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Spectral properties of Dirac operators with singular potentials

We investigate the spectral properties of Dirac operators with singular potentials which are constructed by means of a cut-off procedure. We prove the invariance of the essential spectrum, establish norm resolvent convergence of the cut-off operators, and prove spectral gap formulas.     

Synthesis and crystal structure of new heterocycles containing 1,2,4-oxadiazole, 1,2,4-oxadiazolone (thione), hydantoin,and mercaptobenzimidazole units

A number of 1,2,4-oxadiazolone and mercapto nitro benzimidazole derivatives containing 1,2,4-oxadiazole and hydantoin moieties have been prepared, and their structures were identified by means of spectral/physical characteristics including X-ray diffraction data.     

Synthesis of Some Azamacrocycles Bearing 1,2,4-Oxadiazole and 1,2,3-Triazole Moieties

Russian Journal of Organic Chemistry - A tetraazacrown ether, 4,9-di(prop-2-yn-1-yl)-1,4,9,12-tetraazacyclohexadecane-2,11-dione, bearing propargyl groups on two nitrogens was synthesized starting...     

Heterogeneous Au/Ru hybrid nanoparticle decorated graphene oxide nanosheet catalyst for the catalytic reduction of nitroaromatics

Research on Chemical Intermediates - Gold and ruthenium nanoparticles have been self-assembled on graphene oxide by using cysteine or glutamic acid junctions as heterogeneous nanocatalysts in the...     

Persistence,Permanence and Global Stability for an n-Dimensional Nicholson System

For a Nicholson’s blowflies system with patch structure and multiple discrete delays, we analyze several features of the global asymptotic behavior of its solutions. It is shown that if the spectral bound of the community matrix is non-positive, then the population becomes extinct on each patch, whereas the total population uniformly persists if the spectral bound is positive. Explicit uniform lower and upper bounds for the asymptotic behavior of solutions are also given. When the population uniformly persists, the existence of a unique positive equilibrium is established, as well as a sharp criterion for its absolute global asymptotic stability, improving results in the recent literature. While our system is not cooperative, several sharp threshold-type results about its dynamics are proven, even when the community matrix is reducible, a case usually not treated in the literature.     

Determining the resonance frequencies of forced vibrations of turbogenerators with foundations

The model method for determination of dynamic properties of framed foundations on plastic scale models is elaborated. Position shifting of resonance peaks has been found by evaluation of different response curves, measured on models. Theoretical and experimental analysis of forced vibrations of complex damped mechanical system with several degrees of freedom has shown that resonance peaks, measured at different points of the same system, correspond to various frequencies of exciting force. To locate eigen frequencies and dangerous resonances from results of measurements, it is necessary to plot the envelope of the set of curves and to determine the positions of its peaks, or, at least, to find the concentration of resonance maxima of all individual curves.