Asymptotic growth of trajectories of multifractional Brownian motion,with statistical applications to drift parameter estimation

We construct the least-square estimator for the unknown drift parameter in the multifractional Ornstein–Uhlenbeck model and establish its strong consistency in the non-ergodic case. The proofs are based on the asymptotic bounds with probability 1 for the rate of the growth of the trajectories of multifractional Brownian motion (mBm) and of some other functionals of mBm, including increments and fractional derivatives. As the auxiliary results having independent interest, we produce the asymptotic bounds with probability 1 for the rate of the growth of the trajectories of the general Gaussian process and some functionals of it, in terms of the covariance function of its increments.     

Hyperbolic Chaos in Systems Based on FitzHugh – Nagumo Model Neurons

In the present paper we consider and study numerically two systems based on model FitzHugh–Nagumo neurons, where in the presence of periodic modulation of parameters it is possible to implement chaotic dynamics on the attractor in the form of a Smale–Williams solenoid in the stroboscopic Poincaré map. In particular, hyperbolic chaos characterized by structural stability occurs in a single neuron supplemented by a time-delay feedback loop with a quadratic nonlinear element.     

Σ3 CSL boundary distributions in an austenitic stainless steel subjected to multidirectional forging followed by annealing

The effect of processing and annealing temperatures on the grain boundary characters in the ultrafine-grained structure of a 304-type austenitic stainless steel was studied. An S304H steel was subjected to multidirectional forging (MDF) at 500–800°C to total strains of ~4, followed by annealing at 800–1,000°C for 30 min. The MDF resulted in the formation of ultrafine-grained microstructures with mean grain sizes of 0.28–0.85 μm depending on the processing temperature. The annealing behaviour of the ultrafine-grained steel was characterized by the development of continuous post-dynamic recrystallization including a rapid recovery followed by a gradual grain growth. The post-dynamically recrystallized grain size depended on both the deformation temperature and the annealing temperature. The recrystallization kinetics was reduced with an increase in the temperature of the preceding deformation. The grain growth during post-dynamic recrystallization was accompanied by an increase in the fraction of Σ3ⁿ CSL boundaries, which was defined by a relative change in the grain size, i.e. a ratio of the annealed grain size to that evolved by preceding warm working (D/D₀). The fraction of Σ3ⁿ CSL boundaries sharply rose to approximately 0.5 in the range of D/D₀ from 1 to 5, which can be considered as early stage of continuous post-dynamic recrystallization. Then, the rate of increase in the fraction of Σ3ⁿ CSL boundaries slowed down significantly in the range of D/D₀ > 5. A fivefold increase in the grain size by annealing is a necessary condition to obtain approximately 50% Σ3ⁿ CSL boundaries in the recrystallized microstructure.     

Synthesis of novel racemic 3,4-dihydroferroceno[c]pyridines via the Ritter reaction

A new approach for the synthesis of functionalized racemic 3,4-dihydroferroceno[c]pyridines via the Ritter reaction of 2-methyl-1-ferrocenylpropan-1-ol with nitriles in the presence of methansulfonic acid was developed. The scope and limitations of the reaction were evaluated. Selected racemic 3,4-dihydroferroceno[c]pyridines were successfully separated by preparative HPLC on a Chiralcel OD-H column. The absolute configuration of the enantiomers was determined by X-ray crystal structure analysis.     

Ni olivine: thermal behavior of liebenbergite

The synthetic samples of nickel olivine were measured in the temperature range 100–630 K by the X-ray powder diffraction method. Temperature dependencies of molar volumes and coefficients of bulk thermal expansion of liebenbergite were determined. Interpolation and extrapolation of the experimental data were performed by the procedure based on the Debye–Mie–Gruneisen theory of solid body in the range from 50 to 2000 K, and the Gruneisen coefficient and Debye temperature were calculated. Heat capacity and its behavior in accordance with temperature were evaluated.

     

Thin-Layer Chromatography of Metal Cations Modified with Amines and Surfactants and the Sorption-Catalytic Detection of Cobalt(II) and Copper(II)

JPC – Journal of Planar Chromatography – Modern TLC - The thin-layer chromatography (TLC) procedures of metal cations, modified with amines and cationic surfactant micelles, followed by...     

Laser ablation of paper: Raman identification of products

Old paper samples are bleached using pulsed laser radiation with a wavelength of 532 nm. The ablation products of five paper samples that differ by composition and production dates are studied using Raman microspectroscopy. Cellulose, protein, calcite, titanium dioxide (anatase, rutile, and brookite), quartz, lazurite, bonattite, and dolomite are identified as ablation products.     

Thermodynamics and kinetics of intramolecular water assisted proton transfer in Na+ -1-methylcytosine water complexes

High-level ab initio predictions of the tautomerization equilibrium and rate constants of water-assisted proton transfer of 1-methyl-cytosine (MeC) to its MeC* imino tautomeric form in the presence of up to two water molecules (W) and the Na(+) cation were carried out. The calculated energy values were used to obtain the thermodynamic parameters and equilibrium concentration of MeC, its rare tautomer, and their complexes with up to two water molecules and the Na (+) cation. The rate constants for the tautomerization were obtained by using the instanton approach (a quasiclassical method based on the least-action principle). Hydration of MeC by one water molecule leads to an increase of the concentration of the MeC* tautomer in the equilibrium mixture and a decrease of the barrier of the MeC* formation (to 15.6 kcal/mol). If the Na(+) cation is present, the tautomeric form is much less favored, and the tautomerization barrier increases to 25.2 kcal/mol. It was found that MeC monohydrate has both the highest equilibrium (2.9 x 10(-2)) and rate (7.9 x 10(5) s(-1)) constants of tautomerization in comparison to the MeC*NaW and MeC*Na2W complexes containing the Na(+) cation. Moreover, this study also allows one to estimate the concentration of MeC present in the cell during DNA synthesis as the unwanted tautomer, which in forming a mismatched base pair can cause spontaneous point mutations. Kinetic simulations have demonstrated that the low values of equilibrium (10(-14)-10(-13)) and rate constants (10(-17)-10(-16) s(-1)) of tautomerization make contribution of the MeC*Na(+)W and MeC*Na(+)2W complexes to the point mutations in DNA unlikely. In contrast to these Na(+) complexes, MeC*W can reach an equilibrium concentration of 2.9 x 10(-2) within 10(-7) s; thus, it can increase the probability of the point mutations.