On Higher-Order Differential Operators with Singularity inside the Interval

Mathematical Notes -     

Reconstruction of Sturm-Liouville differential operators on A-graphs

We study the inverse problem of spectral analysis for Sturm-Liouville operators on A-graphs. We obtain a constructive procedure for solving the inverse problem of reconstruction of coefficients of differential operators from spectra and prove the uniqueness of the solution.     

Higher-Order Differential Equations Having a Singularity in an Interior Point

Ordinary differential equations of an arbitrary order having a non-integrable singularity inside the interval are considered 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.     

Modeling of drying in films of colloidal particles

The process of film formation on a solid substrate from polymer colloid dispersion during solvent evaporation has been investigated by means of the Monte Carlo simulation method. Colloid particles are modeled as hard spheres. Time evolution of the colloid density distribution and coverage of the solid substrate are studied. Both density and structure of colloid film is shown to depend strongly on the evaporation rate. At a low evaporation rate, the coexistence of hexagonal and tetragonal domains of dried colloid monolayer has been observed. The results of monolayer structure are in good agreement with the confocal scanning laser microscopy observations of Dullens et al. (2004).     

Effect of the acrylic acid content on the permeability and water uptake of poly(styrene-co-butyl acrylate) latex films

In this contribution, a theoretical modeling of the latex film formation is presented and compared to experimental results: water vapor permeability and latex film capacitance are studied as a function of acrylic acid content in poly(styrene-co-butyl acrylate) latex films. It has been shown that both water uptake and water vapor permeability are mainly affected by film morphology which in turn is defined by intercolloidal interaction and drying rate.     

Reconstructing parameters of a medium from incomplete spectral information

The problem of the synthesis of a stratified medium with specified amplitude and phase properties is investigated. The wave propagation in the medium is described by a system of differential equations. The synthesis problem considered in the paper relates to inverse problems of spectral analysis with incomplete spectral information. Using the contour integral method we study properties of spectral characteristics and obtain algorithms for the solution of the synthesis problem for differential equations with singularities.     

On the Inverse Problem for Differential Operators on a Finite Interval with Complex Weights

Mathematical Notes - Inverse problems of spectral analysis for second-order differential operators on a finite interval with complex-valued weights and with an arbitrary number of discontinuity...     

An inverse problem for Sturm-Liouville operators on arbitrary compact spatial networks

An inverse spectral problem is studied for Sturm-Liouville differential operators on arbitrary compact graphs (spatial networks). A uniqueness theorem of recovering operators from their spectra is proved, and a constructive procedure for the solution of the inverse problem is provided.     

Inverse problems for first-order integro-differential operators

Mathematical Notes - Inverse spectral problems for first-order integro-differential operators on a finite interval are studied, the properties of spectral characteristics are established, and...