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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。

The elegance and apparent usefulness of the new theory led to a string of Nobel prizes for its creators, and many of the theory's adepts also received more mundane rewards: Armed with their new models and formidable math skills — the more arcane uses of CAPM require physicist-level computations — mild-mannered business-school professors could and did become Wall Street rocket scientists, earning Wall Street paychecks.

这个新理论的优雅性和表面上的有用性，给它的创造者带来了一系列诺贝尔奖，而该理论的许多行家里手们，也获得了更为世俗化的回报：一些温文尔雅的商学院教授以簇新的模型和令人敬畏的数学技能来做武装——因为 CAPM 较深奥的应用要求物理学家水平的计算——可能而且的确摇身一变成了华尔街的火箭科学家，拿起华尔街水平的薪水。

Well, there he lay, and thought and thought, and all at once it was just as if someone kissed his eyes and mouth: he slept, and yet he did not sleep; it was as though the old washerwoman gazed on him with her mild eyes and said

他躺在那上面，想了许多事情。忽然觉得有人吻他的眼睛和嘴。他似乎睡着了，又似乎没有睡着。他好像觉得那个洗衣老太婆的温柔的眼睛在看他，并且对他说

This can be a mild case which clears itself or with the help of washes and medication.

这可能是一个温和的情况下它清除自身或与药物帮助洗涤和。

The success of the crop was attributed both to an unusually mild winter and to the "virtual disappearance of the spaghetti weevil."

备受尊敬的该频道的节目主持人 Richard Dimbleby 在节目中说这次的大丰收主要归功于罕有的温和天气以及"象鼻虫的消除"。

Well-meant admonitions.5. Mild, kind, yet earnest reproof.

告诫，劝谏温和的，和善的，但诚挚的谴责

County on behalf of rice wine, wine-colored, golden, mellow mild, hot drinks taste the best.

代县黄酒，酒色金黄，温和醇香，热饮味道最佳。

Supposing you were to say twelve months for the theft, which is mild; and three years for the furious driving, which is lenient; and fifteen years for the cheek, which was pretty bad sort of cheek, judging by what we've heard from the witness-box, even if you only believe one-tenth part of what you heard, and I never believe more myself—those figures, if added together correctly, tot up to nineteen years

三项加在一起，总共是十九年——

Mellow woodiness with hints of herbs and subtle honey with a mild and toasted tobacco taste leaving a pleasant smooth woody and sweet aftertaste.

温和的木味，少量的香草为和淡淡的蜜香甜，温和的烤烟味，这些味道都留给人一种惬意顺滑的木甜余味。

This new method features mild reaction conditions and facile work-up.

3%。结论：该合成方法反应条件温和后处理简单，是一条经济的合成路线。

He paid $5,000 for this cupcake.

他我这个纸杯蛋糕花了5000美元。

I mean, if you want to, that is

我的意思是，如果你们想吃的话。