variables separation 中文意思是什麼

Method of separation of variables and boundaryvalue problem of the isosceles - right triangular waveguide

分離變量法與等腰直角三角形波導的邊值問題

The governing equations of the problem are derived in hamiltonian form by using variable substitution and variational principle. then the methods of separation of variables and conjugate symplectic eigenfunction expansion are developed to solve the equations of plate bending problem. the result can be derived by analytical method

在平面彈性問題中，由變量代換及變分原理，方程可導向哈密頓體系，從而通過分離變量法及共軛辛本徵函數向量展開法，以解析的方法來進行求解。

The chemical variables affecting the separation and extraction recovery were studied

探討了影響濁點萃取的因素。

The vector magnetic potential of a system consisting a line electric current and an infinite long magnetic dielectric column is calculated with the method of separation of variables and method of images, it is pionted out that the vector magnetic potential of a system consisting a line electric current and a magnetic dielectric plane, an ideal paramagnetic column, a superconductor column, and a line electric current in homogeneous magnetic field can all be deduced from our calculation

摘要用鏡象電流法和分離變量法計算了線電流與無限長磁介質圓柱系統的磁矢勢，指出線電流與無限大磁介質分界平面、線電流與超導體圓柱、均勻外磁場中有磁介質圓柱系統時的磁矢勢都可以由線電流與磁介質圓柱系統的磁矢勢的極限情形給出。

Abstract : to facilitate the design, teaching and research of asphalt pavements, the article founded the models of displacement and tensile stress of three - layer system by using separation of variables, analysis and synthesizer. based on the analysis of common pavement structures and their equivalent conversion, the regression formulas of displacement and tensile stress are obtained successfully, furthermore the formulas applied in multi - layer system are checked. a great number of results of regression formulas show good accuracy for engineering application and theory research

文摘:為方便瀝青路面結構設計生產、教學、科研之用，本文採用分析綜合法與分離變量法建立了彈性三層體系應力位移顯式模型；並在分析常見路面結構層厚度及其當量換算和模量變化范圍的基礎上，成功求得了三層體系路表彎沉、上層滑動應力、上層連續應力、中層應力逼近公式；精度分析表明本文逼近公式精度很好，完全可推廣應用於多層體系，滿足工程設計和有關理論研究的需要

The research work of this thesis consists of the following major parts : 1. according to the target problem, the current operation status of the separation section of a plant was analysed. the major controllable independent variables, dependent variables and the object function of optimization problem was formed

主要作了以下幾方面的工作： （ 1 ）針對該廠氣體分離裝置的運行狀況，進行了深入細致的分析，確定了主要的可控自變量集、因變量集和需要優化的目標函數的組織。

In this dissertation, with the aid of many types of constructive transformations and symbolic computation, some topics in nonlinear waves and integrable system are studied, including exact solutions, painleve integrability, backlund transformation, darboux transformation, symmetry ( similarity reduction ), conditional symmetry, lax integrable hierarchy, liouville integrable n - hamilton structure, constraint flow, involutive system, lax representation, r - matrix, separation of variables and integrable couplings. chapter 2 and 3 are devoted to investigating exact solutions of nonlinear wave equations : firstly, the basic theories of c - d pair and c - d integrable system are presented

本文以構造性的變換及符號計算為工具，來研究非線性波和可積系統中的一些問題：精確解（如孤子解、周期解、有理解、 dromion解及compacton解等） 、 panileve可積性、 backlund變換、 darboux變換、對稱（相似約化） 、條件對稱、 lax可積族、 liouville可積的n - hamilton結構、約束流、對合系統、 lax表示、 r -矩陣、變量分離及可積的耦合系統

There are many kinds of ways to solve the electrostatic field of two - dimensional laplace ’ s equation or the poisson ' s equation, like the separation of variables, green ’ s function or alternative means. but if their boundary shapes are quite complex, it is extremely difficult to use these usual methods, and, in general, it is impossible to work out even there is such peculiar instance as analytic solution, or obtains the approximate solution

對二維拉普拉斯方程或泊松方程的平面場的解法有多種，如分離變量法、格林函數法或者其他方法，但如果它們的邊界形狀比較復雜，用這些通常的方法求解會非常困難，即使對于存在有解析解的特殊情況，一般說來也不可能求出，而且求得的只能是近似解。

However, linearization of the boussinesq equation 624 science in china : series d earth sciences allows the derivation of analytical solutions valid for specific cases. here we follow the methodology of brutsaert 20 22 to linearize the diffusion term in : 22cossin, hkpdhkhnttffxfx where p is the linearization constant taken to be 0. 5 usually and d l is the mean aquifer depth. the clas - sical separation of variables method for partial differ - ential equations is adopted to give the analytical solu - tion of eq

