liouville 中文意思是什麼

liouville 解釋
利烏維爾
  1. A liouville theorem for a class of elliptic systems

    一類橢圓型方程組的劉維爾定理
  2. An extension form of liouville ' s theorem about analytic functions for general harmonic functions is proved

    摘要證明復變函數中的劉維爾定理在調和函數中的一種推廣。
  3. Analysis of asymptotic behavior of a regular sturm - liouville problem

    問題本徵的漸近分析
  4. Using riemann - schwarz ' s symmetry principle of complex functions, the above problems are transformed into riemann - hilbert boundary problems. by combining the analysis of singularity of complex functions, generalized liouville ' s theorem, cauchy model integral and residue theorem, the general solutions of above problems are presented

    創造性運用復變函數解析延拓原理，將上述問題轉化為riemann - hilbert邊值問題，結合復應力函數奇性主部分析方法、廣義liouville定理、 cauchy型積分和留數定理，獲得了上述問題的一般解答。
  5. In this paper, we convert the complex third order eigenvalue problems into the real third order eigenvalue problems. then, based on the euler - lagrange equation and legendre transformation, a reasonable jacobi - ostrogredsky coordinate system have been found, then using nonlinear method, the lax pairs of the real bargrnann and neumann system are nonlinearized, so as to be a new finite - dimensional integrable hamilton system in the liouville sense is generated. moreover, the involutive representations of the solution for the evolution equations are obtained

    本文將復的三階特徵值問題轉化為實的三階特徵值問題，利用euler - lagrange方程和legendre變換，找到一組合理的實的jacobi - ostrogredsky坐標系，從而找到與之相關的實化系統，再利用曹策問教授的非線性化方法，分別將三階特徵值問題及相應的lax對進行非線性化，從而得到bargmann勢和neumann勢約束系統，並證明它們是liouville意義下的完全可積系統，進而給出了bargmann系統和neumann系統的對合解。
  6. In this dissertation, with the aid of many types of constructive transformations and symbolic computation, some topics in nonlinear waves and integrable system are studied, including exact solutions, painleve integrability, backlund transformation, darboux transformation, symmetry ( similarity reduction ), conditional symmetry, lax integrable hierarchy, liouville integrable n - hamilton structure, constraint flow, involutive system, lax representation, r - matrix, separation of variables and integrable couplings. chapter 2 and 3 are devoted to investigating exact solutions of nonlinear wave equations : firstly, the basic theories of c - d pair and c - d integrable system are presented

    本文以構造性的變換及符號計算為工具，來研究非線性波和可積系統中的一些問題：精確解（如孤子解、周期解、有理解、 dromion解及compacton解等） 、 panileve可積性、 backlund變換、 darboux變換、對稱（相似約化） 、條件對稱、 lax可積族、 liouville可積的n - hamilton結構、約束流、對合系統、 lax表示、 r -矩陣、變量分離及可積的耦合系統
  7. The unconstrained and constrained linear matrix equations and related least squares ( l - s ) problems have been of interest for many applications, including particle physics and geology, control theory, the inverse sturm - liouville problem, inverse problems of vibration theory, digital image and signal processing, photogrammetry, finite elements and multidimensional approximation

    例如在粒子物理學和地質學， sturm - liouville逆問題，自動控制理論的逆問題，振動理論的逆問題，數碼影象和信號處理，航空投影測量學，有限元及多維逼近問題等方面都有重要的作用。
  8. The tu ' s scheme is extended to the generalized dirac spectral problem with an arbitrary function, the generalized kaup - newell spectral problem and the new 3x3 spectral problem with five potentials such that their lax integrabie integrabie hierarchies of equations and liouville integrabie hamilton structures are obtained. chapter 7 is devote to higher - order constraint flow, involutive system, lax representation, r - matrix and the separation of variables

    第六章研究了lax可積的新的方程族和liouville可積的n - hamilton結構方面的問題：將屠格式推廣到新的含有任意函數的廣義dirac族的譜問題、廣義kaup - newell譜問題及含有五個位勢函數的3 3譜問題，研究了它們的lax可積的方程族和liouville可積的hamilton結構。
  9. Finite element method of the eigenvalues of sturm - liouville ' s problem

    問題特徵值的有限元方法
  10. A note on liouville theorem

    關于劉維爾定理的一個注記
  11. Liouville ' s theorem

    劉維定理
  12. In this paper, we analyze the nonlinear response of a three - level a model system, using a perturbation theory based on the liouville equation. of motion and considering the lorentz local field effect

    本文中，我們考慮了lorentz局域場效應的影響，在liouville運動方程的基礎上用微擾理論分析了一個三能級系統的非線性響應。
  13. Then the nonlinearization procedure is applied to the eigenvalue problem of mkdv - nls hierarchy. under bargmann constraint, it is shown that lax pairs are nonlinearized to be two finite - dimensional liouville completely integrable system

    同時，應用非線性化技巧，證明了在bargmann約束下， mkdv - nls方程族的lax對可被非線性化為兩個有限維liouville完全可積系。
  14. Starting from isospectral problems, tu ' s scheme is applied to generate a well - known generalized burgers equation hierarchy, a class of new mkdv - nls equation hierarchy and a family of discrete nonlinear evolution equations. they are shown to be liouville integrable hamiltonian systems

    從等譜問題出發，利用屠格式導出了著名的廣義burgers方程族和一類新的mkdv - nls方程族，及一族離散的非線性演化方程，且證明了它們均是liouville可積的廣義hamilton方程族。
  15. 3. as for the existence of positive solutions, the cone theory and the fixed point index of condensing mapping are employed, and the results of the existence of positive solutions are obtained in the case of superlinear and sublinear. the conclusions extend and improve the existence theorem which lou ben - dong extablished in 1996 about the question of sturm - liouville of banach spaces

    三、對于正解存在性問題，我們應用凝聚映射的不動點指數理論，分別在超線性與次線性情形下進行討論，獲得了一些正解存在的結果，主要結果推廣和改進了1996年louben - dong對banach空間sturm - liouville問題所建立的存在性定理。
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