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.

     

Sharp asymptotics of the <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> approximation error for interpolation on block partitions

Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing optimal approximating spline for each function proved to be very hard. In fact, no polynomial time algorithm of adaptive spline approximation can be designed and no exact formula for the optimal error of approximation can be given. Therefore, the next natural question would be to study the asymptotic behavior of the error and construct asymptotically optimal sequences of partitions. In this paper we provide sharp asymptotic estimates for the error of interpolation by splines on block partitions in \mathbbR^d{\mathbb{R}^d} . We consider various projection operators to define the interpolant and provide the analysis of the exact constant in the asymptotics as well as its explicit form in certain cases.     

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.     

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.     

Asymptotic multiphase Σ-solutions to the singularly perturbed Korteweg–de Vries equation with variable coefficients

The paper deals with constructing the asymptotic solution to the singularly perturbed Korteweg–de Vries equation with variable coefficients. The notion of an asymptotic multiphase Σ-solution is proposed, and an algorithm of its construction in a neighborhood of the point t = 0 is given. Some theorems concerning the exactness, with which such local asymptotic solution satisfies the equation under study are proved.     

Effects of Spiro-Cyclohexane Substitution of Nitroxyl Biradicals on Dynamic Nuclear Polarization

Spiro-substituted nitroxyl biradicals are widely used as reagents for dynamic nuclear polarization (DNP), which is especially important for biopolymer research. The main criterion for their applicability as polarizing agents is the value of the spin–spin exchange interaction parameter (J), which can vary considerably when different couplers are employed that link the radical moieties. This paper describes a study on biradicals, with a ferrocene-1,1′-diyl-substituted 1,3-diazetidine-2,4-diimine coupler, that have never been used before as DNP agents. We observed a substantial difference in the temperature dependence between Electron Paramagnetic Resonance (EPR) spectra of biradicals carrying either methyl or spirocyclohexane substituents and explain the difference using Density Functional Theory (DFT) calculation results. It was shown that the replacement of methyl groups by spirocycles near the N-O group leads to an increase in the contribution of conformers having J ≈ 0. The DNP gain observed for the biradicals with methyl substituents is three times higher than that for the spiro-substituted nitroxyl biradicals and is inversely proportional to the contribution of biradicals manifesting the negligible exchange interaction. The effects of nucleophiles and substituents in the nitroxide biradicals on the ring-opening reaction of 1,3-diazetidine and the influence of the ring opening on the exchange interaction were also investigated. It was found that in contrast to the methyl-substituted nitroxide biradical (where we observed the ring-opening reaction upon the addition of amines), the ring opening does not occur in the spiro-substituted biradical owing to a steric barrier created by the bulky cyclohexyl substituents.     

One-step synthesis of substituted 6-amino-5-cyanospiro-4-(piperidine-4')- 2H,4H-dihydropyrazolo[3,4-b]pyrans

Three-component condensation of 4-piperidinones (7), 5-pyrazolones (8), and malononitrile (4) proceeds chemically and electrochemically and is a convenient one-step means of synthesis of substituted 6-amino-5-cyanospiro-4-(piperidine-4')-2H,4H-dihydropyrazolo[3,4-b]pyrans (12). The electrochemical reactions proceed under milder conditions and with yields 12-15% greater than those of the reactions catalyzed by chemical bases.     

A new reaction of phosphorylated N-sulfonylimines with hydrophosphoryl agents involving C → N transfer of phosphoryl groups

Hydrophosphoryl nucleophilic agents add to the CN bond of N-sulfonyltrichloroacetimidoylphosphonates to give unstable C,C-diphosphorylated adducts, which undergo competitive 1,2-C → N phosphorotropic rearrangement and dehydrochlorination with the formation of aza-Perkow reaction products, C,N-diphosphorylated dichlorovinylsulfonamides. This is the first reliably identified case of an aza-Perkow transformation for acid phosphites and their initial nucleophilic attack at the C atom of the azomethine bond in the aza-substrates.     

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...