對于方程2 ， brutsaert進行了如下的線性化處理20 22 22cossin ， hkpdhkhnttffxfx ? ? ? ? ? ? 3這里p是線性化常數一般取值為0 . 5 20 ， 21 ，而d l是整個潛水面的平均厚度的線性化參數，下面採用science in china ser . d earth sciences第4期? ?田向軍等:基於boussinesq - storage方程同時考慮水分儲存和入滲的地下徑流機制377的是偏微分方程理論中比較經典的分離變量法來給出以上這個經過線性化處理后的方程的解析解

The solving steps are as follows : the field is divided into three regions by the cylindrical surface of the finite - length cylinder and the location of the delta - coils. because " the surface current source is placed at the interface, the non - homogenous restricted equation on the magnetic vector potential is transformed into the homogenous helmholtz equation. by using the method of separation of variables to solve equation and according to the interface conditions and the condition at infinity to determine the unknown constants, the expressions for the magnetic vector potential of the three regions are solved out

在求解過程中，假定放置式圓柱線圈是由無窮多個對稱圓環線圈密饒而成，首先求解含有有限長磁芯的通電對稱圓環線圈的電磁場：以有限長圓柱磁芯的側面和圓環線圈所在圓柱面為分界面將場域劃分為三個小區域，由於場源放置在內邊界面上，使得關于矢量磁位的非齊次約束方程轉化成齊次亥姆霍茲方程，利用分離變量法求解，根據分界面鄭州大學碩十研究生畢業論文摘要條件以及無限遠條件確定待定常數，從而得到各場區矢量磁位的表達式。

By using the method of separation of variables, a recursive formula was derived for the electromagnetic fields in a circular coaxial cable with a radial conductor plate and filled with multilayered homogeneous isotropic media, and the relationship between the first and the nth layers of the electromagnetic fields was determined

摘要採用分離變量方法，推導了有徑向導體板、填充均勻的多層各向同性介質的同軸線各層電磁場之間的遞推關系，得到了第1層與第n層介質中電磁場的關系方程。

According to thinking the joints of plates as elastic boundary supports to plates and by using of the method of separation of variables, betti ' s reciprocal theorem of work, the solution of dynamic equation can be deserved

運用變分法，分離變量法，互等功定理等數學工具求解板的運動方程，可得出彈性地基上考慮接縫傳荷能力的道面板在移動荷載下的動力響應（解析解） 。

( 2 ) because of t he variability of rock subjected to outside action, three new conceptions : postive damage basic damage and negative damage, are suggested, which can deal with the condition that rock density became large. ( 3 ) the present damage variables based on ct number mostly include ct average number of the rock without damage, which is difficult to measure, so a new damage variable, which includes the average ct number is proposed, on the other hand, strain equal theory is generalized because the one put foreword by lemaitre is not good enough to use. ( 4 ) a axial damage constitutive equation is proposed and testified. ( 5 ) with the circle times, the damage propagation laws of two different rocks, subjected to circle of freezing and thawing, are studied, and in the analysis process, traditional analysis method including average ct number and is used, some important conclusions are reached : inner damage of soft rock containing a large mount of apertures is largely propagating with the time increasement of circle, however, at the preliminary time, the hard rock containing a small mount of aperture is a little propagating, at late time, the influence become large ; ( 6 ) zone separation and statistics frequency put forward is used to analysized the three different damage propagation in the open circumstance, when they are subjected to the different circle times of freezing and thawing, in which the temperature variability is linear, different freezing rate, and different freezing temperature, and no water is supplied during the test

