homogeneous equation 中文意思是什麼

homogeneous equation 解釋
齊次多程
  • homogeneous : adj. 1. 同種的，同質的，同性的，相似的。2. 純一的，均質的；均勻的。3. 【數學】齊性的，齊次的。adv. -ly ,-ness n.
  • equation : n. 1. 平衡，均衡；平均，相等。2. 【數學】方程式，等式。3. 【天文學】（時）差；均分，等分。4. 【化學】反應式。
  1. In this paper, i consider the traveling wave solutions and peakons of the generalized camassa - holm ( gch ) equation and give the express of the solitons of this equation. the peakons and their figures of the gch equation are given with the mathematic software for m - 1, m = 2 and m = 3 in particular ; for m = 3, i get the generalized dissipative camassa - holm equations by adding a dissipative term and find two types exact traveling wave solutions of this equations. i also apply the homogeneous balance method into the gch equation so that i get a group of smooth solutions for m = 2 and m = 3 and the backlund transformation for m - 3 of the gch equation

    本文研究廣義camassa - holm （ gch ）方程的行波孤立子解及尖峰孤立子解，給出gch方程的行波孤立子解的表達式，特別的，對m = 1 、 m = 2 、 m = 3時利用mathematica數學軟體進行計算，解出了gch方程的尖峰孤立子解，並給出了此時gch方程的尖峰孤立子解的圖形，使數值分析和理論相結合；對m = 3時的gch方程增加一耗散項u _ （ xx ）后得到廣義耗散camassa - holm方程，並解出此方程的兩類精確行波解；本文將齊次平衡法應用到gch方程中，解出m = 2 、 m = 3時的gch方程的一組光滑解，同時應用此方法得到了m = 3時的gch方程的backlund變換。
  2. Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation

    壓電熱彈性體的變分原理及正則方程和齊次方程
  3. In the second section of chapter 2, the fact that the essential interest rates of all nodes differ from each other is discussed, a non - homogeneous differential equation model of interest rate - amount of circulating fund is established, and it is proved that the sum of the weighted interest rates of each node in the financial network still remains a constant and that the difference of the instant interest rates between two nodes will finally approach the difference between their basic interest rates. in the third section of chapter 2, the differential equation model of interest rate - amount of circulating fund in an open system is studied, the laws of changes of interest rate are taken into account when fund is injected into or withdrawn from the node or when fund is injected into the network or withdrawn from the network, and the stability of equilibrium solution is proved based upon lyapunov stability theory. in the last, the equation model of interest rate - amount of circulating fund in the financial network with time delay is studied, and a necessary and sufficient condition for the existence of periodic solution is obtained to the interest rate - amount of circulating fund equation with delay

    本文第二章首先建立了封閉系統的利率?流通量微分方程模型，證明了各結點利率加權和為常數即金融市場利率均衡原理，以及各結點利率極限為整個網路平均利率；其次在各結點基本利率不相同的情況下，建立了非齊次利率?流通量微分方程模型，證明了金融網路各結點利率加權和仍是一個常數，並證明了各結點兩兩之間的即時利率之差最終將穩定地趨于其基本利率差；此外，還研究了開放金融網路利率?流通量方程模型，考慮了結點自身追加資金和提走資金的情形以及網路外部注入資金和向外部轉移資金情形下的利率變化規律，用lyapunov穩定性理論證明了模型均衡解的穩定性；最後，還研究了具有時滯的金融網路利率?流通量方程模型，並給出了具有時滯金融網路的利率流通量方程具有周期解的充要條件。
  4. The specified solution formula derivation of second order non - homogeneous linear differential equation with constant coefficients

    二階常系數非齊次線性微分方程特解公式的推導
  5. In this paper, we study the finite iterated order of growth and the iterated convergence exponent of the zero sequence of nonzero meromorphic solutions of second order homogeneous linear differential equation, and obtain some precision evaluation

    摘要研究了二階齊次線性微分方程非零亞純解的迭代級與零點迭代收斂指數，得到了它們的精確估計。
  6. In chapter 2, we discuss the problem of the relationship between the solution of non - homogeneous linear differential and small function. in chapter 3, we investigated the relationship between exponent of convergence to zero - sequence of the solution of certain homogeneous linear differential equation f ( k ) + a ( z ) f = 0 and the order of growth of a ( z )

    其中第二部分討論了非齊次線性微分方程解取小函數的收斂指數，第三部分研究了齊次線性微分方程f ~ （ k ） + a （ z ） f = 0的解的零點收斂指數與a （ z ）的級的關系
  7. This is a homogeneous linear equation, which always has the trivial solution w≡0.

