龐加萊 的英文怎麼說
中文拼音 [pángjiālāi]
龐加萊
英文
henri poincaré-
Why not poincare
為什麼不是龐加萊總統The most important property for hamiltonian systems is the poincare and liuville ' s conservation law of phase areas, i. e., the phase flow is a one - parameter symplectic transformation
哈氏系統最重要的性質是龐加萊-劉維爾的一系列相面積的守恆律，即系統的相流是一個單參數的保辛變換。The numerical results from the phase portraits, the period - doubling bifurcation and the poincare sections show that external stochastic excitation always masks the regular motions of a deterministic system and plays a dissipative role to the motions of the system, which causes the chaotic motions of the system to arise easily, though the period - doubling bifurcation is delayed
系統的相圖、倍周期分岔圖以及龐加萊映射圖等方面的數值結果表明，外加隨機激勵的作用往往掩蓋原確定性系統內在的規則運動，對原確定性系統的運動具有較典型的分散作用，可延緩系統的倍周期分岔，也可使得系統內在隨機行為提前發生，即可使得系統更容易出現混沌運動。Grigory perelman, a reclusive russian mathematician who solved a key piece in a century - old puzzle known as the poincar conjecture, was one of four mathematicians awarded the fields medal today
格雷高利、佩雷爾曼，一位解決了一個被稱為龐加萊猜想的世紀性難題的關鍵部分的俄羅斯數學隱士，是今天四位菲爾茲獎得主之一。Proving the conjecture false would have cast doubt on much of modern mathematics ? and everything that depends on it
一旦證明猜想是偽命題，那將使人們對現代數學的許多部分產生質疑? ?當然也包括基於龐加萊猜想的一切。When we research the chaotic character of conservative system in classical mechanics, the easiest and most effective method is the poincare surface of section ( pos ) of the orbits in phase space which abide by the classical hamiltonian
人們研究經典保守系統的混沌特徵時，最簡便有效的方法是計算相空間軌道的龐加萊截面。The qualitative work including : research the phase trajectory of the system 、 poincare map 、 power spectral and auto - correlation. the quantitative work including : calculation of ratio of period 、 calculation of fractional dimension and coefficient of lyapunov, especially ratio of period and the maximum lyapunov exponent. the results show that chaos occurs in the movement of system
定性的研究工作有：研究系統運動的相軌圖、龐加萊映射圖、功率譜圖和自相關函數圖；定量方面的研究工作有：周期比的計算、分維數的計算和lyapunov指數的計算，並著重進行了周期比和最大lyapunov指數的計算。General topology has gone through over one hundred years ' development since it was initiated to become a independent science branch by poincare from the end of the 19th century to now
一般拓撲學從19世紀由龐加萊開創為一個獨立的科學分支至現在已經歷了一百多年的發展歷史。When the potential is interaction, because of the symmetry of the hamiltonian, the poincare surface of section ( pos ) of the orbits in the classical phase space is integrable, which is corresponding to the poisson distribution in the quantum manifestation, our compute accords with this distribution
當粒子間為占勢作用時，由於哈密頓的對稱性，系統對應的經典相空間軌道的龐加萊截面圖表現出可積的性質，這在量子上對應著能級統計分佈為無規譜的poisson分佈，我們通過基矢展開的方法求得的能級正符合這個分佈。Based on comprehending the definition of chaos and its concepts, several description methods of chaos are discussed, including poicare mapping, power spectrum and lyapunov exponent, and so on
在理解混沌的含義和幾個概念基礎上，重點討論了混沌運動的幾種刻劃方法，包括龐加萊映射、功率譜與lyapunov指數等。But because there is the uncertainty principle in quantum mechanics, the particle ' s momenta and coordinates ca n ' t be determined at the same time, we ca n ' t use the orbits in phase space to describe quantum chaos
但是在量子力學中，由於不確定關系，粒子的動量和坐標不能同時被確定，所以經典龐加萊截面取法就不適用了。Considering the actual experiment condition, we use the poincare surface of section, which is the elementary method in the study of classical chaos, to investigate how the different relative energy and tiled angle influence on the particle ' s motion in the potential well. 2
考慮到實際的實驗數據，分別改變粒子的初始能量和磁場的傾斜角度，採用經典混沌研究的主要工具，即經典相空間的龐加萊截面方法來研究不同能量和傾角對系統中粒子運動的影響。To understand the poincar conjecture, start by thinking of any object existing in a three - dimensional world
要理解龐加萊猜想，當始於對三維世界存在的一切物體的認識。Poincar ' s conjecture is important not for its practical applications, but because a vast quantity of mathematical work assumes that it is true
龐加萊猜想的重要不僅在於它的實際應用性，還因為巨量的數學工作是基於假定龐加萊猜想是正確的。Pioncare says : if we should predict the future of math, the proper way is to know the history and development of the subject
龐加萊認為： 「如果我們希望預知數學的將來，適當的途徑是研究這門學科的歷史和現狀」 。分享友人