查询词典 dimensional equation

In this paper, the problem of an arbitrarily shaped planar crack which is perpendicular to the interface of bimaterial and loaded by interior normal pressure is studied by means of the method of hypersingular integral equation in three dimensional fracture mechanics.

利用三维断裂力学的超奇异积分方程方法，对双材料空间中重直于界面的平片裂纹Ⅰ型问题进行了研究。

Through solving the Navier-Stokes equation, three dimensional transonic unsteady flow in isolated rotor blade was simulated.

本文通过数值求解Navier-Stokes方程，计算了跨音速压气机转子叶排内三维非定常粘性流动。

By the methods of reducing order and Euler s eigenvalues,we obtain the general solution formula to one kind of systems of three dimensional second order ordinary differential equation with constant coefficients.

采用降阶和特征根方法，给出了一类三维二阶常系数微分方程组的通解公式，并通过算例与拉氏变换法进行了比较。

With the method of the Lie group transformation,the symmetry of the equation governing one dimensional finite strain consolidation is discussed and,from the point of the symmetry,the feasibility to obtain the analytical solution of these nonlinear partial differential equations is discussed.

介绍了基于连续介质理论和混合物理论的大应变固结理论的发展，论述了两种一维大应变固结理论之间的差异及其一致性。

On each subspace the Dirac equation is equivalent to a two dimensional system of ordinary differential equations of first order.

在每一个子空间中狄拉克方程等效为一阶线性微分方程组的两个空间系统。

Based on dynamic equilibrium equations of three-dimensional elasticity, a state equation was established for orthotropic foundation plates using double Fourier series, in which no assumption about stress or displacement modes was made. Analytical solutions and frequency equations of unified formulas were presented for thin and thick laminated foundation plates.

从三维弹性力学动力平衡方程入手，抛弃应力或位移模式的人为假定，利用Fourier双重级数，建立了正交各向异性地基板的状态方程，并分别给出了地基上任意层厚薄板静力问题的统一解析式和动力问题的频率方程。

As an application, the completeness of the eigenfunction system of the infinite dimensional Hamiltonian operator corresponding to a wave equation is given.

作为应用，还给出了波动方程导出的无穷维Hamilton算子特征函数系的完备性。

The influences of the shock thickness and Alfven waves on the particle acceleration by diffusive shock waves are numerically studied through solving one-dimensional diffusive equation including the second-order Fermi effect. It is shown that the spectral index of the energetic particles strongly depends on the shock thickness. For example, the spectral index increases from 2.1 to 3.7 in the low energy range of 3-10 MeV and from 2.5 to 5.0 in the high energy range of 20-60 MeV as the thickness increases. The spectral index decreases from 4.3 to 3.1 as the particle injection energy increases. The spectral index decreases from 4.0 to 1.8 at the quasi-steady stage with the enhancement of the compression ratio from 2 to 4. The results indicate that under the influence of Alfven waves, the energetic particle spectrum at lower energy becomes flat and the spectral index decreases from 2.5 to 0.6 in the low energy range of 3-10 MeV and from 11.6 to 5.0 in the high energy range of 20-60 MeV. At the same time, the rollover energy reaches 19.6 MeV. The spectral index decreases from 5.8 to 2.9 as the energy density of Alfven waves increase. All these results are basically consistent with the theoretical models, as well as the observations of typical energetic particle events.

通过数值求解包含二阶费米加速的一维扩散方程，探讨在准平行激波条件下激波厚度和级联阿尔芬波对粒子加速的影响，研究粒子分布函数的演化与激波厚度和阿尔芬波强度的内禀关系，计算结果表明：(1)考虑激波厚度时，谱指数明显依赖于激波厚度，随着厚度从0.32增大到2.56，低能端(3-10MeV)谱指数逐渐从2.1增加到3.7，高能端(20-60MeV)谱指数从2.4增大到5.0，能谱逐渐变软；当初始注入粒子动量增大1.3倍，质子能谱指数从4.3减小到3.1，且与零厚度激波加速的谱指数差值缩小；厚度不变时，随着压缩比从2增加到4，准稳态分布时低能端(3-10MeV)粒子能谱指数逐渐从4.0减小到1.8谱变硬；(2)在级联阿尔芬波的影响下，随着时间的增大，粒子在低能处(3-10MeV)的谱指数从2.5减小到0.6高能端(20-60MeV)谱指数从11.6减小到5.0，能谱变硬，拐点能量值从7.5MeV增大到为19.6MeV；随着波的能量密度增大，谱指数从5.8减小到2.9，这表明阿尔芬波强度越大，加速效率越高，通过与激波厚度解析结果和高能粒子事件的观测能谱比较发现两者是一致的，说明数值模拟结果是可靠的。

The three-dimensional motion equation of the cable-damper system is established and discretized by the finite difference method.

建立斜拉索—阻尼器系统的三维运动方程，并采用有限差分法进行离散化。

The new method- expansion method-proposed by Wang Ming-hang and others is promoted to high-dimensional nonlinear evolution equation.

将王明亮等人提出的一种新方法－扩展法推广到高维的非线性演化方程。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新