Results 131 to 140 of about 15,028 (168)

The integrated inverse spectral problem

Journal of Molecular Structure, 1994
Abstract The concept of the integrated inverse spectral problem is discussed. Force constants and electro-optical parameters of molecules and half-widths of spectral bands may be simultaneously determined as a result of solving this problem. A novel expression based on the correlation factor and penalty function is offered as a solution to the ...
openaire   +1 more source

Spectral and scattering inverse problems

Journal of Mathematical Physics, 1978
The reconstruction of a differential operator form discrete spectra is reduced to its reconstruction from an S-matrix. This method makes it possible to solve the singular Sturm–Liouville problems which determine certain modes of a sphere. The results pave the way for handling studies in which information on modes and scattering results would all be ...
openaire   +1 more source

On an inverse spectral problem

Russian Journal of Mathematical Physics, 2017
The author considers the inverse spectral problem of reconstructing a function \(Q\) appearing in \[ (Qy')' +\lambda (y(x)-ky''(x))=0\text{ for }0\leq x \leq 1, \] where \(y\) is subject to \[ y(0)=y(1)=0,\, \int_0^1 y(x)dx=0 \] for \(k>0\). The sought \(Q\) is normalized by \(\int_0^1 Q(x)dx=1\) and the question is to find \(Q\) that minimizes the ...
openaire   +2 more sources

Inverse spectral problem for quantum graphs

Journal of Physics A: Mathematical and General, 2005
Summary: The inverse spectral problem for the Laplace operator on a finite metric graph is investigated. It is shown that this problem has a unique solution for graphs with rationally independent edges and without vertices having valence 2. To prove the result, a trace formula connecting the spectrum of the Laplace operator with the set of periodic ...
Kurasov, Pavel, Nowaczyk, Marlena
openaire   +2 more sources

New inverse spectral problem and its application

1997
The origin of inverse spectral problems lies in natural science, but the problems themselves are purely mathematical. At the beginning these problems attracted attention of mathematicians by their nonstandard physical contents. But we think that today their place in mathematical physics is determined rather by the unexpected connection between inverse ...
Anne Boutet de Monvel, Vladimir Marchenko   +1 more
openaire   +1 more source

Windowed Spectral Regularization of Inverse Problems

SIAM Journal on Scientific Computing, 2011
Regularization is used in order to obtain a reasonable estimate of the solution to an ill-posed inverse problem. One common form of regularization is to use a filter to reduce the influence of components corresponding to small singular values, perhaps using a Tikhonov least squares formulation.
Julianne Chung, Glenn Easley, Dianne P. O'Leary   +2 more
openaire   +1 more source

Lq -inverse spectral problems for semilinear Sturm–Liouville problems

Nonlinear Analysis: Theory, Methods & Applications, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Inverse Spectral Problems for Transmission Eigenvalues

2013
We previously encountered transmission eigenvalues and their role in inverse scattering theory in Chap. 6. We now return to this topic and consider the inverse spectral problem for transmission eigenvalues in the simplest possible case, i.e., when the inhomogeneous medium is an isotropic spherically stratified medium in ℝ3 and the eigenfunctions ...
Fioralba Cakoni, David Colton
openaire   +1 more source

Spectral Analysis of an Inverse Problem

2013
In this chapter we treat the solution of systems of linear equations in finite dimension spaces. This can be seen as examples of inverse reconstruction problems of Type I.We present a mathematical analysis of these linear inverse problems of finite dimension based on the spectral theorem.We study several aspects and behaviour of well-established ...
Francisco Duarte Moura Neto, Antônio José da Silva Neto   +1 more
openaire   +1 more source

Riemann Hypothesis and Inverse Spectral Problems

2012
In this chapter, we provide an alternative formulation of the Riemann hypothesis in terms of a natural inverse spectral problem for fractal strings. After stating this inverse problem in Section 9.1, we show in Section 9.2 that its solution is equivalent to the nonexistence of critical zeros of the Riemann zeta function on a given vertical line.
Michel L. Lapidus, Machiel van Frankenhuijsen   +1 more
openaire   +1 more source