Laplace approximations for sums of independent random vectors

Let X _i , i∈N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a mapping B→R. Under a central limit theorem assumption, an asymptotic evaluation of Z _n = E (exp (n Φ (∑ _{i =1} ⁿ X _i /n))), up to a factor (1 + o(1)), has been gotten in Bolthausen [1]. In this paper, we show that the same asymptotic evaluation can be gotten without the central limit theorem assumption. Received: 19 September 1997 / Revised version:22 April 1999     

Stellatic acid: a new class of sesterterpenoid; X-ray crystal structure

The complete structure of a unique tricyclic sesterterpene, stellatic acid, was established by X-ray diffraction of its p-bromophenacyl ester.     

Avenic acid,a new amino acid possessing an iron chelating activity

A new amino acid derivative possessing an iron chelating activity was isolated from root washings of water cultured $\text{Avena sativa}$ under iron deficient conditions. The structure of this compound, avenic acid A has been determined as 2(S),3′(S),3″(S)-N-[3-(3-hydroxy-3-carboxypropylamino)-3-carboxypropyl]-homoserine (1) on the basis of chemical and spectroscopic evidence.     

Non-Darcian effects on conjugate natural convection between horizontal concentric cylinders filled with a porous medium

An analysis is presented of steady conjugate free convection between two horizontal concentric cylinders filled with a fluid-saturated porous medium; the innermost cylinder surface is maintained at a high temperature and the outermost cylinder surface at a lower one. The velocity-pressure-gradient relation is taken to be nonlinear, with departure from the linear Darcy situation measured by a parameter F₀. The investigation is based on the numerical solution, by a finite-difference method, of the full momentum and energy equations. The streamline and isotherm patterns as well as the local and mean Nusselt numbers are plotted for several physical parameters to show some of the flow and heat transfer characteristics. It is found that all parameters play an important role in the flow and heat transfer characteristics. The model can be applied to a variety of engineering problems.     

Malliavin calculus, geometric mixing, and expansion of diffusion functionals

Under geometric mixing condition, we presented asymptotic expansion of the distribution of an additive functional of a Markov or an ε-Markov process with finite autoregression including Markov type semimartingales and time series models with discrete time parameter. The emphasis is put on the use of the Malliavin calculus in place of the conditional type Cramér condition, whose verification is in most case not easy for continuous time processes without such an infinite dimensional approach. In the second part, by means of the perturbation method and the operational calculus, we proved the geometric mixing property for non-symmetric diffusion processes, and presented a sufficient condition which is easily checked in practice. Accordingly, we obtained asymptotic expansion of diffusion functionals and proved the validity of it under mild conditions, e.g., without the strong contractivity condition. Received: 7 September 1997 / Revised version: 17 March 1999     

Polarization dependence of the optical absorption of single-walled carbon nanotubes

Anisotropic optical absorption properties of single-walled carbon nanotubes (SWNTs) are determined from a vertically aligned SWNT film for 0.5-6 eV. Absorption peaks at 4.5 and 5.25 eV are found to exhibit remarkable polarization dependence and have relevance to optical properties of graphite. A method for determining a nematic order parameter for an aligned SWNT film based on the collinear absorption peak at 4.5 eV is presented, followed by the determination of the optical absorption cross section.     

Cycloaddition reaction of pyrimidine-dienols with dienophiles. A new approach to quinazolines

A new synthetic approach to quinazolines bearing a carboxy group is described. Reaction of 5-carbonyl substituted 1,3,6-tri-methyluracils (I) with dimethyl acetylenedicarboxylate or electron-deficient olefines affords quinazoline derivatives (III-VI) $\text{via}$ pyrimidine(Z)-dienols (II) formed by base-catalyzed isomerization.     

Infrared spectroscopic studies of polymer transitions. III. Effects of sodium ion on glass transitions in styrene-based ionomers

The glass transition in styrene-based ionomers was investigated by means of infrared spectroscopy and differential scanning calorimetry (DSC). Transition temperatures were determined from the temperature dependence of the peak absorbances of the 1700 and 1745 cm^?1 bands. These transition temperatures agreed with glass transition temperatures (T_g) determined by DSC. With increasing degree of ionization, T_g and the enthalpy ΔH of the residual intermolecular hydrogen bonding increased. The values of T_g obtained were analyzed by the theory of Fox and Loshaek for the effect of crosslinks. It is concluded that sodium ions probably from ionic domains and act as crosslinks to reinforce the residual hydrogen bonding and may increase T_g. The absorbance at 1560 cm^?1 (ν_COO^?) did not change at T_g. This suggests that the glass transition observed here is not due to the onset of the mobility in ionic domains, as has been proposed for ethylene-based ionomers on the basis of dielectric measurements.