasi - contractive mapping pair.

在完备凸度量空间中，运用广义的Ishikawa迭代序列列逼近拟压缩映射对的公共不动点。

"Yes, now you can give yourself airs," she said, you have got what you wanted.

"对了，您现在高兴了，"她说道，这是您所期待的。

Then the LORD said to me: Rebel Israel is inwardly more just than traitorous Judah.

上主于是对我说：＂失节的以色列比失信的犹大，更显得正义。