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.     

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.     

A new three-component one pot reaction of trinitromethane, epoxides and alkenes via dinitronitronates: synthesis of highly functionalized 3,3-dinitroisoxazolidines

A novel approach to acyclic alkyldinitronitronates using nucleophilic opening of epoxides with the trinitromethyl anion is presented. The scope and limitations of this synthetic procedure are presented. A series of highly functionalized 3,3-dinitroisoxazolidines were synthesized as mixtures of diastereomers.     

Partial-wave analysis of the ωπ0-system at high masses

A partial-wave analysis of the ω ωπ⁰-system produced in the π^- p→ωπ⁰ n reaction at 38 GeV/c beam momentum has been performed. A new 5^?- meson state,ρ ₅(22350), with a massM=2330±35 MeV and a width Γ=400±100 MeV, is observed. The analysis also confirms the 1^?- ρ(2150) meson, a radial-orbital excitation of the ρ(770), observed earlier by the GAMS Collaboration.     

Syringaldazine

The prostaglandin H synthase (PGHS) reaction has been studied with syringaldazine as the electron donor. Kinetic parameters of the reaction agreed with those for commonly used electron donors. The sensitivity of the PGHS activity detection in the presence of syring aldazine increases 10 times. A sensitive spectrophotometric assay for polyunsaturated fatty acid (PUFA) detection using syringaldazine as a new electron donor has been proposed.     

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.     

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...