Higher order asymptotics in estimation for two-sided Weibull type distributions

We consider the estimation problem of a location parameter on a sample of size n from a two-sided Weibull type density % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GaamOzaiaacIcacaWG4bGaeyOeI0IaeqiUdeNaaiykaiabg2da9iaa% doeacaGGOaGaeqySdeMaaiykaiGacwgacaGG4bGaaiiCaiaacIcacq% GHsislcaGG8bGaamiEaiabgkHiTiabeI7aXjaacYhadaahaaWcbeqa% aiabeg7aHbaakiaacMcaaaa!52AD!\[f(x - \theta ) = C(\alpha )\exp ( - |x - \theta |^\alpha )\] for –<x<, –<< and 1<a<3/2, where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gaam4qaiaacIcacqaHXoqycaGGPaGaeyypa0JaeqySdeMaai4laiaa% cUhacaaIYaGaeu4KdCKaaiikaiaaigdacaGGVaGaeqySdeMaaiykai% aac2haaaa!4B0E!\[C(\alpha ) = \alpha /\{ 2\Gamma (1/\alpha )\} \]. Then the bound for the distribution of asymptotically median unbiased estimators is obtained up to the 2a-th order, i.e., the order % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GaamOBamaaCaaaleqabaGaeyOeI0IaaiikaiaaikdacqaHXoqycqGH% sislcaaIXaGaaiykaiaac+cacaaIYaaaaaaa!4444!\[n^{ - (2\alpha - 1)/2} \]. The asymptotic distribution of a maximum likelihood estimator (MLE) is also calculated up to the 2a-th order. It is shown that the MLE is not 2a-th order asymptotically efficient. The amount of the loss of asymptotic information of the MLE is given.     

Total synthesis of ingenol

Total synthesis of ingenol, a diterpene isolated from the genus Euphorbia, was accomplished on the basis of the novel key reactions. The highly strained ingenane skeleton was constructed through an intramolecular cyclization reaction of an acetylene dicobalt complex followed by a rearrangement reaction of an epoxy alcohol. The C(3),C(4),C(5)-triol moiety was introduced by a stereoselective double dihydroxylation reaction of a diene having C(2)-C(3) and C(4)-C(5) double bonds.     

Catalytic deprotection of protected alcohols in water using low-loading and alkylated polystyrene-supported sulfonic acid

Catalytic deprotection of various protected alcohols was efficiently conducted using a hydrophobic low-loading and alkylated polystyrene-supported sulfonic acid (LL-ALPS-SO3H) in water as the sole solvent. Transprotection of an alcohol from a silyl ether to the corresponding benzylic ether or ester also proceeded smoothly in water.     

The stereoregularity of polyacrylonitrile and its dependence on polymerization temperature

The stereoregularity of polyacrylonitrile was studied by NMR spectroscopy. The methylene protons in isotactic configuration are equivalent in dimethylformamide-d₇ solution and are nonequivalent in dimethylsulfoxide-d₆ solution. In the case of the latter solution the difference in chemical shift between the isotactic methylene protons is 6.6 cps. The stereoregularity of polyacrylonitrile-α-d instead of polyacrylonitrile was determined on the dimethylformamide-d₇ solution. In the radical polymerization all the polyacrylonitrile-α-d's that polymerized at temperatures between 80 and ?78°C. have a configuration consisting of about 50% of isotactic diads and, accordingly, the stereoregularity of polyacrylonitrile does not depend upon the polymerization temperature. Analysis of the NMR spectra of isotactic polyacrylonitrile prepared from acrylonitrile–urea canal complex was also carried out. The NMR spectra of meso- and dl-2,4-dicyanopentanes, dimer models of isotactic and syndiotactic polyacrylonitriles, respectively, were analyzed by a computer program proposed by Bothner-By.     

Stereoregularity and polymerization mechanism of polymethacrylonitriles determined by 13C-NMR spectroscopy

Carbon-13 nuclear magnetic resonance (¹³C-NMR) spectra of polymethacrylonitriles prepared under various conditions were measured. In acetone solution, the α-methyl carbon absorptions were split into triads and partially into pentads, and the methylene carbon absorptions into tetrads. In trifluoroacetic acid solution, the α-methyl carbon absorptions were split into pentads and the cyano carbon absorptions into triads. The triad, tetrad, and pentad tacticities determined from ¹³C-NMR spectra were compared with dyad tacticities determined from proton NMR spectra. The stereoregularity of the polymers which are γ-ray-initiated in liquid phase at temperatures near melting point (?35.8°C) and in the solid state differs from that of the polymers radically initiated at ?20 to 80°C. The stereoregularity and the conversion suggest the existence of an ionic mechanism in the polymerization at low temperatures.     

