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Resonant forced oscillations in systems with periodic nonlinearities
Discrete and Continuous Dynamical Systems. 2013. Vol. 33. No. 1. P. 239-254.
We present an approach to study degenerate ODE with periodic nonlinearities; for resonant higher order nonlinear equations L(p)x=f(x)+b(t), p=d/dt, with 2pi-periodic forcing b and periodic f we give multiplicity results, in particular, conditions of existence of infinite and unbounded sets of 2pi-periodic solutions.
Alexander M. Krasnosel’skii, Discrete and Continuous Dynamical Systems - Series S 2013 Vol. 6 No. 4 P. 999-1016
Autonomous higher order differential equations with scalar nonlinearities, periodic with respect to the main phase variable under appropriate generic conditions, have an infinite sequence of isolated cycles with amplitudes growing to infinity and periods converging to some specific value T. ...
Added: February 11, 2013
Pereskokov A., Математические заметки 2012 Т. 92 № 4 С. 583-596
The eigenvalue problem for the perturbed resonant oscillator is considered. A method for constructing asymptotic solutions near the boundaries of spectral clusters using a new integral representation is proposed. The problem of calculating the averaged values of differential operators on solutions near the cluster boundaries is studied. ...
Added: November 26, 2012
M.V. Karasev, E.M. Novikova, Russian Journal of Mathematical Physics 2013 Vol. 20 No. 3 P. 283-294
The Penning trap Hamiltonian (hyperbolic oscillator in a homogeneous magnetic field) is considered in the basic three-frequency resonance regime. We describe its non-Lie algebra of symmetries. By perturbing the homogeneous magnetic field, we discover that, for special directions of the perturbation, a secondary hyperbolic resonance appears in the trap. For corresponding secondary resonance algebra, we ...
Added: November 17, 2013
M.V.Karasev, E.M.Novikova, Russian Journal of Mathematical Physics 2015 Vol. 22 No. 4 P. 463-468
We study dynamics of a charge in the planar Penning trap in which the direction of magnetic field does not coincide with the trap axis. Under some combined resonance condition on the deviation angle and magnitudes of magnetic and electric fields, the trajectories of a charge are near-periodic. We describe the reduction to a top-like ...
Added: October 22, 2015
M.V. Karasev, E.M. Novikova, Theoretical and Mathematical Physics 2014 Vol. 179 No. 3 P. 729-746
We discuss the choice of physical parameters of a quantum Penning nanotrap under the action of a perturbing inhomogeneous Ioffe magnetic field and also the role of frequency resonance modes. We present a general scheme for constructing the asymptotic behavior of the eigenstates by the generalized geometric quantization method and obtain the reproducing measure in ...
Added: October 16, 2015
Ivanov A. I., Орлов О., Демин А. В. et al., М. : Слово, 2012
В работе использован подход, заключающийся в применении результатов теории функций комплексного переменного для нахождения внутренних причин колебательных процессов тонуса вегетативной нервной системы (ВНС) человека. Установлены отдельные причины возникновения колебаний тонуса ВНС, численно характеризующегося индексов Кредо. Найдено объяснение возникновения отдельных сильно выделяющихся значений индекса Кредо как резонансных явлений. Пособие предназначено для научных работников, физиологов и врачей, ...
Added: February 8, 2013
М.В. Карасев, Е.М. Новикова, Теоретическая и математическая физика 2014 Т. 179 № 3 С. 406-425
The choice of physical parameters of the quantum Penning nanotrop with a perturbing in homogeneous magnetic Ioffe field is discussed, as well as the role of the resonance frequency modes. The general scheme for constructing the asymptotics of eigenstates by themethods of generalized geometric quantization is presented. The reproducing measure in theintegral representation of eigenfunctions ...
Added: March 8, 2014
Samovol V. S., Математические заметки 2012 Т. 92 № 5 С. 731-746
In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of the linearized system has two pure imaginary eigenvalues, all other eigenvalues lying outside the imaginary axis. The reducibility of such systems to pseudonormal form is studied. ...
