Results 51 to 60 of about 11,416,461 (242)

Multi‐MeV Electron Occurrence and Lifetimes in the Outer Radiation Belt and Slot Region During the Maximum of Solar Cycle 22

Space Weather, Volume 23, Issue 10, October 2025.
Abstract The Combined Release and Radiation Effects Satellite (CRRES) observed the response of the Van Allen radiation belts to peak solar activity within solar cycle 22. This study analyses relativistic and ultra‐relativistic electron occurrence and loss timescales within the CRRES High Energy Electron Fluxometer (HEEF) data set, including during ...
R. T. Desai, J. Perrin, N. P. Meredith, S. A. Glauert, S. Ruparelia, W. R. Johnston   +5 more
wiley   +1 more source

Shape invariance through Crum transformation

, 2006
We show in a rigorous way that Crum's result on equal eigenvalue spectrum of Sturm-Liouville problems can be obtained iteratively by successive Darboux transformations. It can be shown that all neighbouring Darboux-transformed potentials of higher order,
Bagchi B. K., Cycon H. L., Darboux G., Gel’fand M., Gendenshtein L., Gendenshtein L., Gesztesy F., Gesztesy F., H. C. Rosu, Ince E. L., José Orlando Organista, Marchenko V. A., Marek Nowakowski   +12 more
core   +1 more source

Finite‐Dimensional Reductions and Finite‐Gap‐Type Solutions of Multicomponent Integrable PDEs

Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.
ABSTRACT The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well‐known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent Camassa–Holm, Dullin–Gottwald–Holm, and Kaup ...
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev   +2 more
wiley   +1 more source

Inverse nodal problem for a class of nonlocal sturm‐liouville operator

Mathematical Modelling and Analysis, 2010
Inverse nodal problem consists in constructing operators from the given nodes (zeros) of their eigenfunctions. In this work, the Sturm‐Liouville problem with one classical boundary condition and another nonlocal integral boundary condition is considered.
Chuan-Fu Yang
doaj   +1 more source

Self‐similar instability and forced nonuniqueness: An application to the 2D euler equations

Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.
Abstract Building on an approach introduced by Golovkin in the ’60s, we show that nonuniqueness in some forced partial differential equations is a direct consequence of the existence of a self‐similar linearly unstable eigenvalue: the key point is a clever choice of the forcing term removing complicated nonlinear interactions.
Michele Dolce, Giulia Mescolini
wiley   +1 more source

Studies on Fractional Differential Equations With Functional Boundary Condition by Inverse Operators

Mathematical Methods in the Applied Sciences, Volume 48, Issue 11, Page 11161-11170, 30 July 2025.
ABSTRACT Fractional differential equations (FDEs) generalize classical integer‐order calculus to noninteger orders, enabling the modeling of complex phenomena that classical equations cannot fully capture. Their study has become essential across science, engineering, and mathematics due to their unique ability to describe systems with nonlocal ...
Chenkuan Li
wiley   +1 more source

Development of a methodology for transitioning from a spectral equation relative to a spatial variable to a differential equation relative to a spectral parameter in the Sturm-Liouville problem for a one-dimensional periodic two-layer photonic crystal

Вісник Харківського національногоуніверситету імені В.Н. Каразіна. Серія: Радіофізика та електроніка
Relevance. In connection with solving the problem of scattering of electromagnetic waves (diffraction problem) on objects such as photonic crystals (one-dimensional periodic unbounded), it is important to study the dispersion relation.
O. V. Kazanko, O. E. Penkina, O. V. Golovko   +2 more
doaj   +1 more source

On the equivalence of discrete Sturm–Liouville problem with nonlocal boundary conditions to the algebraic eigenvalue problem

Lietuvos Matematikos Rinkinys, 2015
We consider the finite difference approximation of the second order Sturm–Liouville equation with nonlocal boundary conditions (NBC). We investigate the condition when the discrete Sturm–Liouville problem can be transformed to an algebraic eigenvalue ...
Jurij Novickij, Artūras Štikonas
doaj   +1 more source

The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator

, 2012
A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm-Liouville problem via the interpolation theory of the
Apagyi B, Barnabás Apagyi, Coz M, De Alfaro V, Gelfand I M, Gelfand I M, Hilk D, Kuberczyk J, Levitan B M, Marchenko V A, Palmai T, Palmai T, Povzner A, Tamás Pálmai   +13 more
core   +1 more source

Variational principles for spectral analysis of one Sturm-Liouville problem with transmission conditions

, 2016
We study certain spectral aspects of the Sturm-Liouville problem with a finite number of interior singularities. First, for self-adjoint realization of the considered problem, we introduce a new inner product in the direct sum of the L2$L_{2}$ spaces of ...
K. Aydemir, O. Mukhtarov
semanticscholar   +1 more source