函數展開 的英文怎麼說

中文拼音 [hánshǔzhǎnkāi]
函數展開 英文
expansion of function
  • 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. Generalized eigenfunction expansion concerning normal operators

    與正常運算元相關的廣義特徵函數展開
  2. Comparison of modal function expansion method with eigenfunction expansion method for prediction of hydroelastic responses of vlfs

    預報超大型浮體水彈性響應的模態函數展開方法和特徵函數展開方法比較
  3. In chapter 8 solutions by eigenfunction expansion to 1 - dimensional problems of mechanics and 2 - dimensional problems of theory of elasticity are researched

    第八章研究1維力學和2維彈性力學問題的特徵函數展開解法。
  4. Equation ( 4 ) is said to belong to limit circle type if all solutions of equation ( 4 ) belong to l ~ ( 2 ) ( simply denoted by l. c. ) equation ( 4 ) is said to belong to lagrange stable if all solutions of equation ( 4 ) belong to ( simply denoted by l. s. ). in chapter 4, we study criteria for the linear nonhomogeneous differential equation belonging to the limit circle type

    方程（ 』 ）稱為極限圓型的，若方程（ 』 ）的所有解都屬于護[ a ， co ） （簡記為l . c . ） ;方程（ 』 ）稱為拉格拉日穩定，若方程（ 』 ）的所有解均屬于lco [ a ， co ） （簡記為l . s . ） .由於方程（ 』 ）解的平方可積性及有界性的研究在微分運算元理論、按微分方程的特徵函數展開理論以及無界區間上受控系統的最佳控制理論等方面具有重要應用
  5. The mostly conclusion of this part is as follows, on the conditon of travelling wave, the exact solitary wave solutions to some nonlinear wave equations such as sawada - kotera equation, kaup - kupershmidt equation, the fifth order kdv equation, fisher - kolmogorov equation, on the help of the computer algebraic system ( maple ), are explicitly established by making use of the hyperbolic function method. this part is maken up of three sections

    本部分的主要結論如下，利用雙曲函數展開法，在行波條件下，對sawada - kotera方程， kaup - kupershmidt方程，五階kdv方程， fisher - kolmogorov方程，等幾類非線性波動方程求解，將其孤立波表示為雙曲函數的多項式，從而將非線性波方程的求解問題轉化為非線性代數方程組的求解問題，並藉助于計算機代數系統求解非線性代數方程組，最終獲得了這些非線性波動方程的若干精確孤立波解。
  6. 2. we present a solution to the scattering of gaussian beams by a concentric multilayered non - confocal spheroidal particle by taking a concentric two - layered one as an example. because the boundaries of these two layers are connected with two different spheroidal coordinate systems, firstly, the electromagnetic fields between the inner and outer boundaries are expanded in terms of the spheroidal vector wave functions with reference to these two systems, and the electromagnetic fields within the inner boundary with reference to the system for it

    2 .以雙層橢球為例，我們提出了一種研究同心非共焦多層橢球粒子散射的方法，首先把兩層橢球之間的電磁場用對應于兩個橢球坐標系的橢球矢量波函數展開，這兩個橢球坐標系分別與兩層橢球的邊界面相聯系，在每層橢球邊界面上分別應用邊界條件，建立關于各展開系數的方程組。
  7. Upon using an artificial neural network ( ann ) a new short - term climate forecast model with the monthly mean rainfall in june in the north of guangxi as predictand is established making empirical orthogonal functions ( eof ) to the 36 predictors ( 15 ssa predictors, 21 500hpa height predictors ) with over 0. 05 significant correlation level of previous 500hpa height and sea surface temperature ( sst ) field, and selecting the high relative principal components, at the same time, a new approach of constructing ann learning matrix is developed. predictive capability between the new model ( principal components ann model ) and linear regression model for the same predictors is discussed based on the independent samples and historical samples

