应用复变函数论的方法，简洁地给出了的一切有理数解和一切整数解公式。
In this paper, the general rational solutions and the general integer solutions of are given.
给出了利用渐近解公式，由模有效折射率的测量值确定波导表面折射率和扩散深度的方法。
A method is given for determining the parameters of a diffused waveguide from the observable values of mode efficient index by using the asymptotic solution equations.
在应力偏张量主值三角函数解的基础上，推导了应力空间内主应力和主方向的通用解析解公式。
Based on the stress partial tensor's trigonometric function answer, the main stress and main direction are established in parsed currency formula, and some special answers and examples are discussed.
你必须用刚学的公式解这些问题。
In solving these problems you must apply the formulas you have just learned.
同时利用带位的奇异积分方程理论得到了这一问题可解的主要条件及指数计算公式。
By the singular integral equation theory we obtain the resolvable sufficient and necessary condition and the formula of counting index for the problem.
指出关于铅球最佳投掷角计算公式中存在的问题，提出了计算这一角度的精确方程和数值解。
The problem of shots optimum putting angle in calculation formulae are pointed out, precise equation and numerical solution of this angle are given.
同时，给出了计算光滑行波解的公式。
The formulas to compute the travelling waves are also educed.
通过解传输线阻抗转移公式和终端输入阻抗的气隙电容表达式的联立方程得出了数值结果。
The numerical results were obtained in a table by solving the combined equation of transmission line impedance transfer equation and terminal input impedance expression in gas capacitance.
当用积分方程法分析桩和其它地学工程问题时，这些公式可以用作一近似的基本解。
These formulae can be used as an approximate basic solution when the integral equation method is employed for the analysis of piles and other geotechnical engineering problems.
得到了波动方程的解的反演公式及等距等式，为再生核理论的应用提供了新的思路。
Then we prove the isometrical identity and inversion formula of the solution of the wave equation.
利用方程的解推出地层应力及破裂参数的计算公式。
Derives the formula for calculating the formation stress and rupture parameters with the solution of the equation.
此公式具有渐进强对偶的特性并且可以保证找到原问题的最优解。
This formulation possesses an asymptotic strong duality property and guarantees a success for identifying an optimum solution.
得到了最大三维应力集中、表面应力集中与相应平面解之间的近似关系和经验公式；
The relationships of the maximum SCF, surface SCF and the corresponding planar solution were found, and the corresponding empirical formulae were obtained by fitting the FE results.
所有这些实际上很难用明确的数学模型及数学公式给出唯一确定解的。
All of these actually difficult to clear the mathematical model and mathematical formulas are the only confirmed solvable.
笔者提出从测角前方交会推演出测边解算前方交会的简便公式，方便可行，比较实用。
A simple formula of side-measured forward intersection is derived from angle-measured forward intersection, which is easy, feasible and practical.
本文还导得动平床情况下的流速分布公式、阻力公式和输沙率公式，使动床的水流运动和输沙过程得以联解。
The formulas of velocity distribution, flow resistance and bed load transport rate are obtained, in which the flow and sediment movement are considered simultaneously.
在通过对任一正整数提出另外一种唯一分解式的基础上，利用初等方法得到了关于立方补数的几个有趣的渐近公式。
On the basis of requesting another factorization of an integer in only one way, two interesting asymptotic formulas on cub complements are obtained through the elementary method.
本文从衍射积分公式出发，利用贝塞尔函数，求得夫琅禾费环孔衍射积分的精确解，并对衍射图样进行分析讨论。
In this paper, diffraction integral equations and Bessel Functions are used to getting perfect solution of Fraunhofer ring aperture diffraction, and the diffraction pattern is analysed.
以半圆形和矩形基坑弹性半平面应力解为基础，推导了基坑周围土体的竖向位移和水平向位移的计算公式。
Based on the elastic semi-plane stress solution of the semicircular excavation and rectangle excavation, deducing the soil displacement equation around the foundation pit.
为此先推导离散格林函数的权模估计和有限元解的渐近不等式展开，然后给出公式的证明。
For this, we derive the weighted estimates for discreet Green function and the asymptotic error expansion inequalities, and then the proofs of the formulas are given.
从衍射积分公式出发，利用贝塞尔函数，求得夫琅禾费环孔衍射积分的精确解，并对衍射图样进行了分析。
Diffracton integral equations and Bessel Functions are used to get perfect solution of Fraunhofer ring aperture diffraction, and the diffraction pattern is analysed.
通过在平面波谱域中比较复射线束叠加场和标准解的方法，导出了球面波和柱面波的复射线束展开系数公式。
In this article, we derive complex expansion formula of spherical and cylindrical waves by comparing the stacking field of complex ray and the close-form solution in the plane spectral domain.
运用目的规划的单纯型方法，得到了模糊方程广义解的计算公式及模糊方程广义解的若干性质。
By use of the simplex method of the goal programming, we obtains the calculation formula and some properties of the generalized solution of fuzzy equation.
另外，论文还根据波浪作用下饱和海床响应的解析解提出了液化最大深度的计算公式。
In addition, an equation for calculation of maximum liquefaction depth is brought up according to analytic solution of saturated seabed under waves.
运用目的规划的单纯型方法，得到了模糊方程广义解的计算公式及模糊方程广义解的若干性质。
By use of the simple method of the goal programming, we obtains the calculation formula and some properties of the generalized solution of fuzzy equation.
本文给出了求非退化线性规划最优解的迭代公式。
In this paper, an iterative formula to solving non-degenerate LP to optimality is given.
通过分析，得到了运动学逆解的解析公式。
Analytical expression of inverse solution for kinematics equation is solved.
在控制器的设计中利用插值法导出了一个超越方程解函数的具有较高精度的近似计算公式。
An approximate formulation with sufficient high precision is obtained from an implicit function in designing the feedback linearization control law.
基于分离变量方法，建立了绕射势的级数解，导出了作用于大直径桩柱上的绕射力的计算公式。
A formal potential solution for the diffraction problem was established, and the computational formulation for the corresponding diffraction force was given.
给出了悬臂压弯构件整体稳定性计算的解析解，并建立了其设计计算的相关公式。
The analytical solution for the stability of cantilevered beam-columns is presented, and the design interaction formula for it is established.
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