二次形式

This paper discusses the broad-sense relation between solution and coefficient of some special kinds of second order variable coefficient and homogeneous linear differential equation,and have a try of giving a general form of common solution and the coefficient decision formula of special solution.

探讨了某些特殊类型二阶变系数齐次线性常微分方程的解与系数的广义关系，尝试了从理论上给出通解的一般形式和特解的系数决定式。

Compared with deterministic systems, the infinitesimal generator for the system is a second-order differential operation. In this dissertation, we designed the quartic control Lyapunov function and systematically design the state-feedback and output feedback adaptive controller using integrator backstepping methodology. The closed-loop system is asymptotically stable in the large.

与确定性系统相比，随机系统的Lyapunov函数的微分运算包含二阶导，所以设计适当形式的控制Lyapunov函数十分关键，本文设计了四次型的控制Lyapunov函数，并应用积分反推技术，给出了状态反馈及输出反馈自适应控制器和鲁棒自适应控制器的设计方法，证明了闭环系统概率意义下的渐近稳定性和有界稳定性。

In Chapter 4 we discuss the solvable theorem of adaptive inverse optimal control problems, and proceed with controller designs of global asymptotic stability in probability, adaptive inverse optimal stabilization in probability and output-feedback adaptive inverse optimal stabilization in probability for strict-feedback stochastic nonlinear continuous systems with additive standard Wiener noises and constant unknown parameters using It〓's differentiation rule and an adaptive backstepping algorithm. Control laws and adaptive laws can be obtained at one time by this design scheme. Many simulations have been performed to validate the properties of the proposed adaptive control scheme.

在第4章中，针对具有标准Wiener噪声扰动和未知定常参数的不确定随机非线性系统，提出并证明了自适应逆最优控制问题可解定理，构造了适当形式的四次型随机控制Lvapunov函数，基于It〓微分规则和自适应Backstepping算法，系统地设计了全局依概率渐近稳定控制器、自适应逆最优控制器、输出反馈逆最优控制器以及在设计中如何处理二阶Hessian矩阵函数的方法，这种方法可同时获得控制律和自适应律，通过实例仿真，表明该控制算法是有效性的。

By using a similarity transformation, the Navier-Stobes equations in the cylindrical co-ordinates for the steady incompressible flow are reduced to an ordinary non-linear differential equation of the third order.

利用相似转换，将不可压缩流体，定常运动，柱坐标形式的纳非尔-斯托克司方程组简化为一三次非线性常微分方程，运用小参数法及适当边界条件求出此方程的解，结果表明，吸吮或吹注对流动的速度分布，沿流程压力下降和摩擦系数均有显著影响，其影响的大小，依赖于吸吮或吹注的性质，程度及二圆管的相对尺度。

At metaphase Ⅰ, 7 bivalents were frequently detected to separate into three groups, with a form of 3+2+2, which indicated that at least four translocation events once occurred.

在中期Ⅰ，7个二价体出现分组分布现象，主要以3+2+2形式存在，表明其至少经历了4次染色体易位。

Daubechies'wavelet frame theorem is extended from one dimension to n dimensions. According to this framework, an example of n-dimensional radial wavelet is given. Differing from tensor product multidimensional wavelet, the radial wavelet is inseparable, locally supported and infinitely differentiable. The family, obtained by dilations and translations from this radial wavelet, constitutes a special type of radial wavelet frame in L〓.

Daubechies的框架定理推广到了n维情形，同时，也按照这一理论框架，给出了高维二进径向小波的具体例子，具有下列性质：ψ是无穷次连续可微的；ψ是局部支撑的，支集为‖x‖≤1；ψ含有分式因子，因此对&奇异点&更为敏感；ψ是不可分的，不同于张量积形式的高维小波；ψ是各向同性的。

Documentary and FabricationWang Anyis discussion on documentary and fabrication which seem to be two different kinds of writing methods practise her novel theory at the same time produce a new kind of novel form and novel-writing possibility.

二纪实与虚构纪实与虚构，是两种看似相悖的小说写作手法，王安忆对纪实和虚构的探讨，既是对自己已有的小说理论的一次实践，又同时创造了一种新的小说形式和小说创作的可能性。

There is no clear date of foundation, but teaching existed at Oxford in some form in 1096 and developed rapidly from 1167, when Henry II banned English students from attending the University of Paris. In 1188, the historian, Gerald of Wales, gave a public reading to the assembled Oxford dons and in 1190 the arrival of Emo of Friesland, the first known overseas student, initiated the University's tradition of international scholarship.

虽然没有牛津大学宣称确切的建校时间，但是它的某种形式的教学活动在1096年就已经存在，从1167年开始迅速发展，当时亨利二世下令禁止英国的学生到巴黎大学。1188年，威尔士的历史学家杰拉德向集会的牛津大学教师作了一次公开的阐释。1190年，荷兰的弗里斯兰省的艾默，第一位著名的留学生，开创了牛津大学国际奖学金的传统。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。