A bounded linear operator T acting on a Hilbert space is called Coburn operator if ker(T ? λ) = {0} or ker(T ? λ)*= {0} for each λ ∈ C. In this paper, the authors define other Coburn type properties for Hilbert space operators and investigate the compact perturbations of operators with Coburn type properties. They characterize those operators for which has arbitrarily small compact perturbation to have some fixed Coburn property.Moreover, they study the stability of these properties under small compact perturbations. 相似文献
We simulate the polarization manipulation of bright-dark vector bisolitons at 1-μm wavelength regime.Through changing the pulse parameters,different kinds of pulse shapes and optical spectra are generated in output orthogonal polarization directions.When the input vector bisoliton is polarization-locked with 1064 nm central wavelength,“1+1”fundamental dark-dark and“2+1”pseudo-high-order bright-dark group-velocity-locked vector solitons can be achieved through changing the projection angle.When the input vector bisoliton is group-velocity-locked with 1063 nm and 1065 nm central wavelengths,“2+1”and“2+2”pseudo-high-order bright-dark group-velocity-locked vector solitons,bright-dark group-velocity-locked vector solitons with chirp-like temporal oscillations are generated.Our simulation results can provide beneficial conduct for polarization manipulation of vector multi-solitons,and have promising applications in quantum information register,optical communications,nanophotonics,and all-optical switching. 相似文献
This paper presents a long-term analysis of one-stage extended Runge–Kutta–Nyström (ERKN) integrators for highly oscillatory Hamiltonian systems. We study the long-time numerical energy conservation not only for symmetric integrators but also for symplectic integrators. In the analysis, we neither assume symplecticity for symmetric methods, nor assume symmetry for symplectic methods. It turns out that these both types of integrators have a near conservation of the total and oscillatory energy over a long term. To prove the result for explicit integrators, a relationship between ERKN integrators and trigonometric integrators is established. For the long-term analysis of implicit integrators, the above approach does not work anymore and we use the technology of modulated Fourier expansion. By taking some adaptations of this technology for implicit methods, we derive the modulated Fourier expansion and show the near energy conservation.