The paper formulates inverse homogenization problem as a problem of recovery of Markov function using diagonal Padé approximants. Inverse homogenization or de-homogenization problem is a problem of deriving information about the microgeometry of composite material from its effective properties. The approach is based on reconstruction of the spectral measure in the analytic Stieltjes representat...

Recently we generalized the max algebra system to the class of nonnegative  tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and i...

A nonclassical skew-selfadjoint system of two linear differential equations is considered, which depends rationally on the spectral parameter. Systems of this type are related to the sine-Gordon equation. We introduce the notion of Wp-functions (Weyl functions) which are defined in a neighborhood of the poles. The main results are theorems on the existence and uniqueness of the Weyl functions, ...

We present new numerical methods for the solution of inverse spectral problem to determine the dielectric constants of core and cladding in optical fibers. These methods use measurements of propagation constants. Our algorithms are based on approximate solution of a nonlinear nonselfadjoint eigenvalue problem for a system of weakly singular integral equations.We study three inverse problems and...

New formulas on the inverse problem for the continuous skewself-adjoint Dirac type system are obtained. For the discrete skewself-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. BorgMarchenko type uniqueness theorems are derived for both discrete and ...

The sine-Gordon equation in light cone coordinates is solved when Dirichlet conditions on the L-shape boundaries of the strip {t ∈ [0, T ]} ∪ {x ∈ [0,∞]} are prescribed in a class of functions that vanish (mod 2π) as x → ∞ at initial time. The method is based on the inverse spectral transform (IST) for the Schrödinger spectral problem on the semi-line x > 0 solved as a Hilbert boundary value pr...

We use an inverse scattering approach to study multi-peakon solutions of the Degasperis–Procesi (DP) equation, an integrable PDE similar to the Camassa–Holm shallow water equation. The spectral problem associated to the DP equation is equivalent under a change of variables to what we call the cubic string problem, which is a third order non-selfadjoint generalization of the well-known equation ...

The hybrid method presented in this paper, is based on the inverse of the belonging joint probability (IBJP) and the power spectral density (PSD) to detect new anomalous in a random signal representing normal state behavior of a given machine. We first compute the power spectral density (PSD) of the normal state signal and then represent this PSD signal by an adequate Gaussian white noise (GWN)...

An overview of the author’s results is given. Property C stands for completeness of the set of products of solutions to homogeneous linear Sturm-Liouville equations. The inverse problems discussed include the classical ones (inverse scattering on a half-line, on the full line, inverse spectral problem), inverse scattering problems with incomplete data, for example, inverse scattering on the ful...