查询词典 integral calculus

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 discrete equation was deduced by control volume integral method, and realized by numerical method.

用控制容积积分法导出了离散方程，并用数值方法进行了求解。

By volume integral can be divided into: large, medium, small and micro.

可分为：大型，中型，小型和微型。

Control Volume Analysis, Integral Methods.

控制体积分析，积分方法。

In order to use the analytical results of three dimensional crack problem of infinite bodies and avoid the volume integral in numerical analysis.

为了充分利用三维裂纹问题的解析结果。以及避免数值分析中出现体积分。

The relative variational rate of the volume and shape of particles is 8.4% and 12.5%, and the contribution to integral volume is 1.68% under the general condition.

一般情况下，颗粒的体积和形状的相对变化率分别为8.4%和12.5%，对总体积变化率的贡献为1.68%。

It avoids the internal resonance phenomenon, and smaller dimensions of the impedance matrix are obtained by comparison with the volume integral equation.

推导一种用于求解介质体散射问题的面积分方程，它克服了内谐振现象，且同体积分方程相比，获得了更小的阻抗矩阵维数。

The term involving the time derivative of the control volume integral represents unsteady effects associated with the fact that values of the parameter within the control volume may change with time.

这条件包含了控制体积积分法内，与在控制容积中的参数可能会随时间改变这个事实所相关的非定常效应。

A negative correlation was found between the change of proximal gastric volume and integral alleviation of dyspepsia symptom in patients with chronic gastritis.

慢性胃炎患者近端胃的体积变化与消化不良症状积分缓解之间呈显著负相关关系。

Volume integral equation method has been used to calculate forward and inverse problems of 3D electromagnetic fields in homogeneous half-space.

0引言在电磁法勘探中，利用体积分方程计算三维地电磁场，由于数据点只分布在电阻率异常区域[1~3]而不是整个三维空间，因而与有限元法和有限差分法相比其计算量相对较小，是进行地电参数正反演计算的有效方法。

The network space is the typical form of abstract space when it comes to the digital stage.

网络空间是抽象空间数字化阶段的典型形式。

The Notarial System,as the system of judicial certification in our country,is both the constructor and the defender of social credit system,It has its special value and function in the social honesty.

公证制度作为我国司法证明制度，既是社会信用体系的建设者，同时也是社会信用的捍卫者，在诚信中有其特殊的价值和功能。