Reduction Principle and Asymptotic Phase for Center Manifolds of Parabolic Systems with Nonlinear Boundary Conditions

We prove the reduction principle and study other attractivity properties of the center and center-unstable manifolds in the vicinity of a steady-state solution for quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on bounded or exterior domains.     

Synthesis and Structure of the Heterocyclic Phosphorus Containing Derivatives of [60] Fullerene

Abstract

Data on the structure of cycloadducts of organophosphorus dipolar reagents and fullerenes arc absent, to our knowledge. We died the reactions and the shucturc of cycloadducts of phosphorylated azidcs and nitrile oxide with [60]fullcrcnc. The cycloaddition of diphcnylphosphinic llzide to fullcrme has bcm determined to lead to the 1 -[(N-diphenylphosphoryl)amino]-2-hydroxy[6O]hllcrme (l), the mixhuc of phosphorylated aziridinofullcrcne (2) and derivative of fullerne (3) with one aziridine fragment and one aminohydmxy-fragment, or to product (4), depending on the conditions of don .     

Heterocyclization of electrophilic alkenes with tetranitromethane revisited: regiochemistry and the mechanism of nitroisoxazole formation

Revised regiochemistry for the heterocyclization of electrophilic alkenes with tetranitromethane (TNM) in the presence of triethylamine, providing rapid access to nitroisoxazoles, is reported. The formation of 5-nitroisoxazoles previously incorrectly assigned as 3-nitro regioisomers, has now been established unambiguously by X-ray crystallography. Empirical computations with ACD/CNMR Predictor, based both on hierarchical ordering of spherical environments (HOSE) and an algorithm of artificial neural networks (ANN), and also Density Functional Theory computations of the ¹³C NMR chemical shifts for the 3- versus 5-nitroisoxazoles are shown to consistently match the spectra of the experimentally observed 5-regioisomers.     

“Slow” wave of zero-sound in degenerate Fermi gas

The dynamic Hartree-Fock theory with point-like interaction is used to calculate the speed of sound and damping factor of a zero-sound wave propagating in a degenerate Fermi gas. This wave propagates slower than Fermi velocity. It is shown, that if the interaction is weak and density is small, then the damping of such a wave can be small. A possibility of discovering such waves in ultracold Fermi gases is discussed.     

Running coupling corrections to non-linear evolution for diffractive dissociation

We determine running coupling corrections to the kernel of the non-linear evolution equation for the cross section of single diffractive dissociation in high energy DIS. The running coupling kernel for diffractive evolution is found to be exactly the same as the kernel of the rcBK evolution equation.     

Synthesis,structure, and the energetic properties of tetraazidopyridine-4-carbonitrile

Chemistry of Heterocyclic Compounds - Nucleophilic substitution of fluorine atoms in 2,3,5,6-tetrafluoropyridine-4-carbonitrile with sodium azide was used to obtain...     

Kinetic approach to partially overlapped thermal decomposition processes

Practical usefulness of the kinetic deconvolution for partially overlapped thermal decomposition processes of solids was examined by applying to the co-precipitated basic zinc carbonate and zinc carbonate. Comparing with the experimental deconvolutions by thermoanalytical techniques and mathematical deconvolutions using different statistical fitting functions, performance of the kinetic deconvolution based on an accumulative kinetic equation for the independent processes overlapped partially was evaluated in views of the peak deconvolution and kinetic evaluation. Two-independent kinetic processes of thermal decompositions of basic zinc carbonate and zinc carbonate were successfully deconvoluted by means of the thermoanalytical measurements in flowing CO₂ and by applying sample controlled thermal analysis (SCTA). The deconvolutions by the mathematical curve fittings using different fitting functions and subsequent formal kinetic analysis provide acceptable values of the mass-loss fractions and apparent activation energies of the respective reaction processes, but the estimated kinetic model function changes depending on the fitting functions employed for the peak deconvolution. The mass-loss fractions and apparent kinetic parameters of the respective reaction processes can be optimized simultaneously by the kinetic deconvolution based on the kinetic equation through nonlinear least square analysis, where all the parameters indicated acceptable correspondences to those estimated through the experimental and mathematical deconvolutions. As long as the reaction processes overlapped are independent kinetically, the simple and rapid procedure of kinetic deconvolution is useful as a tool for characterizing the partially overlapped kinetic processes of the thermal decomposition of solids.