可解方程

Based on this, to avoid using the Green′s formula on infinite domain, an infinitely differentiable function with compact subset is constructed and some important results to a especial solution of the inhomogeneous field equation are obtained.

在此基础上，为了避免使用无限区域上的 Green公式，通过构造紧支集上的无穷可微函数，获得满足非齐次控制微分方程的特解的重要结果。

As known, using the porential theory Green's tormulae and the fundamental solutions wecan reduce the harmonic and biharmonic elliptic boundary value problems to integral equationson the boundary.

我们熟知，利用位势理论或由Green公式及基本解出发区域内调和及重调和边值问题可归化为边界上的积分方程。

According to the boundary condition of the actual rectangular plates, it is very easy to get the characteristic equation for the problem through the boundary value of the generalized solution.

根据实际矩形板的边界条件，再应用弹性矩形薄板稳定问题的广义位移解的边界值，很容易便可得到该稳定问题的特征方程。

Using the results, some oscillatory criteria for solutions of the hyperbolic equation with distributed deviating arguments can be established.

运用本文结果可建立一类具有连续分布偏差变元的双曲方程解的振动准则。

For the ill conditioned load flow caused by the error produced in the transformation from electricity quantities to average power, direct current load flow and sensitivity vector are presented to find out the ill node, then by adjusting the load curve and generation curve in a certain principle, which is shown in detail with several flow charts, a new operation mode is reestablished to ensure the convergence of the calculation. Optimal multiplier method is proposed to work out the least square solution according to ill conditioned structural power network. The electricity quantities flow method enhances the reliability and accuracy of the calculation of the power transmission losses.

该方法可根据当前输电网中各个变电站24小时的电量记录，利用电量潮流计算对输电网总线损和各条线路损耗进行计算，使计算的精度满足降损措施分析和指标考核的要求；并且对于由负荷出力曲线转化成平均功率计算潮流时引入的误差，进而导致潮流计算不收敛的情况，采用直流潮流法，依据相角对有功功率的灵敏度向量判断出"网络异常点"，并且给出了解决此种情况的方法流程图；针对结构病态的电力系统潮流计算不收敛的情况，运用非线性约束优化方法中的最优乘子法求解潮流方程的最小二乘解，从而解决了电量潮流法计算理论线损时的收敛性问题，增强了该方法的适用性。

Ablish two decision theorems of relative compactness for unbounded function groups in an infinite interval.

sect；2.3我们建立了判定无穷区间上抽象无界连续函数组和抽象无界可微函数组相对紧性的充分必要条件，并对无穷区间上抽象二阶微分方程两点边值问题无界解的存在性做了研究。

The research on the explicit solution and integrability are helpful in clarifying the movement of matter under the nonlinear interactiveties and play an important role in scientifically explaining of the corresponding physical phenomenon and engineering application.

非线性演化方程精确解和可积性的研究有助于弄清物质在非线性作用下的运动规律，对相应物理现象的科学解释和工程应用将起到重要作用。

Adopting generalized Jordan block and algebra equivalence transform method, all of the transfer functions at different load points can be transformed to state-space description with time variable. The steady robustness of three different mode of control systems were researched by mathematic analysis. It shows that: for the high order inertia controlled object with the characteristic of nonlinear and time-variable that described by the set of transfer functions, the Luenberger function observer established according to its any algebra equivalence state-space description, if some conditions can be met, there would be a matrix of T with n′n satisfied the Sylvester matrix equation TA- FT=GC.

采用广义约当块及代数等价变换方法，可将分段的传递函数描述转换为变参数的状态空间描述，对3种典型控制系统的稳定鲁棒性所进行的理论研究表明，对同一组传递函数描述的具有非线性和时变特性的高阶惯性受控对象，依据其任一代数等价的状态空间描述所构建的Luenberger函数观测器，在满足一定的条件时，存在n′n解阵T满足Sylvester矩阵方程TA- FT=GC。

This thesis is devoted to study the properties of the solutions of some specialrefinable equations,such as properties of multi-refinable,global linear independence,local linear independence and local polynomial property,etc,by using fractal theory,measure theory and theory of generalized functions.

本文的主要目的是通过用分形几何中的一些想法以及测度论和广义函数中的一些知识来研究一些特殊的细分方程的解的一些性质，如多重可细分性、整体线性无关性、局部线性无关性和局部多项式性质等。

If 〓 is an absolutely continuousmeasure and is represented by a measurable function f on Q,then u is said tobe the generalized solution of(1),and 〓 to be the parabolic Monge-Amperemeasure.

定义1由legendre变换定义了一个Q上的测度〓（4）其中〓为〓空间中的Lebesgue测度，若〓是一个绝对连续测度且在Q上由可测函数〓表示，则称u为方程（1）的广义解、称测度〓为抛物型Monge-Ampère测度。

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。