Non-Archimedean Analysis on the Extended Hyperreal Line *R_dand the Solution of Some Very Old Transcendence Conjectures over the Field Q

In 1980 F. Wattenberg constructed the Dedekind completion *Rd of the Robinson non-archimedean field *R and established basic algebraic properties of *Rd. In 1985 H. Gonshor established further fundamental properties of *Rd. In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completion *Rd in transcendental number theory were considered. Given any analytic function of one complex variable , we investigate the arithmetic nature of the values of at transcendental points . Main results are: 1) the both numbers and are irrational;2) number ee is transcendental. Nontrivial generalization of the Lindemann-Weierstrass theorem is obtained.

高强辐射场下不同孔阵的金属腔体屏蔽效能研究

提高屏蔽腔体的屏蔽效能可增强民用航空机载电子系统的高强辐射场(HIRF)防护能力。基于Robinson模型,提出一种可计算带有非中心孔阵金属屏蔽腔体屏蔽效能的修正模型。选用民航机载通信设备作为研究对象,运用修正模型计算其屏蔽效能,与三维电磁仿真软件的结果对比验证了所提模型的正确性。此外,通过软件仿真分析了HIRF作用下不同孔阵、频率、位置对设备内部电场分布的影响。仿真结果可为民航机载电子设备的屏蔽壳体设计以及内部敏感器件布局提供参考。