poincare 1.普安卡雷(姓氏)。2.J.H. Poincare 普...
1.普安卡雷(姓氏)。 2.J.H. Poincare 普安卡雷〔1854-1912，法國數學家〕。 3.Raymond Poincare 朋加萊〔1860-1934，法國政治家，曾代總統〕。 “henri poincare“ 中文翻譯： 彭加勒“poincare conjecture“ 中文翻譯： 龐加萊猜想“poincare elements“ 中文翻譯： 龐加萊根數“poincare group“ 中文翻譯： 龐加萊群“poincare henri“ 中文翻譯： 亨利・普安卡雷“poincare lake“ 中文翻譯： 潘卡雷湖“poincare lemma“ 中文翻譯： 龐加萊引理“poincare manifold“ 中文翻譯： 龐加萊廖“poincare matrix“ 中文翻譯： 龐加菜矩陣“poincare model“ 中文翻譯： 龐加萊模型“poincare series“ 中文翻譯： 龐加萊級數“poincare sheroid“ 中文翻譯： 龐加萊橢球體“poincare sphere“ 中文翻譯： 鮑英卡勒偏振球; 鮑英卡勒球“poincare transformation“ 中文翻譯： 龐加萊變換“euler poincare formula“ 中文翻譯： 歐拉 龐加萊公式“euler poincare relation“ 中文翻譯： 歐拉 龐加萊公式“euler-poincare equation“ 中文翻譯： 歐拉-龐加萊方程“generalized poincare conjecture“ 中文翻譯： 廣義龐加萊猜想“jules henri poincare“ 中文翻譯： 彭加勒“poincare half plane“ 中文翻譯： 上半平面“universite henri poincare“ 中文翻譯： 一大“poincar correction“ 中文翻譯： 龐加萊改正“poin the wing“ 中文翻譯： 生活之翼“poin“ 中文翻譯： 波因; 內嵌; 嵌入; 突然出現; 一種性質未定的抗生物質,為從膿毒扁桃體炎病例中培養出來的鐮孢屬霉菌fusarium sporotrichiella var. paoe bilai所產生,在體外有抗葡萄球菌和鏈球菌的作用“poimula“ 中文翻譯： 波伊穆拉“poimkov“ 中文翻譯： 波伊姆科夫
Poincare ' s criticism on “ the expected reason “ , justification for the existence of mathematical object and opposition to the postulate of real infinite provide the developmental approach for the intuitionism in philosophy of mathematics 摘要彭加勒對邏輯主義“預期理由”的批判，對數學對象存在性的辯護和對實無窮假設的反對，都為數學哲學中直覺主義學派的發展開辟了道路。 |
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Henri poincare “ , , “ la physique ne nous donne pas seulement l ' occasion de resoudre des problemes . . . elle nous fait pressentir la solution . “ , 物理不僅僅給我們以解決問題的機會, … …而且還使我們預料到它的解. |
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poinciana |
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Especially , when the isocline of x is monotone decreasing in 0 < x < 1 , the svstem has no limit cycle and is globally stable ; next , we construct a saddle bifurcation at the boundary equilibrium and a degenerated bogdanov - takens bifurcation at the interior equilibrium by choosing appropriate parameter values in the following two sections , where our work are based on the theory of central manifolds and normal torms . we prove that is a codimention 3 focus - type equilibrium . system ( 6 . 1 ) will have two limit cycles at some appropriate bifurcation parameter values , and have homoclinic or double - homoclinic orbits at some other appropriate bifurcation parameter values ; at last , we study the qualitative properties of the system at infinite in the poincare sphere 因為系統在( 0 ， 0 )點處沒有定義，這給研究其在( 0 ， 0 )附近的動力學性質帶來了困難，我們應用文獻[ 17 ]中關于研究非線性方程奇點的系列理論和方法，圓滿解決了這一問題，給出了第一象限內當t +或t -時，在全參數狀態下系統的軌線趨于( 0 ， 0 )點的所有可能情況，其相圖也得以描繪；并且，系統不存在極限環的幾個充分條件我們也予以列出，當x的等傾線在0 x 1范圍內遞減時，系統不存在極限環，全局漸近穩定；然后，我們以中心流形定理和正規型方法為主要工具，巧妙選擇參數，分別構造了一個余維2的鞍點分岔和一個余維3退化bogdanov - takens分岔，證明了平衡點是余維3的焦點型平衡點，存在參數， m ，的值使得系統( 6 . 1 )有兩個極限環，還存在參數， m ，的另外值使得系統( 6 . 1 )有同宿軌或雙同宿軌。 |
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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，并著重進行了周期比和最大lyapunov指數的計算。 |
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Recently , there are some methods are utilized to study it , such as the modified lindstedt - poincare method , frequency - incremental method , stroboscopic method etc . more and more , scientists pay attention to it , as the study of solving partial differential equation is very important for the development of mechanics 目前主要的近似求解方法有改進l - p方法、頻率增量法、改進的諧波平衡法、頻閃法等等。由于求解偏微分方程對于力學的發展起了很重要的作用，求解偏微方程特別是非線性偏微分方程引起了很多力學工作者的注意。 |
