查询词典 reducible equation

A quasi one-dimensional, time dependent system model based on the parallel compressor theory was used to compute the effect of inlet distortion on turbine engine stability; Through Modifying steady state continuum equation, momentum equation and energy equation, the effect of power extraction and additional bleed on turbine engine running line was computed. Unsteady state continuum equation, momentum equation and energy equation were solved for computing the effect of acceleration on turbine engine running line.

其中，进气畸变对发动机气动稳定性影响的计算采用平行压气机模型，基于李亚普诺夫理论的方法完成；附加引气、功率提取对发动机气动稳定性的影响采用通过对发动机转子间质量、动量、能量守恒方程进行修正的方法进行；加速过程对发动机气动稳定性的影响采用欧拉方法求解动态的质量、动量、能量守恒方程的方法完成；最后采用&层迭&的方法进行各种降稳因素的综合评估。

Taking the active network as a research task, the input accessibility, the Coates graph of matrix and graph transmission etc are used to analyze the relation between reducibility of the coefficient matrix of the state equation and the electric separability of the network or the electric accessibility of the network for the first time, acquiring sufficient and necessary conditions that coefficient matrix of the state equation is reducible. Network Graph Theory, Matrix Theory and System Theory over F etc are used to derive the structural controllability criterion of the passive network over F for the first time. Then according to these theoretic results, the structural controllability problems of the active network over F are studied, acquiring several structural controllability conclusions of the active network.

率先将状态方程的输入可达、矩阵的Coates图、流图传输系数等概念和方法引入到对F上有源电网络的研究，研究了网络状态方程的系数矩阵的可约性与网络电气可断性或电气可达之间的关系，研究了F上有源电网络的能控性问题，获得了状态方程的系数矩阵可约的充分必要条件、F上有源电网络系统的结构能控性判据等新的结论。

The finite difference is used to approximate differential operation; the reflectance map equation described by the first order nonlinear differential equation is transformed into an algebraic equation about the unknown surface heights, and then the objective equation is constructed by the reflectance map equation and gradient information of image. Moreover, the Newton iterative algorithm is utilized to obtain the numerical solution and 3D shape of the surface.

采用有限差分近似微分运算，将一阶非线性微分方程所描述的反射图方程转化为关于未知表面高度的代数方程，再由反射图方程和图像梯度信息构造目标方程，进而用Newton迭代算法求出该方程的数值解，得到表面三维形状。

We develop and apply the Hirota bilinear-θfunction method,Jacobi elliptic function expansion method,linear superposition method and F-expansion method respectively to solve many 2+1 dimensional nonlinear wave models including 2+1 dimensional 2DsG equation,the coupled ZK equation,2+1 dimensional KdV equation,2+1 dimensional long wave short wave resonance interaction equation and 2+1 dimensional dispersive long wave equation,abundant Jacobi elliptic function doubly periodic solutions are derived.These solutions show various periodic wave shapes and special periodic characters.

发展和应用Hirota双线性-θ函数方法，雅克比椭圆函数展开法，线性叠加法，F-函数展开法等分别求解2+1维2DsG方程，耦合ZK方程，2+1维KdV方程，2+1维长波短波共振相互作用方程，2+1维色散长波方程，获得丰富的雅克比椭圆函数双周期波解，描述了一些周期波形态及周期特性。

In the solution of the problems in algebraic equation, differential equation and integral equation, we usually resort the sotution of equation to the fixed point of mapping in metric space. The contraction mapping principle can be used to solve many problems of the existence and uniqueness of equation solution.

在代数方程、微分方程和积分方程的求解问题中，通常把所求的解归结为度量空间中映射的不动点，然后应用压缩映象原理来统一处理许多方程解的存在性和唯一性问题。

On the basis of gas migration equation -Darcy Law,coal seam gas content equation -parabola equation ,ideal gas state equation and the continuity equation s of the gas flow,a dynamic model of gas unilateral flow in the coal seam is set .

