算子方程

It proves the singular transport operator generates a strongly continuous C_0 semigroup V(t0)and the weak compactness properties of the second-order remained term of the Dyson-Phillips expansion for the C_0 semigroup V(t0)in L1 space,and to obtain the spectrum of the singular transport operator only consist of,at most,finitely many isolate eigenvalues which have a finite algebraic multiplicity in trip Γ.

证明了这类方程相应的奇异迁移算子产生C0半群和该半群的Dyson-Phillips展开式的二阶余项是弱紧的，从而得到了该迁移算子的谱在区域Γ中仅由至多有限个具有限代数重数的离散本征值组成等结果。上饶师院数学与计算机系江西上饶334001；南昌大学数学系江西南昌330047袁邓彬

The operator can bedetermined through some ancilla differential equations.Using this operator,theexact solution of the ion's motion can be obtained.

通过对一组辅助的微分方程的求解，可以得到演化算子中的各个参数，并可用这一演化算子精确求解囚禁离子的含时量子运动。

In the second chapter, the suspension bridge equation on unbounded domainR1 is considered. Applying with the method of decomposing operator and thetheory of constructing some compact operator in weighted space, the existenceof global attractor is obtained.

在第二章中，运用带权空间构造一类紧算子和算子分解的方法，研究了该方程在无界区域R1上的情形，得到了其全局吸引子的存在性。

In the frame of TTE, this work proves that the resolvent operator of compound KDV equation is computable.

本文在TTE的框架下，运用算子理论和方法，证明了组合KdV方程的解算子是可计算的，从而可以。。。

This paper is to research singular transport equations with anisotropic continuous energy homogeneous slab geometry for periodic boundary condition in slab geometry.

在Lp1周期边界条件下各向异性、连续能量、均匀介质的奇异迁移方程，证明了其相应的奇异迁移算子产生C0半群和该C0半群的Dyson-Phillips展开式的二阶余项是紧的，从而该算子的谱在区域Γ中由具有限重的离散本征值组成等结果。

In this thesis, we express one dimension wave equation by arithmetic theory and prove D'Alembert Solution in the light of method on one stage linear partial differential equations.

本文从另一角度即算子的方法，将弦振动方程写成算子的形式，再根据一阶线性偏微分方程的求解方法，最终推导出D'Alembert公式。

Poisson's equation:In space where the source density is ρ, the Laplacian of a : potential U is 2 U = 4πρK, where is the operator del and K is a constant (gravitational constant in case of mass and gravitational potential).

泊松方程：在源密度为ρ的空间中，位场 U 的拉普拉斯算子为： U = 4πρK，。在米-千克其中为 del 算子，K 为常数(质量的万有引力常数和重力势)秒单位制中应去掉常数 4π。

This paper is the continuance of that of Lewalle (2001). Lewalle has made use of Gaussian wavelet to obtain the N-S equations with flexion as fundamental quantity in the infinite domain. In that work, Lapalace operator has been degraded to one-order operator. Moreover the resulted N-S equations take the form of diffusion equations with local bilinear mutual interaction kernel.

本文是Lewalle工作的继续，Lewalle利用高斯子波，得到了以弯曲度为基本量的无穷域中N-S方程，此时Lapalace算子降低为一阶导数，并且N-S方程变形为具有局部化双线性相互作用的扩散方程的形式。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

An example of these maximal monotone operators is the subdifferential of a closed convex function.

这种多值极大单调算子的一个特殊例子是闭凸函数的下微分算子，所以本文考虑的多值随机微分方程包含了在凸区域内具有反射边界的随机微分方程。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。