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     

Reaction of α-chloroketones with 1,4-dianion of acetophenone n-ethoxy-carbonylhydrazone

1,4-Dianion of acetophenone N-ethoxycarbonylhydrazone (2) reacts with α-chloroketones such as phenacyl chloride, 1-chloroacetone, 3-chloro-2-butanone, and 1,3-dichloroacetone to give pyrazoline derivatives in good yields. In the reactions of 2-chlorocyclohexanone and 3-chloro-2-norbornanone with 2, cis-chlorohydrin and exo-chlorohydrin were selectively obtained, respectively.     

Strong uniqueness for the plate equations

In this paper we show the strong uniqueness for the plate equations. By using the idea due to Lebeau we transform the given operator to the elliptic operators to which we apply the Carleman estimates given by Alinhac and Lerner.

     

Absolute stereochemistry of the triol moiety of gymnoprenols

Absolute configuration of the triol portion in gymnoprenols, the polyisoprenepolyols obtained from mushroom $\text{Gymnopilus spectabilis}$, has been established as 2S and 3R by a stereocontrolled synthesis of the enantiomer of a chemical degradation product of gymnoprenol.     

Kinetics of esterification of palmitic acid with isobutyl alcohol on ion-exchange resin pellets

Cylindrical pellets were made by mixing ion-exchange resin particles with binding powders and heating to 140°C. To compare catalytic activities of these resin pellets with those of resin particles and sulfuric acid, the esterification of palmitic acid with isobutyl alcohol was carried out in a batch reactor. The rate equation for sulfuric acid could be applied to ion-exchange resins although the values of parameters were different.     

Revision of the absolute configuration of triol moiety of gymnoprenols

The absolute configurations of triol moiety of gymnoprenol-A, -B and gymnopilin have been revised as 2R,3S, on the basis of the synthesis of (2S,3R)-lactone diacetate (1a) from (R)-(-)-linalool.     

Synergistic N‐Heterocyclic Carbene/Palladium‐Catalyzed Reactions of Aldehyde Acyl Anions with either Diarylmethyl or Allylic Carbonates

Benzylation and allylation of aldehyde acyl anions were enabled by the merger of a thiazolium N‐heterocyclic carbene (NHC) catalyst and a palladium/bisphosphine catalyst in a synergistic manner. Owing to the mildness of the reaction conditions, various functional groups were tolerated in the substrates.