根据基本假设，对煤层瓦斯流动规律进行了研究，运用瓦斯运动方程—达西定律、煤层瓦斯含量方程—抛物线方程、理想气体状态方程以及气体流动的连续性方程，建立了煤层单向瓦斯流动的动力学模型，并根据边界条件和初始条件，对动力学模型进行了求解，推导出煤壁单位面积的瓦斯涌出量的计算公式，分析了瓦斯涌出量的影响因素，利用测得的数据，进行了实例计算，并用vc编制了计算机程序。

In order to obtain more general solution of second order linear differential equation with constant coefficients, which is important in theory and practice, on the basis of knowing a special of the second order linear differential equation with constant coefficients and by using the method of variation of constant, the second order linear differential equation with constant coefficients is transferred to the reduced differential equation and a general formula of the second order linear differential equation with constant coefficients is derived.

为了更多地得到理论上和应用上占有重要地位的二阶常系数线性非齐次微分方程的通解，这里使用常数变易法，在先求得二阶常系数线性齐次微分方程一个特解的情况下，将二阶常系数线性非齐次微分方程转化为可降阶的微分方程，从而给出了一种运算量较小的二阶常系数线性非齐次微分方程通解的一般公式，并且将通解公式进行了推广，实例证明该方法是可行的。

Thirdly, according to the development of the frozen soil, the coupling model of single freezing pipe of axial symmetry of temperature field, stress field and moisture migration is put forward firstly. Then, by means of the progressing principle of potential field, the coupling model of temperature field, stress field and moisture migration which is under the condition of the multi-freezing pipes is extended. At last, the energy balance equation, stress balance equation, quality balance equation, geometric equation, physical equation, initial and boundary conditions etc are adopted to give the analytic solution to the problem of plane axial symmetry of single freezing pipe.

第三，在对室内试验和现场实测结果研究的基础上，分析了土体冻结过程中温度场、应力场、水分场耦合原理，并按照冻土体形成发展过程，首先建立了单一冷源冻结轴对称温度、应力、水分场耦合模型；接着利用势场的迭加原理，将单一冷源情况的三场耦合问题推广到多冷源情况的三场耦合；最后根据能量守恒平衡方程、应力平衡方程、质量守恒平衡方程、几何方程、物理方程、初始及边界条件，解出了单一冷源平面轴对称问题的解析解。

Under the condition of the slide between pile and soil around pile is taked into account,five equations are established, including the equation of compatibility between the settlement of pile cap soil and the settlement of pile cap; the equation of compatibility between the settlement of pile head soil and the settlement of pile head; the physical equation between the settlement of soil around pile shaft and the settlement of pile shaft;the equation of equilibrium between loads on the pile cap, side frictional stress and restraints of pile head; the equation of compatibility between the deformation of the pile body and the subtraction between the settlement of pile cap and the settlement of pile heap.

桩身单元和土单元存在着相互作用，在允许桩土相对滑移的前提下，建立桩顶土体沉降与桩顶沉降的协调方程、桩底土体沉降与桩端沉降的协调方程、桩土相对位移与桩侧摩阻力的物理方程、桩身力的平衡方程、桩身压缩和桩顶沉降与桩端沉降之差的协调方程。

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.

为了确定方程的解集，本文利用交既约元与不可缩短的有限交分解等工具，同样地先求出简单形式的型矩阵方程的所有极大解，然后讨论方程与方程之间的关系，在此基础上，在B的每个元素均有不可缩短的有限交分解的情况下，求出了方程的所有极大解，从而完全确定了方程的解集。

"Bird Man's Diary, Butting on the Love Island", Changsha, China

2008年"鸟人日记，顶在爱情岛"，中国长沙

As long as they were in the service of a family of wizards, their magic would remain dormant.

只要他们一天为家庭服务，他们的法力就潜藏不动。