查询词典 mapping theorem

After a detailed discussion of the variation theorem for upper bound calculation of eigenvalues, many standard procedures for determining lower bounds to eigenvalues are presented with chemical applications in mind.

本文将介绍无元素葛勒金法，此无元素法为利用变动最小二乘法所求的近似函数引入葛勒金弱式推导。可克服有限元素在工程上的限制。

In the thesis a novel formulation of variable-domain variational principle for fluidmechanics has been successfully deduced,and the Kelvin's theorem has beenextended to steady compressible ones.

本文还排导得到了一个新型的变域变分公式，并把Kelvin原理推广到定常可压无旋流体。

It is consistent with the results obtained by central manifold theorem or variational method.

这与用中心流型定理或变分法证明离散呼吸子的存在性得到的结果相同。

Based on the decomposition theorem for vector space with module structure and rational canonical form of matrix, a kind of new block diagonal controllably canonical forms are inferred when the time invariant linear multivariable system is completely controllable, which the system matrix is similar to a block diagonal and has an analogy with its rational canonical form. Compare with current controllability canonical forms, this kind is easier to analyse the system constructional characteristic. The process of proof gives an effective solution method.

基于向量空间的模结构分解和矩阵的有理标准形给出了定常多输入线性系统一类新的块对角可控规范型，其中的系统矩阵相似与一个块对角矩阵，该块对角矩阵类似于矩阵的有理标准形，与现在有的可控规范型比较，更容易反映系统的结构特征，证明步骤给出了求解方法。

The versal unfolding theorem obtained in this paper by using DA-algebras tools introduced by Damon not only includes many corresponding results but also cancels the stronger demand on the codimension of a bifurcation Problem in some of relevant references to establish more general unfolding theory.

本文第二章进一步研究在(来源：AB00c6C论文网www.abclunwen.com)接触等价群作用下上述等变分歧参数及其开折的稳定性问题，得到了这类分歧问题是稳定的等价于它是无穷小稳定的结论，并且用横截性条件刻画了这类分歧问题的稳定性。

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。

Using the divergence theorem, converted the area integral of the flux of stress for the surface force to a volume integral of the divergence of stress.

应用散度定理，将通量应力的面积积分转换成应力散度的体积积分。

Moreover, we design a testing method based upon Wald theorem for the specification of model, thus greatly facilitates and extends the specification test of Panel Data model.

此外，本文设计了一种基于Wald定理的模型设定检验方法，极大的方便和拓展的Panel Data模型的设定检验。

For diffusive Predator-Prey model with Holling-Ⅲ functional response without time delay, shooting argument together with LaSalle's Invariance Principle and the Hopf bifurcation theorem are applied to prove the existence of traveling wave solutions and small amplitude traveling wave train solutions.

在数学理论的研究中，行波解可以揭示方程本身的许多重要性质；在实际应用中，行波解可以很好的表现自然世界中的振荡现象。因此，对反应扩散方程行波解的研究具有非常重要的意义。

Finally,usingHodge decomposition theorem,domain variations theory and capacitytheory,we prove that the continuity of very weak solutions of a classof nonlinear elliptic equations on varying domains.

最后，使用Hodge分解、区域拓朴和容量理论，我们证明了一类非齐次半线性椭圆型方程很弱解关于区域的连续依赖性。

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。