1) generalized Riccati transformation
广义Riccati变换
1.
Oscillatory properties for solutions of a class of nonlinear hyperbolic partial functional differential equation with several delays were studied,and the new sufficient conditions for oscillation of these equations were obtained under the first boundary value condition by using the method of differential inequalities and the generalized Riccati transformation.
研究一类非线性时滞双曲型偏泛函微分方程解的振动性,利用微分不等式方法和广义Riccati变换,获得了该类方程在第一类边值条件下振动的新的充分条件,所得结果通过实例加以阐明。
2.
By using Green theorem and the generalized Riccati transformation,some sufficient criteria for oscillation of all solutions of such equations are obtained under two different boundary value conditions.
考虑一类非线性中立双曲型时滞偏泛函微分方程的振动性,利用Green定理和广义Riccati变换获得了这类方程在两类不同边值条件下所有解振动的若干充分判据。
3.
In the paper,we investigated a class of second order neutral delay differential equations with nonlinear second order part,and by using generalized Riccati transformation obtained sufficient conditions for the oscillations of them.
研究一类二阶部分为非线性的二阶中立型时滞微分方程,利用广义Riccati变换获得了该类方程解振动的充分条件。
2) Riccati transformation
Riccati变换
1.
Riccati transformation is used to consider third nonlinear difference equation of the form△[an△(bn△(xn - qn-r))] + qnf(xn-σ) = 0, (1)a new suffisanle criterion for oscillation behavior of all solutions of (1) is obtained and an example is given to explain the use of this criterion.
应用Riccati变换法对三阶非线性中立型差分方程 Δ[α_nΔ(b_nΔ(χ_n-p_(n-r)))]+q_nf(χ_(n-c)=0 (1)进行讨论,得出了方程解的振动性的一个充分性判据,并给出了具体实例。
2.
A sufficient condition on the oscillation of the second order nonlinear neutral dynamic equations is given bying generalized Riccati transformation and using analytic method and technique,and a property of a certain perturbed nonlinear dynamic equation is considered.
运用广义Riccati变换给出时标上二阶非线性中立型动力学方程振动的充分条件,进一步研究了具扰动项的动力学方程解的性态。
3.
Oscillatory properties of solutions of a class of nonlinear hyperbolic partial functional differential equations with multi-delays are studied and some new sufficient conditions for the oscillation of all solutions of the equations are obtained under two boundary value conditions by using the method of differential inequalities and Riccati transformation.
讨论一类多滞量非线性双曲型偏泛函微分方程解的振动性,利用微分不等式方法和Riccati变换,获得了该类方程在两类不同边值条件下振动的新的充分条件,通过实例对所得结果加以阐明。
3) Generalized partial Riccati transformation
偏Riccati变换
4) Riccati transformation
Riccati变换法
1.
Equivalence between generating function method and Riccati transformation method for LQ terminal control
LQ终端控制的生成函数法与Riccati变换法的等价性
5) generalized Riccati equation
广义Riccati方程
1.
On Integrability Conditions of Generalized Riccati Equation——To discuss about it with Mr.Zhao Linlong;
关于广义Riccati方程的可积条件——与赵临龙先生商榷
2.
The generalized Riccati equation is introduced in a class of uncertain nonlinearly generalized interconnection systems with saturation input to design the decentralized and generalized robust stabilization controllers relevant to such systems.
采用广义Riccati方程,对一类具有输入饱和的不确定非线性广义交联系统,给出了一种分散广义鲁棒镇定控制器的设计。
3.
This paper considers one kind of generalized Riccati equation.
考虑一类广义Riccati方程,通过函数变换,在所给条件下,将这类方程等价地化为变量分离方程,从而得到了该方程可积的三个充分性判据,并给出方程通解的参数表达形式,扩大了Riccati方程的可解性范围。
6) generalized Riccati technique
广义Riccati技巧
1.
By using the generalized Riccati technique,the averaging technique and differential inequalities,the oscillation for a class of higher-order nonlinear functional differential equations is discussed,and some new oscillation criteria are obtained.
利用广义Riccati技巧、积分平均与完全平方技巧以及微分不等式理论,讨论了一类高阶非线性泛函微分方程的振动性,并得到一些新的振动准则。
2.
By using the generalized Riccati technique,the averaging technique,the oscillation for a class neutral delay difference equations is discussed and new oscillation criteria are obtained.
利用广义Riccati技巧与完全平方技巧,讨论了一类中立型差分方程的振动性并得到一些新的振动准则。
3.
By the generalized Riccati technique,the averaging technique and differential inequalities,the oscillation for a class of high order nonlinear differential equations is discussed and new oscillation criteria are obtained.
利用广义Riccati技巧、积分平均与完全平方技巧以及微分不等式理论 ,讨论了一类高阶非线性微分方程的振动性并得到一些新的振动准则。
补充资料：Radon变换和逆Radon变换
Radon变换和逆Radon变换
X线物理学术语。CT重建图像成像的主要理论依据之一。1917年澳大利亚数学家Radon首先论证了通过物体某一平面的投影重建物体该平面两维空间分布的公式。他的公式要求获得沿该平面所有可能的直线的全部投影(无限集合)。所获得的投影集称为Radon变换。由Radon变换进行重建图像的操作则称为逆Radon变换。Radon变换和逆Radon变换对CT成像的意义在于，它从数学原理上证实了通过物体某一断层层面“沿直线衰减分布的投影”重建该层面单位体积，即体素的线性衰减系数两维空间分布的可能性。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条