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The Poincaré Index on Singular Varieties
J, 2022 In this paper, we discuss a few simple methods for computing the local topological index and its various analogs for vector fields and differential forms given on complex varieties with singularities of different types.
Alexander G. Aleksandrov
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Nonlinear Spectral Singularities for Confined Nonlinearities [PDF]
Physical Review Letters, 2013 5 pages, 1 figure, to appear in Phys.
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Nonlinear spectral singularities and laser output intensity [PDF]
Journal of Optics, 2017 Abstract The mathematical notion of spectral singularity admits a description in terms of purely outgoing solutions of a corresponding linear wave equation. This leads to a nonlinear generalization of this notion for nonlinearities that are confined in space.
Hamed Ghaemi-Dizicheh +2 more
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International Journal of Mathematics and Mathematical Sciences, 2004 We investigate the spectrum of the differential operator Lλ defined by the Klein-Gordon s-wave equation y″+(λ−q(x))2y=0, x∈ℝ+=[0,∞), subject to the spectral parameter-dependent boundary condition y′(0)−(aλ+b)y(0)=0 in the space L2(ℝ+), where a≠±i, b are ...
Gülen Başcanbaz-Tunca
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Spectral walls in multifield kink dynamics
Journal of High Energy Physics, 2021 We show that spectral walls are common phenomena in the dynamics of kinks in (1+1) dimensions. They occur in models based on two or more scalar fields with a nonempty Bogomol’nyi-Prasad-Sommerfield (BPS) sector, hosting two zero modes, where they are one
C. Adam +4 more
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Spectral singularities of a general point interaction [PDF]
Journal of Physics A: Mathematical and Theoretical, 2011 We study the problem of locating spectral singularities of a general complex point interaction with a support at a single point. We also determine the bound states, examine the special cases where the point interaction is P-, T-, and PT-symmetric, and explore the issue of the coalescence of spectral singularities and bound states.
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Numerical solution of two dimensional harmonic boundary problems containing singularities by conformal transformation methods [PDF]
, 1971 Numerical solutions to a class of two dimensional harmonic mixed boundary value problems defined on rectangular domains and containing singularities are obtained using conformal transformation methods.
Whiteman, J R, Papamichael, N
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Abstract and Applied Analysis, 2010 Let 𝐴 denote the operator generated in 𝐿2(ℛ+) by the Sturm-Liouville problem: −𝑦+𝑞(𝑥)𝑦=𝜆2𝑦, 𝑥∈ℛ+=[0,∞), (𝑦/𝑦)(0)=(𝛽1𝜆+𝛽0)/(𝛼1𝜆+𝛼0), where 𝑞 is a complex valued function and 𝛼0,𝛼1,𝛽0,𝛽1∈𝒞, with 𝛼0𝛽1−𝛼1𝛽0≠0.
Elgiz Bairamov, M. Seyyit Seyyidoglu
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Autoregressive models of singular spectral matrices
Automatica, 2012 This paper deals with autoregressive (AR) models of singular spectra, whose corresponding transfer function matrices can be expressed in a stable AR matrix fraction description [Formula: see text] with [Formula: see text] a tall constant matrix of full column rank and with the determinantal zeros of [Formula: see text] all stable, i.e. in [Formula: see
Anderson, Brian +3 more
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Error Estimates for the Nearly Singular Momentum-Space Bound-State Equations
Advances in Mathematical Physics, 2020 We present errors of quadrature rules for the nearly singular integrals in the momentum-space bound-state equations and give the critical value of the nearly singular parameter.
Yang-Hong Zhang, Jiao-Kai Chen
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