expansion equation 中文意思是什麼
expansion equation
解釋
展開式-
This equation can be derived using taylor's expansion.
此方程可用泰勒展開式導出。 -
Fitting the experimental data into the general effective media ( gem ) equation, a theoretical percolation curve was gained. a mathematical model was proposed which is based on the gem equation and the dilution effect of filler volume fraction due to thermal volume expansion
使用有效介質普適方程（ gem方程）對實驗數據進行擬合，得到導電復合材料的理論滲流曲線，根據gem方程和基體的體積膨脹，建立起一個數學模型。 -
In the thesis, the fundamental formula of ffd method derives from the square root that is approximated by a continued fraction expansion in the one - way wave equation. optimizations of the parameters of the finite - difference operator improve the validity of the method
本論文用連分式近似單程波波動方程中的平方根導出ffd演算法的基本公式，並對ffd演算法中的有限差分運算元進行了系數優化，進一步提高了計算的有效性。 -
The main results achieved in this thesis can be summarized as follows : 1. by means of the fourier series expansion, an approximate analytical propagation equation of flattened gaussian beams ( fgbs ) passing through an apertured paraxial abcd optical system is derived, and illustrated with numerical examples, when the transmissivity of the aperture is t ( x ) = cos ( x )
用傅立葉級數展開法研究了平頂高斯光束通過有光闌限制的近軸abcd光學系統的傳輸特性，導出了光闌透射率為t （ x ） = cos （ x ）時的近似解析傳輸公式，硬邊光闌的情況可作為= 0的特例得到。 -
The new jacobi elliptic function expansion method by the long - short wave interaction equation
橢圓函數新的展開法求解 -
For the ten years of late, the cellular automata has made the new progress in hydy nimiee dynamices. by gaining the moment equations from lattice boltzmann equation and using chapman - enskog expansion, the fluid dynamices equation and energy equation of 13 - bit lattice gas automata model with polyvelocity have been deduced. the validity of the model using for non - isothermal fluid dynamics has been proved
近十年來，細胞自動機已在流體力學的研究中取得了進展，應用13 - bit多速格子氣自動機模型，在由格子boltzmann方程求得矩方程的基礎上，根據chapman - enskog展開方法，導出了該模型的宏觀熱流體力學方程，從理論上證明了所建模型對熱流體力學問題描述的正確性。 -
The nonparallel linear stability of the two - dimensional and three - dimensional disturbance waves are studied by the parabolized stability equation which is developed in recent years and the local method based on the landau expansion
採用近年來新發展的拋物化穩定性方程和利用landau展開式的局部法方程，分別研究二維和三維線性非平行流穩定性問題。 -
By using the asymptotic analysis method and the diagonalization technique, considers the singular perturbation of boundary value problem for system of third order nonlinear integro - differential equation. under appropriate assumptions, the existence of the solution of perturbation problem has been proved and a asymptotic expansion of the solution and the estimation of the corresponding remainder term are geven as well
研究三階非線性積分微分方程組邊值問題的奇攝動.在適當的條件下，利用漸近分析方法和對角化技巧，證得解的存在性並給出解的漸近展開式及其餘項估計 -
In this paper, we expand eigenvalue of poisson equation using bilinear element, by the formulation of the error expanition, we can conclude that it is a upper bound. and by two numerical example, we computer the approximate eigenvalue of poisson equation in square and l - shape domains, then we analyses the approximate eigenvalue. we also extraplate the error expansion and enhance the accuracy of the eigenvalue form the second order to the forth order
本論文對poisson方程的特徵值採用雙線性元進行展開，得到了誤差展開式，通過誤差展開式，我們能得到特徵值是上界。通過數值算例，計算方形與l形區域上的poisson方程的近似特徵值，並對數據進行分析，驗證了理論的正確性，然後通過對誤差展開式外推，收斂級數可以從二階提高到四階，得到了高精度的解。 -
In the third chapter, we introduce geometric expansion of convex planar curves. we discuss the evolution equation using minkowski ' s support function with the speed function of curvature and show that the shapes of curves become round asymptotically when the initial closed curves is smooth and convex
限制曲線在外法向上的演化速度是另一類特殊的曲率函數，研究相應的方程，我們得到了在初始為凸的閉簡單光滑曲線的條件下，曲線的最後形狀是漸近地趨於一個圓。 -
The integrands in the dispersion equation are not integrable in general, so we used the asymptotic expansion solution to analyze the behavior of the dispersion relation at the singularity and mapped the dispersion relation curves approximately the system composed of collisionless particles which obey maxwellian distribution or all kinds of degenerate distribution, even in their mixture system, their dispersion relation are analogous
一般來說，色散方程中的被積函數都是難以求積的，本文是用函數逼近法分析色散方程在奇點處的行為，並大致劃出色散關系曲線。由無碰撞粒子組成的系統，不管初始分佈是maxwell分佈還是各種簡並分佈，甚至是這些分佈的混合體，色散關系都是相似的。 -
