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The world seems to be exponentially spirally downwards with calamities and problems being borne faster than solutions can be thought up.

不断冒生的灾难与问题让人来不及解决，世界性的恶性循环正在加速进行。

And it was proved that the stabilization controller through the proposed method could guarantee all the states of n-dimensional system exponentially converge to the origin.

并证明了利用该方法设计的控制器可使得高维链式系统各状态指数收敛于原点。

BACKGROUND: Recently, the interest in micellization of amphiphilic star-shaped polymer has exponentially increased in the field of drug delivery.

摘要背景：近年来，在药物载体材料领域，两亲性星形聚合物的自组装胶束化引起了人们的关注。

As a result, CDNF algorithm had better performance than tableaux by saving spatial cost linearly or even exponentially.

因此，CDNF算法比Tableau算法能节省线性甚至指数倍于输入概念描述长度的空间代价。

The results show that the absorbed SO_2 per unit volume of slurry is related exponentially to the slurry pH.

根据试验结果，提出了单位体积浆液吸收SO2的量与浆液的pH值呈幂函数关系。

Russell([17]) has showed that, a compact perturbation, generated from unitary operator groups in infinite-dimensional linear Hilbert spaces, is unable to make the perturbed semigroup exponentially stable.

Russell([17])曾指出，无限维Hilbert空间中的酉算子群对生成的紧扰动不能使被扰动半群具有指数稳定性。

In the context of the string theory landscape, the overall number of different universes is expected to be exponentially greater than the total number of vacua in the landscape.

当然，作为一直以来倾向相信暗能量其实是全息暗能量的我来说Linde等人的多元宇宙完全是多余的垃圾-当然是超级庞大的垃圾场。

Some sufficient conditions are presented, which all solutions of the proposed neural network are globally exponentially convergent to the unique solution of the linear variational inequality problem.

得到了一些保证该神经网络的所有解全局指数地收敛到线性变分不等式问题的解的充分条件。

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。

Root length density of Abies fabri, whose root system is horizontal, decreased exponentially with increasing of soil depth.

峨眉冷杉属于水平根系树种，其根长密度随土层深度的增加呈指数递减。

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。