次方程的英文

• equation of n th order

• 次    order; sequence
• 方程    equation
• 二次方程    binomial equation; quadratic equation; quadraticequation; quadric equation
• 二次方程的    quadratic
• 二次方程式    quadratic equation
• 非齐次方程    inhomogeneous equation; nonhomogeneous equation
• 高次方程    equation of higher degree
• 立方次方程    cubic equation
• 六次方程    sextic equation
• 七次方程    polynomial; septic equation
• 齐次方程    homogeneous eqation; homogeneous equation
• 全二次方程    complete quadratic (equation)
• 三次方程    cubic equation
• 三次方程式    cubic equation
• 双二次方程    biquadratic equation
• 四次方程    biquadratic; biqudratic equation; quartic equation
• 四次方程式    biquadratic
• 同次方程式    homogeneous equation
• 无因次方程    dimensionless equation
• 五次方程    quintic equation
• 一次方程    equation of the first degree; equationofthefirstdegree; first order equation; first-order equation; linear equation; simple equation
• 一次方程式    simple equation
• 因次方程    dimension equation; dimensional equation
• 因次方程式    dimensional equation
• 隐二次方程    implicit quadratic equation

• The method that simple cubic equation was changed from general to standard was introduced and the distribution of standardized real root was illustrated , which solved the problem of the distribution of any real root for simple cubic equation
  摘要介绍了一元三次方程一般式化为标准式的方法，结合图形给出了标准式的实数根的分布情况，从而解决了任意一元三次方程的实数根的分布的问题。
• The production reason of extraneous roots is analyzed and the improved method is proposed , that is the degree of the variables during the elimination process is reduced by searching relations among the vectors , so that a 46 degree univariate polynomial equation can be obtained directly
  分析了产生增根的原因并提出了消元过程中避免增根的改进措施，即寻找相关向量之间的关系，在消元过程中降低变量的次数，直接得到一元46次方程。
• As for nonlinear problem , the approximation schemes and the error analysis of pti are investigated , in order to avoid the computation of inverse matrix , the pti with dimensional expanding is proposed . the methods of constant , linear , sinusoidal approximation are proposed for the transformation of non - homogenous terms
  通过增维技术，该算法将非齐次方程齐次化，从而避免了矩阵求逆，并给出非齐次项常数近似、线性近似和正弦余弦近似的处理方法。
• Combined with the formerly fitted expressions of the second virial coefficient , some multi - parameter virial equations are proposed . among them , a quintic virial equation was chosen to predict the vapor - liquid equilibria of some very polar fluids , and the results are notably better than those of the usual cubic equations
  结合前面得到的第二维里系数拟合式，作者提出了几种多参数维里方程，并用其中的五次方程预测了一些强极性流体的汽液平衡，结果显著地优于常见的立方型方程。
• The weighted number of solutions of equation , r ( b ) , is expressed as the sum of a integral on [ 0 , 1 ] and a remainder term . using the circle method , the integral on the interval [ 0 , 1 ] is divided into the integrals on major arcs and minor arcs respectively , j and j . the section 3 gives a transformation for sj ( a ) and simplifies /
  把三次方程的加权解个数r ( b )表示为[ 0 , 1 ]上的积分加上余项，然后利用圆法，把区间[ 0 , 1 )上的积分变成优弧和劣弧的积分和第三节，给出s _ i ( )的一个变换，并化简把的主项被分成m _ 1 ， m _ 2和m _ 3
• This method is also valid for identifying the circuit and branch defect of first group spatial linkages based on the equivalent of circuit properties of the first group spatial linkages and its equivalent sphere four - bar linkage base on the property of the solutions of quartic equation , the conclusion that the number and order of branch between two adjacent stationary positions of the input link are derived . then , the new method to identify circuits of spatial single - loop linkages with four closures is presented . all types of the manner on which the branches coalesce at the stationary positions of the input link are obtained and the procedures to determine the type automatically are developed
  基于一元四次方程解的性质，得到了在输入构件两个相邻瞬时静止位置之间机构的分支的数目和大小顺序不变的结论，进而提出了识别具有四个封闭形的空间单环机构回路的新方法一一死点法，综合出了输入构件位于瞬时静止位置时机构分支结合情况的所有类型及其自动判别方法，研究了由所有结合的分支信息自动生成回路的算法，首次解决了此类机构回路与回路缺陷的自动识别。
• Because the questions of partial differential equations make green function method studied difficultly for student , the variation of parameters formula and ordinary differential equation are put forward . initial value of ordinary differential equation and the boundary value of ordinary differential equation are discussed . green function with time and green function without time are introduced and theirs equations and conditions are calculated
  基于偏微分方程问题造成学生学习green函数方法的困难，我们以常微分方程为切入点，从学生熟悉的参数变动法解非齐次方程出发，讨论了非齐次常微分方程的初值问题和边值问题，引入含时green函数和与时间无关的green函数，得出它们应满足的方程与条件，分析这些green函数最一般的性质及物理含义，从而验证了通常green函数方法在数学上的合理性，在此基础上总结并规范了green函数方法解决问题的基本思想和步骤。
• It is shown that a system of linear equations is resolved to obtain the rotational parameters by using of seven couple of conic curves in image sequences when the motion of a rigid object is pure rotational . when the motion of a rigid object is pure translation , a system of non - linear equations is resolved using iterative method , or using the method for resolving quartic equation . the translation parameters with a scale factor may be determined and the translation direction can be obtained
  研究结果表明，在纯旋转运动分析中，最少利用图像序列中7条对应二次曲线，可以线性地求解刚体旋转运动参数；在纯平移运动分析中，只需利用图像序列中1条对应二次曲线就可以求解刚体相对平移运动参数(即平移方向) ，分别用非线性迭代法和一元四次方程解法求解了刚体相对平移运动参数(即平移方向) 。
• In chapter 2 , we study the regularity of solutions of some second order differential equations . in chapter 3 , we study the regularity of solutions of higher order non - homogeneous differential equations where coefficients are rational functions or super entire functions . in chapter 4 , we study the regularity of solutions of higher order homogeneous differential equations where coefficients are super meromorphic functions
  其中第二章研究了某些二阶方程解的正规性；第三章在系数分别为有理函数和超越整函数的情况下研究了高阶非齐次方程解的正规性；第四章在系数为超越亚纯函数的情况下研究了高阶齐次方程解的正规性；第五章则是假设在方程系数为正规亚纯函数的条件下得到的解的增长性方面的结果。
• In chapter 2 , we study the further results on the properties of growth of solutions of one kind of higher order linear differential equations with entire coefficients , when there is one coefficient that is main dominating to the properties of the solutions , we obtain precise estimate of hyper - order of solutions of equations either homogeneous or non - homogeneous and relations between the solutions and functions with smaller growth
  本文研究了某些高阶线性微分方程解的增长性问题。其中第二章研究了一类高阶整函数系数微分方程解的增长性的进一步结果，当存在某个系数对方程的解的性质起主要支配作用时，得到了齐次与非齐次方程解的超级的精确估计及方程的解与小函数的关系。