Topological Limit of Trajectories of Intervals of Simplest One-Dimensional Dynamical Systems

We consider dynamical systems generated by continuous maps of an interval into itself. We investigate the asymptotic behavior of the trajectories of subsets of the interval. In particular, we prove that if the -limit set of an arbitrary trajectory is a fixed point, then the topological limit of the trajectory of any subinterval exists.     

On the lowest order electroweak corrections to spin-12 fermion scattering: (I). The one-loop diagrammar

Based on a gauge model of the electroweak interaction the total set of all one-loop diagrams for scattering of $\text{spin}\text{-}\text{1}\text{2}$ fermions is calculated. Throughout the calculations, the type of fermions (?, ν, …) and of heavy vector bosons (W^±Z⁰, …) is not specified. Derivation of finite parts of each diagram is carried out under the restriction that all invariants of the amplitude are much larger than all fermion masses squared. This allows us to use the expression obtained at arbitrary high energies where weak and electromagnetic interaction strengths are comparable.     

XPS spectra of vanadium-doped disulfides CuCrS<Subscript>2</Subscript>

The charged state of atoms in layered cation-substituted disulfides CuCr_1?x V _x S₂ (x = 0?0.4) was studied using X-ray photoelectron spectroscopy. The study was performed with polycrystalline powder and ceramic samples of chromium-copper disulfides. CuCr_1?x V _x S₂ samples were shown to comprise differently charged atoms of chromium, copper and vanadium, the charged state of which varies with the concentration of vanadium cations (x).     

The Inclusion Properties of a New Watersoluble Sulfonated Calix[4]resorcinarene towards Alkylammonium and N-Methylpyridinium Cations

The inclusion behaviour of a new water-soluble sulfonated calix[4]resorcinarene towards alkylammonium and N-methylpyridinium cations has been investigated on the basis of ¹H NMR spectroscopy and pH-potentiometry data. The inclusion of the N-methylpyridinium cation has been found to be dependent on pH with the preferable inclusion of the methyl substituent in alkaline and the aromatic ring in neutral aqueous media.     

XPS spectra of free nitroxyl radicals and their electronic structure

The N(1s) and O(1s) XPS spectra of stable nitroxyl radicals and molecules with a related heterocycle structure: 4,4,5,5-tetramethyl-2-phenyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl, 4,4,5,5-tetramethyl-2-(3-nitrophenyl)-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl, 4,4,5,5-tetramethyl-2-(2-hydroxyphenyl)-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl, 4,4,5,5-tetramethyl-2-(2-hydroxy-3-nitrophenyl)-4,5-dihydro-1Himidazole-3-oxide-1-oxyl, and 4,4,5,5-tetramethyl-2-phenyl-4,5-dihydro-1H-imidazole-3-oxide were studied. The possibility to apply X-ray electron spectra for investigation of the charge electron and spin density distribution on free radical atoms and at their coordination by a metal is considered.     

Synthesis and photophysical properties of silica nanoparticles based on europium(iii) complexes

Monodisperse 280?C480 nm silica particles doped with europium complexes with thenoyltrifluoroacetylacetone and adducts with some phosphine oxides as luminophores were prepared for the first time by the optimized Stober procedure using surfactants. The size and the polydispersity of the obtained particles depend on the luminophore incorporated in the polymer template. The photophysical properties of aqueous dispersions of the europium(iii)-doped silica particles were studied by the luminescence method.     

Stereochemistry of Seven-Membered Heterocycles: XLIII. Steric Structure of Diastereoisomeric 8,8-Dichloro(dibromo)-4-R-3,5-dioxabicyclo[5.1.0]octanes

Dichloro- and dibromocyclopropanation of 2-substituted 1,3-dioxacyclohept-5-enes according to Makosza resulted in formation of the corresponding 4-substituted 8,8-dichloro(dibromo)-3,5-dioxabicyclo[5.1.0]octanes in good yields. Ultrasonic activation of the process considerably shortened the reaction time. According to the ^{1 3}C NMR spectra, the chair-twist equilibrium is essentially displaced toward the chair conformer for the exo isomers and toward the twist conformer for the endo structures. Similar results were obtained by AM1 semiempirical calculations which indicated that the CCl···O interaction largely determines the conformational equilibrium. The state of the diastereoisomer epimerization equilibrium depends on the size of the substituent at the acetal carbon atom.