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We show that ${\mathcal M}(G,R)$ is a symmetric tensor category, i.e., the motive of the product of two projective homogeneous G-varieties is a direct sum of twisted motives of projective homogeneous G-varieties.
      
We also study the problem of uniqueness of a direct sum decomposition of objects in ${\mathcal M}(G,R).$ We prove that the Krull--Schmidt theorem holds in many cases.
      
For a split reductive algebraic group, this paper observes a homological interpretation for Weyl module multiplicities in Jantzen's sum formula.
      
The new interpretation makes transparent for GLn (and conceivable for other classical groups) a certain invariance of Jantzen's sum formula under "Howe duality" in the sense of Adamovich and Rybnikov.
      
From elements of the invariant algebra C[V]G we obtain, by polarization, elements of C[kV]G, where k ≥ 1 and kV denotes the direct sum of k copies of V.
      
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The assignment of aberration tolerances for optical systems suffering from wave-front aberrations greater than λ/4 is worth further studying. In this paper it is shown that "low" contrast resolving power of optical systems can be taken as an appropriate criterion for assessing image quality, where the optical transfer function can be evaluated approximately in terms of the sums of Legendre polynomials. Accordingly, the best program of aberration correction and tolerences in the case where certain aberration...

The assignment of aberration tolerances for optical systems suffering from wave-front aberrations greater than λ/4 is worth further studying. In this paper it is shown that "low" contrast resolving power of optical systems can be taken as an appropriate criterion for assessing image quality, where the optical transfer function can be evaluated approximately in terms of the sums of Legendre polynomials. Accordingly, the best program of aberration correction and tolerences in the case where certain aberration constants are inevitably present and others are adjustable in optical design can be obtained. The results so obtained as applied to aberrations of small magnitude comparable to λ/4 conform well to the Strehl Deffinitionshelligkeit method.

具有大象差的光学系统象差公差问题一直还未得到很好解决。本文中提出以低对比分辨本领作为光学系统的质量指标,并将光学系统的传递函数近似表示为正交多项式之和,象差任意大小的光学系统的最佳校正方案和公差之值就可以求出。在小象差情况下,所得的结果与Strehl判断的结果基本一致。

This paper suggests an approximation method for solving the problems of diffraction due to perfectly conducting cylinder, the section of which is a smooth curve C of arbitrary form. The principle of the method is similar to that of H. Bremmer[8]: The field of diffraction due to a cylinder with a polygonal section (which is an inscribed polygon of the curve C) is expanded into a series. The first term of the series is the geometrical field. The second term of the series is the sum of the elementary diffraction...

This paper suggests an approximation method for solving the problems of diffraction due to perfectly conducting cylinder, the section of which is a smooth curve C of arbitrary form. The principle of the method is similar to that of H. Bremmer[8]: The field of diffraction due to a cylinder with a polygonal section (which is an inscribed polygon of the curve C) is expanded into a series. The first term of the series is the geometrical field. The second term of the series is the sum of the elementary diffraction fields due to the wedges of the polygonal cylinder. These fields are taken as those of Sommerfeld's problem, i.e., both sides of each wedge are infinitely extended. Each of these elementary fields falls on the neighbour wedge and is diffracted by the latter, and this diffracted field in turn falls on the next neighbour wedge and is again diffracted by the latter, etc. The field diffracted by the wedges one after another in such a way is called the main tangential elementary field. The third term of the series is the sum of these main tangential elementary fields. The field diffracted by wedge A, being diffracted again by the neighbour wedge B, reflects back on wedge A again, and then propagates in this direction progressively in a manner mentioned above. Such a field is called once-reflected elementary field. The fourth term of the series is the sum of these once-reflected elementary fields, etc. In general, the m-th term of the series is the sum of the (m-3) times-reflected elementary fields. Every elementary diffracted field due to any wedge is taken as the solution of Sommerfeld's problem for this wedge in the manner mentioned above. As the sides of the inscribed polygon approach to zero, the inscribed polygon approaches to the curve C, and each term of the series becomes an integral, the limit of the summation of the series approaching to the rigorous solution of the initial problem.