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Nature of the singular point of plane poincare mapping that is established by equation ( 1 ) is analyzed . relationship between the three parameters and homoclinic orbit and heteroclinic orbit of the hamilton system corresponding to this sort of equation is discussed . the adequate and essential condition of the existing homoclinic orbit or heteroclinic orbit for the hamilton system is presented 分析了方程( 1 )建立的平面poincare映射的奇點性質，討論了此類方程對應的hamilton系統的同宿軌道和異宿軌道與三個參數o 、夕、尸的關系，給出了hamilton系統存在同宿軌道或異宿軌道的充分必要條件。 |
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For innovation diffusion model with three products , the global stability of the unique positive equilibrium is proved , by using the generalized poincare - bendixson theory and the competitive system theory . the threshold between the extinction and existence of the product without advertisement in the market is considered . for four products , the local stability of the unique positive equilibrium is proved through hurtwiz theory 當三個產品在市場中競爭時，利用推廣的poincar - bendixson定理以及競爭系統理論，我們證明了模型有一個全局穩定的正平衡點，并得到一個沒有廣告宣傳的產品占有市場或被淘汰的閾值，當四個產品擴散時，利用hurwitz定理，我們證明了唯一正平衡點是局部穩定性的。 |
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In chapter 3 , the poincare mapping is introduced to the study on oblique - impact vibrating systems . the periodic vibro - impacts and their stability are analyzed by using shaw ' s method and the local impact mapping near a periodic vibro - impacting motion is analyzed by using the discontinuity bypass mapping . furthermore , several possible bifurcations in the oblique - impact vibrating system are illustrated through a numerical example ( 2 )在第三章中建立了斜碰撞振動系統的poincar映射，研究了通過該映射方法確定系統周期運動及其穩定性，并具體計算了給定周期運動附近的局部碰撞映射，分析了斜碰撞振動系統可能存在的各種分叉行為。 |
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The stability of period response of nonlinear rotor - bearing systems is analyzed by employing the newmark and shooting methods . the bifurcation rules of period response of elastic rotor system with multi - degree of freedom are obtained . the motion characteristic of the rotor system is determined according to the fractal dimension of poincare mapping of phase aspect and frequency spectrums at certain speed and physic parameter of rotor 對于這三個模型,本文采用了計算速度較快的newmark方法求解系統的響應,用poincare映射、軸心軌跡和頻譜圖分析各個轉子-軸承系統在特定參數下的運動特征,通過分岔圖研究了轉子?軸承系統隨某些參數(轉速、不平衡量分布、軸承質量等)變化時的系統響應。 |
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By means of the precise integration method with lagrangian interpolation the trajectory of the shaft center , the poincare mapping and the bifurcation graphs are numerically given . the results predicted by the floquet theory are checked and the long - term dynamic behavior of the system is predicted . it is shown that the system has rich nonlinear behaviors at some m combination of the four parameters , for examples , multi - frequency subharmonic resonance , as well as chaos phenomenon from doubling bifurcation and twice hopf bifurcation 通過lagrange插值精細積分法數值給出系統的軸心軌跡圖、 poincar映射圖、分叉圖，檢驗floquet理論預測結果并預測系統的長期性態，顯示系統在四個參數組合的某些范圍內具有豐富的非線性特性，還存在多形式次諧波解，以及由倍周期分叉、二次hopf分叉通往混沌的現象。 |
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The discussing process follows the steps below : first , suppose the system ( 1 ) has only one finite singular point ( 0 , 0 ) . then we can assume b50 = 0 , which special direction is determined by equation g ( 0 ) - 0 , introduce poincare transformation to discuss infinite singular points , according to the coefficient conditions , list all possible infinite singular points and special directions , judging their type , drawing out all kinds of phase portraits 本文主要內容為：一、假設系統( 1 )只有唯一的有限遠奇點( 0 ， 0 ) ，則不妨設b _ ( 50 ) = 0 ，其特殊方向由示性方程g ( ) = 0給出，引進poincare變換研究無窮遠奇點，再根據各定理中的系數條件，列出系統所有可能的無窮遠奇點和特殊方向，并判斷其類型，由此畫出系統的各種可能的全局相圖。 |
