Browsing by Subject "Eigenvalues"
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Item Open Access Characteristic equations for the lasing Modes of infinite periodic chain of quantum wires(IEEE, 2008-06) Byelobrov, V. O.; Benson, T. M.; Altıntaş, Ayhan; Nosich, A.I.In this paper, we study the lasing modes of a periodic open optical resonator. The resonator is an infinite chain of active circular cylindrical quantum wires standing in tree space. Characteristic equations for the frequencies and associated linear thresholds of lasing are derived. These quantities are considered as eigenvalues of specific electromagnetic-field problem with "active" imaginary part of the cylinder material's refractive index - Lasing Eigenvalue Problem (LEP). ©2008 IEEE.Item Open Access EFIE and MFIE, why the difference?(IEEE, 2008-07) Chew W.C.; Davis, C. P.; Warnick, K. F.; Nie, Z. P.; Hu, J.; Yan, S.; Gürel, LeventEFIE (electric field integral equation) suffers from internal resonance, and the remedy is to use MFIE (magnetic field integral equation) to come up with a CFIE (combined field integral equation) to remove the internal resonance problem. However, MFIE is fundamentally a very different integral equation from EFIE. Many questions have been raised about the differences.Item Open Access Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators(Optical Society of America, 1994) Özaktaş, Haldun M.; Mendlovic, D.The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform. The order of the fractional Fourier transform is proportional to the Gouy phase shift between the two surfaces. This result provides new insight into wave propagation and spherical mirror resonators as well as the possibility of exploiting the fractional Fourier transform as a mathematical tool in analyzing such systems.Item Open Access Random walks on symmethric spaces and inequalities for matrix spectra(Elsevier, 2000-11-01) Klyachko, A.Using harmonic analysis on symmetric spaces we reduce the singular spectral problem for products of matrices to the recently solved spectral problem for sums of Hermitian matrices. This proves R.C. Thompson’s conjecture [Matrix Spectral Inequalities, Johns Hopkins University Press, Baltimore, MD, 1988]. © 2000 Elsevier Science Inc. All rights reserved.Item Open Access Random walks on symmetric spaces and inequalities for matrix spectra(2000) Klyachko, A.A.Using harmonic analysis on symmetric spaces we reduce the singular spectral problem for products of matrices to the recently solved spectral problem for sums of Hermitian matrices. This proves R.C. Thompson's conjecture [Matrix Spectral Inequalities, Johns Hopkins University Press, Baltimore, MD, 1988]. © 2000 Elsevier Science Inc.