积分变量

Line integrals are used extensively in the theory of functions of a complex variable.

在复变量函数理论中广泛使用线积分。

Their application of convex body and geometry probability is the important theory in integral geometry and convex geometry, One can study the geometric invariants and geometric probability and other issues.

它们在凸体和几何概率中的应用是积分几何和凸几何的重要理论，通过它们可以研究几何不变量和几何概率等相关问题。

The complex variable boundary element-free method is a direct numerical method of the meshless method of boundary integral equation.

复变量边界无单元法是边界积分方程的无网格方法的直接列式法，容易引入边界条件，且具有更高的精度。

The time-dependent Dirichlet boundary condition was used to describe the variation of water head during water level fluctuation.

模型的求解采用效率较高的积分有限差分法进行空间离散，并编制了全隐式联立求解的计算程序，通过变换主要变量，实现了饱和与非饱和的相互转变，采用随时间变化的Dirichlet边界条件精确模拟水位波动时的变水头边界条件。

In order to solve the problem,We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential manifold. The travel time are expressed as polynomials of the horizontal offset between the two points, and the single-square-root operator in frequency-wavenumber domain are expressed as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddle-point method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量(地面点到地下相点的水平距离)的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

In order to solve the problem, We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddlepoint method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量（地面点到地下相点的水平距离）的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

And a model of layer—disperising dual medium is established (2) Some new theories and methods, such as Fourier dual integral transformation and half numeral value analytic method and so on, are used to establish the calculating formula in this paper.

2本文在理论推导上，应用了数学、力学和数学物理方程方面的新理论和新方法，如：二重富里叶积分变换、板壳理论、分离变量法以及半解析数值方法等，使本论文在理论推导过程上，增加了理论的严密性和逻辑性。

By studying double-power integral, the geometric invariants and geometric probability can studied from the perspective. In particular, more complicated geometric probability can be resolved with the double-power integral inequality.

通过对双弦幂积分的研究，可以从新的角度更进一步的研究几何不变量和凸几何，特别是双弦幂不等式能解决更为复杂的几何概率问题。

The Gibbs phenomenon should be considered in interpreting the numerical curve of the transient solution with infinite integral derived by the method of separation of variables.

计算结果表明，在求解由分离变量法所得的无穷积分解析解的数值曲线时，吉布斯现象的存在具有普遍意义。

The deduced integral invariant is employed to study the 3D predator-prey Lotka-Volterra systems and some new results are obtained.

利用此积分不变量，对三维捕食被捕食 LVS解的渐近性进行讨论，得到了平衡点全局渐近稳定的新条件，推广了已有LVS正平衡点全局渐近稳定的结

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。