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There are series of papers studying the solvability of an incompressible, viscous, instationary fluid contained in a domian bounded entirely by a free surface. In 1977, Solonnikov proved its local solvability in a Holder space for any initial date but without surface tension. In 1984, he considered the same problem in a Sobolev space with surface tension being taken into account. In I992, Mogilevskii and Solonnikov treated the same problem in a Holder space, where the coefficient of surface tension is not a constant. There are also short-time existence results for the solvability of an incompressible, vicous, unsteady fluid bounded above by a free surface and below by a fixed bottom which approach horizontal planes at infinity. In 1981, Beale proved its local solvability in a Sobolev space for any initial date but without surface tension. In 1983, Allain were concerned with the same problem in R〓 with surface tension but under the assumption that the initial fluid domain was near a horizontal strip. In 1987, he obtained the same result without the preceding assumption. In 1996, Tani solved the same problem in R with surface tension. For the solvability of an incompressible viscous instationary fluid in Ω R bounded inside by a free surface S and outside by a rotating boundary S, in 1995 Ciuperca proved its local existence in a Sobolev space for any initial date but without surface tension. In this paper, we consider the same problem with surface tension.

对于边界完全是由自由边界组成的有界区域中粘性不可压流体的非定常运动问题,Solonnikcv于1977年在忽略表面张力情况下证明了初值问题小时间解在Holder空间的存在性,于1984年在有表面张力情况下证明了初值问题问题小时间解在Sobolev空间的存在性,Mogilevskii和Solonnikov于1992年在表面张力系数可以不是常数情况下证明了初值问题小时间解在Holder空间的存在性;对于上面是自由边界、下面是固定边界且两边界在无限处趋于水平的无限区域中粘性不可压流体的非定常运动问题,Beale于1981年在忽略表面张力情况下证明了初值问题小时间解在Sobolev空间的存在性,Allain于1983年在有表面张力情况下证明了R中初值问题小时间解在Sobolev空间的存在性,但其中假定初始区域近似是个水平条,他于1987年去掉了这个假定得到同样的结果,Tani于1996年在有表面张力情况下证明了R中初值问题小时间解在Sobolev空间的存在性;对于R中内面是自由边界、外面是旋转边界S的有界区域中粘性不可压流体的非定常运动问题,Ciuperca于1995年在忽略表面张力情况下证明了初值问题小时间解在Sobolev空间的存在性,本文考虑了在有表面张力情况下初值问题可解性问题。

Secondly, the research methods of the pallet loading problem are induced. Branch and Bound Method is analysed. Upper bounds for the Pallet Loading Problem are summerizaed.

接着,归纳了装盘问题的研究方法,分析了分支定界方法,重点总结了装盘问题中的定界算法。

On the assumption that the constraint field is not empty and bounded, using the branch and bound theory, an algorithm is presented to solve the by branching the upper-level decision variable.

在可行域非空有界的条件下,运用分支定界方法的思想,对上层决策变量进行分支,又提出了一个求解混合整数线性双层规划的分支定界算法。

We make the following assumption for When 2 is positive definite matrix, different estimators about matrix of regression coefficients and inefficiency of Least squares estimate have been discussed in many documents. Considered 2 is nonnegative definite matrix, this thesis derives Best linear unbiased Estimate of parameter matrix B and estimable parameter function KBL under the meaning of matrix nonnegative definite and the property of maximum probability of BLUE is investigated.

当∑>0时,众多文献讨论了回归系数阵的各种估计及LSE的有效性,本文考虑了当∑≥0的情形,给出了回归系数阵B及其可估参数函数KBL的在矩阵非负定意义下的最优估计,研究了它的一个最大概率性质,并且讨论了最小二乘估计成为最佳线性无偏估计的充分必要条件,在此基础上给出了均值矩阵的最小二乘估计与BLUE的偏差估计,定义了LSE相对于BLUE的一个相对效率,并给出了它的界。

First, for a given integer value of the objective function, the lower and upper bounds of the variables were determined by the optimum simplex tableau of the linear programming relaxation problem. Then the conditions on the bounds were added to the constraints as cuts to the associated objective function hyperplane. Finally, a branch procedure of the branch-and-bound algorithm was applied to finding a feasible solution on the objective function hyperplane.

对于给定的目标函数整数值,首先利用线性规划松弛问题的最优单纯形表确定变量的上、下界,然后将变量的上、下界条件加入约束条件中对相应的目标函数超平面进行切割,最后应用分支定界算法中的分支方法来搜寻目标函数超平面上的可行解。

In this paper,a quadratic programming method based on semidefinite programming is given to solve the design of FIR filters with discrete coefficients in the light of literature 6,which can give a better bound than a semidefinite programming relaxation method.Based on the model,the Branch-and-Bound algorithm is used to solve this problem.

基于离散系数滤波器设计问题已有的半定规划松弛模型,利用文献[6]的方法给出了该问题的二次规划松弛模型,该模型能给出比半定规划模型更好的界,然后运用分支定界方法求解该模型。

It is uniphase and has amorphous structure.

非晶态合金在原子排布上完全不同于晶态金属,它没有晶粒和晶界,是单相无定形结构,没有像晶体那样的结构缺陷,如晶界、孪晶、位错、层错等。

Next, after analyzing the nets′relationship in three layer channel routing, setting up the objective function toward channel area minimization, we propose some new terms, for example, the withstand bound columns, valid complete cover net sets, TRACK valid routing, etc.. The conceptions and natures of static bound of nets, dynamic bound of unrouted net set and the lower bound value of the horizontal tracks are discussed; and the methods of calculating static bound, dynamic bound and lower bound are put forward.

文章接着分析了线网在三层通道区布线中的相互关系,为了以完成布线所需通道区面积最小化为目标解决三层通道区布线问题,提出了柱界列、完全有效覆盖线网集、TRACK有效布线等一些新的概念,讨论了三层通道区布线问题中线网定界、未布线网集动界和水平通道数Lower-Bound等概念和它们的性质,给出了定界、动界、Lower-Bound值的计算方法。

The multi-stage Tabu Search fits for the situation where the problem has middle size, the quality of solution is important, and the speed is not restricted too much.(4) The combined algorithm which shares the advantages of HR and TS—high speed and high quality—is the most practicable one for middle-scale problems.

通过仿真实验对分枝定界算法、基于运行的启发式算法、多阶段禁忌搜索算法和组合算法进行一系列的对比研究,得出以下几点结论:(1)分枝定界算法只适用于问题规模小且对计算时间要求不高的场合,它是一种最优化算法;(2)启发式算法适合于求解大规模问题,尤其是实际应用中遇到的大型问题,对计算时间要求较高而对解的质量只要满意即可。

Quasi-convex relaxation algorithm, which aims to solve ordinary constraint global optimization problems, is produced by a combination of branch-and-bound method with quasi-convex lower bound and quasi-concave upper bound functions developed from quasi convex-concave extension. This algorithm extends the interval algorithm with box constraint to general constraint global optimization problem.

利用拟凸-凹扩张中构造出的函数的拟凸下界函数和拟凹上界函数,与分枝定界方法相结合,建立了求一般约束全局优化问题的拟凸松弛算法,这一算法是将盒子约束的区间算法推广到一般约束优化问题中。

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