解集

The main problem studied in this thesis are properties of positive solutions to a semi-linear parabolic system with non-local nonlinear sources and null Dirichlet boundary conditions. We give the analysis about asymptotic property: blow-up rate, blow-up set and blow-up profiles.

本论文主要研究了具有非局部源的半线性抛物系统并附加Dirichlet零边值的解的性质，得到了系统古典解的渐近性分析：blow-up速率、blow-up集，边界层估计等问题。

The method generates the feasible set that satisfies the constraint condition with chaotic optimal algorithm, fines out the optimal trade-off solution from the non-inferior solution set with the favor of interactive decision-making, and furthermore, makes an actual case study on the reservoirs along the downstream of Luanhe River.

该方法利用混沌优化算法生成满足约束条件的可行集，再采用交互式决策偏好的方法从非劣解集中寻找最佳权衡解；并对滦河下游水库群进行了实例研究。

This paper deals with global existence and blow-up profiles for the solutions of some classes of reaction-di...

本文讨论几类反应扩散方程解的定性性质：具有局部源的初值问题和具有非局部源的初边值问题解的整体存在性和有限时刻爆破的条件，同时爆破，爆破集，爆破解的爆破率、渐近行为等。

We also introduce and study a new system generalized nonlinear variational inclusions for fuzzy mappings in Hilbert space.

我们利用极大单调映象的预解算子技巧，建立了这类模糊映象的变分包含组与非线性集值映象的不动点问题之间的等价关系，再利用Nadler的不动点定理给出了这类变分包含组的解的存在性定理。

By extending the concepts of supremum and infimum in real space to the casein any finite-dimensional Euclidean space a weak supremum set and infimumset theory with respect to cones for the set in finite-dimensional Euclideanspace is developed,and several similar properties to the set in real space are ob-tained,with the concepts of this weak supremumset,w-D-conjugate maps and w-D-subdifferentials theory for the point-to-setmap are developed,and its several properties and its relationships with weakefficient solutions of the multiobjective programming are studied.

推广实空间中上、下确界的概念至任意有限维欧氏空间，建立了有限维欧氏空间中集合的锥弱上、下确界集理论，得到了与实空间中十分相似的性质。借助于这一理论，应用上、下确界的概念，给出了点集映象的w-D-共轭映象及w-D-次微分理论，并研究了它们的若干特性及其与弱有效解之间的关系，此外还讨论了弱鞍点问题。

Second order differential inclusion; boundary condition; usc multivalued map; fixed point; monotone map; Yosida approximation; solution tube; upper-lower solutions; critical point; PS-condition; C-condition; Sobolev space

基础科学，数学，数学分析二阶微分包含；集值边界；上半连续集值映照；不动点；单调算子； Yosida逼近；解管道；上下解；临界点； PS-条件； C-条件； Sobolev空间

In the first part, the thesis firstly constructs the production possibility sets deduced from constant, nonincreasing, nondecreasing and nondetermined returns to scale. Based on the above point, the thesis systematically deduces the models of DEA which evaluate production efficiency for exogenously fixed inputs and the models of ADEA (Allocative Data Envelopement Analysis) which evaluate cost, revenue, profit efficiencies and allocation efficiency in production possibility sets, and then discusses the solution properties of these mathematics models.

在第一部分中，首先以生产规模收益率不变、非增、非减和不确定四种情形下的生产可能集的构成为出发点，系统地归纳出在这四种生产可能集上评价具有固定不变输入或输出生产有效性的DEA模型及其相应情形下评价生产成本、收入、利润和生产配置有效性的ADEA模型，并讨论了这些数学规划模型解的性质。

Finally, an example is given to illustrate the influence of the impulse on population dynamics by numerical simulation.

第二节利用k-集压缩理论研究脉冲时滞Logistic模型正周期解的存在性，给出正周期解存在的充分条件。

Based on the method of multi-objective fuzzy optimization and the overhead traveling crane design, a mathematical model of fuzzy optimization for main box beam section is established. A fuzzy goal anthology is constructed. The fuzziness of multi-objective function and constraints is defined. The transformation of the fuzzy constraints set to normal constraints set in real number domain is realized by applying optimal level cut set method. The optimal solution and optimal constraint value of sub-objective function in the feasible field are found using the genetic algorithms.

应用多目标模糊优化方法，以工程设计中桥式起重机箱形主梁设计为实例，建立了桥式起重机箱形主梁多目标模糊优化设计的数学模型，构造了模糊目标集，确定了多目标函数的模糊性和约束的模糊性，并应用最优水平截集法实现了模糊约束到实数论域上的集合转换，从而用遗传算法寻求到子目标函数在可行域空间的最优解和约束最优值。

Without utility function, group preference relation on alternative set was constructed in this paper by means of efficient numbers of a lternatives, which are described by Pareto efficient solutions of a group of mul tiobjective decision making problems respectively considered by decision makers.

一些学 者曾借助群体效用函数引进群体多目标决策问题有关效用解的概念，并且给出若干求解的方法。本文撇开效用函数的介入，直接依据由各多目标决策问题的Pareto有效解表示的供选方案的有效数，引进了决策群体在供选方案集上的偏爱关系。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失