在研究過程中本文主要做了以下工作： （ 1 ）針對巖石損傷變化較小時，運用ct均值和方差分析不方便的缺陷，本文提出運用對ct數范圍劃分區段的方法，根據各區段統計頻率的變化規律來分析損傷擴展狀況； （ 2 ）針對巖石受到外部作用的多變性，本文提出了基準損傷，正損傷，負損傷的概念，在某種程度上考慮了巖石受到外部作用時的壓密情況； （ 3 ）現有的基於ct數的損傷變量大多需要用到巖石基體的ct均值，這實際上是很難觀測到的，因此本文建議了一個可運用巖石初始狀態ct均值的損傷變量，由於現有的勒邁特教授應變等價原理使用上的不便，本文在其基礎上進行了推廣； （ 4 ）建議了一個可用巖石初始狀態ct數和彈性模量的單軸損傷本構方程，並用算例進行了驗證； （ 5 ）對兩種不同巖石在開放環境下受到凍融循環作用且融化過程中補水時，內部損傷隨凍融循環次數增加的擴展規律進行了探討，主要運用了常規的ct均值和ct方差的分析方法進行分析，試驗發現：對于孔隙率和含水率較高，密度和強度較低的軟弱巖石，凍融循環次數對損傷結構的擴展有明顯的影響，而對于孔隙率和含水率較低，密度和強度較高的硬巖，凍融循環次數對其損傷結構擴展初期由於含水率低的原因，影響不是太大，而後期由於水補給后，含水率較高的原因，凍融影響逐漸增大； （ 6 ）運用了本文提出的區段劃分和統計頻率的方法，深入地分析了開放環境下的線性溫度變化的凍融循環次數，凍結溫度，凍結速度不同巖石作用時，其內部損傷隨凍融循環次數，凍結速度和凍結溫度變化的擴展規律，需要指出的是除了在試驗前飽水外，凍融過程中沒有補水。

In this paper, an experimental investigation of the removal of volatile organic compounds ( voc ) from dilute aqueous solutions was presented by vacuum membrane distillation ( vmd ). experiments were carried out using aqueous mixtures of ethanol with hollow fiber module. the influences of operating variables such as feed concentration, flow rate, temperature and downstream pressure on the flux and separation factor were investigated

本文對膜蒸餾脫除水溶液中的揮發性有機化合物（ voc ）進行了試驗研究；文中以乙醇水溶液為研究對象，採用真空膜蒸餾法，膜材料為中空纖維膜，研究膜通量及分離因子與原料液的溫度、濃度、流速，冷側壓力的關系，並對真空膜蒸餾的傳熱傳質機理進行了初步探討。

By using the method of separation of variables and limited fourier and laplace transform, the analytical results are obtained

運用分離變量法和有限傅立葉變換和拉普拉斯變換，將系統運動微分方程轉換為線性方程組，求出撓度和內力解析解。

Third, the mode solution is obtained using the separation of variables. the last, the mode transition property is discussed when the plane wave transmit in the step - index optical fiber

再次，利用分離變量法推導出平面波在階躍光纖中傳播的模式表達式，討論了光波在光纖中傳播的模式特性。

By adopting appropriate transformation, this paper transform the heat conduction equation with internal heat source into a non - source heat conduction equation, and then solve the problem successfully by the method of separation of variables

其關鍵方法是：通過將電場量引入溫度場方程，作適當變換，把含內熱源的熱傳導方程轉化為不含內熱源的熱傳導方程，然後採用分離變量法進行求解。

The tu ' s scheme is extended to the generalized dirac spectral problem with an arbitrary function, the generalized kaup - newell spectral problem and the new 3x3 spectral problem with five potentials such that their lax integrabie integrabie hierarchies of equations and liouville integrabie hamilton structures are obtained. chapter 7 is devote to higher - order constraint flow, involutive system, lax representation, r - matrix and the separation of variables

第六章研究了lax可積的新的方程族和liouville可積的n - hamilton結構方面的問題：將屠格式推廣到新的含有任意函數的廣義dirac族的譜問題、廣義kaup - newell譜問題及含有五個位勢函數的3 3譜問題，研究了它們的lax可積的方程族和liouville可積的hamilton結構。

Based upon practical engineering applications, the variant separating - variable algorithms of hyper - surface fitting for arbitrary multivariate scattered data are presented by separating positional variables in a spatial domain from certain physical variables such as time, mach number, angle of attack and so on, followed by their comparison. when compared with existing scatted data interpolation algorithms, the new ones are more effective. a sufficient condition to exchangeable order of separation is obtained and order of continuity on the hyper - surfaces above is discussed

三、以實際工程應用為背景，將具有某種物理意義的量（如時間、 ma數、迎角等）與空間位置變量分開處理，給出任意散亂數據超曲面擬合變量分離的各種演算法，對它們進行了演算法的分析比較，獲得了分離次序可交換性的充分條件，給出了變量分離法構造的超曲面的光滑階。

Now, we adopt the centrifugal separation to do with it, which is often a typical and complex industrial process because of the characteristics of non linearity, interactions between process variables and the lack of knowledge concerning their control, especially foundation of the relevant formulation of precise mathematics model

許多技術方法用於固液分離（ sls ）過程，但黃河泥沙分離過程作為典型的復雜工業過程，至今沒有一套完整有效的分離方法。此分離過程具有非線性、大時滯、時變、干擾大特點無法建構精確的數學模型。