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unit voltage中文是什么意思

  • 單位電壓

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  • 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(wèn)題都可轉(zhuǎn)化為求解電路電壓的問(wèn)題:給出了計(jì)算平面格點(diǎn)上dirichlet問(wèn)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(jì);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?duì)應(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(shí),則x點(diǎn)的電壓v _ x表示對(duì)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(guò)a的總傳導(dǎo)率之比。
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