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Complex Transmission Eigenvalues in One Dimension [PDF]
Abstract and Applied Analysis, 2014 We consider all of the transmission eigenvalues for one-dimensional media. We give some conditions under which complex eigenvalues exist. In the case when the index of refraction is constant, it is shown that all the transmission eigenvalues are real if ...
Yalin Zhang +3 more
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Double, borderline, and extraordinary eigenvalues of Kac-Murdock-Szeg\"o matrices with a complex parameter [PDF]
, 2019 For all sufficiently large complex $\rho$, and for arbitrary matrix dimension $n$, it is shown that the Kac--Murdock--Szeg\H{o} matrix $K_n(\rho)=\left[\rho^{|j-k|}\right]_{j,k=1}^{n}$ possesses exactly two eigenvalues whose magnitude is larger than $n$.
Fikioris, George +1 more
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Eigenvalues of complex unit gain graphs and gain regularity [PDF]
Special MatricesA complex unit gain graph (or T{\mathbb{T}}-gain graph) Γ=(G,γ)\Gamma =\left(G,\gamma ) is a gain graph with gains in T{\mathbb{T}}, the multiplicative group of complex units.
Brunetti Maurizio
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Eigenvalue-based entropy in directed complex networks
PLOS ONE, 2021 Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer.
Yan Sun +3 more
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Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We study the eigenvalue problem −u''+V(z)u=λu in the complex plane with the boundary condition that u(z) decays to zero as z tends to infinity along the two rays arg z=−π/2± 2π(m+2), where V(z)=−(iz)^m−P(iz) for complex-valued polynomials P of degree at ...
Kwang C. Shin
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Complex Eigenvalues for Binary Subdivision Schemes [PDF]
, 2008 Convergence properties of binary stationary subdivision schemes for curves have been analyzed using the techniques of z-transforms and eigenanalysis. Eigenanalysis provides a way to determine derivative continuity at specific points based on the eigenvalues of a finite matrix.
Christian Kuehn
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Coquaternionic Quantum Dynamics for Two-level Systems [PDF]
Acta Polytechnica, 2011 The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory are investigated. It is shown that the time evolution exhibits three different characteristics, depending on the values of the parameters of the Hamiltonian.
D. C. Brody, E. M. Graefe
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On eigenvalues of random complexes [PDF]
Israel Journal of Mathematics, 2016 Extended full version of an extended abstract that appeared at SoCG 2012, to appear in Israel Journal of ...
Gundert, Anna, Wagner, Uli
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Mathematics, 2022 A rigorous approach was employed for the accurate evaluation of the electromagnetic interaction between a thin metallic rod and a two-dimensional (2D) slotted cavity.
Elena D. Vinogradova, Paul D. Smith
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Entropy, 2022 Complex eigenvalues of random matrices J=GUE+iγdiag(1,0,…,0) provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel.
Yan V. Fyodorov +2 more
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