Exact solution to the transcendental equation in the waveguide method of investigation of dielectrics

Authors

  • A. Ye. Dubinov Russian Federal Nuclear Center. All-Russian Research Institute of Experimental Physics, Russian Federation
  • S. K. Saikov Russian Federal Nuclear Center. All-Russian Research Institute of Experimental Physics, Russian Federation

DOI:

https://doi.org/10.3103/S0735272705060105

Abstract

The analytical solution is obtained for a transcendental equation related to measurement of complex permittivity of solid and liquid substances when the measurement is performed by the waveguide method in the microwave range.

References

  1. BRANDT, A.A. Investigation of Dielectrics at Microwave Frequencies [in Russian]. Moscow: GIFML, 1963.
  2. BURNISTON, E.E.; SIEVERT, C.E. The use of Riemann problems in solving a class of transcendental equations. Math. Proc. Cambridge Philosophical Society, v.73, n.1, p.111-118, 1973. DOI: http://doi.org/10.1017/S0305004100047526.
  3. LUCK, R.; STEVENS, J.W. Explicit solutions for transcendental equations. SIAM Rev., v.44, n.2, p.227-233, 2000. DOI: https://doi.org/10.1137/S0036144501386111.
  4. MARKUSHIN, V.E.; ROSENFELDER, R.; SCHREIBER, A.W. The $W_t$ transcendental function and quantum mechanical applications. arXiv: math-ph/0104019v2, 10 Jan. 2003.

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Published

2005-06-10

Issue

Vol. 48 No. 6 (2005)

Section

Research Articles