The theorem for semisimple Hopf algebras

We give an algebraic version of a result of G. I. Kac, showing that a semisimple Hopf algebra of dimension , where is a prime and , over an algebraically closed field of characteristic 0 contains a non-trivial central group-like. As an application we prove that, if , is isomorphic to a group algebra.

     

Fan-type theorem for path-connectivity

A graphG is said to bek-path-connected if every pair of distinct vertices inG are joined by a path of length at leastk. We prove that if max{deg _G ^x , deg _G ^y }k for every pair of verticesx,y withd _G (x,y)=2 in a 2-connected graphG, whered _G (x,y) is the distance betweenx andy inG, thenG isk-path-connected.     

Synthesis of Six-Membered Compounds by Environmentally Friendly Cyclization Using Indirect Electrolysis

[Ni(cyclam)](ClO(4))(2)-catalyzed indirect electroreduction of olefinic bromides produced six-membered compounds in low to high yields. The synthetic intermediate 49 of Ipecac and Corynanthe alkaloids was obtained in 88% yield in a highly stereoselective manner. Lactam 66, the synthetic precursor of tacamonine, was prepared in 49% yield as a mixture of two diastereoisomers. The electrolysis of the bromoacetates gave the debrominated compounds in good yields.     

Identification of Shiga toxins in Shiga toxin-producing Escherichia coli using immunoprecipitation and high-performance liquid chromatography-electrospray ionization mass spectrometry

We developed a rapid and reliable identification method for Shiga toxins in Shiga toxin-producing Escherichia coli (STEC) using immunoprecipitation and high-performance liquid chromatography-electrospray ionization mass spectrometry (HPLC-ESI-MS). Polyclonal antisera specific for Shiga toxin 1 (Stx1) and Shiga toxin 2 (Stx2) were raised in rabbits so as to be used for the immunoprecipitation. The immunoprecipitaion was carried out by mixing sample solutions with 50 microl each of the antisera to Stx1 and Stx2 followed by allowing the mixed solutions to stand for 30 min. The quantity required to obtain the immunoprecipitate was more than 0.5 microg of Shiga toxins. HPLC-ESI-MS analysis of the resulting immunoprecipitates provided accurate molecular weight information on Shiga toxins, leading to direct evidence for the presence of these toxins. It requires at most two days to perform our procedure from toxin extraction to measurement of HPLC-ESI-MS whereas the previous method using isolation procedures required about two weeks to complete. The usefulness of the present method has been demonstrated by identifying Stx1, Stx2 and a variant of Stx2 (Stx2e) in the immunoprecipitates prepared from STEC strains.     

Development of versatile cis- and trans-dicarbon-substituted chiral cyclopropane units: synthesis of (1S,2R)- and (1R,2R)-2-aminomethyl-1-(1H-imidazol-4-yl)cyclopropanes and their enantiomers as conformationally restricted analogues of histamine

The cyclopropane ring can be used effectively in restricting the conformation of biologically active compounds to improve activity and also to investigate bioactive conformations. We designed (1S,2R)- and (1R,2R)-2-aminomethyl-1-(1H-imidazol-4-yl)cyclopropanes (1 and 2, respectively) and their enantiomers (ent-1 and ent-2) as conformationally restricted analogues of histamine. The four types of chiral cyclopropanes bearing two differentially functionalized carbon substituents in a cis or trans relationship on a cyclopropane ring, (1S,2R)-2-(tert-butyldiphenylsilyloxy)methyl-1-formylcyclopropane (7) and (1R,2R)-2-(tert-butyldiphenylsilyloxy)methyl-1-formylcyclopropane (8) and their enantiomers (ent-7 and ent-8), were developed as the key intermediates for synthesizing 1, 2, ent-1, and ent-2. The reaction between (R)-epichlorohydrin [(R)-12] and phenylsulfonylacetonitrile (13a) in the presence of NaOEt in EtOH followed by treatment with acid gave the chiral cyclopropane lactone 11a with 98% ee in 82% yield. Compound 11a was converted into both the cis- and trans-chiral cyclopropane units 7 and 8, respectively, via reductive desulfonylation with Mg/MeOH as the key step. The corresponding enantiomers, the cis-substituted ent-7 and the trans-substituted ent-8, were also prepared starting from (S)-epichlorohydrin [(S)-12]. The four conformationally restricted target histamine analogues 1, 2, ent-1, and ent-2 were successfully synthesized from 7, 8, ent-7, and ent-8, respectively. The chiral cyclopropane units 7, 8, ent-7, and ent-8 should be useful as versatile intermediates for synthesizing various compounds having an asymmetric cyclopropane structure.     

