A variant of an infinite-dimensional local limit theorem

Let _n be a sequence of independent, identically distributed random elements in a separable Banach space X, for which the CLTholds: the normalized sums (₁+...+_n)/n^1/2 converge weakly to the Gaussian random element . It is proved that, under certain conditions on the distribution of ₁ and on the measurable mappingf: X R¹, the distribution of the random variable converges in variation to the distribution of the variablef().Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 46–50, 1989.     

Changes in the conformational parameters of 1-allylbenzotriazole in a mixed halide π-complex [CuCl0.85Br0.15(C6H4N3CH2=CH2)] under the action of bromine atoms

Single crystals of [CuCl_0.85Br_0.15(C₆H₄N₃CH₂=CH₂)] (I) were obtained by alternating current electrochemical synthesis; their X-ray structural investigation has been carried out (DARCh automatic diffractometer, MoK _α radiation, θ/2θ scanning; 1460 reflections with F ≥ 4σ(F), R = 0.0517). The crystals are monoclinic, their space group is P2₁/c, a = 7.292(3) Å, b = 17.947(8) Å, c = 7.398(4) Å, β = 93.56(4)°, V = 966(1) ų, Z = 4). Complex I is close in structure to the previously investigated compound [CuCl(C₆H₄N₃CH₂=CH₂)] (II). In both structures, the trigonal-pyramidal surroundings of the copper atom include two halide atoms (one is apical), a nitrogen atom, and a C=C group. The Cu₂X₂ dimers are associated into {[Cu₂X₂(C₆H₅N₃CH₂=CH₂)]}_n layers due to the bridging function of the 1-allylbenzotriazole molecule. In spite of the similar coordination polyhedra of the metal atoms and identical bridging function of the ligand molecule in I and II, the differences in the conformation parameters of the allyl group π-coordinated by the copper(I) atom (trans-like in I and cis-like in II) caused by the presence of bromine atoms in the coordination sphere predetermine different structures of the organometallic [Cu₂X₂(C₆H₅N₃CH₂=CH₂)]₄ tetramer subunits in the layers and, as a consequence, formation of different crystal structures. Original Russian Text Copyright ? 2005 by E. A. Goreshnik, B. M. Mykhalichko, and V. N. Davydov __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 46, No. 1, pp. 174–178, January–February, 2005.     

Raman spectroscopic study of the hydration of short-chain poly(oxyethylene)s C <Subscript>1</Subscript>E<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>C <Subscript>1</Subscript> (<Emphasis Type="Italic">n</Emphasis>=1−4)

The hypothesis that the degree of hydration of poly(oxyethylene) (POE) in aqueous solution depends on the mole ratio of water molecules to ether oxygen atoms in the molecule has been verified by studying the isotropic Raman spectra in the O−H stretching region for four short-chain POEs (C ₁E _n C ₁ withn=1−4). Excellent coincidence of the O−H stretching Raman band for all four POEs studied in the range of mole ratio H₂O/O _ether from 25 to 0.6 was observed, thus confirming the assumption stated above. A conclusion that all ether oxygen atoms in the POE molecule participate in hydrogen bonding with water molecules has been made.     

Electron-stimulated production of molecular hydrogen at the interfaces of amorphous solid water films on Pt(111)

The electron-stimulated production of molecular hydrogen (D(2), HD, and H(2)) from amorphous solid water (ASW) deposited on Pt(111) is investigated. Experiments with isotopically layered films of H(2)O and D(2)O are used to profile the spatial distribution of the electron-stimulated reactions leading to hydrogen within the water films. The molecular hydrogen yield has two components that have distinct reaction kinetics due to reactions that occur at the ASW/Pt interface and the ASW/vacuum interface, but not in the bulk. However, the molecular hydrogen yield as a function of the ASW film thickness in both pure and isotopically layered films indicates that the energy for the reactions is absorbed in the bulk of the films and electronic excitations migrate to the interfaces where they drive the reactions.     

Efficient Resolution of Some Monoprotected Derivatives of Corey Lactone

Racemic monoprotected at primary hydroxy group Corey lactones were resolved using (1S,2R,5R)-6,6-dimethyl-4-oxo-3-oxabicyclo-[3.1.0]hexan-2-ol as a chiral auxiliary reagent of hemiacylal chemotype.     

The unique structure of [(C4H9)4N]3[Pb(NO3)5]—one step forward in understanding transport properties in tetra-n-butylammonium-based solid electrolytes

Structural Chemistry - The crystal and molecular structure of tris(tetrabutylammonium) pentanitratoplumbate(II) was determined and characterized by single-crystal and powder X-ray diffraction and...     

The effect of electrode rotation on pitting passivity breakdown of metal in sodium chloride solution

The effect of electrode rotation on the initiation and development of pitting passivity breakdown of two steels and nickel in the chloride solutions is studied. The effect of rotation is most pronounced for the development of pitting on steels in the neutral unbuffered NaCl solution. The electrode rotation has almost no effect on the pitting development in the nickel/NaCl + NaOH solution sistem. The discussion of experimental results is presented.