dynamical symmetry 中文意思是什麼

dynamical symmetry 解釋
動力學對稱性
  • symmetry : n. 對稱；勻稱；調和；勻稱美。 bilateral symmetry 左右對稱。 radial symmetry 輻射對稱。
  1. Hi the aspect of symmetry analyzing to the hopfield model neural network with hebbian learning, we study on the dynamical behavior of the state space under the action of isometric transformation group g = z2 ? n, and prove the invariant property of the energy orientation ? / / " ) of the state space under the action of g. we find that the symmetry relationship of the network is sx - sw = sh when the active function of the neuron is odd, where sx is the symmetry of the patterns set x under hebbian learning rule, sh is the symmetry of the network and sw is the symmetry of the weight matrix w of the network

    ） s _ n為手段，研究了網路狀態空間在群g作用下各點的運動情況，證明了群g作用下的不變性。證明了當神經元的激活函數f為奇函數時， hebb法則下存儲樣本集x的對稱性s _ x 、網路對稱性s _ h以及連接矩陣對稱性s _ w三者之間滿足s _ x = s _ w = s _ h的關系；同時，我們還證明了：網路穩定態集vf同一s _ h軌道中的兩個穩定態的動力學行為（能量和吸引域大小）相同；兩個等距網路h和h 1 = g ? h ， （ ? ） g （
  2. Phase transition from u ( 3 ) to o ( 4 ) in the model is also analyzed in detail. finally, the vibron model is used to describe diatomic molecules. fitting to vibrational energy spectra is performed using both transitional theory and dynamical symmetry limit theory within the same framework

    利用建立在該嚴格解基礎上的計算程序討論了u （ 4 ）振動子模型的過渡區理論對雙原子分子振動能譜的描述，並與o （ 4 ）極限的計算結果做了比較。
  3. What we do at this aspect are : firstly, we describe the permutation symmetry of the structure of some special networks and the corresponding attractor sets with some geometric graphs in euclidean space, which are called attractors graph and geometrized structure graph of the networks respectively ; the geometrizing conditions are also given ; we study the dynamical behavior of the networks using the geometrized structure graph and attractors graph of the network ; moreover, we propose an approach to construct a big - size network with some small - size network with symmetry by the method of direct - sum, direct - produce and semidirect - produce. we also study the dynamical properties " relation between the big - size network and the small - size networks. all those results will provide some theoretical basis for designing a special large - scale network

    本文在這方面所做的工作如下：首次將一些特殊網路的結構和吸引子集的置換對稱性用三維歐氏空間中的一些幾何圖來表示，分別稱之為幾何結構圖和吸引子圖；給出了網路對稱性的幾何化條州即相應的對稱性群為可遷群） ：並惜助網路的幾何結構圖和吸弓吁圖分析網路的動力學性質；此外，我們提出了用簡單的具有一定對稱性的小網路按照群的直和、半直積和直積的方式組合成較大的網路的方法，探討了這些小網路和所組成的大網路的一些動力學性質的關系，如穩定態的個數、各穩定態的回憶性質等，為較大網路的設計提供一些理論依據。
  4. We also prove the following properties : the stable states of the network in the same sh orbit have a same dynamical behavior, such as the size of attraction basin and the energy ; the relation of the symmetry of two isometric networks h and h ' = g - h is s ' h = g - sh - g ~ } for any isometry g, where sh and s ' h are the symmetry of h and h " respectively ; the isometry will not change the dynamical properties of the stable states set of the corresponding networks ; etc.

    ） g的對稱性s _ h和s _ n的關系為s _ h = g ? s _ h ? g ~ （ - 1 ） ；等距變換不會改變網路穩定態集的動力學性質等一系列的結論。所有這些研究結果表明了hebb學習法則是通過調整網路的連接矩陣，使得其的結構的對稱性包含存儲樣本集的對稱性這一存儲機理。
  5. By using the bifurcation theory of planar dynamical systems and the method of detection functions, this paper gives a configuration of limit cycles forming compound eyes. with the help of numerical analysis ( using maple ), it is shown that there exist parameter groups such that a polynomial vector field of degree 7 has at least 49 limit cycles with z8 - symmetry

    然後，利用平面動力系統的分支理論以及判定函數法，考慮z _ 8 -等變的擾動hamilton向量場，在計算機數學軟體（ maple ）的幫助下，我們得到結論： 8次平面向量場至少有49個極限環，形成具有z _ 8 -對稱性的極限環分佈。
  6. It also can use to reduce the computing freedoms of the weight matrix in associative memory designing by applying the symmetry relations of the network. regarding the artificial neural network as a dynamical system with symmetry will bring the corresponding geometric approach

    利用這種對稱性關系，既可以揭示「學習就是尋找樣本集對稱性」這一學習的內涵，又可以在聯想記憶網路的分析與設計中減小連接權計算的復雜度。
  7. In the second part, we try to apply orthogonal polynomial approximations to the dynamical response problem of the duffing equation with random parameters under harmonic excitations. we first reduce the random duffing system into its non - linear deterministic equivalent one. then, using numerical method, we study the elementary non - linear phenomena in the system, such as saddle - node bifurcation, symmetry break bifurcation, phenomena in the system, such as saddle - node bifurcation, symmetry break bifurcation, period - doubling bifurcation and chaos

    本文第二部分嘗試將正交多項式逼近方法應用於隨機duffing系統，提出與之等價的確定性非線性系統的新概念，並用數值方法對該系統在諧和激勵下的鞍結分叉、對稱破裂分叉、倍周期分叉、和混沌等各種基本非線性響應進行了初步探討。
  8. In the fourth part, by using the bifurcation theory of planar dynamical systems and the method of detection functions, the paper gives a configuration of limit cycles forming compound eyes. with the help of numerical analysis ( usi ng maple ), it is shown that there exist parameter groups such that a z7 - equivariant planar polynomial vector field of degree 7 has at least 36 limit cycles with z7 - symmetry

    然後，對於一組特定的參數值，研究了它的相軌線的變化趨勢；第四部分指出：在一定的條件下，利用平面動力系統分支理論以及判定函數法，在計算機數學軟體（ maple ）的幫助下，得到結論： 7次z _ 7 -等變平面向量場至少有36個極限環，形成具有z _ 7 ?對稱性的極限環分佈。
分享友人
分享到 Line

分享到臉書