Electronic structures and NMR of some hydroxycarbonium ions

The proton and isotropic (¹³C) magnetic resonances of some hydroxycarbonium ions (HCHOH⁺, CH₃CHOH⁺ (CH₃)₂COH⁺ HCO₂H₂⁺, CH₃CO₂H₂⁺, and CH₃OH₂⁺) are discussed in relation to their electronic structures computed by means of the INDO—SCF method. The proton and carbon-13 chemical shifts, which depend directly on the local diamagnetic and paramagnetic contributions respectively, are reasonably explained by the electronic structures of the hydroxycarbonium ions relative to those of the corresponding parent molecules. The Fermi contact interaction term is found to be well reflected in the hydrogen-hydrogen and carbon-hydrogen coupling constants, and the differences in the coupling constants between rotational isomers of the ions are discussed from the viewpoint of their electronic properties.     

Metal chelation-controlled twisted intramolecular charge transfer and its application to fluorescent sensing of metal ions and anions

Two fluorescent ligands, N-(2-(5-cyanopyridyl))cyclen (L5) and N-(2-pyridyl)cyclen (L6) (cyclen = 1,4,7,10-tetraazacyclododecane), were designed and synthesized to control twisted intramolecular charge transfer (TICT) by metal chelation in aqueous solution. By complexation with Zn(2+), L6 exhibited TICT emissions at 430 nm (excitation at 270 nm) in 10 mM HEPES (pH 7.0) with I = 0.1 (NaNO(3)) at 25 degrees C due to the perpendicular conformation of a pyridine ring with respect to a dialkylamino group, which was fixed by Zn(2+)-N(pyridine) coordination, as proven by potentiometric pH, UV, and fluorescence titrations and X-ray crystal structure analysis. We further describe that the 1:1 complexation of ZnL6 with guests such as succinimide, phosphates, thiolates, and dicarboxylates, which compete with a nitrogen in the pyridine ring for Zn(2+) in ZnL6, induces considerable emission shift from TICT emissions (at 430 nm) to locally excited emissions (at ca. 350 nm) in neutral aqueous solution at 25 degrees C.     

A new synthetic method of 3-acyltetronic acid derivatives and its application to the synthesis of isoaspertetronin a (isogregatin A)

A new synthetic method of 3-acyltetronic acid derivatives from the corresponding 3-bromo compound via lithiation with n-BuLi followed either by acylation with acid chloride or better by first reacting with aldehyde and then subsequent oxidation with active MnO₂ is described. A revised structure $\text{10}$ for aspertetronin A(gregatin A) was presented based on the synthesis of the proposed structure $\text{8}$ and spectral comparison of a model compound $\text{12}$ with the natural product.     

Determination of proteins in urine by high-performance liquid chromatography with spectrophotometric detection using a pyrogallol red-molybdate complex

A high-performance liquid chromatographic method with spectrophotometric detection was developed for the determination of proteins in urine. The proteins were separated on an anion-exchange column and eluted with a Tris-HCl buffer with a gradient of sodium chloride concentration and pH. The separated proteins were mixed with a pyrogallol red-molybdate complex reagent and determined spectrophotometrically. Urinary proteins were well separated without desalting the urine. The reproducibility was satisfactory.     

Product analyses of ozone mediated nitration of benzimidazole derivatives with nitrogen dioxide: formation of 1-nitrobenzimidazoles and conversion to benzotriazoles

Several benzimidazole derivatives having electron-withdrawing or -donating substituent(s) at the benzene moiety were used as models of the imidazole moiety of purine bases and their nitration with nitrogen dioxide and ozone (so-called Kyodai nitration) were examined. Products were extracted from the reaction mixture with AcOEt and their structures were analyzed. 1-Nitrobenzimidazole derivatives and unexpected 1-nitrobenzotriazole derivatives were identified. Although the yields of 1-nitrobenzimidazole derivatives were quite low, these were all new compounds that could be obtained only by Kyodai nitration. It was speculated that benzotriazoles were formed via 1-nitrobenzimidazoles and subsequent nitration toward benzotriazoles resulted in the formation of 1-nitrobenzotriazoles.