球諧函數 的英文怎麼說

中文拼音 [qiúxiéhánshǔ]
球諧函數 英文
spheric harmonic function
  • 球 : 名詞1 （以半圓的直徑為軸 使半圓旋轉一周而成的立體; 由中心到表面各點距離都相等的立體） sphere; glo...
  • 諧 : Ⅰ形容詞1 （和諧） in harmony; in accord; in tune 2 （詼諧） humorous Ⅱ動詞（商量好; 辦妥） come t...
  • 函 : 名詞1. [書面語] （匣; 封套） case; envelope 2. （信件） letter 3. （姓氏） a surname
  • 數 : 數副詞（屢次） frequently; repeatedly
  • 函數 : [數學] function函數計算機 function computer; 函數計算器 function calculator; 函數運算 functional operation
  1. The angular part of a continuum wave function is, of course, a spherical harmonic.

    連續譜波函數的角度部分當然是球諧函數。
  2. These are called spherical harmonics.

    這些叫做球諧函數。
  3. Firstly, in spherical coordinate system, the sovp formulation for the time - harmonic electromagnetic fields of the current dipole in conductive infinite - space is derived, using reciprocity theorem and transforming relations between special functions. then, selecting appropriate coordinate system, using superposition principle, the boundary - value problem of modified magnetic vector potential on the problem of a time - harmonic current dipole in spherical conductor is solved and analytical solution is obtained. finally, by means of the addition formulas of legendre polynomial and spherical harmonics function of degree n and order 1, the analytical solution in spherical coordinate system specially located is transformed into that in spherical coordinate system arbitrarily located

    首先利用特殊函數間的轉化關系和互易定理推導得到了無限大導體空間中球坐標下時諧電流元電磁場的二階矢量位形式：然後利用疊加原理，選擇合適坐標系，求解了導體球中時諧電流元的修正磁矢量位邊值問題，得到了問題的解析解；最後依據不同坐標系下電磁場解的轉化原理，藉助勒讓德多項式和n次1階球諧函數的加法公式，將坐標系特殊安放時的電磁場解析解變換到坐標系一般安放時的解析解，給出了球內電場和球外磁場的並矢格林函數。
  4. The addition formula of spherical harmonics function of degree n and order 1 is derived using the relations between coordinate varieties after coordinate rotating and the property of the associated legendre polynomial. the relations among the magnetic vector potential, the modified magnetic vector potential and the second - order vector potential ( sovp ) are shown going forward one by one. it is explained that the solutions of electromagnetic fields in different coordinate systems can be transformed and an example having analytical solution is given

    利用坐標旋轉后球坐標變量間的關系和連帶勒讓德多項式的性質推導得到了n次1階球諧函數的加法公式；以遞進的方式說明磁矢量位、修正磁矢量位與二階矢量位的關系，寫出了引入二階矢量位的過程；以時諧場矢量邊值問題為例，闡明了不同坐標系下電磁場解的相互轉化原理，給出了一個解析解的轉化例子；在球坐標下，引入了較球矢量波函數更普遍的兩類矢量函數，給出了其在球面上的正交關系。
  5. It also roundly researched the solution of the helmholtz equation in the circumrotating ellipsoidal coordinates, and discussed how to calculate the solution of the electro - magnetic field in the circumrotating ellipsoidal coordinates using special functions, and researched circumrotating ellipsoidal cavity ’ s latent value and quality parameter using arithmetic simulation, finally we compared the ellipsoidal cavity with the spheriform cavity. the main content of this thesis are as following : 1. calculated the distribution of the electro - magnetic field inside the ellipsoidal cavity based on maxwell equations and boundary conditions, and confirmed the syntonic mode inside the ellipsoidal cavity using arithmetic methods

    本文從maxwell方程及其邊界條件求解出橢球腔內的電磁場分佈，較為全面的研究了旋轉橢球坐標系下赫姆霍茲方程的解的問題，討論了用特殊函數來求解旋轉橢球坐標系下電磁場的解，並通過數值模擬研究了旋轉橢球諧振腔的本徵值和品質因數，並和球形諧振腔做了比較，主要內容為: 1 .用maxwell方程及其邊界條件求解出橢球腔內的電磁場分佈，並且分析了橢球腔內的諧振模式。
  6. Based on the extended boundary condition method and addition theorem of vector spherical functions, this paper study the light scattering problems of aggregate spheres from the angles of a single sphere, two - sphere system and multi - spheres system

