symplectic 中文意思是什麼

Symplectic solutions of annular sector plate clamped along two circular edges with circumfluent coordinate treated as

環扇形板彎曲問題中環向模擬為時間的辛體系

High accuracy symplectic scheme for the schr dinger type equation

方程的高精度辛格式

Multi - symplectic method for the dirac equation

方程的多辛格式

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

( 2 ) the causation that the caustic phenomena of electromagnetic wave propagation in two - dimension concave reflectors occurs and the types of singularities in caustic fields are investigated, and the conclusion that there are two types of singularities ( fold and cusp ) in caustic fields in two - dimension concave reflectors is obtained ; by symplectic geometrical method, formulations of computing wave fields in and far away from caustic fields in two - dimension concave reflectors are deduced, and the results are plotted in pictures. ( 3 ) the cause of the caustic phenomena of electromagnetic wave propagation in three - dimension concave reflectors and the types of singularities in caustic fields is discussed, and the conclusion that there are three main types of singularities ( fold, cusp and swallowtail ) in caustic fields in three - dimension concave reflectors is obtained ; by symplectic geometrical method, the formulae of computing wave fields in and far away from caustic fields in three - dimension concave reflectors are deduced. particularly, the wave fields in ellipsoid concave reflector are computed, and the results displayed in special sections are given

論文主要包括三個方面： （ 1 ）分析了凹面反射的焦散現象，給出了不同凹面反射的焦散圖； （ 2 ）分析了二維凹面反射波動場焦散現象產生的原因及焦散區奇性的種類，得出了二維凹面反射波動場焦散區奇性主要有折疊（ fold ）和尖點（ cusp ）兩種的結論，利用辛幾何方法構造了圓錐曲面反射波動場非焦散區和焦散區的通用計算公式，並給出了圓柱面、橢圓柱面及雙曲柱面反射的計算結果； （ 3 ）分析了三維凹面反射波動場焦散現象產生的原因及焦散區奇性的種類，得出了三維凹面反射波動場焦散區奇性主要有折疊（ fom 、尖點kusp和燕尾k ）三種的結論，提出了利用辛幾何方法計算三維凹面反射波動場非焦散區和焦散區的計算方法，並給出了三軸不等橢球體凹面反射波動場的計算結果剖面圖。

Iterative methods for symplectic algorithm of wave equation

波動方程辛演算法的迭代求解

The governing equations of the problem are derived in hamiltonian form by using variable substitution and variational principle. then the methods of separation of variables and conjugate symplectic eigenfunction expansion are developed to solve the equations of plate bending problem. the result can be derived by analytical method

在平面彈性問題中，由變量代換及變分原理，方程可導向哈密頓體系，從而通過分離變量法及共軛辛本徵函數向量展開法，以解析的方法來進行求解。

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。

The main studies are as follows : ( 1 ) the hamiltonian mechanics and equations are deduced from the lagrange mechanics. the symplectic quality of the hamiltonian system is discussed. the formulations of the symplectic integrator method are constructed, especially the explicit symplectic schemes for the separable hamiltonian system and the symplectic partitioned runge - kutta ( prk ) method for the generic hamiltonian system

本文對該方法進行了初步的研究和計算應用，具體展開了以下幾方面的工作： （ 1 ）從lagrange力學出發引入hamilton力學和hamilton正則方程的概念，討論了hamilton系統的辛性質，給出了構造辛演算法的基本原理，並重點介紹了線性可分hamilton系統的顯式辛格式和一般hamilton系統的辛prk方法。

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。

We use the pseudo - symplecticity to interpret the inexactness, and pseudo - symplectic order to magnitude of inexactness. by using the pseudo - symplectic b _ series and p - series theories, the relation between the pseudo - symplecitc order q and iteration number k can be established

我們使用擬辛p - series理論與擬辛的b - series理論，建立了擬辛階q與迭代次數k之間的對應關系。

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。

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。

In this paper, the symplectic direct decomposition of complex symplectic linear spaces is given. these results laid foundations for further research on normal forms of complex symplectic matrices

給出了復辛線性空間的辛直和分解，這些結果為將來進一步研究復辛矩陣的標準形打下了基礎

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。

In this paper, by means of the euler systems on the symplectic manifold, the bargmann system and the neumann system for the 4f / lorder eigenvalue problems : are gained. then the lax pairs for them are nonlinearized respectively under the bargmann constraint and the neumann constraint. by means of this and based on the euler - lagrange function and legendre transformations, the reasonable jacobi - ostrogradsky coordinate systems are found, which can also be realized

本文主要通過流形上的euler系統，討論四階特徵值問題所對應的bargmann系統和neumann系統，藉助于lax對非線性化及euler - lagrange方程和legendre變換，構造一組合理的且可實化的jacobi - ostrogradsky坐標系? hamilton正則坐標系，將由lagrange力學描述的動力系統轉化為辛空間（ r ~ （ 8n ） ， ）上的hamillton正則系統。

The nil radical for symplectic ternary algebras

辛三代數的冪零根

The problems are changed into a series of symplectic eigenvalue problems under the duality system

在辛系統中，問題被化為系列本徵解問題。

In the systematic system, a direct method solution for symplectic eigenvalue problems is put forward. the symplectic method updated the solving system of the viscoelasticity to a new platform

在辛體系下建立了一種辛本徵解直接方法，將粘彈性力學求解方法和思路上升到一個新的平臺。

( 3 ) the symplectic integrator method is applied to time evolution of the scalar wave equation

（ 3 ）將辛演算法運用到標量波動方程的時域模擬中。