Saratov, Russia
Saratov, Russia

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Chetverikov A.P.,Saratov University | Ebeling W.,Humboldt University of Berlin | Velarde M.G.,Complutense University of Madrid
International Journal of Quantum Chemistry | Year: 2010

We present a model for nonlinear excitations in bio(macro)-molecules stable at room temperature and offering a possible mechanism for electron transfer over long distances (e.g., 100 Å and beyond). It is based on the excitation of generally supersonic solitons in a heated one-dimensional lattice with Morse interactions in a temperature range from low to physiological level. We study the influence of these supersonic excitations on electrons moving in the lattice. The lattice units (considered as "atoms") are treated by classical Langevin equations. The densities of the core electrons are in a first estimate represented by Gaussian densities, thus permitting to visualize lattice compressions as enhanced density regions. The evolution of excess, added free electrons is modeled in the tight-binding approximation using first Schrödinger equation and, subsequently, the assumption of local canonical equilibrium corresponding to an adiabatic approximation. The relaxation to thermal equilibrium is studied in a perturbative approach by means of the Pauli master equation. © 2009 Wiley Periodicals, Inc.


Freiling G.,University of Duisburg - Essen | Yurko V.A.,Saratov University
Tamkang Journal of Mathematics | Year: 2010

Inverse nodal problems are studied for second-order differential operators on graphs with a cycle and with standard matching conditions in the internal vertex. Uniqueness theorems are proved, and a constructive procedure for the solution is provided.


Freiling G.,University of Duisburg - Essen | Yurko V.A.,Saratov University
Inverse Problems | Year: 2010

Sturm-Liouville differential operators in a finite interval with boundary conditions depending polynomially on the spectral parameter are studied. We establish the properties of the spectral characteristics and investigate three inverse problems of recovering the operator either from the so-called Weyl function, or from discrete spectral data or from two spectra. For these inverse problems we provide procedures for constructing their solutions by the method of spectral mappings. © 2010 IOP Publishing Ltd.


Freiling G.,University of Duisburg - Essen | Ignatyev M.,Saratov University
Inverse Problems | Year: 2011

A scattering problem is studied for second-order differential operators on noncompact graphs with a cycle and with standard matching conditions in the internal vertices. Moreover, a uniqueness theorem for a corresponding inverse problem is proved. Problems of this type appear in various applications of mathematical physics, in particular in connection with the study of the properties of Aharonov-Bohm rings connected to one or several wires. © 2011 IOP Publishing Ltd.


Yurko V.,Saratov University
Tamkang Journal of Mathematics | Year: 2014

We study boundary value problemsoncompact graphswitha cycle for second-order ordinary differential equations with nonlinear dependence on the spectral parameter. We establish properties of the spectral characteristics and investigate inverse spectral problems of recovering coefficients of the differential equation from spectra. For these inverse problems we prove uniqueness theorems and provide procedures for constructing their solutions.


Yurko V.,Saratov University
Inverse Problems in Science and Engineering | Year: 2016

An inverse spectral problem is studied for differential pencils on graphs with a rooted cycle and with standard matching conditions in internal vertices. A uniqueness theorem is proved, and a constructive procedure for the solution is provided. © 2016 Taylor & Francis


Non-self-adjoint Sturm-Liouville differential operators on the half-line with a boundary condition depending polynomially on the spectral parameter are studied. We investigate the inverse problem of recovering the operator from the Weyl function. For this inverse problem we provide necessary and sufficient conditions for its solvability along with a procedure for constructing its solution by the method of spectral mappings.


Ignatyev M.,Saratov University
Tamkang Journal of Mathematics | Year: 2011

A scattering problem is studied for second-order differential operator on onevertex noncompact graph with a cycle and with standardmatching conditions in the vertex. A uniqueness theorem for a corresponding inverse problem is proved and a procedure for solving the problemis provided.


Fedoseev A.,Saratov University | Fedoseev A.,Russian Academy of Sciences
Tamkang Journal of Mathematics | Year: 2011

Arbitrary order ordinary differential equations on the half-line having a nonintegrable singularity inside are studied under additional matching conditions for solutions at the singular point. We construct special fundamental systems of solutions for this class of differential equations, study their asymptotical, analytical and structural properties and the behavior of the corresponding Stokes multipliers. These fundamental systems of solutions are used in spectral analysis of differential operators with singularities. We study the inverse problem of recovering differential equation from the given Weyl-Yurkomatrix and prove the corresponding uniqueness theorem.


Yurko V.,Saratov University
Tamkang Journal of Mathematics | Year: 2012

Non-selfadjoint Sturm-Liouville operators on a finite interval with nonseparated boundary conditions are studied. We establish properties of the spectral characteristics and investigate an inverse problem of recovering the operators from their spectral data. For this inverse problem we prove a uniqueness theorem and provide a procedure for constructing the solution.

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