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In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

YE Zhong-xing, ZENG JinDept. of Applied Math., Shanghai Jiaotong Univ., Shanghai 200030, ChinaAbstract: Genetic algorithm, evolutio nary programming and evolution strategies are all based on the idea of natural e volution. Those algorithms are differentiated by the way of getting new generat ion. But the new one is related with the last generation only.

摘 要：遗传算法、进化规划和进化策略这三类进化算法都是基于对自然进化的模拟，其区别在于产生下一代群体的规则不同，但下一代群体的产生又都是仅依赖于其父代，因而进化算法的运行过程可以视为一个Markov过程，其状态转移矩阵可以表示成一个统一的形式。

The dominant vortical structure in the wake of the impinging jet in crossflow is primarily dependent on the velocity ratio.

横流冲击射流中形成的主要尾迹涡结构主要依赖于流速比。

Other all systems soft ware and application software must depend on the support of the operating system .

其它所有的系统软件和应用软件都必须依赖于操作系统的支持。

The ratio and the magnitude of warpage depend on the compound properties.

封装的翘曲率及翘曲幅度依赖于模塑料的特性。

This paper implements the Dealer Management System based on WebWork,Spring and Hibernate architecture.

这种管理不仅依赖于企业及经销商的员工，同时也需要企业及经销商稳

That used to be bad for business in Xinjiang, the most westerly region of China, which formerly depended on the trade route between central Asia and the densely populated cities in the far east.

这样恶劣得条件曾经给中国西部边陲省份新疆的商业活动带来了很大的阻碍。以前新疆地区的商业是依赖于中亚和内地人口密集的城市之间的贸易往来而得以发展的。

Business relies heavily on information technology – and Westwood graduates help fill this crucial need.

业务依赖于信息技术的大量-维斯特伍德毕业生和帮助填补这一迫切需要。

For example, constant modulus of levy and the increments of a Wiener Process all depend on this inequality.

关于Wiener过程增量的尾概率的估计不等式在讨论Wiener过程增量的性质中十分有用，像Levy连续模定理及Wiener过程增量有多大的证明都依赖于这一不等式。

For example, constant modulus of levy and the increments of a Wiener Process.

关于Wiener过程增量的尾概率的估计不等式在讨论Wiener过程性质中十分有用，像Levy连续模定理及Wiener过程增量有很多的证明都依赖于这一不等式。

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。