Groups generated by 3-state automata over a 2-letter alphabet. II

This is the second in a series of papers presenting results on the classification of groups generated by 3-state automata over a 2-letter alphabet. Among the examples treated here, one can find automata generating the free product of 3 cyclic groups of order 2, a virtually free abelian group of rank 3, a solvable group of derived length 3, some virtually torsion-free weakly branch groups, and other interesting self-similar groups. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 50, Functional Analysis, 2007.     

The role of water H-bond imbalances in B-DNA substate transitions and peptide recognition revealed by time-resolved FTIR spectroscopy

The conformational substates B(I) and B(II) of the phosphodiester backbone in B-DNA are thought to contribute to DNA flexibility and protein recognition. We have studied by rapid scan FTIR spectroscopy the isothermal B(I)-B(II) transition on its intrinsic time scale. Correlation analysis of IR absorption changes occurring within seconds after a reversible incremental growth of the DNA hydration shell identifies water populations w(1) (PO(2)(-)-bound) and w(2) (non-PO(2)(-)-bound) exhibiting weaker and stronger H-bonds, respectively, than those dominating in bulk water. The B(II) substate is stabilized by w(2). The water H-bond imbalance of 3-4 kJ mol(-1) is equalized at little enthalpic cost upon formation of a contiguous water network (at 12-14 H(2)O molecules per DNA phosphate) of reduced ν(OH) bandwidth. In this state, hydration water cooperatively stabilizes the B(I) conformer via the entropically favored replacement of w(2)-DNA interactions by additional w(2)-water contacts, rather than binding to B(I)-specific hydration sites. Such water rearrangements contribute to the recognition of DNA by indolicidin, an antimicrobial 13-mer peptide from bovine neutrophils which, despite little intrinsic structure, preferentially binds to the B(I) conformer in a water-mediated induced fit. The FTIR spectra resolve sequential steps leading from PO(2)(-)-solvation to substate transition and eventually to base stacking changes in the complex. In combination with CD-spectral titrations, the data indicate that, in the absence of a bulk aqueous phase, as in molecular crowded environments, water relocation within the DNA hydration shell allows for entropic contributions similar to those assigned to water upon DNA ligand recognition in solution.     

On the interpolation of analytic mappings

Let (E ₀,E ₁) and (H ₀,H ₁) be two pairs of complex Banach spaces densely and continuously embedded into each other, E ₁ ? E ₀ and H ₁ ? H ₀ and also let $\left\| x \right\|_{E_0 } \leqslant \left\| x \right\|_{E_1 } $ . By E _θ = [E ₀, E ₁]_θ and H _θ = [H ₀, H ₁]_θ we denote the spaces obtained by the complex interpolation method for θ ∈ [0, 1], and by B _θ(0,R) we denote an open ball of radius R in the space E _θ. Let Φ: B ₀(0,R) → H ₀ be an analytic mapping taking B ₁(0,R) into H ₁, and let the estimates $\left\| {\Phi (x)} \right\|_{H_\theta } \leqslant C_\theta \left\| x \right\|_{H_\theta } for allx \in B_\theta (0,R)$ hold for θ = 0, 1. Then, for all θ ∈ (0, 1), the mapping Φ takes the ball B _θ(0,r) of radius r ∈ (0,R) in the space E _θ into H _θ and $\left\| {\Phi (x)} \right\|_{H_\theta } \leqslant C_0^{1 - \theta } C_1^\theta \frac{R} {{R - r}}\left\| x \right\|_{E_\theta } ,x \in B_\theta (0,r). $ .     

Estimates of Riesz Constants for the Dirac System with an Integrable Potential

We consider the Dirac operator on the interval [0, π] with an integrable potential P = (p_ij (x)) _i,j=1 ² and strongly regular boundary conditions U. It is well known that for any integrable potential P the system {y_n}_n∈Z of root functions of the strongly regular operator L_P,U is a Riesz basis in the space H = L₂[0, π] × L₂[0, π]. We obtain estimates, uniform on every compact set of potentials, of the Riesz constants ||T||||T^?1||, where T is the operator of transition to an orthonormal basis.     

