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Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics.

角动量：算符，对易代数，本征值和本征态，球谐函数。

Finally we also study some operators in spinor QED which give gauge independent matrixelements when acting on some specific states.

最后我们还研究了旋量电动力学中的一些算符，这些算符作用到某些特定态上时也给出规范无关的矩阵元。

"The MLS is our response to numerous requests for a mid-web press splicer and is an ergonomic solution that operators find particularly user friendly," reports David Wright, Vice President of Sales and Marketing.

"在大联盟是我们回应的中卷筒纸印刷机熔接机的许多要求，是符合人体工程学的解决方案，运营商发现，特别是用户友好的，"报告大卫赖特，销售副总裁和市场营销。

Applicable to a variety of industries and the operators of the spraying.

适用于多种行业的喷涂和机械操作。

On the other hand, for operators, standardized management and operation of more conducive to their development.

另一方面，对经营者来说，规范化的管理和经营更加有利于他们的发展。

And developers, logging companies, and strip-mine operators on the edge of the swamp can easily upset the delicate balance of nature in the area.

在沼泽边缘的开发商，伐木公司和露天开采商轻易地就能破坏这个地区大自然微妙的平衡关系。

Therefore, it's natural to estimate those values of operators such as 〓, log mf and so on in order to investigate the weighted inequalities for the minimal operator We discuss them under two conditions respectively: In one-weight case, we establish the relative weighted inequalities under the condition of A〓-weight and A〓-weight respectively, and the equivalent condition has been found between the strong -type weighted inequality and the property of W〓-weight; while in the case of two-weight condition, we characterize the equivalent relations between the weak type weighted inequality and the property of W〓-weight, the strong -type weighted inequality and the property of W〓-weight.

我们分两种情况分别加以讨论：单权情况下，我们分别刻画了A∞权和A〓权条件下关于〓，log mf等的强型加权不等式，并证明了关于鞅的极小算子的强型加权不等式与对应的W〓权性质之间的某些等价关系；在双权情况下，我们刻画了关于极小算子的弱型加权不等式与W〓权以及强型加权不等式与W〓权之间的等价关系。

By means of the concept of η-subdifferential, this paper employs a new method and constructs resolvent formula of η-subdifferential operators.

本文用一种新颖的方法，借助于η-次微分的概念，构造η-次微分算子的预解式来逼近问题的解。

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。

In this paper, by using the notable Mountain Pass Lemma of critical point theory, some sufficient conditions for the existence and multiplicity of periodic and subharmonic solutions to a class of second order nonlinear functional difference equations with Jacobi operators are obtained.

论文研究了一类具有Jacobi算子类型的二阶非线性泛函差分方程(1)的周期解和次调和解的存在性与多重性。首先将方程（1）的解的存在性问题转化为某个泛函临界点的存在性问题，然后验证此泛函满足著名的山路引理的条件，从而得到论文的主要结论。

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。