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theorem
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  定理
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  theorem
In the case of 3-dimensional commutative algebras a new proof of a recent theorem of Katsylo and Mikhailov about the 28 bitangents to the associated plane quartic is given.
      
If the additive group of complex numbers acts algebraically on a normal affine variety, then the associated ring of invariants need not be finitely generated, but is an ideal transform of some normal affine algebra (Theorem 1).
      
If the variety is a complex affine space and the ring of invariants is isomorphic to a polynomial ring, then the action is conjugate to a translation (Theorem 3).
      
On the other hand, there is a locally trivialGa-action on a normal affine variety with nonfinitely generated ring of invariants (Theorem 2).
      
As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras.
      
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In a paper by Klein, it is pointed out that for the quantum mechanical ergodic theorem (time average = average over states) to be valid, all integrals of motion R must satisfy the condition

在Klein的一篇论文中,他指出了当量子系统的ergodic定理成立时,所有的运动积分R必须满足以下的条件: sum from r″to (α′γ″|R|β′γ″=常数δ_α′β′,(1)式中α′,β′,…等代表我们所研究的系统的态,γ″,ρ″…等代表舆我们的系统共同平衡的外界的态。在这篇短文中,我们指出:Klein的讨论在一点是可以怀疑的,而用了另一个方法来讨论ergodic定理。这样,我们证明了(1)式只是在引入另一个假定——外界各态有同一个几率——后才是充分的,而在一般情形下,我们须要更强的条件,例如 (α′ρ″|R|β′γ″)=常数δ_α′β′δ_(ρ″γ″)。(2) 以上相当於没有运动积分的情形。有运动积分的情形也在本文中作了讨论。

In this paper we studied the Maxwell's equations in imhomogeneous and anisotropic media as an operator. It is defined in a bounded region, which can be comprehended as a resonant cavity in micro-wave technique. But these cavities are filled with ferrite, plasma or other gyrotropic medium, all these new media become more and more important in practice. We proved that under some concrete conditions imposed on μ, e and restrictions on the boundary value, the operator of Maxwell's equations becomes a symmetric one....

In this paper we studied the Maxwell's equations in imhomogeneous and anisotropic media as an operator. It is defined in a bounded region, which can be comprehended as a resonant cavity in micro-wave technique. But these cavities are filled with ferrite, plasma or other gyrotropic medium, all these new media become more and more important in practice. We proved that under some concrete conditions imposed on μ, e and restrictions on the boundary value, the operator of Maxwell's equations becomes a symmetric one. The symmetry and self-adjoint property give much convenience in eigenfunction expansion problems. Besides, we derived the orthogonality of characteristic oscillation and reciprocity theorem in general.

在本文中,把在不均匀各向异性介质中的麦克斯韦方程看作算符,它定义在一个有界区域,可以被理解为微波技术中的谐振腔。但在这腔中充填着铁氧体,等离子体或其他各向异性介质,这些介质在应用中日益重要。文中证明了在某些、边界条件下,算符成为对称。而对称性和自伴性在本征函数展开中带来很多方便;此外我们推导了本征振动的正变性和互易定理。 如果不满足对称性,引入伴谐振腔的概念,所谓伴谐振腔在几何形状上和原来的腔相同,但、和边界条件不一样。它和自伴谐振腔在正交性和互易定理上有某些相似之处。

Utilizing a theorem from the variational principles, after transforming boundaries of a transmission line into simpler ones, we can find upper and lower bounds to the correct value of the characteristic impedance of the line, so that the lengthy calculation in the ordinary variational method is avoided. Impedances of the rectangular line with central cylindrical inner conductor, the trough line with the slab line as a special case and the multi-conductor cable are calculated.

本文提出对于传输线的特性阻抗的一个新计算方法,即利用变分法的一个定理求出特性阻抗的准确值的上限及下限,但在计算过程中不是应用变分法的常用方法来进行处理,而是利用函数变换法来进行处理。这种方法可以估计特性阻抗的准确值的上限及下限,如果上下限值差别不大,则其平均值即可取作此特性阻抗的近似值,并且准确度很高。文中对于具有圆柱形内导体的矩形线、对称全矩形线、槽形线及平板线的特性阴抗分别进行计算,并举例求出数值与已发表的文献进行比较,最后对多心电续的特性阻抗也进行近似计算。

 
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