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Letters in Mathematical Physics, ISSN 0377-9017, 8/2013, Volume 103, Issue 8, pp. 919 - 925
In this paper we prove that the spectra of the Mathieu–Hill Operators with potentials ae−i2π x  +be i2π x and ce−i2π x  +de i2π x , where a, b, c and d are... 
Geometry | spectrum | isospectral operators | Theoretical, Mathematical and Computational Physics | 34L05 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | Mathieu–Hill operator | Physics | 34L20 | Mathieu-Hill operator | PHYSICS, MATHEMATICAL | Invisibility | Mathematics - Spectral Theory
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2013, Volume 405, Issue 2, pp. 453 - 465
The Hill operators Ly=−y″+v(x)y, considered with complex valued π-periodic potentials v and subject to periodic, antiperiodic or Neumann boundary conditions... 
Potential smoothness | Hill operator | Riesz bases | MATHEMATICS | MATHEMATICS, APPLIED | DIRAC OPERATORS | GAPS | INSTABILITY ZONES
Journal Article
Journal of Spectral Theory, ISSN 1664-039X, 2017, Volume 70, Issue 3, pp. 699 - 732
We consider the Stark operator perturbed by a compactly supported potential (of a certain class) on the real line. We prove the following results: (a) upper... 
Resonances | Trace formula | Stark operators | MATHEMATICS, APPLIED | trace formula | LADDER | FIELD | resonances | POTENTIALS | ONE-DIMENSION | MATHEMATICS | HILL OPERATOR | POLES | HAMILTONIANS | REAL LINE | SCATTERING | SCHRODINGER-OPERATORS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 11/2013, Volume 255, Issue 10, pp. 3233 - 3283
We study in various functional spaces the equiconvergence of spectral decompositions of the Hill operator L=−d2/dx2+v(x), x∈[0,π], with Hper−1-potential and... 
Singular potentials | Hill–Schrödinger operators | Spectral decompositions | Equiconvergence | Hill-Schrödinger operators | INTERVAL | SERIES | EIGENFUNCTION-EXPANSIONS | 1D DIRAC OPERATORS | REGULAR BOUNDARY-CONDITIONS | MATHEMATICS | STURM-LIOUVILLE OPERATORS | CONVERGENCE | ASYMPTOTICS | LINEAR-DIFFERENTIAL EQUATIONS | Hill-Schrodinger operators
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 05/2017, Volume 14, Issue 5
In this paper, we investigate the spectrum and spectrality of the one-dimensional Schrodinger operator with a periodic PT-symmetric complex-valued potential. 
PT-symmetric periodic potential | real spectrum | Schrödinger operator | HILL OPERATORS | COMPLEX | Schrodinger operator | TRANSLATION | PHYSICS, MATHEMATICAL | DIFFERENTIAL-OPERATORS | Mathematics - Spectral Theory
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 2/2017, Volume 207, Issue 2, pp. 895 - 980
We study the quasi-periodic Schrödinger operator $$\begin{aligned} -\psi ''(x) + V(x) \psi (x) = E \psi (x), \quad x \in {\mathbb {R}}\end{aligned}$$ - ψ ′ ′ (... 
Mathematics, general | Mathematics | MATHEMATICS | VARIABLES | ABSOLUTELY CONTINUOUS-SPECTRUM | POTENTIALS | HILLS EQUATION | KDV | Toruses | Operators | Approximation | Mathematical analysis | Multiscale analysis | Estimates | Multiscale methods | Fourier analysis | Schroedinger equation
Journal Article
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, ISSN 1815-2406, 05/2018, Volume 23, Issue 5, pp. 1434 - 1475
Throughout this paper, we study the spectrum of a periodic Schrodinger operator on a zigzag super carbon nanotube, which is a generalization of the zigzag... 
Carbon nanotube | zigzag nanotube | quantum graph | Hill operator | supergraphene | spectral gap | Floquet-Bloch theory | band structure | SPECTRA | GAPS | PHYSICS, MATHEMATICAL | EFFECTIVE MASSES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2017, Volume 447, Issue 1, pp. 84 - 108
The one-dimensional Dirac operator with periodic potential V=(0P(x)Q(x)0), where P,Q∈L2([0,π]) subject to periodic, antiperiodic or a general strictly regular... 