Synthesis of potent beta-secretase inhibitors containing a hydroxyethylamine dipeptide isostere and their structure-activity relationship studies

Several beta-secretase inhibitors were designed based on hydroxyethylamine dipeptide isostere (HDI) structures and were synthesized by a methodology using the aza-Payne rearragement and O,N-acyl transfer reactions to study their structure-activity relationships. Among these pseudopeptides, effective compounds were developed as the first beta-secretase inhibitors containing the HDI transition state mimic with potent enzyme inhibitory activity (IC50 < 100 nM).     

Photoinduced electron-transfer systems consisting of electron-donating pyrenes or anthracenes and benzimidazolines for reductive transformation of carbonyl compounds

Photoinduced electron-transfer reactions of several ketone substrates were studied to evaluate the utilities of 1,6-bis(dimethylamino)pyrene (BDMAP), 1,6-dimethoxypyrene (DMP), 9,10-bis(dimethylamino)anthracene (BDMAA), and 9,10-dimethoxyanthracene (DMA) as electron-donating sensitizers cooperating with 2-aryl-1,3-dimethylbenzimidazolines. BDMAP and DMP generally led higher conversion of ketones and better yield of reduction products compared to BDMAA and DMA.     

The effect of humidity on thermal process of zinc acetate

The thermal decomposition of zinc acetate dihydrate Zn(CH₃CO₂)₂·2H₂O in some humidity-controlled atmospheres has been successfully investigated by novel thermal analyses, which are sample-controlled thermogravimetry (SCTG), thermogravimety combined with evolved gas analysis using mass spectrometry (TG–MS) and simultaneous measurement of differential scanning calorimetry and X-ray diffractometry (XRD–DSC). The thermal processes of anhydrous zinc acetate in dry gas atmosphere by conventional linear heating experiment initiated with the sublimation around 180 °C, followed by the fusion and the decomposition over 250 °C. SCTG was useful to interpret clearly the successive reaction because the high-temperature parallel decompositions were effectively inhibited. The thermal behavior changed dramatically by introducing water vapor in the atmosphere and the thermal process was quite different from that in dry gas atmosphere. Zinc oxide (ZnO) was formed only in a humidity-controlled atmosphere, and could be easily synthesized at temperatures below 300 °C. XRD–DSC equipped with a humidity generator revealed directly the crystalline change from Zn(CH₃CO₂)₂ to ZnO. A detailed thermal process of Zn(CH₃CO₂)₂·2H₂O and the effect of water vapor are discussed.     

A new synthetic route to 2-substituted naphtho[2,3-b]furan-4,9-dione2-Substituted Naphtho[2,3-b]furan-4,9-dione

4,9-Dimethoxynaphtho[2,3-b]furan 9 was obtained in 91% yield via the reductive methylation of naphtho[2,3-b]furan-4,9-dione 2 . After treatment of 9 with butyllithium, the mixture was allowed to react with N,N-dimethylacetamide, followed by oxidization with cerium(IV) diammonium nitrate to give 2-acetylnaphtho[2,3-b]furan-4,9-dione 1 . 2-Formylnaphtho[2,3-b]furan-4,9-dione 13 and 2-trimethylsilyl-naphtho[2,3-b]furan-4,9-dione 14 were also obtained from 9 by a similar method. The halodesilylations of 14 easily gave 2-iodonaphtho[2,3-b]furan-4,9-dione 16 , 2-bromonaphtho[2,3-b]furan-4,9-dione 17 , and 2-chloronaphtho[2,3-b]furan-4,9-dione 18 in 82%, and 93% and 83% yield, respectively. Furthermore, the nitrodesilylation of 14 gave 2-nitronaphtho[2,3-b]furan-4,9-dione 3 in 77% yield.