使问题的维数，对各级渐近解而言，降低了一维。
For every order of the asymptotic solution, the dimensionality of the problem has been decreased by one.
同时给出了输入输出维数相等时的解耦并完全线性化的充要条件。
When the output vector dimensions equal to the input vector dimensions, the necessary and sufficient conditions for decoupling and complete linearization to nonlinear system are given.
电源优化问题具有高维数、非线性、随机性等特点，常规的优化算法难以求解到最优解。
The generation expansion optimization is high dimension, nun-linear, randomness problems. The convention algorithm hardly finds the best solution.
得到一类高维混合问题解的唯一性有离散现象，并与此问题的一维情况下解唯一性的离散值做了比较，得到了不同之处，说明维数对离散值有一定的影响。
The discrete phenomena of uniqueness on a class of mixed problem is discussed, and we prove there is discrete phenomena, and it is related to every coefficient of the equation.
针对粒子群算法用于高维数、多局部极值点的复杂函数寻优时易陷入局部最优解现象，提出一种改进的带扰动项粒子群算法并进行收敛性分析。
Traditional particle swarm optimization(PSO) algorithms often trap into local minima easily when used for the optimization of high-dimensional complex functions with a lot of local minima.
介绍了导出平均场加一般对力核多体问题粒子数守恒严格解的无穷维李代数方法。
By using an algebraic method related to su(3) Lie algebra, exact solutions of the eigenvalue problem of the reduced Hamiltonian are derived analytically.
介绍了导出平均场加一般对力核多体问题粒子数守恒严格解的无穷维李代数方法。
By using an algebraic method related to su(3) Lie algebra, exact solutions of the eigenvalue problem of the reduced Hamiltonian are derived analytically.
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