We study an inverse scattering problem for the Helmholtz equation on whole line. The goal of this paper is to obtain a Gelfand–Levitan–Marchenko (GLM)-type Jost solution that corresponds 1D differential operator. assume simplicity refraction index compact support. Using asymptotic behavior solutions with respect wave-number, we derive generalized Povzner–Levitan representation in space tempered...

Electromagnetic mass shifts, equal-time commutators (ETC), and their relation are analyzed, using the Jost-Lehmann representation for the forvrard Compton amplitude, The divergences in 6m are determined by Lorentz scal@rs associated with the ETC (when these exist). These results are illustrated by models with currents bilinear and linear in canonical fields. Existence of the ETC implies that th...

We derive curvature estimates for minimal submanifolds in Euclidean space for arbitrary dimension and codimension via Gauss map. Thus, SchoenSimon-Yau’s results and Ecker-Huisken’s results are generalized to higher codimension. In this way we improve Hildebrandt-Jost-Widman’s result for the Bernstein type theorem.

A system of linear integral equations is presented, which the analog Marchenko equations, to solve inverse scattering problem for associated with DNLS (derivative nonlinear Schrödinger) equations. The corresponding direct and problems are analyzed, recovery potentials Jost solutions from solution described. When reflection coefficients zero, some explicit formulas provided in terms a pair const...

In this article we develop the direct and inverse scattering theory of Ablowitz-Ladik system with potentials having limits equal positive modulus at infinity. particular, introduce fundamental eigensolutions, Jost solutions, coefficients, study their properties.We also discuss discrete eigenvalues corresponding norming constants. We then go on to derive left Marchenko equations whose solutions ...

The decay of the parameters {an, bn} for a Jacobi operator J on `(N) is related to the analyticity of the Jost function u(z; J) associated with J , which is in turn related to the spectral measure dμ of J . Damanik and Simon demonstrated the equivalence between the exponential decay of these parameters and the analyticity of the Jost function on a disk whose radius is given by the rate of decay...

Presenting an impressive model based on a large body of evidence, J. T. Jost, J. Glaser, A.W. Kruglanski, and F. J. Sulloway (2003) proposed that political conservatism uniquely serves epistemic, existential, and ideological needs driven by fears and uncertainties. The authors offer an alternative view based on conceptual considerations, historical events, features of communist ideology and pra...