Potential smoothness | Dirac operator | Riesz basis property | SCHRODINGER OPERATOR | MATHEMATICS | ZAKHAROV-SHABAT SYSTEM | MATHEMATICS, APPLIED | DIRICHLET EIGENVALUES | ADJOINT HILLS OPERATORS | INSTABILITY ZONES
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2012, Volume 50, Issue 1, pp. 64 - 78
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2012, Volume 396, Issue 1, pp. 243 - 255
The Mathieu operator L(y)=−y″+2acos(2x)y,a∈C,a≠0, considered with periodic or anti-periodic boundary conditions has, close to n2 for large enough n, two... 
Spectral gap asymptotics | Mathieu operator | INSTABILITY-INTERVALS | HILL OPERATORS | MATHEMATICS | MATHEMATICS, APPLIED | SCHRODINGER | ZONES
Journal Article
Operators and Matrices, ISSN 1846-3886, 03/2016, Volume 10, Issue 1, pp. 57 - 71
First we study the spectral singularity at infinity and investigate the connections of the spectral singularities and the spectrality of the Hill operator.... 
Spectral operator | Spectral singularities | Spectral expansion | Hill operator | MATHEMATICS | spectral expansion | spectral singularities | SCALAR TYPE | spectral operator | TRANSLATION | DIFFERENTIAL-OPERATORS
Journal Article
Russian Mathematics, ISSN 1066-369X, 07/2017, Volume 61, Issue 7, pp. 1 - 10
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.3103/S1066369X17070015 We... 
asymptotics | Hill operator | perturbation
Journal Article
Pattern Recognition Letters, ISSN 0167-8655, 05/2014, Volume 41, Issue 1, pp. 34 - 42
•The proposed Hill-Climbing algorithm incorporates an acceleration operator.•The acceleration operator improves the exploration capability of the... 
Feature selection | Hill climbers | Pattern recognition | Typical testors | FEATURE-SELECTION | PATTERN-RECOGNITION | CT-EXT | FAST IMPLEMENTATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algorithms
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 07/2012, Volume 253, Issue 2, pp. 400 - 437
Under the assumption that V∈L2([0,π];dx), we derive necessary and sufficient conditions in terms of spectral data for (non-self-adjoint) Schrödinger operators... 
Periodic and antiperiodic boundary conditions | Riesz basis | Non-self-adjoint Hill operators | Secondary | Primary | BASIS PROPERTY | STURM-LIOUVILLE OPERATOR | ROOT FUNCTIONS | SPECTRAL DECOMPOSITIONS | SCALAR TYPE | ORDINARY DIFFERENTIAL-OPERATORS | POTENTIALS | HILL OPERATORS | MATHEMATICS | ALGEBRO-GEOMETRIC SOLUTIONS | EQUATION
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2009, Volume 247, Issue 2, pp. 364 - 400
This paper is a continuation of Zhang [M. Zhang, Continuity in weak topology: Higher order linear systems of ODE, Sci. China Ser. A 51 (2008) 1036–1058; M.... 
Extremal value | Singular integral | [formula omitted] ball | Eigenvalue | Period function | Variational method | Potential | Sturm–Liouville operator | MATHEMATICS | L-p ball | HILLS EQUATIONS | P-LAPLACIAN | STABILITY | Sturm-Liouville operator
Journal Article
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, ISSN 0253-4142, 06/2017, Volume 127, Issue 3, pp. 471 - 516
In this paper, we study the spectra of Schrodinger operators on zigzag carbon nanotubes, which are broken by abrasion or during refining process. Throughout... 
Carbon nanotube | zigzag nanotube | MATHEMATICS | quantum graph | Hill operator | spectral gap | Floquet-Bloch theory | band structure | SPECTRA | QUANTUM GRAPHS | Schrodinger equation | Research | Mathematical research | Quantum theory | Nanotubes
Journal Article
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, ISSN 0532-8721, 08/2019, Volume 62, Issue 2, pp. 255 - 283
In this paper, we study the spectral structure of periodic Schrodinger operators on a generalization of carbon nanotubes from the point of view of the quantum... 
Carbon nanotube | MATHEMATICS | Band structure | MATHEMATICS, APPLIED | Zigzag nanotube | Quantum graph | Spectral gap | Hill operator | Floquet-Bloch theory
Journal Article
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