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The discrete 0-1 programming problem is translated into continuous nonlinear optimization problem by polish function, and the nonlinear optimization problem is solved by contraction algorithm.

3利用过滤函数近似处理连续体拓扑优化问题，使用缩并解法实现了对连续体拓扑优化问题的求解。

In this algorithm, at first the reactive power optimization problem is converted to integer nonlinear programming problem with discrete control variables which are solved by IGA; then by use of PDIP algorithm, the continuous variables which can match with the obtained most are solved, and the reactive power optimization is changed into a nonlinear programming problem with continuous control variables.

首先通过改进遗传算法求解无功优化问题中的离散变量，然后采用原对偶内点法求解与已获得离散变量最匹配的连续变量。

Brief the; of commonly used method that narrated research to sort solid coupling problem discussed iterative method of dry mode law, across and LS-DYNA finite yuan of software analysis law, the theoretical calculation that is problem of coupling drifting solid offerred new method and train of thought, the analysis of problem of convection solid coupling has fair referenced value.

简要叙述了探究流固耦合新问题的常用方法；讨论了干模态法、交叉迭代法以及LS-DYNA有限元软件分析法，为流固耦合新问题的理论计算提供了新的方法和思路，对流固耦合新问题的分析有一定的参考价值。

The linear function applicable scope is broad, when the reservoir turnover water volume and the time, the student leaves the staircase mouth population and the time and the time and the motion communication speech spends the comparison and so on the relational question has the important application;The study linear function, may deepen in the life the linear question understanding and the understanding, is helpful in solves some simple function problem; The linear function some problem solving method has the universality in mathematics, the linear function related theory may use for to solve some other mathematics problem, For instance the dual linear equation group, a Yuan inequality, a Yuan quadratic equation most value question and some complex mathematics question, the light is studies the linear function the theory is insufficient, the key is can utilize actual the linear function goes is our final goal.

一次函数的适用范围广，在蓄水池的进出水量与时间、学生出楼梯口人数与时间与时间和移动通讯的话费比较等的关系问题时均有重要的应用；学习一次函数，可以加深生活中线性问题的认识与理解，有助于解决一些简单的函数问题；一次函数的一些解题方法在数学中具有普遍性，一次函数的有关理论可以用来解决一些其它的数学问题，比如二元一次方程组、一元一次不等式、一元二次方程的最值问题及一些复杂的数学问题，光是学习一次函数的理论是不够的，关键是能把一次函数运用到实际中去才是我们最终的目的。

Since the sub-problem is strict convex and separable, the dual problem is especially effective for large scale problem.

由于我们得到的子问题是严格凸和可分的，从而获得的对偶问题简单易解，因此这一方法尤其适合处理大规模问题。

The numercial simulation has been carried out, and the experimental results show that this method has been improved significantly comparing with the traditional one in nonlinear optics. Secondly, a second order system of semilinear elliptic equations, which comes from a mathematics model of the electric potential distribution of a media surrounded with the protein, is transformed into a variational problem, the existence of solution of it is proved by using variational principle and Trudinger—Moser inequality, and the relation between the solutions of variational problem and the solutions of its dual problem is obtained.

首先，讨论了非线性光学中的二次谐波产生的耦合方程组，利用变分法证明了耦合方程组非平凡解的存在性，然后进行了数值模拟，实验结果表明文中方法比经典的非线性光学中的方法有较大的改进，这对优化光倍频器件的设计将有所帮助；其次，将一类二阶半线性椭圆型方程组转化为一个变分问题，然后利用变分法和

Harmonic measurement is an important embranchment of harmonic problem. It is not only the main basis of studying the harmonic problem, but also the starting point of analyzing the problem.

谐波测量是谐波问题的一个重要分支，它是谐波问题研究的主要依据，也是研究分析问题的出发点。

Firstly, we consider the problem of the representation formula for the transition probability density of a right process under Girsanov transform. Secondly,we consider the problem of the MEMMs (minimal entropy martingale measure)for Markov switching Levy processes, and justify that the minimal entropy martingale measure is obtained by some regime switching Esscher transform. At last,we consider the problem of the invariant measure and the ergodic property of recurrent right processes. This paper includes 5 chapters.

首先，我们考虑了满足一定条件的右过程在Girsanov变换下的转移概率密度的表达式问题；其次，我们考虑了由Markov调制的Lévy过程的最小相对熵鞅测度的问题，证明了其最小相对熵鞅测度是某个状态转换Esscher变换；最后，我们考虑了右过程的不变测度及其遍历性的问题。

In the last chap-ter,the natural integral equation and natural boundary element method forharmonic problem on exterior elliptic domain are introduced.Then,based onthis,the natural boundary reduction method for a kind of exterior problem ofanisotropic constant coefficients elliptic equation is discussed, the natural inte-gral equation and its solving method on circular boundary and elliptic bound-ary are obtained.These results can be directly applied in coupled methodand DDM for exterior boundary value problem.

最后，讨论了椭圆外区域调和问题的自然积分算子即D-N算子及自然边界元方法，并基于此研究了一类各向异性常系数椭圆型方程外问题的自然边界归化方法，首次得到其在圆周边界及椭圆边界上的自然积分方程及其求解方法，并将这些结果直接应用于外边值问题的耦合算法。

At first, numerical simulation are made on the temporal developing gas-phase mixing layer where the convective mach number is in the region of subsonic(0.5) and transonic(0.8). For the temporal problem where Mc is 0.5, researches where the computational field contains different numbers of initial disturbances(so-called n period problem) are made respectively, and vortex's types of evolution in mixing layer including different numbers of initial disturbances are investigated; For the temporal problem where Mc is 0.8, the distinct shock let structure is obtained, and its mechanism is analyzed at the same time.

文中首先对对流马赫数为亚声速(0.5)、跨声速(0.8)的时间发展单气相混合层作了数值研究，对Mc为亚声速单气相时间发展混合层，分别研究了计算域包含不同数目的初始扰动周期问题，考查了不同周期数的混合层中涡的不同演化方式；对Mc为跨声速的单气相时间发展混合层，得到了清晰的小激波结构，同时分析了小激波的形成机理。

Analog output can display output results.

可以模拟输出显示输出效果。

It implied that RAPD technique pro vided a new alternative for checking irradiation induced effects.

对扩增产物进行数据分析，结果表明RAPD技术能够检测出辐射后唐菖蒲基因组变异情况，可用于对唐菖蒲辐射后基因变异的分析。