可解方程

We can realize the special Abel equation integrability and accurate solution by computer.

实现了计算机对该类方程可积性及其精确解的自动判定。

We characterize the optimal value function as the viscosity solution of the associated Hamilton-Jacobi-Bellman equation and we prove that there exists an optimal barrier strategy which is optimal among all admissible dividend strategy in some special cases.

通过HJB方程的粘性解理论来刻画最优值函数，并证明了一些特殊情形下界策略在所有可允许的分红策略中是最优的。

In this chapter,we will give the relation between attainability of this LQ problem and the stabilizing solution of one kind of algebraic Riccati equation.

我们给出了这类二次最优控制问题的可达性和一类代数黎卡提方程的稳定解之间的联系。

That the coefficient matrix of the reduced linear correction equation has arrow-shaped block structure and can be accurately decomposed into 25 sets of low-dimension linear equations by two algorithms was proposed.

该文指出其修正方程系数矩阵可具有箭形分块结构，可采用两种方法将其精确解耦为25个低维线性方程组。

In a steady compressible flow, if the method of stream function is applied, the stream is satisfied by a specific boundary value problem for partial differential equation of quasilinear elliptic type when the flow is subsonic.

可压缩流动；马赫数；西安交通大学；函数方法；流函数；有限元解；稳定的可压缩流动中，若用流函数方法，当流动是亚音速时，则流函数满足一种特殊的拟线性椭圆型方程的边值问题。

By using the theories of conservation of momentum,conservation of energy and hydrokinetics,a mathematical model for describing the relationship among the fluid parameters,the formation parameters and the vibrant operation parameters was established.The analytic solutions of one-dimensional and radial transfusion equation for compressive and single-phase fluid flow through the compressive formation were obtained.The effects of each parameter on the vibrant operation were also gotten.On the basis of the above results,the computation models were established.

应用动量守恒、能量守恒、流体动力学等基本原理，建立了地层参数、流体参数和振动作业参数之间相互耦合的数学模型，求出了单相微可压缩流体在可压缩地层中的平面一维和平面径向渗流方程的解析解，得到了各项参数与振动作业效果之间的关系，为振动采油的数值模拟提供了初始压力分布表达式。

The powerful function of a new computer language MATLAB, produced by the America Mathworks company, is the mathematical software system for the calculation in science engineering. It can efficiently solve problems in science and engineering such as numerical linear hypercomplex system, digital approximation, optimization, numerical quadrature etc. It also has characters of beautiful interface and convenience for users.

MATLAB是Mathworks公司推出的适用於科学和工程计算的数学软件系统，可高效地解决数值线性代数、微分方程数值解、数值逼近、最优化、数值积分等科学和工程问题，且具有可视化图形处理、使用方便、开放式多功能於一体的新一代计算机语言。

The numerical solution showed that the control strategy in this paper was effective.

数值模拟结果表明，文中的控制策略是可行的，而且可通过文中的方法可得到矩阵黎卡提方程的精确解(在计算机有效精度范围内)。

The first conclusion infers the sufficient condition with the aid of thealgebra Riccati equation solution and the semi-group theory nature which the systemmay optimize;Next discussed when the system operator characteristic vector forms theRiesz base,causes control function concrete mathematical expression which its systemmay optimize;Finally summarized the system to be possible to optimize the researchnewest conclusion and the research forecast.

第一个结论借助代数Riccati方程的解及半群理论性质推导出系统可最优化；其次讨论了系统算子的特征向量形成Riesz基时，使其系统可最优化的控制函数的具体数学表达式；最后总结了系统可最优化研究的最新结论和研究展望。

In order to obtain more exact analytical solution to study the output characteristics of double-clad fiber lasers,according to the continuous-wave rate equations of fiber lasers,using typical parameters of double-clad fiber lasers,the contribution of the re-emission effect arising from the interaction between the upper-level atoms and pump light was estimated.Taking into account the predominant part of the re-emission to improve the accuracy of the integration approximated rate equations,the integration of the product of the loss and radiation should be found and explicit analytical expressions for the output of the DCFLs and gradient efficiency of the pump radiation,were deduced,and certain issues of concern were discussed.

为了求得用于研究双包层光纤激光器输出特性的更为精确的解析解，根据稳态速率方程组，针对典型的双包层光纤激光器参量，在估计了上能级粒子再发射项和抽运光产生的影响后，采用保留再发射贡献主导部分的办法以提高可积分近似方程的精确度，明确地提出了要获得光纤激光器输出功率的解析表达式的关键在于求出损耗系数与光场乘积的积分值，简洁地求得了输出功率和抽运光斜线效率的显函数解析表达式，并对其相关问题进行了讨论，以915nm，920nm和975nm的抽运光为例，当输出激光为1090nm时，得出975nm抽运光产生的斜率效率最高并可高达约87%。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。