solution to an equation 中文意思是什麼

solution to an equation 解釋
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  • solution : n. 1. 溶解；溶液，溶體，溶劑。2. （補輪胎用的）橡膠水；〈美國〉藥水。3. 解決，解答 （of; for; to）; 解釋；（數學等的）解法，解式。4. 免除，解除。5. 【醫學】消散，消退。
  • to : adv 到某種狀態；〈特指〉到停止狀態；關閉。 ★也常和動詞結合，略去其後賓語，而構成成語： The door i...
  • an : an1indef. art. 見 a 條。1. 〈方、口〉 ＝ and. 2. 〈古、方〉 ＝ （and） if.
  • 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. A novel catalytic property of hemin is described. in ammonium buffer medium of ph 8. 08. 9, hemin has an ability to catalyze the decoloration of bromopyro - gallol red. oxygen dissolved in solution plays a role as an oxidant in the reaction. with sodium dodecylbenzenesulfonate and ethanol as effect - enhancing agents, the catalytic system obeys the michaelis - menten equation of enzymatic catalysis. the michaelis constant, catalytic constant and specificity constant of the system are estimated by lineweaver - burk plot to be 3. 710

    在ph 8 . 08 . 9氨性緩沖介質中， hemin催化溶解氧氧化溴鄰苯三酚紅的褪色反應。在sdbs和30 %乙醇的增效作用下，催化體系服從michaelis - menten方程。用lineweaver - burk作圖法求得米氏常數催化常數和專一性常數分別為3 . 710
  2. As far as the discussion about the structures is concerned, to some extent, it may be said to be an application to the backlund transformation : fix a solution qn to the system ( l. 3 ), construct a group of solutions qn different from qn through the backlund transformation, and then prove that qn is convergent to qn. in the section 4, it is vital for us to find out the fixed solution n to the equation ( 3. 1 ) in the theorem3. 2, which is completed in the lemma4. 2 and theorem4. 3

    第四節對方程（ 1 . 3 ）的解的性態的討論，在一定程度上也可說是對定理3 . 2的一個應用：給定方程的一個解q _ n ，然後通過貝克朗變換構造了一系列不同於q _ n的解q _ n ，之後證明了q _ n收斂于q _ n 。
  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in an open system is studied, the laws of changes of interest rate are taken into account when fund is injected into or withdrawn from the node or when fund is injected into the network or withdrawn from the network, and the stability of equilibrium solution is proved based upon lyapunov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. An existence theorem of solution to a nonlinear cantilever beam equation

    非線性懸臂梁方程解的一個存在定理
  5. We reduce the cauchy problem of equations ( 8 ), ( 9 ) to an equivalent integral equations by the fundamental solution of a second order partial differential equation. then using the contraction mapping principle and the extension theorem of the solution we prove the existence and uniqueness of the global generalized solutions and the existence and uniqness of the global classical solution

    先是通過一個二階偏微分方程的基本解，把imbq型方程組歸） ， p ）的初值問題轉化為等價的積分方程組，然後利用壓縮映射原理、解的延拓定理等證明了歸） ，問的初值問題的整體廣義解和整體古典解的存在唯一性
  6. On the other hand, the conformal deformation ' s problem is to find a metric on h2 ( - 1 ), conformal to g, with the given function k as its gaussian curvature, that is, it is important for us to study the solvability of the conformal gauss curvature equation in geometry analysis. the problem that the conformal gauss curvature equation may have a solution for every nonegative holder continuous function k ( x ) is also an open problem

    ） = e ~ （ 2u ） g使k是（ ? ）的高斯曲率，即共形高斯曲率方程的可解性研究是幾何分析中的一個重要問題。當預定的函數k取正值時，共形高斯曲率方程解的存在性命題作為一個猜測至今未得到解決。
  7. Then the application of cauchy - inequality is illustrated by proving a proposition or an inequation, solving a triangle, and finding a solution to an equation or the maximum value & minimum value of a function

    然後給出了柯西不等式在命題證明、不等式證明、求解三角形問題、函數最值、解方程等方面的應用。
  8. In this paper, river water quality prediction is integrated with water pollution control measures. two parameters, water environmental capacity and pollution index are selected for pollution control measures. the objective is achieved after the development of simulation model using one - dimensional advection dispersion equation. the model algorithm and computer program is an improvement over the existing water quality models, since the model solution involves four point implicit upwind schemes for water quality prediction and pollution control measures at each grid point. model simulation results the assessment of water environmental capacity that yield the acceptable and realistic pollutants concentration in order to maintain water quality objectives. the pollution and overall pollution index of the river is suggested for integrating number of contaminants variables into one index. study provides the mathematical and scientific procedure for water quality management. the new approach is helpful for the water pollution control and to study the impacts of waste effluents on the river system for strategic planning purposes

