scholarly journals WIENER-HOPF ANALYSIS OF FINITE-LENGTH IMPEDANCE LOADING IN THE OUTER CONDUCTOR OF A COAXIAL WAVEGUIDE

2008 ◽  
Vol 5 ◽  
pp. 241-251 ◽  
Author(s):  
Feray Hacivelioglu ◽  
Alinur Büyükaksoy
Keyword(s):  
Finite Length ◽  
Coaxial Waveguide ◽  
Outer Conductor

scholarly journals Analysis of a Coaxial Waveguide with Finite-Length Impedance Loadings in the Inner and Outer Conductors

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Feray Hacıvelioğlu ◽  
Alinur Büyükaksoy
Keyword(s):  
Reflection Coefficient ◽  
Boundary Value Problem ◽  
Finite Length ◽  
Formal Solution ◽  
Coaxial Waveguide ◽  
Algebraic Equations ◽  
Coaxial Cylinders ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Band Stop Filter

A rigorous Wiener-Hopf approach is used to investigate the band stop filter characteristics of a coaxial waveguide with finite-length impedance loading. The representation of the solution to the boundary-value problem in terms of Fourier integrals leads to two simultaneous modified Wiener-Hopf equations whose formal solution is obtained by using the factorization and decomposition procedures. The solution involves 16 infinite sets of unknown coefficients satisfying 16 infinite systems of linear algebraic equations. These systems are solved numerically and some graphical results showing the influence of the spacing between the coaxial cylinders, the surface impedances, and the length of the impedance loadings on the reflection coefficient are presented.

On mappings with finite length distortion on Riemann surfaces

2019 ◽  
Vol 33 ◽  
Author(s):  
Serhii Volkov ◽  
Vladimir Ryazanov
Keyword(s):  
Finite Length ◽  
Riemann Surfaces ◽  
Boundary Behavior ◽  
Main Tool ◽  
Natural Generalization ◽  
Finite Distortion ◽  
Lipschitz Mappings ◽  
Geometric Function ◽  
Mappings With Finite Distortion ◽  
Length Distortion

The present paper is a natural continuation of our previous paper (2017) on the boundary behavior of mappings in the Sobolev classes on Riemann surfaces, where the reader will be able to find the corresponding historic comments and a discussion of many definitions and relevant results. The given paper was devoted to the theory of the boundary behavior of mappings with finite distortion by Iwaniec on Riemannian surfaces first introduced for the plane in the paper of Iwaniec T. and Sverak V. (1993) On mappings with integrable dilatation and then extended to the spatial case in the monograph of Iwaniec T. and Martin G. (2001) devoted to Geometric function theory and non-linear analysis. At the present paper, it is developed the theory of the boundary behavior of the so--called mappings with finite length distortion first introduced in the paper of Martio O., Ryazanov V., Srebro U. and Yakubov~E. (2004) in the spatial case, see also Chapter 8 in their monograph (2009) on Moduli in modern mapping theory. As it was shown in the paper of Kovtonyuk D., Petkov I. and Ryazanov V. (2017) On the boundary behavior of mappings with finite distortion in the plane, such mappings, generally speaking, are not mappings with finite distortion by Iwaniec because their first partial derivatives can be not locally integrable. At the same time, this class is a generalization of the known class of mappings with bounded distortion by Martio--Vaisala from their paper (1988). Moreover, this class contains as a subclass the so-called finitely bi-Lipschitz mappings introduced for the spatial case in the paper of Kovtonyuk D. and Ryazanov V. (2011) On the boundary behavior of generalized quasi-isometries, that in turn are a natural generalization of the well-known classes of bi-Lipschitz mappings as well as isometries and quasi-isometries. In the research of the local and boundary behavior of mappings with finite length distortion in the spatial case, the key fact was that they satisfy some modulus inequalities which was a motivation for the consideration more wide classes of mappings, in particular, the Q-homeomorphisms (2005) and the mappings with finite area distortion (2008). Hence it is natural that under the research of mappings with finite length distortion on Riemann surfaces we start from establishing the corresponding modulus inequalities that are the main tool for us. On this basis, we prove here a series of criteria in terms of dilatations for the continuous and homeomorphic extension to the boundary of the mappings with finite length distortion between domains on arbitrary Riemann surfaces.

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