Asymptotic expansions of the distributions of some test statistics for Gaussian ARMA processes

Let {X_t} be a Gaussian ARMA process with spectral density f_θ(λ), where θ is an unknown parameter. The problem considered is that of testing a simple hypothesis H:θ = θ₀ against the alternative A:θ ≠ θ₀. For this problem we propose a class of tests , which contains the likelihood ratio (LR), Wald (W), modified Wald (MW) and Rao (R) tests as special cases. Then we derive the χ² type asymptotic expansion of the distribution of T up to order n⁻¹, where n is the sample size. Also we derive the χ² type asymptotic expansion of the distribution of T under the sequence of alternatives A_n: θ = θ₀ + /√n, ε > 0. Then we compare the local powers of the LR, W, MW, and R tests on the basis of their asymptotic expansions.     

Distribution of hydrogen vibrations in LaH2.28 and LaH2.99

The hydrogen vibrational modes in LaH_x samples have been investigated by pulsed neutron spectroscopy. The results are compared with a simple model emphasizing strong HH forces and the lack of stoichiometry in LaH_2.28.     

Phase transitions in RbCaF3. II: Neutron scattering

The 196 K phase transition of RbCaF₃ has been identified as a phonon condensation at the R point (cubic [111] zone boundary). Above the transition temperature, a ridge of scattering extending from the [110] zone boundary (M point) to the R point was observed, corresponding to a line of soft phonons from M₃ to R₂₅. Below the transition the scattering at M decreases rapidly with temperature, indicating a lattice stabilization which causes the ridge of scattering to disappear.     

The site distribution of Ti and V and the metal-metal interaction in the ternary system (V,Ti)5S8

The phase relations of the ternary system V_1?xTi_xS_1.57 are presented on the basis of X-ray diffractometry. The site distribution of Ti and V atoms in the structure is clarified through an NMR absorption study at room temperature. The phase relations and the site distribution of Ti and V, which appear to be closely related to each other, are discussed in terms of the metal-metal interaction of the face-shared octahedra in the metal-deficient distorted NiAs structure.     

Magnetic field effect on the hydrogen abstraction of xanthone from xanthene in SDS micelles

The magnetic field effect (<800 G) on the hydrogen abstraction of xanthone from xanthene in SDS aqueous micellar solutions was studied using laser flash photolysis. The rate of triplet-singlet intersystem crossing of the radical pair of xanthone ketyl and 9-xanthenyl formed upon photolysis decreases from 1.4 × 10⁶ s^?1 at O G to 0.4 × 10⁶ s^?1 at 640 G.     

Cp2TiCl2-catalyzed regio- and chemoselective one-step synthesis of gamma-substituted allylsilanes from terminal alkenes using dianion-type zincate (SiSiNOL-Zn-ate)

A regio-/chemoselective silylation reaction of various functionalized terminal alkenes in the presence of titanocene dichloride, based on a newly designed dianion-type zincate, was developed. The present silylation of terminal alkenes is a powerful tool for the one-pot generation of regiocontrolled functionalized allysilanes, which are available for various transformation reactions, such as hydroxyalkylation, epoxidation, and hydroboration.     

Inductive effect-assisted chain-growth polycondensation. synthetic development from para- to meta-substituted aromatic polyamides with low polydispersities

The polycondensation of m-(octylamino)benzoic acid esters (1) with base was investigated in order to extend the synthesis of well-defined condensation polymers from para-substituted polymers to meta-substituted ones. We expected that the aminyl anion of 2 would deactivate the ester moiety at the meta position of 2 owing to the strong inductive effect of the anion, resulting in, not self-polycondensation, but chain-growth polycondensation. The methyl ester monomer 1a polymerized with lithium hexamethyldisilazide (LiHMDS) in the presence of phenyl benzoate (3a) as an initiator at 0 degrees C to afford a polymer with a low polydispersity, but the product contained a small amount of self-condensation polymer. On the other hand, the polymerization of the ethyl ester monomer (1b) with phenyl 4-methylbenzoate (3b) proceeded through chain polymerization without self-polycondensation. The Mn values of the polymers increased linearly in proportion to the [1b]0/[3b]0 ratio, and the Mw/Mn ratios remained narrow over the entire [1b]0/[3b]0 range. Furthermore, a block copolymer of N-alkylated poly(m-benzamide) and poly(p-benzamide) with a low polydispersity was synthesized by the monomer addition method under this polymerization condition.     

Photocatalytic activity of R3MO7 and R2Ti2O7 (R=Y, Gd, La; M=Nb, Ta) for water splitting into H2 and O2

The photocatalytic activities of R3MO7 and R2Ti2O7 (R=Y, Gd, La; M=Nb, Ta) strongly depended on the crystal structure. Overall, photocatalytic water splitting into H2 and O2 proceeded over La3TaO7 and La3NbO7, which have an orthorhombic weberite structure, Y2Ti2O7 and Gd2Ti2O7, which have a cubic pyrochlore structure, and La2Ti2O7, which has a monoclinic perovskite structure. All of these materials are composed of a network of corner-shared octahedral units of metal cations (TaO6, NbO6, or TiO6); materials without such a network were inactive. The octahedral network certainly increased the mobility of electrons and holes, thereby enhancing photocatalytic activity.     

Regiocontrolled intramolecular cyclizations of carboxylic acids to carbon-carbon triple bonds promoted by acid or base catalyst

We systematically investigated, for the first time, the relationship between regioselectivity and acid/base effects in the cyclization reactions between carboxylic acids and carbon-carbon triple bonds. We found novel acid- and base-promoted cyclizations to selectively give isocoumarin or pyran-2(2H)-one and phthalide or furan-2(5H)-one skeletons, respectively, and established a catalytic version of regioselective heterocyclic ring synthesis. Density functional theory calculations and application to a short route to thunberginol A were also described. [reaction: see text].