本文对于任意形状的光滑柱状理想导体的衍射提出一种级数解法。方法的原理与层变媒质的Bremmer级数相似:先以内接多面稜柱代替上述光滑柱体;将此稜柱产生的衍射场展为一个级数。级数之首项为几何光学场;级数之第二项为稜柱的所有各稜产生的元衍射场之和,其中每个元衍射场皆取Sommerfeld问题的解,即将该稜之两侧面视为半无限大的平面。上述每一元衍射场皆投射在其相邻稜上,并在相邻稜上发生衍射;这一衍射场随之又投射在下一个相邻稜上而发生衍射;依此类推。按此方式依次被各稜所衍射的场称为“主掠射元场”。级数之第三项即为这些主掠射元场之和。被某一稜A衍射而后又在相邻的稜B上衍射的某一元场,同样会回射到A上;然后以上述“主掠射”方式传递下去,这样的场称为“一次反射元场”。级数的第四项即为这些一次反射元场之和。依此类推。一般说来,级数之第m项(m>3)为m-3次反射元场之和。元场在任何一稜上的衍射皆取Sommerfeld解。当内接多面稜柱之面数趋向无穷,且每面之宽度趋向零时,多面稜柱即趋于光滑柱体,且级数每一项的求和变为一个积分。这时该级数总和之极限即为原问题之解。 对级数之前三项单独进行了推导。对于一般的第m项(m>3),导出...

本文对于任意形状的光滑柱状理想导体的衍射提出一种级数解法。方法的原理与层变媒质的Bremmer级数相似:先以内接多面稜柱代替上述光滑柱体;将此稜柱产生的衍射场展为一个级数。级数之首项为几何光学场;级数之第二项为稜柱的所有各稜产生的元衍射场之和,其中每个元衍射场皆取Sommerfeld问题的解,即将该稜之两侧面视为半无限大的平面。上述每一元衍射场皆投射在其相邻稜上,并在相邻稜上发生衍射;这一衍射场随之又投射在下一个相邻稜上而发生衍射;依此类推。按此方式依次被各稜所衍射的场称为“主掠射元场”。级数之第三项即为这些主掠射元场之和。被某一稜A衍射而后又在相邻的稜B上衍射的某一元场,同样会回射到A上;然后以上述“主掠射”方式传递下去,这样的场称为“一次反射元场”。级数的第四项即为这些一次反射元场之和。依此类推。一般说来,级数之第m项(m>3)为m-3次反射元场之和。元场在任何一稜上的衍射皆取Sommerfeld解。当内接多面稜柱之面数趋向无穷,且每面之宽度趋向零时,多面稜柱即趋于光滑柱体,且级数每一项的求和变为一个积分。这时该级数总和之极限即为原问题之解。 对级数之前三项单独进行了推导。对于一般的第m项(m>3),导出了一个递推公式。最后,对该级数之收敛条件进行了探讨。

The general formulas for computing actual shielding factors of high-conductivity overhead ground wires hung on power and tele-communication lines are given. These formulas are derived from a system of finite difference equations representing the relation between the currents in successive sections of the multiply-grounded shielding conductors, and the subsequent substitution of terminal conditions corresponding to the particular circuit arrangement under consideration. It is found that the actual shielding factor...

The general formulas for computing actual shielding factors of high-conductivity overhead ground wires hung on power and tele-communication lines are given. These formulas are derived from a system of finite difference equations representing the relation between the currents in successive sections of the multiply-grounded shielding conductors, and the subsequent substitution of terminal conditions corresponding to the particular circuit arrangement under consideration. It is found that the actual shielding factor can be written as the sum of the intrinsic shielding factor t0 and a correction term evaluating the effect of finite conductance of the ground connections. It is also shown that the shielding factor formulas given in Engineering Report No. 26 of the joint subcommitte on development and research of the Edison electric institute and the Bell telephone system are only special cases of the general formulas given in this article.

本文分别就良导体架空地线架设在电力线路上和电信线路上的两种情况,给出了架空地线对于电信线路的实际屏蔽系数的普遍公式。这些公式的推导,是用有限差分方程组代表多点接地的屏蔽导线的相邻两档之间电流的关系,再代入相应的边界条件而解出。所得实际屏蔽系数的公式可以写成架空地线的固有屏蔽系数t_0和一个考虑了接地电阻影响的校正项之和。同时并证明了爱迪生电气协会和贝尔电话系统共同发展和研究小组的工程报告第26号中所列出的屏蔽系数公式是本文普遍公式的一个特殊情况。

 
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