    本文通過對廣西北部6月平均降水量（預報量）同北半球月平均500hpa高度場和北太平洋月平均海溫場進行相關普查，選取了前期36個同預報量相關顯著水平達到0 . 05以上的預報因子（ 15個海溫場預報因子， 21個高度場預報因子） ，並運用自然正交函數展開方法對這36個前期預報因子展開，取其中同預報量相關程度高的主成分，結合人工神經網路技術，提出了一種新的構造人工神經網路學習矩陣的方法，建立了一種新的短期氣候預測模型。
  8. This thesis in theory deals with electromagnetic wave scattering by multilayered confocal and non - confocal spheroidal particles illuminated by gaussian beams, in which the main contributions are as follows : 1. in the case of multilayered confocal spheroidal particles, the scattered fields as well as the fields within each layer are obtained in terms of infinite series with spheroidal vector wave functions by using an appropriate expansion of the incident gaussian beam. by virtue of the boundary conditions, we write the set of equations for determining the unknown expansion coefficients and then solve it

    本文從理論上研究了多層共焦和非共焦橢球粒子對高斯波束的散射，主要成果如下： 1 .我們研究了多層共焦橢球粒子對高斯波束的散射，把入射高斯光，散射場，各層橢球內的電場和磁場用適當的橢球矢量波函數展開，應用電磁場邊界條件，寫出確定各展開系數的方程組，求出散射場系數，進而求出散射場及散射截面。
  9. The mathematics - mechanization method is applied the field of differential equations. many algorithm for constructing solitary wave solutions for a class of nonlinear wave equations are given, and implemented in a computer algebraic system, such as the hyperbolic tangent function method and the hyperbolic function method etc. exact solitary wave solutions of a great deal of nonlinear equations are gained

    將機械化數學方法應用於偏微分方程領域，建立了構造一類非線性波方程的精確孤立波解的許多演算法，如，雙曲正切函數展開法，雙曲函數方法等，並在計算機數學系統上加以實現，因而推導出了一批非線性波方程的精確孤立波解。
  10. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of jacobi polynomials

    為了求解對偶積分方程，將裂紋面上的位移差函數展開為雅可畢多項式的級數形式。
  11. There were troubles in the continuity of the function and of its - derivative divided by band - mass on the boundary. in the theoretical calculation, the wave function is relative to the physical properties of the impurity greatly, the envelop function f ( x, y ) is expanded in terms of the one - dimensional linear harmonic oscillator function in this paper. it satisfies the continuity of the function and of its - derivative divided by the band - mass, so it improves the precision of the function and binding energy

    與以往工作不同的是，以前選用的x ， y方向電子的包絡函數f （ x ， y ）是一維有限深量子阱中波函數的乘積，在邊界上波函數的連續性和粒子流的守恆條件存在問題；而在理論計算中，波函數的選取與雜質的物理性質有密切關系，本文選取的電子的包絡函數是用一維線性諧振子的波函數展開而成的，在邊界上能夠同時滿足波函數的連續性及粒子流（ 1 / m ~ * ） f ' （ x ， y ）的守恆條件，從而使得波函數和束縛能的精確度得到了改進。
  12. Chapter5 : the recently developed method of hyperbolic tangent function expansion is extended and new function transformation is applied to construct some new solitary solutions of kdv equation and klein - gordon equation and the jacobi elliptic function expansion method, which is advanced in 2001, and the extended method of doubly jacobi function expansion are used to construct the exact solutions of a kind of nonlinear evolution equations

    第五章對近年來發展起來的雙曲正切函數展開法加以改進，採用新的變換函數，得到了kdv方程和非線性klein - gordon方程的一些新的孤立波解。其次，分別採用2001年提出的jacobi橢圓函數展開法和本文由此擴展而來的雙橢圓函數展開法，求解了一大類非線性發展方程，得到了一系列新的周期解。
  13. And the newly developed method of lame function method in solving the multi - order approximate equations of nonlinear evolution equations is also discussed. and following equations are solved in this method : nonlinear schr dinger, bbm equation, zakharov equation, kp equation, boussinesq equation and cubic nonlinear schr dinger

