1,3-Dipolar cycloadditions of anhydro-5-hydroxyoxazolium hydroxide generated from 2-piperidinecarboxylic acid. Isolation of the primary adduct and synthesis of tetrahydroindolizines

1,3-Dipolar cycloaddition reactions of anhydro-5-hydroxyoxazolium hydroxide 3 generated from 2-piperidinecarboxylic acid and acetic anhydride, with dimethyl and diethyl acetylene-dicarboxylates, dibenzoylacetylene, p-benzoquinone, and 1,4-naphthoquinone gave the corresponding tetrahydroindolizines. In the case of the reaction with p-benzoquinone, the dihydroindolizine 12 was also formed. The primary N-bridged lactone intermediate 4 was isolated from the reaction of 2 with dibenzoylacetylene. Several attempted conversions of these tetrahydroindolizines into the corresponding aromatic indolizines were fruitless.     

Catalytic asymmetric epoxidation of α,β-unsaturated carboxylic acid imidazolides and amides by lanthanide–BINOL complexes

Highly enantioselective catalytic asymmetric epoxidation of α,β-unsaturated carboxylic acid imidazolides and simple amides was developed. In the presence of 5–10 mol% of lanthanide–BINOL complexes, the reaction proceeded smoothly with high substrate generality. In particular, in the cases of α,β-unsaturated amides, there was nearly perfect enantioselectivity (>99% ee). The corresponding epoxides were successfully transformed into many types of useful chiral compounds such as α,β-epoxy esters, α,β-epoxy amides, α,β-epoxy aldehydes, α,β-epoxy β-keto ester, and α- and β-hydroxy carbonyl compounds. B3LYP density functional studies were performed to predict substrate reactivity.     

Equidistribution of Eisenstein Series in the Level Aspect

We prove an equidistribution property of the Eisenstein series for congruence subgroups as the level goes to infinity. This is an analogy of the phenomenon called quantum ergodicity.     

An anionic strategy for three- and four-component coupling reactions leading to ketone frameworks based on vinylogous conversion of dilithio ketone alpha,beta-dianions

[reaction: see text] Ketone alpha,delta-dianions are generated by vinylogous extension of ketone alpha,beta-dianions with alkenes such as vinylarenes, vinylsilanes, and vinyl sulfides, which then undergo reactions at the delta and alpha positions with different electrophiles, creating ketone frameworks. This work represents a cascade-type anion method that achieved three- and four-carbon component assembly reactions leading to ketones.     

Controlling the solid-state luminescence of gold(I) N-heterocyclic carbene complexes through changes in the structure of molecular aggregates

Thermally stable, solid-state luminescent organic materials are highly desired for the development of practical applications.Herein we synthesized new gold(I) complexes with N-heterocyclic carbene ligands, which have the ability to form strong metalorganic bond. Consequently, their thermochemical stability is enhanced at temperatures around 300 °C. Precise design of the molecular structure of the ligands, with a focus on ensuring low steric hindrance around Au atoms in order to limit disturbances to Au/Au interactions, provided a complex with a densely packed crystal with a shorter intermolecular Au–Au distance(3.17 ?)than the typical distance. In the solid state, this complex exhibited strong aurophilic interactions, which generated intense phosphorescence even in air at room temperature(quantum yield=16%) in spite of absence of any phosphorescence in solution.This behavior is characteristic for solid-state luminescence referred to as aggregation-controlled emission. Furthermore, the gold(I) complex displays capacity for mechano-and vapo-chromism—that is, the ability to change color reversibly in response to the application of external stimuli. We believe that the proposed design framework, which involves controlling thermal stability and luminescence property separately, provides a new opportunity for the development of practical applications using solid-state luminescent organic molecules.     

Generalized GIPSCAL re-revisited: a fast convergent algorithm with acceleration by the minimal polynomial extrapolation

Generalized GIPSCAL, like DEDICOM, is a model for the analysis of square asymmetric tables. It is a special case of DEDICOM, but unlike DEDICOM, it ensures the nonnegative definiteness (nnd) of the model matrix, thereby allowing a spatial representation of the asymmetric relationships among ??objects??. A fast convergent algorithm was developed for GIPSCAL with acceleration by the minimal polynomial extrapolation. The proposed algorithm was compared with Trendafilov??s algorithm in computational speed. The basic algorithm has been adapted to various extensions of GIPSCAL, including off-diagonal DEDICOM/GIPSCAL, and three-way GIPSCAL.     

Familywise decompositions of Pearson’s chi-square statistic in the analysis of contingency tables

Advances in Data Analysis and Classification - Pearson’s chi-square statistic is well established for testing goodness-of-fit of various hypotheses about observed frequency distributions in...