Spectral Analysis for an Indefinite Singular Sturm-Liouville Problem

Direct and inverse problems of spectral analysis are studied for an indefinite singular boundary value problem coming from astrophysics. We establish properties of the spectrum, prove completeness and expansion theorems and investigate the inverse problem of recovering the differential equation from the given spectral characteristics.     

Structural analysis and probing the conformational space of dansylamide by means of gas-phase electron diffraction and quantum chemistry

Dansylamide is perhaps the most ubiquitous fluorophore due to its donor-acceptor bifunctionality and its ability to form intra- and intermolecular hydrogen bonding. Among the diversity of its applications is the development of new generation of biosensors for the in vivo monitoring of traces of metals. The structure and conformational stability of dansylamide in the gas phase were investigated for the first time by a combined gas-phase electron diffraction-mass spectrometry (GED/MS), complemented by quantum chemical calculations. GED data indicate that different skewed conformers exist at T?=?464 K, which are characterized by the deviation of two S–N bonds from the perpendicular orientation relative to the naphthalene plane. Maybe the most indicative structural parameters for electronic interactions between the donor-acceptor substituents and the aromatic naphthalene and the subsequent stabilization of the favorable skewed eclipsed-syn conformer are the dihedral angles C₉–C₁–S–N and C₁₀–C₅–N–C with the experimentally determined values of 66.8° (32) and 68.1° (72), respectively. The role of –SO₂NH₂ by forming intramolecular hydrogen bonds was scrutinized by employing the natural bond orbital approach (NBO), quantum theory atoms in molecules (QTAIM), and molecular electrostatic potential (MESP). The non-planarity of the naphthalene skeleton due to the electronic interactions with the substituents and its consequence for the fluorescence activity of dansylamide have been discussed.     

Constrained equilibrium as a tool for characterization of deformable porous media

A new method for characterizing the deformable porous materials with noncritical adsorption probes is proposed. The mechanism is based on driving the adsorbate through a sequence of constrained equilibrium states with the insertion isotherms forming a pseudocritical point or a van der Waals-type loop. In the framework of a perturbation theory and Monte Carlo simulations we have found a link between the loop parameters and the host morphology. This allows one to characterize porous matrices through analyzing a shift of the pseudocritical point and a shape of the pseudospinodals.     

On the determination of differential equations with singularities and turning points

The inverse problem of synthesizing parameters of differential systems having a finite number of arbitrary order singularities and turning points is investigated. We establish properties of the spectral characteristics, prove a uniqueness theorem and provide a prodcedure for constructing the solution of the inverse problem.     

Inverse problems for matrix Sturm-Liouville operators

Inverse spectral problems for nonselfadjoint matrix Sturm-Liouville differential operators on a finite interval and on the half-line are studied. As a main spectral characteristic, we introduce the so-called Weyl matrix and prove that the specification of the Weyl matrix uniquely determines the matrix potential and the coefficients of the boundary conditions. Moreover, for a finite interval, we also study the inverse problems of recovering matrix Sturm-Liouville operators from discrete spectral data (eigenvalues and “weight” numbers) and from a system of spectra. The results thus obtained are natural generalizations of the classical results in inverse problem theory for scalar Sturm-Liouville operators. Dedicated to the memory of B. M. Levitan     

A Facile and Efficient Synthesis of Organocyclosiloxanes

A new facile preparative method for the synthesis of organocyclosiloxanes is reported. Ring closure of the dichlorosilanes with NaHCO 3 and pyridine gave mixture of organocyclosiloxanes with cyclotrisiloxane as a main product.     

Inverse problems for differential operators of any order on trees

Inverse spectral problems for ordinary differential operators of any order on compact trees are studied. As the main spectral characteristics, Weyl matrices, which generalize the Weyl m-function for the classical Sturm-Liouville operator are introduced and studied. A constructive solution procedure for the inverse problem based on Weyl matrices is suggested, and the uniqueness of the solution is proved. The reconstruction of differential equations from discrete spectral characteristics is also considered.     

Dielectric properties of thin films of partially deuterated betaine phosphite with large- and small-block structures

Ferroelectric thin films of partially deuterated betaine phosphite (DBPI) have been grown by evaporation on NdGaO₃ substrates with a preliminarily deposited structure of interdigitated electrodes. The block structure of the films is a texture in which the polar axis b is oriented in the plane of the film and the a* axis is perpendicular to this plane. Typical dimensions of the single-crystal blocks in DBPI films substantially exceeds the distance between the interdigitated electrodes (d = 50 μm). However, DBPI films in which the block structure has characteristic dimensions of the order of d have also been grown. Investigations of the dielectric properties of the films have demonstrated that the dimensions of the block structure have little effect on the behavior of a small-signal dielectric response, which, in the phase transition region, is characterized by a strong anomaly of the capacitance of the structure at T = T _c and by a glass-like behavior of the capacitance C and dielectric loss tangent tanδ in the temperature range of 120–200 K. By contrast, the low-frequency strong-signal dielectric response (dielectric hysteresis loops) in the structures with small blocks differs significantly from that observed for large-block structures. The difference in the frequency behavior of the hysteresis loops in the large-block and small-block structures is associated with the limitation of motion of domain walls in the case of small blocks.