查询词典 solution set of equation

In this method, the parameters to be estimated are divided into two sections, the number of equation dimension is reduced by half, so the solution of equation is simplified, and the working efficiency is greatly raised.

在这种解算方法中，由于将待估参数分成了两部分，使原本庞大的高维方程组的解算得以简化，把待求参数的维数减半，大大提高了工作效率。

The major implementations of the developed model include: Pseudo-spectral and finite-difference schemes are employed to approximate the spatial-differential operators in the horizontal and vertical directions, respectively. A second-order Runge-Kutta method is adopted to integrate in time for the velocity field and the free-surface elevation. The solenoidal condition of the velocity field is satisfied by solving the transformed pressure Poisson equation. A modified secant method is used to accelerate the iterative solution of the non-separable Poisson equation.

模式的主要数值方法包括：分别以拟频谱法以及二阶有限差分法近似控制方程与边界条件中的水平与垂直导数；以二阶Runge-Kutta法进行非稳态的自由液面位移与流场速度的时间积分；利用改良式割线叠代法求解计算区间中不可分离的压力Poisson方程式，以满足不可压缩流条件。

Some references indicated that the reachability of a Petri net can be analyzed by solving its state equation and judging whether or not there exists a legal firing sequence whose firing number vector is a solution of the state equation, but it is somewhat difficult to achieve.

已有文献提出通过解petri网的状态方程并判定是否存在以它的某个解为发生数向量的合法引发序列来分析petri网的可达性，这往往有一定的困难。

Under the assumption that a differential Riccati equation is solvable, an exponential reduced-order observer is developed by means of coordinate transformation and the gain matrix of the proposed observer depends on the solution of the differential equation.

在一微分Riccati方程有正定解的前提下，通过坐标变换方法对该类系统提出了一种指数型降维观测器设计方法，该观测器的增益矩阵取决于微分Riccati方程的正定解。

Based on them, we calculated precisely some enegy levels of P-wave and D-wave of a helium atom, presented and proved the general interdimensional degeneracies for a quantum N-body system, derived the general spherical spinor functions and the exact solution to the Dirac equation for the hydrogen atom, and proved uniformly the Levinson theorem for the Dirac equation in D-dimensions.

在此基础上，我们精确计算了氦原子P波和D波若干较低能级，建立和证明了量子N体系统不同维数状态间最普遍的简并，推导出任意 D 维空间广义球旋函数和Dirac方程氢原子的精确解，统一地提出和证明了任意 D维空间Dirac方程Levinson定理的一般形式。

In the study of the Lagrange stability of impact motion, we give some conditions of the bouncing solution of the asymptotically linear equation which is bounded or unbounded. Outside of a large disc, using the symplectic transformation of the Hamilton system to estimate the iteration of the successor map. Applying the Moser's small twist theorem, we get the invariant curves and then give the proof of the bouncing solutions which is bounded. We will estimate the successor map of the equation directly for proving the unboundedness of the bouncing solutions.

在碰撞运动的Lagrange稳定性的讨论中，给出了渐近线性方程碰撞解有界或无界的条件，在充分大的圆盘外，通过Hamilton系统的辛坐标变换的角度平均来估计后继映射的迭代，应用Moser小扭转定理得到不变曲线从而给出在一定条件下碰撞解有界的证明，碰撞解无界性的证明将采用直接估计后继映射的方法给出。

However, we can not get the film parameters directly because the ellipsometer equation is a transcendental equation. We can hardly get the analytical solution for film parameters from the measured ellipsometric parameters Ψ and Δ. Therefore, to find an algorithm to inverse the measured data Ψ and Δ becomes a primary but important problem.

但是通过椭圆偏振测量只能得到椭偏参数Ψ和Δ，由椭偏参数求解薄膜结构参数的椭偏方程是一个超越方程，很难得到精确的解析解，因此一般采用数值反演迭代不断逼近测量数据，将最优解作为测量结果。

From the self-consistent solution of 2-D Poisson equation and Schrdinger equation,the electron states and pinch-off behavior in quantum well channel of GaN HFET under longitudinal and transversal electric field were investigated.

从自洽求解二维泊松方程和薛定谔方程出发，研究了纵、横向电场作用下GaNHFET沟道中的电子态和夹断特性。

The cavitated bifurcation equation that describes cavity formation and growth in the interior of the sphere is obtained. It is proved that there exists a unique bifurcation point on the trivial solution of the cavitated bifurcation equation.

本文利用分岔理论和动力学理论中的基本观点、方法和结论，对具有缺陷的超弹性材科组成的球体内部的空穴生成和增长的拟静态问题以及空穴生成后随时间的运动规律等方面进行了系统的研究，得到了一些新的结论，同时给出了相应的数值分析。

The "compressed sparse row data format" is adopted to save storage and the "mode multiplication" is used to improve the computation efficiency, so that the finite integration equation is obtained with low storage and high efficiency. To solve the finite integration equation, which is a large-scale sparse algebraic eigenvalue problem under the condition specified, the Krylov subspace iteration method is introduced and the shift-invert Arnoldi method is proposed to exclude the unphysical static electro-magnetic solution and get the needed eigensolution around the specified eigenvalue.

采用"行索引稀疏格式"压缩存贮技术节约内存，采用大型稀疏矩阵的模式乘法，提高矩阵计算效率，高效获得了离散电场分量满足的有限积分方程；针对有限积分特征方程的求解，论文介绍了大型稀疏矩阵Krylov子空间迭代方法，并提出了位移求逆Arnoldi算法，以排除非物理的静态电磁场解，获得指定频率附近的特征值。

Sodium citrate; calcium carbonate; calcium hydroxide; potassium bicorbonate; magnesium carbonate; ferrous sulphate; Zinc sulphate; copper sulphate; manganese sulphate; potassium iodide; sodium selenite.

柠檬酸钠；碳酸钙；氢氧化钙；碳酸氢钾；碳酸镁；硫酸亚铁；硫酸锌；硫酸铜；硫酸锰；碘化钾；亚硒酸钠。

All this to say that I'm glad filmmaking hasn't become completely ironic. I can enjoy an ironic film as much as the next person, but they usually involve a message of some sort. One that's delivered in a smirkingly clever way that requires little in the way of talent.

所有这些都是说，我很高兴电影制作没有变成完全讽刺艺术，我可以和下一个人一样享受讽刺电影的乐趣，虽然他们经常会被划归到一定级别，技术方面不需要很高的才能。