Added: December 13, 2012
Protasov V., Systems and Control Letters 2016 Vol. 90 P. 54-60
We prove the existence of positive linear switching systems (continuous time), whose trajectories grow to infinity, but slower than a given increasing function. This implies that, unlike the situation with linear ODE, the maximal growth of trajectories of linear systems may be arbitrarily slow. For systems generated by a finite set of matrices, this phenomenon ...
Added: February 22, 2016
V.S. Samovol, Доклады Академии наук 2012 Vol. 85 No. 1 P. 122-124
In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has two purely imaginary eigenvalues, while the other eigenvalues lie outside the imaginary axis. We study the reducibility of such systems to pseudonormal form. We prove that the problem of finitely smooth ...
Added: November 27, 2012
О.В. Благодырева, М.В. Карасев, Е.М. Новикова, Наноструктуры. Математическая физика и моделирование 2013 Т. 9 № 1 С. 5-18
We discuss physical parameters of quantum Penning nanotraps. In the case of 3:(-1) resonance between transverse frequencies of the trap we describe the reproducing measure on symplectic leaves corresponding to irreducible representations of non-Lie symmetry algebra with qubic commutation relations. Nonhomogeneity of the magnetic field and anharmonicity of the electric potential of the trap, after ...
Added: November 20, 2013
Karasev M., Russian Journal of Mathematical Physics 2017 Vol. 24 No. 3 P. 326-335
The Schrödinger operator for a spinless charge inside a layer with parabolic confinement profile and homogeneous magnetic field is considered. The Lorentz (cyclotron) and the confinement frequencies are assumed to be equal to each other. After inclination of the layer normal from the magnetic field direction there appears a pseudospin su(2)-field removing the resonance degeneracy ...
Added: September 26, 2017
Samovol V. S., Доклады Академии наук 2012 Vol. 85 No. 1 P. 122-124
In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has two purely imaginary eigenvalues, while the other eigenvalues lie outside the imaginary axis. We study the reducibility of such systems to pseudonormal form. We prove that the problem of finitely smooth ...
Added: November 27, 2012
Семенякин Н. С., Modern Physics Letters A 2014 Vol. 29 No. 35
In this paper, we investigate phase flows over ℂn and ℝn generated by vector fields V = ∑ Pi∂i where Pi are finite degree polynomials. With the convenient diagrammatic technique, we get expressions for evolution operators ev{V|t} : x(0) ↦ x(t) through the series in powers of x(0) and t, represented as sum over all ...
Added: April 4, 2018
Zakharov D., Гуткин Б. С., Krupa M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2018 Vol. 97 No. 6 P. 062211-1-062211-5
We analyzed a generic relaxation oscillator under moderately strong forcing at a frequency much greater that the natural intrinsic frequency of the oscillator. Additionally, the forcing is of the same sign and, thus, has a nonzero average, matching neuroscience applications. We found that, first, the transition to high-frequency synchronous oscillations occurs mostly through periodic solutions ...
Added: October 4, 2018
Grushin V. V., Математические заметки 2017 Т. 102 № 6 С. 816-827
Asymptotic formulas are obtained for a class of integrals that are Fourier transforms of rapidly oscillating functions. These formulas contain special functions and generalize the well-known method of stationary phase. ...
Added: January 13, 2018
Grushin V. V., Russian Journal of Mathematical Physics 2019 Vol. 26 No. 3 P. 344-351
Formulas for the asymptotics of some class of integrals of rapidly oscillating functions that generalize the well-known stationary phase method, which were obtained in the previous paper of the author, are applied to integrals arising in the well-known tsunami hydrodynamic piston model in the case of a constant pool bottom. As a result, asymptotic formulas ...
Added: October 14, 2019
Колпаков И. Ю., Вестник Пермского национального исследовательского политехнического университета. Прикладная математика и механика 2013 № 11 С. 32-47
In work conditions of solvability of a boundary value problem for equation with a perturbed argument are received. For receiving conditions of solvability the boundary value problem write down on the corresponding space in the form of one quasilinear operator equation to which the theorem of existence of the solution with a condition on area ...
Added: April 7, 2015
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017