A new method for solving the relativistic inverse stellar structure problem is presented. This method determines a spectral representation of the unknown high-density portion of the stellar equation of state from a knowledge of the total massesM and radii R of the stars. Spectral representations of the equation of state are very efficient, generally requiring only a few spectral parameters to a...

We consider stability and approximate reconstruction of Riemannian manifold when the finite number of eigenvalues of the LaplaceBeltrami operator and the boundary values of the corresponding eigenfunctions are given. The reconstruction can be done in stable way when manifold is a priori known to satisfy natural geometrical conditions related to curvature and other invariant quantities.

A spectral stochastic approach to the inverse heat conduction problem (IHCP) is presented. In IHCP, one computes an unknown boundary heat flux from given temperature history data at a sensor location. In the stochastic inverse heat conduction problem (SIHCP), the full statistics of the boundary heat flux are computed given the stochastic nature of the temperature sensor data and in general acco...

This paper develops and implements a new algorithm for calculating wave trace invariants of a bounded plane domain around a periodic billiard orbit. The algorithm is based on a new expression for the localized wave trace as a special multiple oscillatory integral over the boundary, and on a Feynman diagrammatic analysis of the stationary phase expansion of the oscillatory integral. The algorith...

The dielectric function of a composite depends on the geometry of the composite and the dielectric functions of the constituent materials. In the Bergman–Milton spectral representation for a two-component composite, all of the relevant geometric information can be captured in a spectral function which is independent of the material properties. Extracting the spectral function from experimental ...

In this paper the spectral problem of third order for the inverse scattering transform (IST) method is solved. For the discrete part of the spectral data, the two-multiple poles are taken into account. The line spectrum of continuum states for the IST method is examined as well. The suggested spectrum approximates in first order the step-function. The scope for the suggested spectral data is de...

The inverse stellar structure problem determines the equation of state of the matter in stars from a knowledge of their macroscopic observables (e.g. their masses and radii). This problem was solved in a previous paper by constructing a spectral representation of the equation of state whose stellar models match a prescribed set of macroscopic observables. This paper improves and extends that wo...

Assume that M is a compact Riemannian manifold of bounded geometry given by restrictions on its diameter, Ricci curvature and injectivity radius. Assume we are given, with some error, the first eigenvalues of the Laplacian ∆ on M as well as the corresponding eigenfunctions restricted on an open set in M . We then construct a stable approximation to the manifold (M,g). Namely, we construct a met...

We reconstruct a rational Lax matrix of size R+ 1 from its spectral curve (the desingularization of the characteristic polynomial) and some additional data. Using a twisted Cauchy–like kernel (a bi-differential of bi-weight (1−ν, ν)) we provide a residue-formula for the entries of the Lax matrix in terms of bases of dual differentials of weights ν, 1−ν respectively. All objects are described in...