interpretation: n. 1.解釋,說明。 2.翻譯。 3.表演,演奏。 put a favourable interpretation on 對…作有利的解釋。 signal interpretation信號解釋。 What is the interpretation of this poem 這首詩的譯文是什么意思?
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 本文證明了任何邊值的dirichlet問題都可轉(zhuǎn)化為求解電路電壓的問題:給出了計算平面格點(diǎn)上dirichlet問題的5種方法:證明了迭代法和松馳法都是指數(shù)收斂的,并分別給出收斂速度的估計;討論了一般電路上的隨機(jī)徘徊,驗(yàn)證了電路與可逆的遍歷markov鏈?zhǔn)且灰粚?yīng)的;給出了電路電壓的概率解釋:當(dāng)把1伏電壓加于a,b兩端,使得v_a=1,v_b=0時,則x點(diǎn)的電壓v_x表示對應(yīng)的markov鏈中,從x出發(fā),到達(dá)b之前到達(dá)a的概率;進(jìn)一步地,給出了逃離概率與有效電阻之間的關(guān)系:從a出發(fā),在到達(dá)b之前到達(dá)a的概率為有效傳導(dǎo)率與通過a的總傳導(dǎo)率之比。