Advances in the Theory of A, B, C Numbers and Its Application to Waveguide Propagation
Harnessing a recently elaborated iterative technique,the dependence of the real positive numbers A1,B1,C1,defined earlier by the positive purely imaginary zeros ζ(c)k,n in x(n = 1,2,3,…)of the Kummer confluent hypergeometric function Φ(a,c;x),(a=c/2-jk-complex,c =3,x = jz,k,z-real,-∞ < k <+∞,z>0),on the real positive parameters |α| and-r0(0 <|α|< 1,-r0 >ζ(c)0,n/2),satisfying certain criterion,is analyzed numerically,stipulating that n = 1 and-r0≥10.The outcomes are pictured in a graphical form.A second limit of the domain of existence of A1,B1 and C1 in the |α|-A1-and-r0-A1-,|α|-B1-and-r0-B1-,and |α|-C1-and-r0-C1-planes,resp.is specified,linked with a representative of the L1(c,n)numbers,akin to the zeros ζ(c)k,n for k→-∞,in addition to the previously found first one,related to ζ(c)0,n/2.It is established also that as for ζ(c)0,n/2<-r0≤10,so for-r0 ≥10,the impact of |α| on A1,of-r0 on B1 and of both |α| and-r0 on C1,is slight.Interpreting physically-r0,|α| and n in a suitable way,the employment of the quantities studied in the computation of the differential phase shift produced by the circular waveguide,wholly filled with ferrite of azimuthal magnetization and propagating normal TE0n mode,is demonstrated.The investigation is a contribution to the theory of A,B,C numbers of which the A1,B1,C1 ones constitute one of the two sub-classes,introduced by now.
Mariana Nikolova Georgieva-Grosse Georgi Nikolov Georgiev
Consulting in Physics and Computer Sciences,Meterstrasse 4,D-70839 Gerlingen,Germany Faculty of Mathematics and Informatics University of Veliko Tirnovo St.St.Cyril and Methodius,BG-5
国际会议
Progress in Electromagnetics Research Symposium 2011(2011年电磁学研究新进展学术研讨会)
苏州
英文
1462-1466
2011-09-01（万方平台首次上网日期，不代表论文的发表时间）