精确解

The new algorithm effectively combines the advantages of ACO and PSO. It adopts the grid method for environment modeling and makes use of the efficiency and succinctness of PSO to obtain the initial distribution of pheromone, reducing the number of iterations and accelerating the convergence. At the same time, by using the parallelizability of ants and distributed parallelized-searching technology, the performance of the algorithm is effectively improved.

该方法有效地结合了粒子群算法和蚁群算法的优点，采用栅格法进行环境建模，利用粒子群算法的快速简洁等特点得到蚁群算法初始信息素分布，以减少迭代次数，加快算法的收敛速度；同时利用蚁群算法之间的可并行性，采用分布式技术实现蚂蚁之间的并行搜索，求解精度高等优点，求精确解。

The free vibration of a nonlinear elastic rectangular plate is explored, considering influence of material nonlinearity and static-load in plane on its dynamic characteristics. Exact solution to free vibration of each mode of the rectangular plate is obtained according to the fixed point theory of partially ordered space. So the whole process of free vibration is described.

对非线性弹性矩形板的自由振动进行了研究，考虑了材料非线性和面内静载对板动力特性的影响，并根据半序空间的不动点理论求得该矩形板在自由振动时各阶模态的精确解，描绘了其自由振动的全过程。

Through the Lagrange's equation,the nonlinear vibration equation of a particle non-harmonic oscillator is established;the curves of the restoring force and potential energy varying with coordinates and phase plot are drawn.

利用拉格朗日方程建立了单质点弹簧振子非线性振动方程，作出了回复力、势能随坐标的变化曲线以及相图。应用第一类完全椭圆积分求出了非线性振动周期的精确解。

As we well know, the symmetry reduction methods related to group theory, such as the Lie point symmetry method, conditional symmetry, generalized conditional symmetry and etc, are effective tools to study the exact solutions of the nonlinear partial differential equations.

众所周知，与群论有关的对称约化方法，如李点对称方法，条件对称方法，一般条件对称方法等，是研究非线性偏微分方程精确解的有效方法。

The influence of the structure and material parameters on static and dynamic characteristics is studied. The three dimensional static analysis is obtained by the power series expansion method for a piezoelectric composite laminates. Three dimensional distribution of bonding stress, displacement and electric potential are presented. The distributions of electric potential across thickness of two kinds piezoelectric materials are discussed.

对于静态问题，采用三维精确解方法，给出了压电层与基体之间剪应力、位移、电势的三维分布图；讨论了工程中常用的两类压电材料在感知和作动情况下沿压电材料厚度方向电势的分布情况，分析了电势可看作线性分布的条件；讨论了压电层和粘结层的厚度及材料特性变化对压电感知和作动效果的影响，并对压电层的厚度作了优化分析。

Based on the linear elastic theory, the piezoelectric theory and magnetostrictive theory, using the power series expansion series method, a three-dimensional resolution of the natural frequencies of a simply supported rectangular laminate is investigated.

基于线弹性理论、压电理论和磁致伸缩理论，使用幂级数和傅立叶级数解法，得到了四边可移简支、磁电复合材料层合板的固有频率的三维精确解。

Plentiful and substantial achievements have been made, which motivate a lot of methods to obtain the exact solutions of solitary wave equations, such as: the homogeneous balance method, the hyperbolic function method, the power series method, besides the traditional methods, such as: the inverse scatting method, the bilinear Hirota method, and the Backlund transformation method etc.

求解孤立波方程精确解的方法除了传统的反散射方法、Hirota双线性方法、Backlünd变换方法外，近年来又涌现了很多新方法，如齐次平衡法、双曲正切法，级数展开法等。

It also states that students "should know how to use quadratic functions to solve extremum problems in everyday life". It seems to me that befe all these, students should be properly taught the technique of completing the square (which underlies the solution of extremum problems of any kind) and the quadratic formula (which would then give *exact* solutions of quadratic equations).

我认为，在学习这些之前，应该适当地教给学生配平方的技巧（它是解决任何最值问题的基础），以及二次求根公式（它能给出二次方程的精确解）。

In this paper, the reciprocal theorem is applied to research on into the bending problem of set squrare with three clamped edges under a concentrated bending moment acting at any of its points, and the accurate solution of this problem is given.

应用功的互等定理研究了在一集中弯矩作用下三边固定三角形板的弯曲问题，给出了该问题的精确解。

In this paper, the reciprocal theorem is applied tO researchon the bending problem of set square with three clamped edges undera concentrated load acting at any of its POints, the accuracy solutionof this problem is given.

应用功的互等定理研究了在一集中载荷作用下三边固定三角形板的弯曲问题，给出了该问题的精确解。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。