基本解释：殆不变集
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To improve research on the generalized convex function,some new characteristics of the prequasi-invex function are figured out by means of the cographical set of function(E(f)=(x,α)∶x∈K,α∈R,f(x)αH)and η-invex set,and its two applications in the mathematical programming problem are proposed.借助于η-不变凸集和函数的上图(E(f)={(x,α)∶x∈K,α∈R,f(x)≤α})得到了预不变拟凸函数的几个新的性质,然后还给出了预不变拟凸函数在数学规划问题中的两个重要应用,从而完善了对此类广义凸函数的研究。
Minty(strong) weak vector variational-like inequality and Stampacchia(strong) weak vector variational-like inequality had the same solution in the case that a matrix-valued function defined on invex set was a continuous invariant pseudomonotone mapping.讨论两类向量似变分不等式解的关系问题,指出当定义在不变凸集上的映射是不变伪单调连续时,Minty(强)弱向量似变分不等式的解和Stampacchia(强)弱向量似变分不等式的解相同。
To improve research on the generalized convex function,some new characteristics of the prequasi-invex function are figured out by means of the cographical set of function(E(f)={(x,α):x∈K,α∈R,f(x)≤α})and-invex set,and its two applications in the mathematical programming problem are proposed.首先给出例子说明了此类广义凸函数的存在性,然后利用强η-不变凸集和函数的上图(E(f)={(x,α):x∈K,α∈R,f(x)≤α})得到了强预不变凸函数的几个重要性质,并用另一方法给出它的一个判别定理的简化证明,最后还给出了强预不变凸函数在数学规划问题中的一个重要应用,从而完善了对此类广义凸函数的研究。
The scheme also makes use of logic rules and invariant sets,the decentralized control laws which respect the rules are guaranteed feasibility and free-collision formation.使用不变集合方法和强制协同的逻辑规则保证了在飞行中UAV之间的碰撞避免。
By using potential well family method,we study the invariant sets and vacuum isolating behaviour of solutions to a class of nonlinear wave equations.应用位势井族方法,研究了一类非线性波动方程的不变集合与解的真空隔离,证明了当初始能量小于位势井深度时,此问题存在不变集合与解的真空隔离现象。