    這是一個齊次線性方程，總是有零解W0。
  8. The treatments simplifies greatly the solution programs which are often performed to solving non - homogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship and the workload of numerical computation at same time

    這類方法大大簡化了人們在分析壓電熱彈性體耦合問題時通常要求解的非齊次微分方程和關于溫度的平衡方程和導熱方程的二階微分方程的繁瑣方法，同時，齊次狀態方程的提出大大減少了數值計算的工作量。
  9. From the mathematical point of view, the difficulty stems from the inability to get, with the traditional global transform like the fourier transform, a simplified differential equation that governs the evolution of the basic function through the non - homogeneous medium

    這些基本函數的全局特性使其在非均勻空間的演化變得十分復雜，從而影響了傳統方法的波場外推精度及效率。
  10. Essential to their utility is the requirement that the evolution of the basic functions through the propagation environment constitutes a simplified problem with an exact or approximate closed form solution to the original wave equation. the evolution of a spatial fourier harmonic through a homogeneous medium is governed by a reduced wave equation, obtained by applying the fourier transform to the helmholtz equation, with a simple and well - known solution - the plane wave

    這些方法均採用一組具有全局特性的基本函數對波場進行分解，如占據整個空間的富氏調諧函數或充滿各個方向的dirac函數（點源） ，並通過求解基本函數滿足波動方程的精確解或近似解來達到波場外推的目的。
  11. From the analytical point of view, with the aid of the numerical simulation, we investigate the propagation properties of optical pulses for the nonlinear schrodinger equation in picosecond regime, the higher - order nonlinear schrodinger equation in femtosecond regime, the nonlinear schrodinger equation with varying gain / loss and frequency chirping in homogeneous optical fibers, and ginzberg - landau equation that describes ultrashort pulses in the presence of self - frequency shift, respectively

    本文從解析的角度出發，同時藉助各種微擾理論和數值分析方法，分別研究描述皮秒光脈沖傳輸的非線性薛定諤方程、飛秒光脈沖傳輸的高階非線性薛定諤方程、非均勻光纖中光脈沖傳輸的含有頻率啁啾和增益損耗項的非線性薛定諤方程以及描述超短光脈沖傳輸的ginzberg - landau方程的解的特性，為進一步實現超高速、大容量的光信息傳輸提供一定的理論依據。
  12. From the aspect of geometry, structure design, manufacture and examine, this paper generally summarizes the gcm ' s study progress in detail, discusses its kinetic rule and the determination of its primary structure parameter, and educes its surface equation and pressure angle equation based on the homogeneous matrix transformation and the conjugate engagement theory of spatial surface. on the basis of geometry study of gcm, the paper makes a comprehensive analysis to the interference phenomenon that will possible exist in the assemble course of two different structure of gcm with the help of matlab software

    本文從運動幾何學、結構設計、動力學、製造和檢測等方面對國內外弧面凸輪機構的研究進展進行了全面綜述，詳細論述了高速凸輪機構的運動規律和弧面凸輪機構基本尺寸的確定，基於空間曲面共軛嚙合原理，通過齊次變換推導了外弧面凸輪的曲面方程和壓力角方程，並提出了對應的廓面修形演算法；提出了內弧面凸輪機構的構想，推導了內弧面凸輪的曲面方程和壓力角方程。
  13. Nurbs curve equation has three kinds of the equivalence form, i. e. rational fraction, rational base function and homogeneous coordinate

    Nurbs曲線方程具有三種等價形式：有理分式表示、有理基函數表示和齊次坐標表示。
  14. An integrable theorem of second order linear non - homogeneous differential equation

    一類二階變系數線性微分方程的積分因子解法
  15. Using the microwave selective heating property for materials, by setup equivalent equation, and first time inducing the electromagnetic field perturbation theory to the design of heating materials for substrate in mpcvd, three temperature distribution modes were established, including temperature distribution comprehensive mode of inhomogeneous plasma, temperature distribution composite mode of composite substrate materials, temperature distribution perturbation mode of composite materials, which ii provided an whole new technology route to the design of substrate heating system in mpcvd and guided the preparation of heating materials for substrate. and then the heating materials for substrate were designed and optimized to obtain large area homogeneous temperature distribution even larger than substrate holder ' s diameter. as an important part, this thesis researched the nucleation and growth of diamond films in mpcvd, systematically researched the effects of substrate pretreatment, methane concentration, deposition pressure and substrate temperature etc experimental technologic parameters on diamond films " quality on ( 100 ) single crystal silicon substrate in the process of mpcvd, characterized the films qualities in laser raman spectra ( raman ), x - ray diffraction ( xrd ), scanning electron microscopy ( sem ), infrared transmission spectra ( ir ), atomic force microscopy ( afm ), determined the optimum parameters for mpcvd high quality diamond in the mpcvd - 4 mode system

