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However, Diophantus\' solution is strictly algebraic, unlike the quasigeometric Babylonian solution.

但是，丢番图的解是严格代数的，而不像巴比伦人的解是拟几何的。

Inhomogeneous hyperbolic conservation law; viscosity solution; weak solution; entropy-entropy flux; maximum principle; Young measure; Dirac measure; compensated compectness

基础科学，数学，数学分析非齐次双曲型守恒律；粘性解；弱解；熵-熵通量；极值原理； Young测度； Dirac测度；补偿列紧理论

Based on the table of matrix element of spectrum decomposition, the Helmhotz matrix can be decomposed by recursion of the direct solution. A numerical comparison has been made with the spectrum LU decomposition and direct solution.

通过与谱法分解和直解法在分解精度和分解速度两方面的比较表明，本文方法与谱法相比，在非均匀介质中亥姆霍兹算子矩阵分解时的精度提高10倍；在计算速度方面，混合方法比简化后的直解法快。

The solution of some practical problems in engineering can be regarded as that of periodic solution of nonlinear autonomous systems according to the opinion of mathematics, The problems of this kind are analysed by means of the direct numerical method in this paper,The simple and convenient Draw Newton Method is applied for solving the parameter vectors in iteration course along with the calculation of a practical engineering problem.

日I崖旨J，'口工程中的一些实际问题往往可以归结为非线性自治系统，例如描述同步发电机暂态稳定性问题的转子摇摆方程，即是一典型的非线性自治系统。虽然可以用各种小参数摄动法求解非线性系统，但是这类方法是依据对线性系统的解进行"摄动"来逼近非线性系统解的。因而当系统

Apparently, the approximate controllability doesn"t hold for generally linear parabolic equations with bounded control. It doesn"t hold for the semilinear heat equations presented there,either. Then, it is proved by analyzing its" solutions that no matter how long the time T is , there are targets that can"t be approximated by the solution of heat equation with Dirichlet boundary conditions;If a given target satisying certain conditions can be reached by the solution of heat equation .

本文先针对两个具体的半线性热方程系统证明了控制加约束后系统是不能控的；然后通过分析方程的解，对带位势及Dirichlet边界条件的热方程系统，无论时间多大，都存在不能控的目标；文中还证明了满足一定条件的目标可达。

Secondly, the solution of the dirichlet's problem is given in semiexplicitformula, and under the special case the exact solution is obtained.

文章所论内容属当今数学的前沿问题，文章较好的解决了某些特定情况下的复杂问题，具有较高的理论意义和学术价值。

It is usually that the solution for the Dirichlet problem can not be obtained actually. With the development of computers, people pay more and more attention to the numerical solution. Many ideas and methods have appeared. Among them the finite element method has become most popular. But the finite element method has some weaknesses and limitations too. First, it is not fit to higher-dimensional problems.

绝大多数Dirichlet问题的解析解往往难以得到，随着计算机技术的发展，Dirichlet问题的数值解法越来越受到人们的重视，新的思想和方法不断涌现，其中有限元法已经发展成为目前求解Dirichlet问题的最主要的数值方法，但是有限元法解决该问题时，存在着一些弱点和局限。

It is usually that the solution for the Dirichlet problem can not be obtained actually. With the development of computers, people pay more and more attention to the numerical solution. Many ideas and methods have appeared. Among them the finite element method has become most popular. But the finite element method has some weaknesses and limitations too.

绝大多数Dirichlet问题的解析解往往难以得到，随着计算机技术的发展，Dirichlet问题的数值解法越来越受到人们的重视，新的思想和方法不断涌现，其中有限元法已经发展成为目前求解Dirichlet问题的最主要的数值方法，但是有限元法解决该问题时，存在着一些弱点和局限。

This paper introduces the food refrigerated theory and the basis of the current industry refrigerated developments in the situation; And then in the long cylindrical-shaped food heat conduction process and the mathematical model using the method of differential thermal conduction equations for discrete, Programming come through long cylindrical-shaped food cooling process numerical solution; After further analysis of numerical solution of the test results; Finally, the impact of the cooling process food all relevant factors, such as moisture content, wind speed and temperature of the cooling medium for in-depth research, while comparing the different shapes of food to food cooling process.

本文首先介绍了有关食品冷冻冷藏的基础理论和目前冷冻冷藏行业的发展的发展概况；然后研究了长圆柱状食品热传导过程的数学模型并利用差分的方法对热传导方程进行离散，通过编程得出长圆柱状食品冷却过程的数值解；之后再分析解对数值解的结果进行验证；最后对影响食品冷却过程的各相关因素，如含水率、风速和冷却介质温度等进行了深入的研究，同时又对比了不同形状的食品对食品冷却过程的影响。

Three solution algorithms for classical transportation continuous/discrete/ mixed network design problems are designed based on particle swarm optimization approach, in which the continuous NDP is studied in detail, discrete and mixed NDP are only described the frameworks of the solution algorithms.2. Generally, road capacity constraints must be added to the lower level problem of classical discrete NDPs bilevel programming model in order to avoid traffic assignment on candidate roads.

本论文研究工作主要有如下几个方面：(1)基于粒子群优化思想设计了求解传统的城市道路交通网络设计问题的算法，其中详细研究了连续网络设计问题，并用两个网络例子进行了数值实验；并给出了离散网络设计问题和混合网络设计问题的求解算法思路和主要步骤。

The work of this paper is as follows: 1. Looking back the progressing history of the linear motor, introducing the features of the elevator driven by linear induction motor, radicating the topic of this paper "the digital frequency variable control of the elevator bi-side direct driven by linear induction motor". The research of this paper covers the conventional VVVF control, space vector based VVVF control, vector control and DTC.

本文主要开展了以下几个方面的工作： 1 回顾了直线电机发展历史，电机的驱动技术演变，特别是针对直线电机的驱动，简要介绍了直线感应电机驱动电梯的优点和不同结构类型，对传统的v／f控制，基于空间矢量法的v／f控制，矢量控制，和基于电压空间矢量的直接转矩控制进行了比较，确立了本课题的研究主题：直线感应电机双边直推式驱动电梯的全数字变频控制。

The article combines with the treatment of a superficial civil air defense work to introduce how the grouting method to improve the performance of the backfill soil.

文章从治理漂浮人防工事的角度提出了注浆技术在改善回填土性质方面的应用，并详细阐述了注浆技术的施工流程。