On the properties of maps connected with inverse Sturm-Liouville problems

Let L _D be the Sturm-Liouville operator generated by the differential expression L _y = ?y″ + q(x)y on the finite interval [0, π] and by the Dirichlet boundary conditions. We assume that the potential q belongs to the Sobolev space W ₂ ^? [0, π] with some ? ≥ ?1. It is well known that one can uniquely recover the potential q from the spectrum and the norming constants of the operator L _D. In this paper, we construct special spaces of sequences ? ₂ ^θ in which the regularized spectral data {s _k } _?∞ ^∞ of the operator L _D are placed. We prove the following main theorem: the map F _q = {s _k } from W ₂ ^? to ? ₂ ^θ is weakly nonlinear (i.e., it is a compact perturbation of a linear map). A similar result is obtained for the operator L _DN generated by the same differential expression and the Dirichlet-Neumann boundary conditions. These results serve as a basis for solving the problem of uniform stability of recovering a potential. Note that this problem has not been considered in the literature. The uniform stability results are formulated here, but their proof will be presented elsewhere.     

Determination of iodotyrosines in food

A procedure is developed for the determination of iodinated amino acid residues—iodotyrosines—in food. The procedure is based on the hydrolysis of proteins of a food sample (meat, dairy products, bakery products, canned juices, etc.) followed by purification by solid-phase extraction. Analytes 3-iodo-L-tyrosine and 3,5-diiodo-L-tyrosine were determined by HPLC with mass spectrometric detection. The parameters of the chromatographic separation of iodotyrosines and the conditions of electrospray ionization are presented.     

Approximation of classes of convolutions by linear operators of special form

A parametric family of operators G _ρ is constructed for the class of convolutions W _p,m (K) whose kernel K was generated by the moment sequence. We obtain a formula for evaluating $E(W_{p,m} (K);G_\rho )_p : = \mathop {\sup }\limits_{f \in W_{p,m} (K)} \left\| {f - G_\rho (f)} \right\|_p .$ . For the case in which W _p,m (K)=W _r,β ^p,m , we obtain an expansion in powers of the parameter ?=?ln ρ for E(W _p,m ^r,β ; G _ρ,r ) _p , where β ∈ ?, γ > 0, and m ∈ ?, while p = 1 or p = ∞.     

A Convenient Synthetic Approach to Phenazone Derivatives Containing a 1,2,4-Triazine or Pyridine Fragment

Russian Journal of Organic Chemistry - An efficient synthetic approach to phenazone derivatives containing a 1,2,4-triazine or pyridine fragment has been proposed on the basis of successive...     

The Effect of the Isocyanate–Hydroxyl Ratio on the Structure and Properties of Hard Polyurethanes

A comprehensive study has been carried out of the structure and rheological and physicomechanical properties of low-temperature curing polyurethane compositions based on polyisocyanate and a blend of hydroxyl-containing oligomers of different reactivity. The maximum curing rate and strength parameters (tensile strength and Young’s modulus) have been shown to be achieved at the ratio of the reacting groups NCO : OH = 1.1.     

Inverse problem of the theory of distribution of the values of entire and analytic curves

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 43, pp. 119–132, 1985.     

Identification of Petroleum Products in Environmental Samples Using Gas Chromatography and Gas Chromatography–Mass Spectrometry

Typical analytical features of petroleum products in environmental samples were considered. Among them are typical shapes of chromatograms; peaks of n-alkanes; the ratio between n-alkanes with even and odd numbers of carbon atoms; peaks of biomarkers (isoprenanes, steranes, triterpanes, etc.); the predominance of methyl- and alkyl-substituted mono-, bi-, and polynuclear aromatic hydrocarbons over unsubstituted aromatic hydrocarbons; and other features. These features altogether enable reliable conclusions about the petroleum origin of the identified pollutants to be made.     

Reconstruction of the potential of the Sturm–Liouville operator from a finite set of eigenvalues and normalizing constants

It is well known that the potential q of the Sturm–Liouville operator L_y = ?y? + q(x)y on the finite interval [0, π] can be uniquely reconstructed from the spectrum \(\left\{ {{\lambda _k}} \right\}_1^\infty \) and the normalizing numbers \(\left\{ {{\alpha _k}} \right\}_1^\infty \) of the operator L_D with the Dirichlet conditions. For an arbitrary real-valued potential q lying in the Sobolev space \(W_2^\theta \left[ {0,\pi } \right],\theta > - 1\), we construct a function q_N providing a 2N-approximation to the potential on the basis of the finite spectral data set \(\left\{ {{\lambda _k}} \right\}_1^N \cup \left\{ {{\alpha _k}} \right\}_1^N\). The main result is that, for arbitrary τ in the interval ?1 ≤ τ < θ, the estimate \({\left\| {q - \left. {{q_N}} \right\|} \right._\tau } \leqslant C{N^{\tau - \theta }}\) is true, where \({\left\| {\left. \cdot \right\|} \right._\tau }\) is the norm on the Sobolev space \(W_2^\tau \). The constant C depends solely on \({\left\| {\left. q \right\|} \right._\theta }\).