For bose system , the critical temperature tc increase with atom number n . and we also found that the dimensionality had a great effect on such system . the condensate fraction is proportional to t3 in 3d , t2 in 2d , whereas t in 1d . this relation is hold for specific heat c 在谐振子势场的调制下，体系的基态粒子数所占的比重、比热均随温度t的d次幂变化，即n _ 0 n ， c t ~ d ，其中d为谐振子势场的维数。
By establishing the direct mapping from the state set to the action set , the planning efficiency is improved . the learning converges to the optimal control strategy . the simulation result shows that the control strategy is optimized and the control performance is improved 同基于传统人工势场法相比，此方法避免了不合理势场方程所引起的局部极小值问题，而且通过学习得到的策略，可以得到从任意起始位置开始的最优路径。
Following are the main content of this thesis : the first part analyses the khatib artificial potential field model in which we take the goal points with mobile robots with the same polarity as the charge and the obstacles with the conversely polarity as the charge 论文的主要研究工作如下:首先,详细地介绍和分析了传统的khatib人工势场模型。该模型将目标点看作与移动机器人带有相反极性的电荷的带电体,障碍物看作与机器人带有相同极性的电荷的带电体。
In addition , the specific heat c have been manipulated under control of dimensionality , i . e the chemical potential have been discussed in lower - dimension system . the results is interesting that , dose not intend to fermi energy f when temperature is very low in 2d , whereas is a constant in 1d 对于低维情况的化学势的讨论，我们得到：在二维情况下，当温度很低时，化学势不再趋于fermi能量；在一维情况下，为常数(谐振子势场的频率一定) 。
At first , path planning of single manipulator is investigated . a method of collision - free path planning based on artificial potential field is proposed ; an effective algorithm to solve zmii ~ 7 ~ masters thesis dead - l ? k 栲 s ? is iii ~ estigai ? to overcome local planning deficien7 ? of artificial potential fields 故首先研究单操作臂机器人路径规划，介绍了一种基于人工势场的避碰路径规划方法，并提出了有效的消解停留方法来克服人工势函数方法局部规划缺陷。
By sufficiently making use of the knowledge of the semiconductor , we have analyzed the transference and scatterance of the carriers as well as their emergence and being captured by disfigurement in crystal lattice from angles of crystal micro mechanism , the structure of the energy band and the crystal potential field 本文充分利用半导体的能带理论，从薄膜晶体结构、能带结构和晶体势场的角度，分析载流子的迁移、散射以及载流子的产生和晶体结构缺陷对载流子的捕获。
