On the Least Number of Fixed Points of an Equivariant Map

The problem on the least number of fixed points of an equivariant map of a compact polyhedron on which a finite group acts is considered. For such a map, the least number of fixed points and the least number of fixed orbits are estimated in terms of invariants of the type of Nielsen numbers. The estimates obtained are sharp. The results are similar to those of P. Wong, but their assumptions are essentially weaker. Some notations are refined. The proofs are constructive.     

Erratum to: Zero Preservation for a Family of Multivalued Functionals,and Applications to the Theory of Fixed Points and Coincidences

Doklady Mathematics - An Erratum to this paper has been published: https://doi.org/10.1134/S1064562421010087     

Perforated cenosphere-supported pH-sensitive spin probes

Porous supports with an accessible internal volume and a shell providing the diffusive migration of pH-sensitive spin probes were obtained for the first time from hollow aluminosilicate cenospheres isolated from the coal fly ash. Using the methods of scanning electron microscopy and electron spin resonance, the morphology of different porous cenosphere modifications and its influence on the diffusion of spin probes from the internal volume were studied. When supporting aqueous solutions of a radical, the characteristic diffusion time for the mesoporous structure of the support is longer by a factor of 3–5 than that for the macroporous structure. Ferrospinel in a content of 6 wt.% do not virtually affect the diffusion rate of spin probes. A constant rate of radical migration of ∼1 μmol min⁻¹, determined by radical solubility in water, is achieved when a radical in the solid aggregate state is supported on the magnetic cenospheres. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 482–487, March, 2008.     

Approximation of coincidence points and common fixed points of a collection of mappings of metric spaces

On a complete metric space X, we solve the problem of constructing an algorithm (in general, nonunique) of successive approximations from any point in space to a given closed subsetA. We give an estimate of the distance from an arbitrary initial point to the corresponding limit points. We consider three versions of the subset A: (1) A is the complete preimage of a closed subspace H under a mapping from X into the metric space Y; (2) A is the set of coincidence points of n (n > 1) mappings from X into Y; (3) A is the set of common fixed points of n mappings of X into itself (n = 1, 2, …). The problems under consideration are stated conveniently in terms of a multicascade, i.e., of a generalized discrete dynamical system with phase space X, translation semigroup equal to the additive semigroup of nonnegative integers, and the limit set A. In particular, in case (2) for n = 2, we obtain a generalization of Arutyunov’s theorem on the coincidences of two mappings. In case (3) for n = 1, we obtain a generalization of the contraction mapping principle.     

Effect of the structure of alkoxy radicals on the mass-spectral fragmentation of dialkyl alkylphosphonates

Basic fragmentation reaction of dialkyl alkylphosphinates under the conditions of electron ionization proceeds in two steps. In the first step occurs cleavage of C-O bond and splitting the olefin radical off. The intermediate ion formed therewith exerts further fragmentation by the similar way. Peaks of the intermediate ions occurs in the spectra of all dialkyl alkylphosphonates except O-methyl derivatives. In the case of branching at α-carbon atoms of alkoxy radicals cleavage of the first carbon-carbon bond of the alkoxy radical unlike the case of alkyl fluorophosphonates, in the intermediate ion rather than in molecular ion and accompanied by the elimination of alkane. These found regularities allow to explain principal fragmentation pathways of a wide series of phosphoric acids esters of general formula (RO) _n P(O)X _n?3 (where X is R, Hal, or OMe) with both linear and branched in α-position alkoxy radicals.     

Leptonic and charged kaon decay modes of the phi meson measured in heavy-ion collisions at the CERN super proton synchrotron

We report on results of a measurement of meson production in central Pb-Au collisions at E(lab) = 158A GeV. For the first time in the history of high energy heavy-ion collisions, phi mesons were reconstructed both in the K+K- and the dilepton decay channels in the same experiment. This measurement yields rapidity densities near midrapidity, from the two decay channels, of 2.05 +/- 0.14(stat) +/- 0.25(syst) and 2.04 +/- 0.49(stat) +/- 0.32(syst), respectively. The shape of the measured transverse momentum spectrum is also in close agreement in both decay channels. The data rule out a possible enhancement of the phi yield in the leptonic over the hadronic decay channel of a factor 1.6 or larger at the 95% C.L. This rules out the discrepancy reported in the literature between measurements of the hadronic and dimuon decay channels by two different experiments.     

Investigation of a Relativistic Magnetron Supplied from a High-Current Linear Induction Accelerator

The physical processes in a system relativistic microwave generator - power supply unit with a strong feedback are investigated. A computer model is constructed to calculate the output parameters of these systems substituted by equivalent circuits. A model is constructed for a linear induction accelerator based on magnetic elements intended for operation with relativistic magnetrons the nonlinear units of the equivalent circuit of which are calculated in the context of the theory of average motion.     

Mass transfer flame resistant working fluids for hydraulic systems

The experience in running mineral oils in hydraulic system allows us to conclude that basically their properties obey requirements: they provide reliability and durability of work of a hydraulic transmission, but have unavoidable disadvantage: flammability.     

Quantitative HPLC determination of main flavonoid content of <Emphasis Type="Italic">Rhododendron adamsii</Emphasis> leaves and stems

The content of main flavonoids from Rhododendron adamsii R. leaves and stems was determined quantitatively using HPLC. It was found that myricetin and quercetin dominated the identified compounds (myricetin, quercetin, dihydroquercetin, rutin) in leaves; dihydroquercetin, in stems (1.1, 1.0, and 2.5 mass% of raw material, respectively). Dihydroquercetin and rutin were found for the first time in R. adamsii. Translated from Khimiya Prirodnykh Soedinenii, No. 1, pp. 26–29, January–February, 2009.