symplectic space 中文意思是什麼
symplectic space
解釋
辛空間- symplectic : 偶對的
- space : n 1 空間；太空。2 空隙，空地；場地；（火車輪船飛機中的）座位；餘地；篇幅。3 空白；間隔；距離。4 ...
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The asteroids are the most important small bodies in the solarsystem, and they mainly lies in the two locations - a main belt between the mars ' s orbit and the jupiter ' s and the near - earth space. the most feature of the orbits of near - earth asteroids ( neas ) is that the semi - major axes of the orbits are nearly equal to that of the earth or the perihelia distances are approximate to or even less than the mean distance between the sun and the earth, thus they could move into inside of the earth ' s orbit, so that they might close approach or even colliside with the earth ( or other planets, such as the venus, the mars, etc. ). the characteristic brings about some difficulties in the numerical research during their orbital evolution, which leads to the failure of the normalization technique in the general removal impact singularities of celestial mechanics methods and the symplectic algorithm which is successfully applied to the investigation in quality. by comparing the computation effects of several common numerical methods ( including symplectic algorithm ), and considering the nature of the movement of the small bodies, the corresponding treatments are provided here to improve the reliability of the computation
小行星是太陽系最重要的一類小天體，主要分佈在兩個區域；火星和木星軌道之間的一條主帶和近地空間.近地小行星軌道的最大特點是其軌道半長徑與地球軌道半長徑相近，或近日距離接近甚至小於日地平均距離，其運動可深入到地球軌道的內部，這將導致該類小行星與地球（還有金星、火星等）十分靠近甚至發生碰撞.這一特徵給其軌道演化數值研究帶來一些困難，包括天體力學方法中一般消除碰撞奇點的正規化處理以及對定性研究十分成功的辛演算法都將在不同程度上失效.通過對幾種常用數值方法（包括辛演算法）計算效果的比較，根據小天體運動自身的特性，給出了相應處理措施，從而可提高計算結果的可靠性 -
Since the linear or nonlinear electromagnetic field equations can be written as an infinite - dimensional hamiltonian system, whose solution can be viewed as a hamiltonian flow in the phase space which preserves the symplectic structure in the time direction. such important features should not be neglected during the construction of numerical methods for the field equations
由於線性或非線性的電磁場方程可以轉化成無限維的hamilton系統，其結果可以看作是定義在相空間里的時間上保持辛結構的hamilton流，因而在對場方程構造數值演算法時就不應忽略這樣重要的性質。 -
This paper is to study harmonic maps into symplectic groups and local isometric immersions into space forms by means of the soliton theory. by realizing an action of the rational loop group on the spaces of corrsponding solutions, we get the backlund transformation and the darboux transformation, and thereby we give the explicit construction for harmonic maps into symplectic groups and local isometric immersions into space forms via purely algebraic algorithm
主要用孤立子理論研究到辛群的調和映射和到空間形式的局部等距浸入，通過有理loop群在其解空間上的dressing作用，給出b icklund變換和darboux變換的顯式表示，從而獲得到辛群及其對稱空間的調和映射和到空間形式的局部等距浸入的純代數構造方法。 -
In this paper, two kinds of bilinear functions have been mainly discussed, and symplectic space been only simple introduced
摘要該文旨在闡述二類雙線性函數的聯系、區別，並初步介紹了辛空間的概念。 -
While the new components having the same numbers with these original physical vectors are introduced and the new components are combined with those original physical components to form a new symplectic space, the ray problem of wave propagation in geometrical optics is converted into the problem of lagrange submanifold in the symplectic space
通過引入波向量（慢度向量） ，將物理空間中幾何光學的射線問題轉化為辛空間中的lagrange子流形（超曲面）問題。 -
Its content may be separated into two parts. the first part contains chapter one and chapter two, which treat of the harmonic maps from surface into symplectic groups and quaternion grassmann manifolds. the second part contains chapter three and chapter four, which treat of local isometric immersions from space forms or riemannian products of space forms into space forms
全文分四章，內容可分為兩部分：第一部分包括第一、二章，主要論涉從曲面到辛群及四元grassmann流形的調和映射；第二部分包括第三、四章，主要論涉從空間形式或空間形式的局部riemann積到空間形式的局部等距浸入。 -
The symplectic integrator method is the new time - domain method which is specialized to a hamiltonian system and can preserve the symple ctic structure of the phase space
辛演算法正是用來保持hamilton系統相空間辛結構的一種新的數值方法，並且在計算精度、時間上具有優越性。
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