Faculty of Applied Sciences | Факультет прикладних наук
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Item Reconstruction of Differential Operators with Frozen Argument(MDPI, 2022-01-09) Dobosevych, O.; Hryniv, RWe study spectral properties of a wide class of differential operators with frozen arguments by putting them into a general framework of rank-one perturbation theory. In particular, we give a complete characterization of possible eigenvalues for these operators and solve the inverse spectral problem of reconstructing the perturbation from the resulting spectrum. This approach provides a unified treatment of several recent studies and gives a clear explanation and interpretation of the obtained results.Item Minimal Solvers for Single-View Lens-Distorted Camera Auto-Calibration(IEEE, 2021-01) Lochman, Yaroslava; Dobosevych, Oles; Hryniv, Rostyslav; Pritts, JamesThis paper proposes minimal solvers that use combinations of imaged translational symmetries and parallel scene lines to jointly estimate lens undistortion with either affine rectification or focal length and absolute orientation. We use constraints provided by orthogonal scene planes to recover the focal length. We show that solvers using feature combinations can recover more accurate calibrations than solvers using only one feature type on scenes that have a balance of lines and texture. We also show that the proposed solvers are complementary and can be used together in a RANSAC-based estimator to improve auto-calibration accuracy. State-of-the-art performance is demonstrated on a standard dataset of lens-distorted urban images. The code is available at https://github.com/ylochman/single-view-autocalibItem On the first trace formula for Schrödinger operators(EMS Press, 2021-03-15) Hryniv, Rostyslav; Mykytyuk, YaroslavWe prove that the so-called first trace formula holds for all Schrödinger operators on the line with real-valued integrable potentials.Item Spectra of PT-symmetric operators under rank-one perturbations(IOP Publishing, 2020-08-18) Hryniv, Rostyslav; Homa, MonikaWe study the spectra of PT-symmetric Hamiltonians H that are rank-one perturbations of a self-adjoint PT-symmetric Hamiltonian H0. We show that the discrete spectrum of H may include any number of complex–conjugate pairs of complex numbers of arbitrary algebraic multiplicity.Item Inverse scattering on the half-line for energy-dependent Schrödinger equations(IOP Publishing, 2020-08-31) Hryniv, Rostyslav; Manko, StepanIn this paper, we study the inverse scattering problem for energy-dependent Schrödinger equations on the half-line with energy-dependent boundary conditions at the origin. Under certain positivity and very mild regularity assumptions, we transform this scattering problem to the one for non-canonical Dirac systems and show that, in turn, the latter can be placed within the known scattering theory for ZS-AKNS systems. This allows us to give a complete description of the corresponding scattering functions S for the class of problems under consideration and justify an algorithm of reconstructing the problem from S.Item Inverse scattering for reflectionless Schrödinger operators with integrable potentials and generalized soliton solutions for the KdV equation(Springer, 2021-01-07) Hryniv, Rostyslav; Mykytyuk, Yaroslav; Melnyk, BohdanУ статті запропоновано повну характеризацію безвідбивних операторів Шрединґера на осі з інтегровними потенціалами, розв'язок оберненої задачі розсіювання, тобто відновлення таких потенціалів за вдасними значеннями та нормівними множниками та побудовано відповідні узагальнені солітонні розв'язки рівняння Кортевега-де ФризаItem Direct and Inverse Spectral Problems for Rank-One Perturbations of Self-adjoint Operators(Birkhauser, 2021-04-09) Hryniv, Rostyslav; Dobosevych, OlesItem Spectra of rank-one perturbations of self-adjoint operators(Elsevier, 2021-01-15) Hryniv, Rostyslav; Dobosevych, Oles
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