Limit theorems for one-dimensional diffusions and random walks in random environments

Summary The limiting behavior of one-dimensional diffusion process in an asymptotically self-similar random environment is investigated through the extension of Brox's method. Similar problems are then discussed for a random walk in a random environment with the aid of optional sampling from a diffusion model; an extension of the result of Sinai is given in the case of asymptotically self-similar random environments.     

Formation and transformation of alkoxy-derived BaGeO3

Beta-BaGeO₃, being high-temperature form, are formed metastably at 630-660 °C from an amorphous material prepared by the simultaneous hydrolysis of barium and germanium alkoxides. The transformation of BaGeO₃ can be summarized as follows; amorphous BaGeO₃

melt. On cooling from the melt, β- BaGeO₃ can be retained at room temperature.     

Reaction of diazonium salts with transition metals : IX. Reaction of vinyltrimethylsilane with arenediazonium tetrafluoroborates under palladium(0) catalysis

Arenediazonium tetrafluoroborates (ArN₂BF₄ where Ar=Ph, 4-MeC₆H₄, 4-BrC₆H₄, 4-IC₆H₄ and 4-NO₂C₆H₄) reacted easily with CH₂=CHSiMe₃ at 25 δC to give ArCH=CH₂, (E-ArCH=CHSiMe₃ and Ar(Me₃Si)C=CH₂ in excellent yields under palladium(O) catalysis. (E)-ArCH=CHSiMe₃ compounds were obtained predominantly and isolated in good yields by using an excess of CH₂=CHSiMe₃ over ArN₂BF₄. Protodesilylation of the reaction mixture afforded styrene derivatives.     

Characterization of iron(III) oxide films used for photoelectrode by means of cems

Thin iron oxides deposited on semi-conductive glass by a spray pyrolysis technique were analysed by Conversion Electron Mössbauer Spectrometry (CEMS). Iron oxide deposited on SnO₂ coated glass was composed of a large grained particles of crystalline α?Fe₂O₃, which showed sextet. The doublet and sextet appeared in CEM spectra of iron oxides deposited on In₂O₃ and WO₃ coated glasses. The sextet was due to α?Fe₂O₃ and the doublet was attributted to the superparamagnetic microcrystalline α?Fe₂O₃ (≈15nm) rather than to spinel compounds of iron. The iron oxide deposited on ZnO coated glass gave a doublet in CEM spectra. It was supporsed to be due to very fine particle of α?Fe₂O₃ (<100nm). It was found that iron oxide films obtained by spray pyrolysis were dependent on the kinds and the temperature of the semi-conductive materials coated on glass.     

Branching one-dimensional periodic diffusion processes

Let X be a nonsingular conservative one-dimensional periodic diffusion process, λ₀ its principal eigenvalue and X a binary splitting branching diffusion process with nonbranching part X. For each α > λ₀ we have two positive martingales Wⁱ_t(α), i = 1, 2, of X attached to the two positive α-harmonic functions of X. The main purpose of this paper is to show that their limit random variables are positive for all α? (λ₀, α_i), where α_i are some constants greater than λ₀.     

Synthesis and properties of 1,4,8,11,15,18,22,25-octaalkoxy-2,3,9,10,16,17,23,24-octakis(phenylthio)phthalocyaninato copper(II)

1,4,8,11,15,18,22,25-Octaalkoxy-2,3,9,10,16,17,23,24-octakis(phenylthio)phthalocyaninato copper(II) was synthesized. They were easily soluble in organic solvents and their Q-bands showed bathochromic shifts about 100 nm compared with unsubstituted phthalocyaninato copper(II). Their properties were examined.     

The six bidecomposable graphs

A graph G is said to be decomposable if G can be decomposed into a cartesian product of two nontrivial graphs. G is bidecomposable if not only G but also its complement G is decomposable. We prove that there are only six bidecomposable graphs; 2K(2), C₄, Q ₃, K(2) ×(K(2) + K(2)) , K(3) × K(3).