Random partitioning over a sparse contingency table

The present article investigates a class of random partitioning distributions of a positive integer. This class is called the limiting conditional compound poisson (LCCP) distribution and characterized by the law of small numbers. Accordingly the LCCP distribution explains the limiting behavior of counts on a sparse contingency table by the frequencies of frequencies. The LCCP distribution is constructed via some combinations of conditioning and limiting, and this view reveals that the LCCP distribution is a subclass of several known classes that depend on a Bell polynomial. It follows that the limiting behavior of a Bell polynomial provides new asymptotics for a sparse contingency table. Also the Neyman Type A distribution and the Thomas distribution are revisited as the basis of the sparsity.     

Total synthesis of antimalarial diterpenoid (+)-kalihinol A

Total synthesis of antimalarial diterpenoid (+)-kalihinol A, isolated from marine sponge Acanthella sp., is achieved. This total synthesis involves regioselective alkylation of an epoxide, construction of a tetrahydropyran ring by iodo-etherification, construction of a cis-decalin ring by intramolecular Diels-Alder reaction, isomerization of cis-decalin to trans-decalin, and subsequent functionalization of the trans-decalin ring.     

Influence of water on molecular forms of rhodamine B in dip-coated thin films

Dip-coated thin films including rhodamine B have been prepared using the sol-gel reaction of tetraethyl orthosilicate under relative humidity of 30% and 60%. They have been aged under relative humidity of 20%, 60%, and 95% for 5 days. According to the absorption spectra, just after the preparation of the films and under higher humidity, a larger amount of the dimers (H-and J-types) were formed in the films. Five days after the preparation of the films and aged under higher humidity, the H-dimer increased. On the other hand, the J-dimer increased, regardless of humidity under which the films were aged.     

Synthesis and Stereochemical Revision of the C31–C67 Fragment of Amphidinol 3

Amphidinol 3 (AM3) is a marine natural product produced by the dinoflagellate Amphidinium klebsii. Although the absolute configuration of AM3 was determined in 1999 by extensive NMR analysis and degradation of the natural product, it was a daunting task because of the presence of numerous stereogenic centers on the acyclic carbon chain and the limited availability from natural sources. Thereafter, revisions of the absolute configurations at C2 and C51 were reported in 2008 and 2013, respectively. Reported herein is the revised absolute configuration of AM3: 32S, 33R, 34S, 35S, 36S, and 38S based on the chemical synthesis of partial structures corresponding to the C31–C67 fragment of AM3 in combination with degradation of the natural product. The revised structure is unique in that both antipodal tetrahydropyran counterparts exist on a single carbon chain. The structural revision of AM3 may affect proposed structures of congeners related to the amphidinols.     

Stereoselective synthesis of methyl (Z)-(4,4-difluoro-2,3,4,5-tetrahydro-1H-1-benzazepin-5-ylidene)acetate using a dianion Horner-Wadsworth-Emmons reagent

Stereoselective synthesis of methyl (Z)-(4,4-difluoro-2,3,4,5-tetrahydro-1H-1-benzazepin-5-ylidene)acetate (1a) is described. Z-selectivity of the Horner-Wadsworth-Emmons (HWE) reaction was obtained based on an investigation of the reaction conditions for introduction of a methylidene group onto the 5-position of benzazepine.     

Reaction between rare earth elements and HFNO2 solution

Rare earth elements react with HFNO₂ solution to produce nitrosylium fluorometallates (NO)_xLnF_x+3. The value of x is 1.0 or 1.5 for light rare earth elements and 0.5 or 1.0 for heavy rare earths. Nitrosylium fluorometallates of rare earth elements can be decomposed into the simple fluoride and nitrosyl fluoride at low temperatures (46–68°C).     

Carbonylation of lithium enolates with carbon monoxide mediated by selenium

[reaction: see text] Lithium enolates of ketones and aldehydes undergo carbonylation with carbon monoxide with the aid of selenium under mild conditions to yield beta-keto and beta-formyl selenol esters after trapping with alkyl iodides. This reaction proceeds via a unique carbonylation mechanism comprised of O-carbonylation and subsequent migration of the SeCO moiety to the alpha-carbon.     

Ni- or Cu-catalyzed cross-coupling reaction of alkyl fluorides with Grignard reagents

n-Octyl fluoride underwent a cross-coupling reaction with n-propylmagnesium bromide in the presence of 1,3-butadiene using NiCl2 as a catalyst at room temperature to give undecane in moderate yields. This alkyl-alkyl cross-coupling proceeded more efficiently when CuCl2 was employed instead of NiCl2. Addition of 1,3-butadiene dramatically improved the yields of the coupling products from primary alkyl Grignard reagents in both Ni- and Cu-catalyzed reactions. Alkyl fluorides efficiently reacted with tertiary alkyl and phenyl Grignard reagents using CuCl2 in the absence of 1,3-butadiene to afford the coupling products in high yields. The competitive reaction of a mixture of alkyl halides (R-X; X = F, Cl, Br) with nC5H11MgBr showed that the reactivities of the halides increase in the order R-Cl < R-F < R-Br. In contrast, in the Cu-catalyzed reaction with PhMgBr, the reactivities increase in the order R-Cl < R-Br < R-F.     

Analytical application of second-harmonic a.c. polarography

Phase-selective second-harmonic a.c. polarography can be used to distinguish two different species having similar reduction potentials. Because each species has a different phase angle depending on the electrode kinetics, a certain phase angle can be chosen to detect only one component in the mixture. In 1 M potassium chloride solution, indium-(III) at the 4 × 10^-6 M level can be determined in the presence of 50-fold amounts of cadmium(II), and zinc(II) at the 2 × 10^-5 M level in the presence of 100-fold amounts of nickel(II).     

Structure and reactivity of a novel parallel thiosulfito (SSO2-S:S') rhodium dinuclear complex

The parallel thiosulfite ligand (SSO2) in a rhodium complex, which is formed by oxygenation of a bridging disulfide, is converted to a bridging hydrocarbyl thiolate ligand and sulfur dioxide gas by the reaction with hydrocarbyl halides.