    該系統可通過沉積參數的精確控制，以控制沉積過程，減少金剛石膜生長過程中的缺陷，並採用光纖光譜儀檢測分析等離子體的可見光光譜以監測微波等離體化學氣相沉積過程；利用微波對材料的選擇加熱特性，通過構造等效方程，並首次將電磁場攝動理論引入到mpcvd的基片加熱材料的設計中，建立了非均勻等離子體溫度場綜合模型、復合介質基片材料的復合溫度場模型及復合介質材料溫度場攝動模型，為mpcvd的基片加熱系統設計提供了一條全新的技術路線以指導基片加熱材料的制備，並對基片加熱材料進行了設計和優選，以獲取大面積均勻的溫度場區，甚至獲得大於基片臺尺寸的均勻溫度區；作為研究重點之一，開展了微波等離體化學氣相沉積金剛石的成核與生長研究，系統地研究了在（ 100 ）單晶硅基片上mpcvd沉積金剛石膜的實驗過程中，基片預處理、甲烷濃度、沉積氣壓、基體溫度等不同實驗工藝參數對金剛石薄膜質量的影響，分別用raman光譜、 x射線衍射（ xrd ） 、掃描電鏡（ sem ） 、紅外透射光譜（ ir ） 、原子力顯微鏡（ afm ）對薄膜進行了表徵，確立了該系統上mpcvd金剛石膜的最佳的實驗工藝參數。
  16. Application of homogeneous k - equation turbulent closure model in the coastal sea

    齊次湍流動能輸運方程封閉模型在淺海動力學中的應用
  17. According to the radar - absorbing model, the performance of rams of various absorber - volume - percentage with various frequency and the radar obsorbing performance of which in various thickness is predicted. according to the radar - absorbing model, the prerequisites of microwave electromagnetic parameters and the border curves for a single - layer homogeneous absorbing coating backed by a perfectly conducting plate to produce zero specular reflection are obtained by the steffensen speedup approach to solve the complex transcendental equation

    以吸波模型為依據，用計算機求解了單層均勻各向同性吸波材料的阻抗匹配條件，通過數值模擬得到了吸波材料阻抗匹配時電磁參數邊界曲線的數值模擬等式和阻抗不匹配時寬帶吸波材料電磁參數的合理搭配規則和頻散特性。
  18. The vertical mixing law of the linear source in the natural river has been studied in the second step. at first the concentration equation of the linear source at different depth has derived. by the theoretical analysis, the relationship between the distance of the vertical homogeneous mixing and the part depth of homogeneous mixing, and the equation calculated distance of whole depth homogeneous mixing for the linear source have been presented

    通過理論推導，得出任意位置上瞬時線源濃度場的解析解表達式；推導得到表面不同深度線源排放時垂向部分均勻混合水深隨縱向距離變化規律的函數關系，並建立了相應變化規律的諾莫圖；導出了表面不同深度線源在全水深均勻混合時的縱向距離的計算公式，應用長江口南通河段實測資料驗證，得到一致結果。
  19. ( 1 ) based on two types of riccati equations, two kinds of new methods are proposed to obtain solutions of nonlinear differential equations. twelve families of exact solutions of wbk equation are found by using one of two methods ; ( 2 ) the homogeneous balance method is improved cind investigated to ( 2 + l ) - dimensional broer - kaup equation such that many families of new solutions are derived. ( 4 ) based on the isospectral lax pair of riccati form for generalized kdv equation with the force term, new darboux transformation and solitary - like wave solutions and rational solutions are obtained ; ( 4 ) by constructing darboux transformation and the superposition formula of generalized variable coefficients kdv equation with the force term, new single solitary - like wave solutions, double solitary - like wave solutions and rational solutions are found for ( 2 + l ) - dimensional generalized kp equation

    第二章和第三章考慮非線性偏微分方程的精確解的構造：首先給出了c - d對和c - d可積系統的基本理論，然後在第三章中具體研究了它們的應用： （ 1 ）基於兩種riccati方程，提出了兩種新的求解非線性微分方程更多解的方法，利用其中的一種方法，得到了wbk方程的12組精確解； （ 2 ）對齊次子衡法進行改進，以致於獲得了（ 2 + 1 ） -維broer - kaup方程的很多新解； （ 3 ）基於帶有外力項的廣義kdv方程的riccati形式的非等譜lax對，提出了該方程的一個新的darboux變換，利用該變換，得到了新的類孤波解和有理解； （ 4 ）通過構造了帶有外力項的變系數kdv方程的darboux變換及疊加原理，獲得（ 2 + 1 ） -維廣義kp方程的新的類單孤波解、雙類孤波解和有理解。
  20. Based on the conception of the network - changing principle and the two - limited resistance, this paper gives the proof of the transient homogeneous equation for high - order linear circuits and the independent among the two - limited resistance

    摘要根據網路變動原理和雙限電阻的概念，用數學的方法證明了高階線性電路的暫態齊次定理的成立。
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