查询词典 consistent equations

In Chapter Ⅲ, by considering functions H k that may not have nonpositive partial derivative on s and employing integral averaging technique and Hardy inequality, the oscillation for a class of high order nonlinear differential equations and high order nonlinear damped differential equations is discussed, new oscillation criteria are established.

第二章利用广义Riccati技巧、积分平均技巧以及微分不等式理论，讨论了一类二阶非线性常微分方程的振动性，得到了若干新的振动准则，并讨论了该方程具有强迫项时解的渐近性态。

Finally, natural frequency is obtained by the existence condition of nontrivial solution of the numerically discrete algebraic equations derived from the integral equations.

最后由积分方程的离散化方程组有非平凡解的条件，求得固有频率。

The main results and novelties of the paper are as follows:Firstly, we study the existence of nontrivial solution for the following nonlinear equations with singular pontential By using variational methods and critical point theory, we construct linking type critical value of this kind of singular elliptic equations, with the properties of the eigenvalue, we estimate the critical value and prove the local condition holds to show the existence of the nontrivial solution.

论文的创新点及主要结果如下：首先研究有界区域上具有奇异位势的非线性方程的非平凡解的存在性，运用变分方法与临界点理论，构造这一类奇异椭圆方程的环绕型临界值，并由特征值的性质给出临界值的估计，同时证明局部条件成立，最终证明方程非平凡解的存在性。

The existence of global weak solution for a class of generalized Ginzburg-Landau equations with an inhomogeneous boundary condition was studied. Some integral indentities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained.

研究具非线性边界条件的一类广义Ginzburg＿Landau方程解的整体存在性·推导了Ginzburg＿Landau方程的非齐次初边值问题光滑解的几个积分恒等式，由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计；通过逼近技巧、先验估计和取极限方法证明了Ginzburg＿Landau方程的非齐次初边值问题整体弱解的存在性

One of the primary methods to solve them is numerical method, and the other is Galerkin method, which change partial differential equations into normal differential equations, and then solve them with the traditional method.

小波分析已成为当前应用数学中迅速发展的新领域，它可以解决Fourier分析不能解决的许多困难问题，是近年来在研究工具及方法上的创新，已成为众多学科共同关注的热点。

The distributions of transversal shearing and normal stresses obtained from constitutive equations and those from equilibrium equations agree with each other very well.

通过这部分的分析，得出了一个重要结论：根据该分析方法，由平衡方程与由物理方程得到的横向剪应力及横向正应力分布相当一致。

The variational principle of generalized potential energy is used to determine the unknown coefficients of above series. The distributions of transversal shearing and normal stresses obtained from constitutive equations and those from equilibrium equations agree with each other very well.

通过这部分的分析，得出了一个重要结论：根据该分析方法，由平衡方程与由物理方程得到的横向剪应力及横向正应力分布相当一致。

In the modeling of growth macroeconomic rational expectations , using the method of quadratic optimal dynamic programming, the steady state equations of Riccati equations under normal conditions is discussed, which makes a firm basis for the modeling of macroeconomic rational expectations .

针对采用二次最优动态规划建立的宏观增长经济合理预期模型，探讨了Riccati递推方程的稳态方程求取问题，推导出了一般情况下的Riccati稳态方程，为建立合理预期数量经济模型奠定了基础。

Now the scientific workers can evaluate them by Group contribution methods,some equations using other normal properties and some equations using the existed equation for other properties.

现有的估算方法主要分为基团贡献法，与某些常用物性相关联的经验或半经验估算式和基于某些求取其它物性的方程的经验或半经验估算式等。

For the LS problem, the method of normal equations needs less computation but its computed solution has poor accuracy. If QR factorization is used, more accurate solution can be got. However, its computation is nearly as twice as the method of normal equations.

对于线性最小二乘问题，混合方法的提出是企图在法方程法与QR分解方法之间取得某种平衡，希望能够节省计算量又同时保持计算解达到较高精度，但后者在理论上并未得到证明。

"The operators will suffer a temporary decrease in the number of consumers and short message services as people may not like having to provide their ID cards for a phone number," Xu Junqi, vice-dean with the Policy-Making Institute of the Telecommunications Research Centre under MII, said yesterday.

信息产业部下属的通信决策研究院副主任徐俊其昨天说：&实行手机实名制后，人们可能不太情愿用身份证注册手机号，所以通信运营商会暂时面临用户减少和短信用户减少的问题。&

I don't believe in make-believe!

我不相信这些虚构的故事。