级数解的英文

• series solution

• "级数"英文翻译    progression; series; number ...
• "解"英文翻译    understand; see
• "可限级数解" 英文翻译 :    finite series solution
• "幂级数解" 英文翻译 :    power series solution
• "幂级数解法" 英文翻译 :    power-series solution
• "有限级数解" 英文翻译 :    finite series solution
• "级数" 英文翻译 :    [数学] progression; series; number of stages; number of steps; stage number◇级数变换 transformation of series; 级数乘法 multiplication of series; 级数解 series solution; 级数求和 summation of series; 级数相乘 multiplication of series
• "参数解" 英文翻译 :    parametric solution
• "常数解" 英文翻译 :    constant solution
• "代数解" 英文翻译 :    algebraic solution
• "对数解" 英文翻译 :    logarithmic solution
• "数解值" 英文翻译 :    arithmetic solution
• "整数解" 英文翻译 :    integer solution; integral solution; whole number solution
• "指数解" 英文翻译 :    exponential solution
• "补充函数解" 英文翻译 :    complementary-function solution
• "代数解法" 英文翻译 :    algebraic method
• "代数解码" 英文翻译 :    algebraic decoding
• "代数解码器" 英文翻译 :    algebraic decoder
• "代数解析" 英文翻译 :    algebraic analysis
• "对数解调器" 英文翻译 :    logarithmic demodulation
• "对数解法" 英文翻译 :    solution by logarithms
• "函数解码器" 英文翻译 :    decoder, function; function decoder
• "隐函数解" 英文翻译 :    implicit solution
• "用代数解答" 英文翻译 :    algebraize
• "有理整数解" 英文翻译 :    rational integral solution

• Series solution of electric field intensity on perpendicular axis of elliptic charged ring
  椭圆形带电环垂直轴上的电场强度级数解
• In this paper , by using the property of fourier series a compound series consisting of trigonometric series and power series is established
  摘要利用由三角级数和幂级数复合构成的函数项级数的有关性质，得到了一类变系数非齐次调和方程边值问题的级数解。
• The boundary value problems of singular perturbation with boundary layer at turning points are discussed . the asmptotic expansion are constructed . and the uniformly valid asmptolic estimation is obtained
  主要讨论了在转点处出现边界层现象的奇异摄动边值问题，构造了形式级数解，得到了一致有效的渐近估计
• Ordinary differential equation , first order differential equations , 2nd order differential equations , power series solution of differential equation , laplace transform , fourier series and transform , matrix , eigen value problem , partial differential equation
  常微分方程式、一阶微分方程式、二阶微分方程式、微分方程式级数解、拉氏转换、复利叶级数与转换、矩阵、本徵值问题、偏微分程式。
• Secondly , the effectiveness and limitation of the classical perturbation , such as the method of multiple scales and the poincare - lindstedt method , are discussed in detail through a duffing oscillator with delayed velocity feedback . it is shown that the two perturbation methods are effective only in solving the approximate solution of the first two orders . an ambiguity or paradox will be encountered when they are used to seeking for the third or higher order approximation of solution
  其次，以一具有时滞速度反馈的duffing系统为例，研究了经典摄动法如多尺度法， poincar - lindstedt法等在求解时滞微分方程级数解时的适用性和局限性问题，指出利用这些方法只能有效求得系统的前两阶近似解，而在求系统的三次以上近似解时会出现矛盾或二义性。
• Using the complex potential method in the plane theory of elasticity of an anisotropic body , a series solution to the stress field of a finite plate containing multiple cracks subjected to arbitrary loads is obtained by means of the faber series expansion , and the stress intensity factors at the crack tips are calculated based on the theories of fracture mechanics . equivalence yield stress is introduced in order to consider the effects of the plastic zones , with which the strip yield criteria is developed in the article so that the effects of structural size and the crack interactions on the stress distribution can be considered accurately . the effects of plate size , crack size and crack distributions on the stress intensity factors as well as the residual strength of the plate are studied detailedly
  采用各向异性体平面弹性理论中的复势方法，以faber级数为工具，得到了含多裂纹有限大板在任意载荷作用下应力场的级数解，并应用断裂力学方法确定裂纹尖端的应力强度因子；引入当量屈服应力考虑裂尖塑性区的影响，提出基于带屈服准则的剩余强度分析模型，能够充分考虑结构尺寸和裂纹之间相互作用对应力场的影响；通过数值计算详细讨论了结构尺寸和裂纹之间位置关系对应力强度因子和结构剩余强度的影响规律，得到了一系列对工程应用具有实用价值的结论。
• Using the complex potential method in the plane theory of elasticity of an anisotropic body , the series solution of finite anisotropic thin plate containing an elliptical inclusion is proposed with the help of faber series . a hybrid element with an elliptical inclusion for anisotropic materials is obtained by using the hybrid variable principle , and the element efficiency is verified by numerical examples . the state of the damage is modeled by an elliptical soft inclusion , and using the point stress criterion based on characteristic curve and yamada - sun etc . criteria , the prediction of the strength of a composite laminate with damage is set up
  首先基于经典层板理论，将复合材料层板的弹性问题化归为均匀各向异性板来求解；采用各向异性体平面弹性理论中的复势方法，以faber级数为工具，给出了有限大含椭圆核各向异性板弹性问题的级数解形式；利用杂交变分原理，成功导出含椭圆核各向异性板杂交应力有限元，并用算例验证了该单元的可行性和有效性；采用含刚度折减椭圆形弹性核的冲击损伤模型，引入基于特征曲线和yamada - sun破坏准则的点应力判据，建立了含损伤复合材料层板剩余强度的分析方法；通过数值计算详细讨论了各种几何参数对损伤层板应力分布、剩余强度的影响，得到了一系列对工程应用具有实用价值的结论。
• The series solution of the eccentric spherical capacitor ’ s capacitance has been obtained based on the bispherical coordinate system and strict derivetion , and through making programe to compute to get the numerical relation between the capacitance and the eccentrity , pionted out that the capacitance not let up but enlarged with the gain of eccentriccity
  四、采用双球坐标系严格求解了偏心球形电容器的电容。得到了它的级数解,求得了偏心球形电容器电容大小随偏心度变化的规律,发现偏心球形电容器电容的大小并不是随偏心率的增加而减小,而是随偏心率的增加而增加的。

• 级数解的日语：きゅうすうかい