Analyticity and uniform stability in the inverse spectral problem for Dirac operators

We prove that the inverse spectral mapping reconstructing the square integrable potentials on [0,1] of Dirac operators in the AKNS form from their spectral data (two spectra or one spectrum and the corresponding norming constants) is analytic and uniformly stable in a certain sense.Comment: 19 page

The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The Limit-Circle Case

We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditions for two real sequences to be the spectra of two different self-adjoint extensions of a Jacobi operator in the limit circle case.Comment: 26 pages. Changes in the presentation of some result

Multidimensional Borg-Levinson Theorem

We consider the inverse problem of the reconstruction of a Schr\"odinger operator on a unknown Riemannian manifold or a domain of Euclidean space. The data used is a part of the boundary $\Gamma$ and the eigenvalues corresponding to a set of impedances in the Robin boundary condition which vary on $\Gamma$. The proof is based on the analysis of the behaviour of the eigenfunctions on the boundary as well as in perturbation theory of eigenvalues. This reduces the problem to an inverse boundary spectral problem solved by the boundary control method

Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials

We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and suggest an algorithm reconstructing the potential from the spectral data that is based on Krein's accelerant method.Comment: 39 pages, uses iopart.cls, iopams.sty and setstack.sty by IO

Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page

Extrinsic Fluorescent Dyes as Tools for Protein Characterization

Noncovalent, extrinsic fluorescent dyes are applied in various fields of protein analysis, e.g. to characterize folding intermediates, measure surface hydrophobicity, and detect aggregation or fibrillation. The main underlying mechanisms, which explain the fluorescence properties of many extrinsic dyes, are solvent relaxation processes and (twisted) intramolecular charge transfer reactions, which are affected by the environment and by interactions of the dyes with proteins. In recent time, the use of extrinsic fluorescent dyes such as ANS, Bis-ANS, Nile Red, Thioflavin T and others has increased, because of their versatility, sensitivity and suitability for high-throughput screening. The intention of this review is to give an overview of available extrinsic dyes, explain their spectral properties, and show illustrative examples of their various applications in protein characterization