    最後介紹在橢圓函數展開法基礎上發展而來的，利用lam函數求解非線性發展方程多級近似解的方法，並且求解了非線性schrdinger方程，非線性bbm方程， zakharov方程， kp方程， boussinesq方程和立方非線性schrdinger方程等方程。
  14. Based on the empirical orthogonal function ( eof ), the characteristics of large scale variations of precipitation anomaly during rainy season ( from jun to aug ) in south - west china for the period 1961 1995 is analyzed, and the teleconnection distribution charac - teristics between sea surface temperature ( sst ) over india ocean and precipitation during rainy season in south - west china were studied by using the method of cca

    用自然正交函數展開方法對1961 1995年西南汛期（ 6 8月）降水大尺度變化特徵進行分析，並在此基礎上用典型相關分析方法研究了1 8月印度洋海溫距平場與西南汛期降水場的遙相關分佈特徵。
  15. By using new dual vectors, dual differential matrix and orthogonality relationship, a new solution method by igenfunction expansion for an elastic system with one continuous coordinate is establishen based on the theory of ordinary differential eguations

    摘要以常微分方程的理論為基礎，利用新的對偶變量、對偶微分矩陣和正交關系，以單連續座標彈性體系為例，建立了與彈性力學求解新體系平行的特徵函數展開解法。
  16. They have a number of desirable properties not possessed by wavelets of daubechies type, namely : they have symmetry property ; the scaling function and physical space representation are identical ; expansion coefficients are easily computed ; in certain respects they are more accurate ; the functions ( but not their derivatives ) can be computed without solving an eigenproblem. the price to be paid for these advantages is the loss of orthogonality, interpolating wavelets are only biorthogonal

    本文主要的研究成果是把一維的某些結論推廣到高維，分為以下四個方面： （ 1 ）使用二元拉格朗日插值法構造二元尺度函數和小波函數，使其具有緊支性、對稱性以及函數展開式的系數易於計算等優點。唯一的缺陷是缺乏正交性。
  17. In this thesis, based on related previous references, using the non - fourier law of heat conduction, applying the image method, expand method of wave function, multiple scattering of thermal waves in materials with subsurface defects are investigated. our research works are concretely as following

    本文在分析了國內外相關文獻的基礎上，基於非傅里葉熱傳導波動方程，採用鏡像方法和波函數展開法，研究了固體介質中亞表面圓柱缺陷和球形缺陷對熱波的多重散射問題。
  18. The stress and local stability constraints are transformed into movable lower bounds of sizes. an inverse variable xt = ? is inducted, and the objective function is expanded as second order taylor approximation while the displacement constriction is expanded as first order taylor approximation. the lemke algorithm is used to get the final design result

    把復雜的應力約束和局部穩定約束轉化為動態尺寸約束，引入倒變量x _ i 1 / a _ i將目標函數展開為二階近似，將位移約束用莫爾積分化為一階近似，用對偶規劃方法將原問題化為等價的二次規劃問題，調用lemke演算法，求得最優設計結果。
  19. ( 3 ) by means of expanding the aperture function into a finite sum of complex gaussian functions, the propagation of fgbs through a paraxial optical abcd system with hard - edged aperture is studied, and the approximate closed - form equations of apertured fgbs are obtained for the first time. the results obtained by using the approximate closed - form equation and collins formula are compared, and the condition under which the approximate closed - form equation is applicable is analyzed

    （ 3 ）利用光闌函數的復高斯函數展開法對截斷平頂高斯光束的傳輸作了研究，首次得到了截斷平頂高斯光束在近軸abcd光學系統中傳輸時的近似解析傳輸公式，通過比較用近似傳物公式和colhns公式直接數值積分所得的結果，得出了近似公式的適用范圍。
  20. In the part of discussion, the suitability of the jacobi elliptic function expansion method is also studied by proposing the " rank ". and we firstly point out that when the " ranks " of every term of the nonlinear evolution equation are simultaneously even or odd, the method can be used to solve the equation

    為了討論了jacobi橢圓函數展開法的適用性問題，我們最先引進「秩」的概念，指出只要非線性發展方程的各項的「秩」滿足相同的奇偶性，就可以用這種展開法求解。
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