Inverse problems for Sturm—Liouville operators with potentials in Sobolev spaces: Uniform stability

Two inverse problems for the Sturm-Liouville operator Ly = s-y″ + q(x)y on the interval [0, fy] are studied. For θ ⩾ 0, there is a mapping F:W ₂^θ → l _B ^θ, F(σ) = {s _k }₁^∞, related to the first of these problems, where W ₂^∞ = W ₂^∞[0, π] is the Sobolev space, σ = ∫ q is a primitive of the potential q, and l _B ^θ is a specially constructed finite-dimensional extension of the weighted space l ₂^θ, where we place the regularized spectral data s = {s _k }₁^∞ in the problem of reconstruction from two spectra. The main result is uniform lower and upper bounds for ∥σ - σ₁∥_θ via the l _B ^θ-norm ∥s − s₁∥_θ of the difference of regularized spectral data. A similar result is obtained for the second inverse problem, that is, the problem of reconstructing the potential from the spectral function of the operator L generated by the Dirichlet boundary conditions. The result is new even for the classical case q ∈ L ₂, which corresponds to θ = 1.     

Markers of the Nature of Ethyl Alcohol: Chromatographic Techniques for Their Detection

A procedure for distinguishing synthetic ethyl alcohols from those obtained by fermentation using gas chromatography-mass spectrometry is discussed. To reveal the nature of alcohols, the following special chemical markers (characteristic components of the impurity composition of synthetic alcohol) are used: 2-butanol, acetone, and crotonaldehyde. It was found that 2-butanol is the most informative marker of synthetic alcohol because it is not present in fermentation alcohols. Acetone and crotonaldehyde are additional markers of synthetic alcohol because they can occur in food alcohols. The results of studying the stability of the above impurity components and crotonaldehyde degradation products are presented.     

Microheterogeneous Polyetherhydroxylurethane Elastomers with Controlled Phase Structure for Structural Adhesives

Russian Journal of Applied Chemistry - Polyetherhydroxylurethane elastomers were prepared from mixtures of epoxy urethane oligomers and diglycidyl urethane, synthesized using isophorone...     

Artifacts in the determination of intravenous anesthetics by gas chromatography-mass spectrometry: Tramadol, the correlation between the structures of metabolites and impurity substances

The simultaneous determination of preparations used for multicomponent intravenous anesthesia (Promedol, tramadol, ketamine, diazepam, Thiopental, and phentanyl) and of their metabolites in blood and urine of surgical patients by chromatography-mass spectrometry was considered. Artifacts due to the Chromatographie interference of various preparations and their metabolites were revealed. The lability of the anesthetics and their metabolites in the course of sample preparation and analysis by gas chromatography (GC) was examined. The degradation products of the test preparations responsible for the generation of false positive results were found. Phentanyl, Promedol, ketamine, tramadol, Thiopental, diazepam, and their metabolites excreted with urine in the free forms were determined in the whole blood and urine of surgical patients. Bound forms of metabolites and the initial medicinal preparations excreted as complexes with glucuronic acid and other acids were also determined in urine. Metabolites and impurity substances in the intravenous anesthetics with similar mass spectra and retention times were distinguished. Methodological recommendations concerning the analysis of difficult-to-separate (by capillary gas chromatography) pairs of substances used for intravenous anesthesia and their metabolites are given. The following pairs of components are difficult to separate: Norpromedol-2-methylamino-5-chlorobenzophenon (a product of diazepam hydrolysis), norketamine-Promedol, and anhydrotramadol (a GC artifact)-ketamine. The cumulation of an impurity substance from the tramadol preparation, identified by us as epoxytramadol, in the body was examined.     

Best linear methods for approximation of bounded harmonic functions

We construct a best linear method for the approximation of bounded harmonic functions on compact subsets of the unit disk. We show that a system of functions orthonormal on the unit circle and optimal for the construction of the best linear approximation method is a Takenaka-Malmquist system. __________ Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 242–251, April–June, 2008.