On the remained term for the central limit theorem

Summary An upper bound for the remainder term of the Edgeworth expansion for the distribution of the normalized sum of independent and identically distributed random variables is given in terms of 3rd and 4th order moments, together with the total variation of the probability density function of the underlying distribution. The Institute of Statistical mathematics     

Quantification of polycyclic aromatic hydrocarbons (PAHs) in human hair by HPLC with fluorescence detection: a biological monitoring method to evaluate the exposure to PAHs

A high-performance liquid chromatographic (HPLC) method with fluorescence detection was developed for the quantification of polycyclic aromatic hydrocarbons (PAHs) in human hair. Fifteen kinds of PAHs classified as priority pollutants by the US EPA were quantified with four perdeuterated PAHs as internal standards. After 50 mg hair samples were washed with n-hexane to remove external contamination of PAHs, the samples were digested in 2.5 M sodium hydroxide. The digests were extracted with n-hexane and then analyzed by HPLC. Eleven kinds of PAHs were identified in hair samples of 20 subjects, and 10 kinds of PAHs were eventually quantified using the internal standards. For anthracene, chrysene and benzo[k]fluoranthene, significant differences were observed between smokers and non-smokers. Although benzo[b]fluoranthene, dibenz[a,h]anthracene, benzo[ghi]perylene and indeno[1,2,3-cd]pyrene were observed in the particulates of indoor and outdoor air, they were not detected in all hair samples. The analysis of PAHs in human hair should be useful as a new biomarker to evaluate the exposure to PAHs.     

Synthesis of 1‐azabicyclic systems by double cyclization

5‐Cyano‐1‐azabicyclo[3.3.0]octane ( 1 ) was prepared in one step from 1,7‐dichloro‐4‐heptanone ( 4 ) under mild conditions. The application of this method for the preparation of 5‐cyano‐4,6‐dimethyl‐1‐azabicy‐clo[3.3.0]octane ( 11 ) gave two diastereomers in equilibrium. The NMR measurements of 11 and its reduced compound 15 showed that the major isomer is the cis‐exo form, and the minor isomer is the trans form. Molecular orbital calculations indicated that the cis‐exo form is more stable than the trans form, in agreement with the experimental results. Furthermore, 6‐cyano‐1‐azabicyclo[4.3.0]nonane ( 17 ) and 1‐azabicy‐clo[4.4.0]decane ( 19 ), both including a six‐membered ring, were prepared from appropriate haloketones by using this double cyclization method.     

Suzuki-Miyaura cross-coupling of benzylic carbonates with arylboronic acids

The cross-coupling of benzylic carbonates with arylboronic acids gave the corresponding diarylmethanes in high yields by use of the palladium catalyst generated in situ from [Pd(eta(3)-C(3)H(5))Cl](2) and 1,5-bis(diphenylphosphino)pentane (DPPPent). The Suzuki-Miyaura reaction using DPPPent-palladium catalyst is applicable to syntheses of a broad range of functionalized diarylmethanes. [reaction: see text]     

Stereoselective synthesis of premisakinolide A, the monomeric counterpart of the marine 40-membered dimeric macrolide misakinolide A

[structure: see text] The first synthesis of premisakinolide A, the monomeric counterpart of misakinolide A, the marine 40-membered macrolide displaying potent activity against a variety of human carcinoma cell lines, has been reported. The strategy was highlighted by a crucial coupling of a tetrahydropyran fragment and an alkynylaluminum reagent having a polypropionate chain, the highly stereoselective cross aldol reaction of segment A and segment B, and the stereospecific construction of the polypropionate structure based on original acyclic stereocontrol.     

Triphenylpyrylium salt-sensitized photoreactions of 1,4-diaryl-2,3-dioxabicyclo[2.2.2]octanes through competitive single electron-transfer pathway and proton-catalyzed pathway

2,4,6-Triphenylpyrylium tetrafluoroborate (TPPBF₄)-sensitized photoinduced electron-transfer (PET) reactions of 1,4-diaryl-2,3-dioxabicyclo[2.2.2]octanes 5 (a: Ar¹ = Ar² = p-MeOC₆H₄, b: Ar¹ = Ar² = p-MeC₆H₄, c: Ar¹ = Ar² = Ph) underwent novel fragmentation through their radical cations to give 1,4-diarylbutan-1,4-diones 6 accompanied by elimination of ethylene. On the other hand, 4-aryl-cyclohex-3-en-1-ones 7, p-substituted phenols 8, and 4-aryl-4-aryloxycyclohexanones 9 were produced through proton-catalyzed pathways when the PET reactions of 5 were performed in the absence of a certain base such as 2,6-di-tert-butylpyridine (DTBP). Particularly, the formation of 9 is consistent with the novel cationic rearrangement involving nucleophilic O-1,2-aryl shifts and C-1,4-aryl shifts.     