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Based on the hydrodynamic , by using momentum theory to the liquid in the flow channel , the computational formula of the air exciting - vibration force is acquired . by using four - step runge - kutta method , the periodic response results of the elastic rotor system with one single - disc are gained . then the dynamic characteristics of the rotor system at the certain rotate speed and the certain physic parameter of system are analyzed by using the phase spaces and poincare maps of this system 基于流體動力學,通過對葉片流道內的流體模型應用動量定理,得到此汽流激振力模型,并采用四階龍格庫塔法,得出了單盤彈性轉子系統的周期響應規律,然后根據系統的相軌跡及poincare映射圖,分析了系統在特定轉速及特定的轉子系統參數下的運動特征。 |
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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，由于哈密頓的對稱性，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布為無規譜的poisson分布，我們通過基矢展開的方法求得的能級正符合這個分布。 |
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Finally , some properties of limits set of the solution of the dde with local monotone in the delay term are given . moreover , using the above discrete lyapunov functional , we prove that the poincare - bendixson theorem holds for some solutions of this dde . in chapter 4 , detail analysis of the global attractor for three particular classes of delay differential equations in concrete applications are given 最后，給出了最終落在時滯項局部單調范圍內的解的極限集的若干性質，并給出了類似于poincare一bendixson定理的結論及其證明，這些結論的證明盡管與mallet一paret的證明方法相似，但是本文的結論將他有關全局單調的理論推廣到局部單調中去了。 |
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Secondly , the effectiveness and limitation of the classical perturbation , such as the method of multiple scales and the poincare - lindstedt method , are discussed in detail through a duffing oscillator with delayed velocity feedback . it is shown that the two perturbation methods are effective only in solving the approximate solution of the first two orders . an ambiguity or paradox will be encountered when they are used to seeking for the third or higher order approximation of solution 其次，以一具有時滯速度反饋的duffing系統為例，研究了經典攝動法如多尺度法， poincar - lindstedt法等在求解時滯微分方程級數解時的適用性和局限性問題，指出利用這些方法只能有效求得系統的前兩階近似解，而在求系統的三次以上近似解時會出現矛盾或二義性。 |
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Two illustrative examples , a duffing oscillator subject to a harmonic parametric control and a driven murali - lakshmanan - chua ( mlc ) circuit imposed with a weak harmonic control , are presented here to show that the random phase plays a decisive role for control function . the method for computing the top lyapunov exponent is based on khasminskii ' s formulation for linearized systems . then , the obtained results are further verified by the poincare map analysis on dynamical behavior of the system , such as stability , bifurcation and chaos 通過兩個實例，即一類參激激勵作用下的duffing系統和一類murali - lakshmanan - chua ( mlc )電路，考察隨機相位在非反饋混沌控制中的影響與作用，利用最大lyapunov指數和poincare截面分析法證實了隨機相位確實可以用來調節系統的混沌行為，即一個小的隨機相位的擾動可能導致系統從有序轉變為無序，也可能使得系統從無序轉變為有序。 |
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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。 |
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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，采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。 |
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The tests , which will take six months , will not be able to say with certainty that the remains are joan of arc ' s , because there is no known dna sample from her to compare them with , said dr . philippe charlier of the raymond - poincare hospital in garches , west of paris 由于圣女貞德家族傳人的真實性還有待考證，因此利用其后代dna進行比較的檢測也就無法實施。查理爾說： “檢測工作需要6個月時間。我們無法確定這些殘骸就是圣女貞德的，因為沒有已知的dna |