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The Sem Representation of Scattering from Perfectly Conducting Targets in Simple Lossy Media
Published in Carl E. Baum, Detection and Identification of Visually Obscured Targets, 2019
which is a meromorphic function of s. Using (3.65) then the coupling coefficients in the lossy medium scale as () ηα(1→i,1→p)=2+sαt11+sαt1ηα(0)(1→i,1→p)
Insertion Loss Filters
Published in Herbert J. Carlin, Pier Paolo Civalleri, Wideband Circuit Design, 2018
Herbert J. Carlin, Pier Paolo Civalleri
The meromorphic function, Sn(u, z), is completely defined to within a multiplicative constant by its zeros and poles. The scaling factor can be chosen so that the frequency in the middle of the transition region, i.e., at z = mu/2 + jπ/4, is unity. We can therefore set the scaling so that Sn(mu,mu/2+jπ/4)=1,orSn(u,u/2+jπ/4)=1
Chapter S4: Special Functions and Their Properties
Published in Andrei D. Polyanin, Valentin F. Zaitsev, Handbook of Ordinary Differential Equations, 2017
Andrei D. Polyanin, Valentin F. Zaitsev
An elliptic function is a function that is the inverse of an elliptic integral. An elliptic function is a doubly periodic meromorphic function of a complex variable. All its periods can be written in the form 2mω1 + 2nω2 with integer m and n, where ω1 and ω2 are a pair of (primitive) half‐periods. The ratio τ = ω2/ω1 is a complex quantity that may be considered to have a positive imaginary part, Imτ>0. $ {\text{Im }}\tau> 0. $
An inverse problem for non-selfadjoint Sturm–Liouville operator with discontinuity conditions inside a finite interval
Published in Inverse Problems in Science and Engineering, 2019
Yixuan Liu, Guoliang Shi, Jun Yan
The symbol denotes the characteristic function of the boundary value problem consisting of the equation (1), the discontinuity conditions (3) and the boundary conditions . The zeros of are expressed in terms of ; it is easy to show that . Then is a meromorphic function with zeros in and poles in .
Carathèodory convergence for Leau and Baker domains
Published in Dynamical Systems, 2021
Adrián Esparza-Amador, Mónica Moreno Rocha
If f is a meromorphic function satisfying for each s>0 where , then: for each there is an invariant Baker domain of f such that, for each , contains a set of the form if then , , as ;for each s>0 there exists t>0 such that f is univalent in , in fact;for each , , there exists such that f is univalent in and ;each contains a singularity of .
Inverse phaseless scattering on the line with partial information
Published in Waves in Random and Complex Media, 2022
In this paper, we consider the complex analysis of scattering operator of one-dimensional Schrödinger equation where that is, the potential V is compactly-supported. We assume that It is well-known that the Jost solutions of (1) satisfy where , , , and satisfy the unitary condition, i.e. Furthermore [1–3], where the Fourier transforms and will be introduced in Section 2. Accordingly, we define the scattering matrix as where is the transmission coefficient, and is the reflection coefficient from the right/left respectively. Moreover, The scattering matrix is meromorphic in , and its poles in are the square roots of -eigenvalues of (1). The construction above is due to Tang and Zworski [2]. The transmission coefficient is a meromorphic function in .