Synthesis of 2H-chromeno[2,3-d]pyrimidine-2,4-(3H)-diones (10-Oxa-5-deazaflavins) and their use in the oxidation of benzyl alcohol

Treatment of 6-phenoxyuracil derivatives with the Vilsmeier reagent (dimethylformamide-phosphorus oxy-chloride) gave the corresponding 5-formyl-6-phenoxyuracil derivatives or their equivalents (5-dimethylamino-methylene-6-phenoxyuracil derivatives). Dehydrative cyclization of the above 5-formyluracils or 5-dimethyl-aminomethyleneuracils with polyphosphoric acid gave the corresponding 2H-chromeno[2,3-d]pyrimidine-2,4(3H)-diones (10-oxa-5-deazaflavins). These 10-oxa-5-deazaflavins showed strong oxidizing power in oxidizing benzyl alcohol even under neutral conditions (without base) to give benzaldehyde, while they were hydro-genated to 1,5-dihydro-10-oxa-5-deazaflavins.     

Asymmetric allylation of unsymmetrical 1,3-diketones using a BINAP-palladium catalyst

[reaction: see text] The chiral palladium complex generated in situ from [Pd(eta(3)-allyl)Cl](2) and (R)-BINAP is a good catalyst for the catalytic asymmetric allylation of 1,3-diketones. The reaction provided chiral 2,2-dialkyl-1,3-diketones with 64-89% ee in high yields (13 examples). Enantiomeric excesses are strongly affected by the gamma-substituent of the allylic substrates. A variety of unsymmetrical 1,3-diketones were alkylated with cinnamyl acetate in good enantioselectivities via use of the BINAP-palladium catalyst (77-89% ee).     

Determination of atmospheric nitrobenzanthrones by high-performance liquid chromatography with chemiluminescence detection.

A method using high-performance liquid chromatography with chemiluminescence detection was developed for analyzing mutagenic nitrobenzanthrone (NBA) isomers in airborne particulates. The method was a modification of our previously described method for analyzing nitropolycyclic aromatic hydrocarbons (NPAHs). The pretreatment and reducing conditions for 1-, 2-, 3- and 10-NBAs were the same as those for NPAHs. In order to separate these NBA isomers, we used a polymeric-type ODS column (Cosmosil 5C-18MS); a mixture of 40% acetonitrile and 60% 10 mM imidazole-HClO4 buffer was employed as the mobile phase at a flow rate of 1 mL/min. The isomers of 1-, 2-, 3- and 10-NBA were determined in chemiluminescence with linear calibration graphs from 0.1 to 4 pmol, from 200 to 4000 pmol, from 1 to 50 pmol and from 10 to 400 pmol, respectively. The detection limits (S/N = 3) of 1-, 2-, 3- and 10-NBA isomers were 0.02 pmol, 35 pmol, 0.3 pmol and 3 pmol, respectively. The method was used to analyze airborne particulates at a heavy traffic site in Kanazawa. 2- and 3-NBAs were detected in the extracts of the particulates, while 1-NBA and 10-NBA were not detected. The atmospheric concentrations of 2- and 3-NBAs were 1.83 pmol/m3 and 24.7 fmol/m3, respectively.     

One-pot synthesis of metalated pyridines from two acetylenes, a nitrile, and a titanium(II) alkoxide

Four-component coupling process involving two acetylenes, a nitrile, and a divalent titanium alkoxide reagent, Ti(O-i-Pr)(4)/2i-PrMgCl, directly yielded titanated pyridines in a highly selective manner. The reaction can be classified into four categories: (i) a combination of an internal acetylene, a terminal acetylene, sulfonylnitrile, and the titanium reagent to yield alpha-titanated pyridines, (ii) a combination of an internal acetylene, a (sulfonylamino)acetylene, a nitrile, and the titanium reagent to yield alternative alpha-titanated pyridines, (iii) a combination of an internal acetylene, a (sulfonylamino)acetylene, a nitrile, and the titanium reagent to yield titanated aminopyridines, and (iv) a combination of an acetylenic amide, a terminal acetylene, a nitrile, and the titanium reagent to yield pyridineamides with their side chain titanated. Some of these reactions enabled virtually completely regioselective coupling of two different, unsymmetrical acetylenes and a nitrile to form a single pyridine. Synthetic applications of these reactions have been illustrated in the preparation of optically active pyridines and medicinally useful compounds.