    本文將水質預測及水污染控制措施有機地結合，選取水環境容量和污染指數作為水污染控制的參數.這樣，一維對流-擴散水質方程的求解除就是實現本研究目的的關鍵.本研究採用的模型在現有的水質模型基礎上有所改進，因為其採用四點隱格式對水質進行預測，推求可接納污染物的環境容量值及為保證水質而限定的污染物濃度值，從而制定相應的水污染控制措施.為整體考慮各種污染物的情況，建議採用河流的污染指數進而推求綜合污染指數.總之，本研究為水質保護提供了科學的計算方法，該法對水污染控制及污水對河道水質的影響是實用有效的
  9. Abstract : in this paper, river water quality prediction is integrated with water pollution control measures. two parameters, water environmental capacity and pollution index are selected for pollution control measures. the objective is achieved after the development of simulation model using one - dimensional advection dispersion equation. the model algorithm and computer program is an improvement over the existing water quality models, since the model solution involves four point implicit upwind schemes for water quality prediction and pollution control measures at each grid point. model simulation results the assessment of water environmental capacity that yield the acceptable and realistic pollutants concentration in order to maintain water quality objectives. the pollution and overall pollution index of the river is suggested for integrating number of contaminants variables into one index. study provides the mathematical and scientific procedure for water quality management. the new approach is helpful for the water pollution control and to study the impacts of waste effluents on the river system for strategic planning purposes

    文摘:本文將水質預測及水污染控制措施有機地結合，選取水環境容量和污染指數作為水污染控制的參數.這樣，一維對流-擴散水質方程的求解除就是實現本研究目的的關鍵.本研究採用的模型在現有的水質模型基礎上有所改進，因為其採用四點隱格式對水質進行預測，推求可接納污染物的環境容量值及為保證水質而限定的污染物濃度值，從而制定相應的水污染控制措施.為整體考慮各種污染物的情況，建議採用河流的污染指數進而推求綜合污染指數.總之，本研究為水質保護提供了科學的計算方法，該法對水污染控制及污水對河道水質的影響是實用有效的
  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. In order to determine the solution set of the equation, by the means of meet - irreducible element and irredundant finite meet - decomposition, we first obtain the maximal solutions to the simple equation in the case that b has an irredundant finite meet - decomposition, and then consider the relation between the equation and the equation, based on this, we obtain the maximal solutions to the equation in the case that each element of the matrix b has an irredundant finite meet - decomposition and so determine its solution set completely

    為了確定方程的解集，本文利用交既約元與不可縮短的有限交分解等工具，同樣地先求出簡單形式的型矩陣方程的所有極大解，然後討論方程與方程之間的關系，在此基礎上，在b的每個元素均有不可縮短的有限交分解的情況下，求出了方程的所有極大解，從而完全確定了方程的解集
  12. This method is proved to be an accurate solution of random vibration equation, in which all cross - correlation items, either between earthquake inputs or between participant modes are involved naturally. compared to conventional method, the computational efficiency of the developed method is much higher

    此法計算結果自動包含了振型間及各輸入分量間的相關項，理論上是隨機振動方程的精確解法，且與傳統方法相比可大大減少計算量，非常適合分析大型網殼這種自振頻率密集結構的隨機地震響應。
  13. An existence theorem of solution to boundary - value problem governed by second - order difference equation

    二階差分方程邊值問題的一個存在定理
  14. In the third chapter, we will study the existence and uniqueness of the classical global solution and generalized global solution to the periodic boundary value problem and the cauchy problem for this kind of equation. in the second chapter, we study the following nonlinear wave equation of higher order : with the initial boundary value conditions or with where a1, a2, a3 > 0 are constants, ( s ), f ( s0, s1, s2 s3, s4 ) are given nonlin - ear functions, u0 ( x ) and, u1 ( x ) are given initial functions. for this purpose, by green ' s function of a boundary value problem for a fourth order ordinary differential equation we first reduce the problem ( 1 ) - ( 3 ) to an equivalent intergral equation, then making use of the contraction mapping principle we prove the existence and uniqueness of the local classical solution for the intergral equation

    本文分三章，第一章為引言；第二章研究一類非線性高階波動方程的初邊值問題的整體古典解的存在性和唯一性，以及古典解的爆破；第三章研究此方程的周期邊界問題和cauchy問題的整體廣義解和整體古典解的存在性和唯一性，具體情況如下：在第二章中，我們研究一類非線性高階波動方程的如下初邊值問題：或或其中a _ 1 ， a _ 2 ， a _ 3 0為常數， （ s ） ， （ s _ 0 ， s _ 1 ， s _ 2 ， s _ 3 ， s _ 4 ， ）為已知的非線性函數， u _ 0 （ x ） ， u _ 1 ， （ x ）為已知的初始函數，為此，我們先用四階常微分方程邊值問題的green函數把上述問題轉化為等價的積分方程，然後利用壓縮映射原理證明此積分方程局部古典解的存在性和唯一性，又用解的延拓法證明上述問題整體古典解的存在性和唯一性，主要結果有：定理1設u _ 0 （ x ） ， u _ 1 （ x ） c ~ 4 [ 0 ， 1 ]且滿足邊界條件（ 2 ） ，若以下條件滿足：其中a ， b月0為常數， w
  15. To assure astringency, some technologies have been used such as iterative penality function methods, assemblage mass matrix, reduced integration algoritlun, newton iteration method with parameters for non - linear equation set, introducing relax factors and double steps solution and so on, and an algorithin for solving the nonlinear equation set of flow field by fem has been presented