    本文基於擴展邊界條件法及矢量球諧函數的加法定理，通過嚴格求解maxwell方程所得到的散射傳輸矩陣，對與入射波波長可比擬的群聚球形粒子的散射問題進行了研究。
  7. In view of the limitation of the traditional inversion theory and method of the gravity and magnetic field, professional an yulin, etc, worked in china university of geoscience, has come into being the theory system of the all - direction imagery for local gravity and magnetic sources after having researched a few years. the theory system broke through the thinking method of traditional theory system, researched all - direction imagery of the 2d local gravity and magnetic sources by means of complex function theory and researched all - direction imagery of the 3d local gravity and magnetic sources by means of spherical harmonic analysis theory, developed greatly the interpretation theory on the gravity and magnetic field

    該理論體系突破了傳統的重、磁場解釋理論體系的思維方式，採用復變函數理論研究二維局部重磁場源全方位成像，採用球諧分析理論研究三維局部重磁場源全方位成像，大大發展了重磁學科解釋理論，可以在起伏地形、有背景疊加和高頻干擾等復雜條件下，直接反演加疊代修改，求解分佈在有限范圍內的二維和三維重磁場源異常場的多種反演問題。
  8. The two components have identical vertical structure and physical process. the global spectral model component uses spherical harmonics as horizontal basis functions

    這兩部分採用相同的垂直結構和物理過程，都用球諧函數作為水平基本函數。
  9. In this paper, the transitional method of the spherical har monics is applied and a new model is gained. the parameters of the new model are geocentric radius, range cross - deviation and polar is decided by different trajectories

    本文對球諧函數的改進主要是採用了換極法，根據不同的彈道重新選擇極點，將球諧函數變換為以地心距、射程角、側向偏差為參數的新的形式。
  10. In this paper, we not only analysed the different effects of the disturbing gravitation on the trajectories of different ranges, but also discussed shortcomeings of the spherical harmonics model by which the external gravitation potential of the earth is shown usually. when the model is applied directly to the calculation of the trajectory, since the recurrent calculation can not be avoided, an increase in orders of model will result on a decrease in the speed of calculation

    本文重點分析了擾動引力對不同射程導彈的落點偏差的影響，並且討論了原有計算擾動引力的球諧函數法在計算速度上的缺陷（由於勒讓德函數的遞推計算，使得隨著模型階數的增加模型的計算速度下降） ，然後對其進行改進使其能更好的適用於彈道計算。
  11. With the recurrent calculation got rid of, the speed of calculation is increased. practical calculations have shown that the new model not only have the high precision but also enables us to enhance the speed of calculation 6 or 7 times. so it is testified that the new model is superior to the spherical harmonics model

    通過將換極后的球諧函數用於彈道計算，得出換極后的球諧函數不僅在計算精度上可達較高要求，而且計算速度也明顯優于未換極的球諧函數（新模型的計算速度是約為換極前模型的6 7倍） 。
  12. First, we concisely recall the formation and development of bose - einstein condensa - tion ' s theory and it ' s experimentation. secondly, we briefly intro - duce some properties of weakly interactive bose gases, and derive the nonlinear gross - pitaevskii equation that is the condensate macroscopic wave function ' s equation. thirdly, we give a exam - pie, an approximation analytical solution of the gross - pitaevskii equation in a spherical symmetric harmonic trap is derived by a perturbation theory approach, this solution is consistent with that numerically obtained

    全文共分為四章：第一章首先簡要的介紹和回顧了玻色-愛因斯坦凝聚理論的產生和發展，以及其實驗研究的過程，然後著重介紹了弱相互作用的玻色氣體的一些性質，並推導出了凝聚體宏觀波函數滿足非線性的gp方程，還以球對稱的諧振子勢為例，用標準的微擾方法求出了定態的gp方程近似解，發現其與已知的數值結果符合得很好。
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