可解方程

Then, the steady-state productivity model for horizontal well in gas reservoir is established. On the basis of solving the model, this thesis deduces the binomial deliverabiliry equation by which absolute open flow potential and inflow performance relationship can be gotten and we can forecast the production performance of horizontal well in gas reservoir.

其次，在建立水平气井稳定渗流的数学模型并求得其解的基础上，推导出了考虑地层伤害及非达西渗流影响水平气井二项式产能方程，通过该二项式产能方程可求出水平气井的绝对无阻流量，绘制流入动态关系曲线来预测生产动态。

Nonlinear wave system; Exact solution; Approximate solution; Soliton; Riccati equation method; Turing machine; Computable function

非线性波系统；精确解；近似解；孤立波； Riccati方程方法；图灵机；可计算函数

MVFK8vP7Ge+Uu0 Nonlinear wave system; Exact solution; Approximate solution; Soliton; Riccati equation method; Turing machine; Computable function

非线性波系统；精确解；近似解；孤立波； Riccati方程方法；图灵机；可计算函数

This paper discusses a variation equation problem in a class of singular stochastic control with stopping time,gives its solution under two different conditions,which is a one order continuous differentiable and concave function,and gives the exact form.

讨论了一类带停时的奇异型随机控制问题中的一个变分方程问题，并且在两种不同的情况下给出了该变分方程的解，即为一阶连续可导凹函数，并在两种情况下给出了此函数的具体形式。

According to the principle of the diameter of a circle corresponding to the right angle and the principle of short side for little angle in right triangle, projecting the initially-chosen point to the hyper-planes of the linear equation group in which every linear equation can be regarded as a hyper-plane and the projection points can be obtained. The initially-chosen point, and one arbitrary projection point, and the solution point are all on the surface of the relative hyper-geometry ball, therein-to, there is a projection point which is nearest to the solution point and it can be regarded as the next iterative initially-chosen point, so the solution problem of the linear equation group can be changed as an iterative problem of approaching the solution on the surface of a hyper-geometry ball.

根据直径对应的圆周角足直角以及直角三角形中短边对小角的原理进一步知道，当将初始点向线性方程组中各个方程所代表的超平面上投影得到投影点时，初始点和其任何一个投影点及方程组的解点都将位于一个相应的超球面上，其中必定存在一个投影点离问题解点的距离最短，即把该点作为下一次迭代的初始点，从而可将线性方程组求解的问题变成球面上逼近解点的迭代问题。

Finally, we study the eventual differentiability of a C_0-semigroup associated to a waveequation with boundary dissipation.

最后，我们讨论了一类具边界耗散的线性双曲型方程生成的算子半群的最终可微性，并利用这个结果得到了方程的解具有最终正则性以及半群满足谱决定增长条件。

At the latter consolidation stage, it was assumed that the water flow only depended on water pressure and was not influenced by the air. Then the independent continuity equation of water was set up to solve variation of water pressure with time. Besides, the water and air were regarded as mixed fluid, and the continuity equation of mixed fluid was set up.

在其后的固结过程中，假定水的流出仅仅取决于水压力，不受气的影响，单独建立水的连续性方程，解水压力随时间的变化；又将水和气看成混合的可压缩流体，建立混合流体的连续性，解混合流体压力随时间的变化。

Many high-rise buildings can be simplied into variable cross-section cantilever beam, which equation of free vibration is variable coefficient differential equation of higher order and there is no general solving process for which in mathematics.

对这类方程，数学上没有提供一般的解法。本文采用的级数解法可求出任何变系数的四阶微分方程，在给定边界条件下的解。

Integrate the load transfer principle and shearing displacement method to set up the load transfer equation between the pile of soil, using the discrete and fitting methods to solve the equation so as to educe the pile displacement of arbitrary section as well as the analytical solution. Comparing the results with the soil settlement solved by the Mair equation, the relative displacement can be gained.

1结合荷载传递原理和剪切位移法的思想建立隧道开挖作用下的桩土荷载传递方程，采用离散和拟合两种方法来对该一元二次非齐次微分方程进行求解，可分别得到桩身任意截面处的桩体位移以及桩身位移的解析解，并与基于Mair公式求得的地面下任意深度处的土体沉降进行比较，即可求出桩与桩侧土之间的相对位移。

By using the classical or nonclassical Lie symmetry method we can get amount of exact solutions of the nonlinear differential equations.

李群方法是研究非线性微分方程的有力工具，应用经典或非经典李群方法，可得到大量非线性微分方程的精确解。

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。