    基於有限元法建立了流場求解列式，為保證其收斂性，採用了迭代罰函數法，集中質量矩陣，縮減積分計算，帶參數的newton迭代求解，引入松馳因子及雙層解法等技術，提出了一套適合流場有限元方程計算的非線性方程求解方法。
  16. The paper hopes to extract a solution of a nonlinear partial differential equation, a quite new model, of low - permeability gas reserves, then studies the penetraial character. the pose of the model has already been proved theoretically [ 4 ], which encourages us to seek an aptitude numerical calculation and to realize the computation

    本文希望對一個低滲透氣藏非線性偏微分方程的數學新模型的求解，來研究具有滑脫效應下的滲透特徵，利用模型的適定性在理論上已經獲證的結果，探尋恰當的數值計算方法並且實現編程實現計算機電算化。
  17. Thus the resistance factor and vibration modes of the soil layer are obtained and used to analysis the pile response. by considering the interaction between the soil layer and the pile with boundary condition of continuity of displacement and equilibrium of force at the interface of soil layer and pile, the dynamic equilibrium equation of pile is solved and an analytical solution for the pile response in frequency domain is yielded, which is used to define complex stiffness and mobility at the level of the pile head. based on the convolution theorem and inverse fourier transform, a semi - analytical solution of velocity response in time - domain subjected to a semi - sine exciting force is given

    首先通過引入勢函數方法對土體位移進行分解，從而將土體動力平衡方程解耦，求解得到了土層的振動模態和阻抗因子，然後利用該解以小應變條件下樁土接觸面上力平衡和位移連續條件來考慮樁土耦合作用，求解樁的動力平衡方程，得到了樁頂的頻域響應解析解、復剛度和速度導納，利用卷積定理和傅里葉逆變換，求得了半正弦脈沖激振力作用下樁頂速度時域響應半解析解。
  18. ( 4 ) as an application of wavelets, the first, wavelet - based solution to ode to be researched, the second, construction the hermite b - spline bases scale functions with boundary conditions on the interval, combining with garlerkin method, to solve differential equation in finite - length beam problem ; the third, m - scaling function solution to ode in dynamics

    （ 4 ）把小波函數用於微分方程的求解中。首先利用插值小波求解常微分方程，其次，滿足邊界條件的小波尺度函數，結合galerkin方法求解結構力學中的微分方程；最後，使用m -尺度函數求解梁結構中的微分方程。
  19. Then a laplace equation can be deduced and through computation, the blade profile coordinates and geometry of the cascade result from an analytical solution. next, an optimization method, taking the geometry parameters of the unclosed profile as its objective functions, is used to obtain an optimized blade profile. and last, the optimized profile is refined with round arcs added in the leading and trailing edges

    本文採用的勢、流函數解析法法中，將無旋方程用新的類無旋方程替代，這樣在計算域上得出速度場的解析關系式，計算得出初始葉型；然後以此初始葉型的幾何參數，例如前尾緣的封閉程度和葉型彎角等為目標函數，通過優化程序對初始速度進行自動調節直到目標函數值最小為止。
  20. This paper deals with the existence of two positive solutions for critical elliptic equations with a changed sign perturbation and with an auxiliary condition. first of all, the super - sub - solution can be obtained by this positive solution and by the auxiliary condition if perturbation is the positive side of the changed sign perturbation, and then the equation has a positive solution by the method of monotone in teraction and by the maximum principle. because that the positive solution of the equation isnt monotone to parameter. although all of the equations have a positive solution to two given parameters, the existence of the positive solutions of its equation to a parameter between the two given parameters cant be proved. finally, if the first positive solution exits the second solution for the equation can be proved by the mountain pass lemma. 7refs

    討論了帶變號擾動並且具有一定附加條件的臨界橢圓方程的兩個正解存在性.首先由變號擾動的正部對應的方程的正解和附加條件構造出原方程的一個上、下解，再由迭代方法和極值原理得到方程的第一個正解.考慮到方程的正解對參數沒有單調性，因此，即使對于兩個使得方程都有正解的參數，但在這兩個參數之間的參數對應的方程不一定有正解.最後，如果方程存在第一個正解，那麼由山路引理可得到方程的另一個正解.參7
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