unit n. 1.个体,一个,一人。 2.(计值、组织、机构)单位;单元;小组,分部;【军事】部队;分队。 3.【机械工程】机组,装置;元件,部件,附件;一组用具[设备]。 4.【数学】单位数;最小整数;基数。 the guerrilla units 游击队。 army units 陆军部队。 international electrical units 国际电力单位 〔volt, ohm 等〕。 the C. G. S. system of units 厘米、克、秒单位制。 a line unit 【电学】接线盒。 the remote control unit 遥控装置。 the drive unit 传动装置。 a point unit 质点。 a missile-borne unit 导弹附件。 an infrared detection unit 【火箭】热探头。 be a unit 〔美国〕一致 (We were a unit on the question. 我们在这个问题上是一致的)。
In this dissertation , we firstly prove that any dirichlet problem is indeed equal to a voltages problem of networks . we give five solutions to dirichlet problem in two dimensions ; among these five solutions , we prove that the iteration solution and the solution of relaxations are exponential convergence , then we estimate their respective convergence rates ; secondly , we discuss random walks on general networks , prove that there is an one to one correspondence between networks and reversible ergodic markov chains ; thirdly , we give probabilistic interpretation of voltages for general networks : when a unit voltage is applied between a and b , making va = 1 and vb = 0 , the voltage vx at any point x represents the probability that a walker starting from x will return to a before reaching b ; furthermore , we study the relationship between effective resistance and escape probability : starting at a , the probability that the walk reaches b before returning to a is the ratio of the effective conductance and the total conductance 本文证明了任何边值的dirichlet问题都可转化为求解电路电压的问题:给出了计算平面格点上dirichlet问题的5种方法:证明了迭代法和松驰法都是指数收敛的,并分别给出收敛速度的估计;讨论了一般电路上的随机徘徊,验证了电路与可逆的遍历markov链是一一对应的;给出了电路电压的概率解释:当把1伏电压加于a , b两端,使得v _ a = 1 , v _ b = 0时,则x点的电压v _ x表示对应的markov链中,从x出发,到达b之前到达a的概率;进一步地,给出了逃离概率与有效电阻之间的关系:从a出发,在到达b之前到达a的概率为有效传导率与通过a的总传导率之比。