查询词典 quadratic

A deterministic global optimization algorithm based on Lagrangian dual is proposed for solving the nonconvex quadratic programming with nonconvex quadratic constraints, which is often encountered in technical design and operational research.

针对带有非凸二次函数约束的非凸二次规划问题，提出了一个基于拉格朗日对偶的确定型全局优化算法，这类优化算法可广泛应用于工程设计和非线性系统的鲁棒稳定性分析等实际问题中。

Elliptic curves discrete logarithm ; elliptic curve domain parameter ; point group ; base point ; quadratic remainder ; quadratic congruence equation

椭圆曲线离散对数；椭圆曲线域参数；点群；基点；平方剩余；二次同余方程

The fact that solution of wave equation is equivalent to the extreme value of quadratic function solution was verified, and the existence and uniqueness of the quadratic function solution was also proved.

证明了波动方程的解和二次泛函极值解的等价性，以及二次泛函极值解的存在唯一性，为其在液压传动中流体瞬变分析的进一步应用提供了理论依据。

Inner point and exterior point of a quadric and its plane of the type of contact plane;2. The article gives a way by which a quadratic curve is processed by a linkage,and then a quadric can be formed by revolving the quadratic curve as a generatrix around the axis.

提出一种利用能够生成二次曲线的连杆机构作辅助装置，将生成的二次曲线作为母线绕轴线旋转而形成旋转二次曲面的方法，从理论上进行了推导，并通过实例说明了该方法的应用。

According to the studied results at present, the studied objects are mainly thin plate and beam about sound radiation mode, a method computed sound radiation mode of complex structure is presented in this dissertation, according to the results of the previous two chapter, a theoretical method to solve acoustical radiation mode and acoustical radiation efficiency of complex structure by boundary element method and acoustical radiation theory is posed, the acoustical radiation power is expressed as a Hermitian quadratic form, while the radiation modes is determined by general eigenvalue decomposing, and then the radiation efficiency is computed via the orthodoxy of radiation modes with regard to impedance matrix and average velocity matrix; lastly, the validity of the method is proved by pulsating sphere and radiating cube with analytical results. According to results of the form three chapter, the structure sound radiation sensitivity is studied in detail, the sound radiation power of structure can be expressed as positive Hermitian quadratic form, the sound radiation sensitivity can be expressed as two parts by partial differential with respect to design variable, which are sensitivity of boundary velocity and impedance matrix, combined with the theory of FEM and BEM, the structure sound radiation can be translated to the analysis of structure dynamic sensitivity and impedance matrix sensitivity. The theory posted in this dissertation is tested by the FEM software ANSYS and the software AAS programmed by author.

在前几章的基础上，通过结构声辐射的模态理论对结构的声辐射的机理进行了深入地探讨，针对目前声辐射模态的研究对象主要是简单的板和梁类结构，提出了一种计算复杂结构声辐射模态的方法，利用前两章研究所得的结论，将边界元方法与广义特征值的理论结合起来研究了复杂结构的声辐射模态与声辐射效率，先将结构的声辐射功率表示为一个正定的厄米特二(来源：ABb7C论文0909网www.abclunwen.com)次型，运用广义特征值分解求解了复杂结构的声辐射模态，然后利用声辐射模态关于阻抗矩阵与均方速度耦合矩阵的正交性，求解了复杂结构的声辐射效率，最后用具有解析解的脉动球与辐射立方体验证了该方法的有效性。

For the first time,the authors apply sequential quadratic programming of inner point as a solver to algorithm of quadratic programming for dynamic optimization of frame structure.

首次将内点序列二次规划法应用于框架结构的动力优化领域，并作为二次规划算法的求解器，改善整个优化问题的运算效率。

The question on bifurcation of limit cycles in quadratic conservative perturbations of a quadratic integrable system is discussed.

研究了一个具有同宿轨的二次可积系统在二次保守扰动下的分支现象。

Establish integrated invertibility theory over it: By R〓R〓 transformation method, we solve the problem of deciding weakly invertibility and finding weak inverse, By founding the bijections between all quadratic form automata and input memory linear finite automata, we find a algorithm to produce all weak inverse quadratic form finite automata.

本文着眼于这些最基本问题，将有限域上的二次型和置换多项式理论引入有限自动机可逆性的研究，构造了一类由二次型构成的非线性有限自动机（3.6定义），称之为二次型有限自动机，我们在其上面建立了与线性有限自动机可逆性理论相对应的完整的可逆性理论：采用线性R〓R〓变换方法，解决了此类有限自动机的弱可逆性判定、求弱逆问题（3.10、3.12定理）、通过建立全体二次型有限自动机与全体输入存储线性有限自动机之间的保持弱逆性的一一对应，给出了产生全部可逆二次型有限自动机的方法。

The main characteristic of this kind of quadratic forms is their orthogonality depends on the linear dependency of the elements which produce them (2. 17 theorem), and this is the very reason we can establish the invertibility theory over quadratic finite automata by R〓R〓 transformation methods.

这类二次型的主要特点是它们的正交性由它们的生成元的线性相关性决定（2.17定理），这是可以用线性R〓R〓变换方法建立二次型有限自动机弱逆性理论的根本原因。

Summary: The concept of matrix and its determinant computing, matrix determinant, matrix sub-block with the elementary transformation, invertible matrix, rank of matrix; vector and its computation, the linear relationship between vector, vector group of rank; linear equations of the nature and structure of linear equations; matrix eigenvalue and eigenvector, similar to matrix and matrix diagonalization conditions, the standard quadratic form with the normal forms, quadratic and symmetric matrix There are qualitative.

内容提要：行列式矩阵的概念及其运算，方阵的行列式，矩阵的分块与初等变换，可逆矩阵，矩阵的秩；向量及其运算，向量间的线性关系，向量组的秩；线性方程组的性质与结构，线性方程组的求解；矩阵的特征值与特征向量，相似矩阵与矩阵可对角化条件，二次型的标准形与规范形，二次型和对称阵的有定性。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。