Effective dielectric response of ellipsoid composites in which the dielectric function of the grains have the form of ( the equation is abbreviated ) ) embedded in a host medium is investigated in dilute limit based on perturbative expansion method, and general expressions for the effective linear dielectric function and ( - 1 ) - order nonlinear susceptibility of the two - phase system are derived in this paper
摘要利用微擾展開法討論了任意階弱非線性橢球顆粒復合體系（假定顆粒組分的介電函數隨場變化，表示為（方程式略） ）的有效介電響應，導出了稀釋極限下兩組分橢球顆粒體系的有效線性和有效（ + 1 ）次非線性系數的一般表示式。 -
Quark medium is regarded as non - harmonic oscillator model, discussing its response to su ( 2 ) non - abelia field, the perturlation expansion method is used to find the first, second and third order approximate solutions to the response equation, and some nonlinear features of the response are preliminarily displayed
將夸克介質視為非簡諧振子模型，討論了它對su （ 2 ）非阿貝爾場的響應，採用微擾迭代法解出了方程的一、二、三級近似解，初步得出了這種響應的一些非線性特徵 -
And beginning with a perturbed nls equation, using a multi - scales perturbation expansion, we get the zero order and the first order equations, discuss the eigenstates of the operator in the equations, induct relevant " derivative states ", form the completeness of the bounded eigenstates of the associated operator in li space, and expand the corresponding parameters in the closure, get a series evolution equations of the coefficients in the expanded formulas, find the first order approximate solution by researching the evolution equations. this paper also gives the basis of this method - the completeness we have formed and the singular perturbation technique
） dinser方程的求解問題，討論了自伴運算元的本徵函數的正交性和完備性，介紹了尋求微分方程的近似解常用的攝動方法，並從帶有某種擾動項的nls方程出發，利用多重尺度的攝動方法得到了方程的零級近似方程和一級近似方程，通過對近似方程中運算元的特徵態的討論，引入適當的「導出態」 ，建立了運算元在l _ 2空間的特徵態的完備性。 -
We expand the eigenvalue of possion equation using wilson nonconforming element. by the formulation of the error expanition, we can not conclude whether it is a upper bound or a lowr bound. but we guess it is a lower bound, and by two numerical example, we find thatwe are right. we also extraplate the error expansion and enhance the accuracy of the eigenvalue from second order to third order
通過數值算例，計算方行與l行區域上的poisson方程的近似特徵值，並對數據進行分析，驗證了我們的推測是正確的，然後通過對誤差展開式外推，收斂階數可以從二階提高到三階，得到了高精度的解。 -
The submarine structure is simplified to single or double infinite cylindrical shell stiffened with rings, bulkheads and stringers, focusing on underwater sound radiation from the single shell. the shell motion is described by donnell ' s theory including excitation forces and reactions of rings, bulkheads, stringers and fluid, which leads to the fluid - structure coupling vibration equation. expressing displacements by velocities, applying modal expansion circumferentially and fourier transformation longitudinally result in the shell ' s modal equations of motion
殼體的運動方程採用較為簡單的donnell理論描述，運動方程中包括了激勵力、加筋結構（環肋、艙壁和縱骨）和流場對殼體的作用力，從而組成流場-結構的耦合振動方程，並進一步將方程中的位移用速度表示，然後沿軸線方向進行fourier變換，將速度和各項荷載沿圓周方向進行模態展開，得到了殼體振動的模態運動方程。 -
For the expansion theorems of self - adjoint dirac operator, it is difficult to prove it by using the method of integral equation
對于自伴dirac運算元的特徵展開定理的證明，用積分方程方法有一定的困難。 -
The standard parabolic equation method was obtained by the decompocition of the scalar wave equation and the expansion of the pseudo - differential operator
通過對傳統波動方程的分解和偽微分運算元的近似展開，獲得了標準拋物線方程。 -
From 1920s up to now, various techniques and methods for wave field decomposition, propagation and migration / imaging have been well developed, such as the kirchhoff asymptotic method, frequency - wavenumber domain phase - shift and phase - shift - plus - interpolation methods, and the one - way wave equation based phase - screen and generalized screen methods, etc. wave field extrapolation in these methods is implemented based on the expansion of the wave field by sets of basic functions like spatial fourier harmonies, modes, and green ' s functions
自上個世紀二十年代至今，波場分解、傳播與偏移成像技術經歷了將近一個世紀的發展，形成了多種不同的方法，如kirchhoff波動方程高頻近似解方法，頻率-波數域的相移（ phase - shift ）方法和相移-內插（ pspi ）方法，以及在混合域中基於單向波動方程的相位屏、廣義屏方法等。 -
The fipwa based on electric integral equation ( efie ) is presented firstly, the green ’ s function expansion with sommerfeld identity ( based on bessel kernel ) is studied and the msdp for two cases is formulated. in order to improve the iteration property and avoid inner resonance, the combined field integral equation ( cfie ) fipwa is then constructed successfully
首先研究了基於電場積分方程的快速非均勻平面波演算法，對索末菲恆等式（基於貝塞爾積分核）展開的格林函數進行了深入研究，分兩種情形解決了修正最陡下降路徑的設計問題。
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