Semiparametric estimation of the long-range parameter

We study two estimators of the long-range parameter of a covariance stationary linear process. We show that one of the estimators achieve the optimal semiparametric rate of convergence, whereas the other has a rate of convergence as close as desired to the optimal rate. Moreover, we show that the estimators are asymptotically normal with a variance, which does not depend on any unknown parameter, smaller than others suggested in the literature. Finally, a small Monte Carlo study is included to illustrate the finite sample relative performance of our estimators compared to other suggested semiparametric estimators. More specifically, the Monte-Carlo experiment shows the superiority of the proposed estimators in terms of the Mean Squared Error. The first author research was funded by the Economic and Social Research Council (ESRC) reference number: R000238212. The second author research was funded by the Ministry of Education, Culture, Sports and Technology of Japan, reference number: 09CE2002 and B(2)10202202.     

Conformation of bicyclo [n.1.0] Derivatives: Part 3. Dioxa- and trioxa-bicyclo[5.1.0] octanes

The conformational geometries and possible interconversion paths for some oxa derivatives of bicyclo[5.1.0] octane have been studied by the molecular mechanics method. The theoretical results are compared with the experimental data for the molecular geometry of bicyclo[5.1.0] octane and 3,5,8-trioxabicyclo[5.1.0] octane, the free energy of activation for cycloheptene epoxide and 3,5-dioxabicyclo[5.1.0] octane, the dipole moments and molar Kerr constants in solution for cycloheptene epoxide, 3,5-dioxa- and 3,5,8-trioxabicyclo[5.1.0] octane.     

Structural investigation of high-valent manganese-salen complexes by UV/Vis,Raman, XANES,and EXAFS spectroscopy

XANES and EXAFS spectroscopic studies at the Mn-K- and Br-K-edge of reaction products of (S,S)-(+)-N,N'-bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexanediaminomanganese(III) chloride ([(salen)Mn(III)Cl], 1) and (S,S)-(+)-N,N'-bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexanediaminomanganese(III) bromide ([(salen)Mn(III)Br], 2) with 4-phenylpyridine N-oxide (4-PPNO) and 3-chloroperoxybenzoic acid (MCPBA) are reported. The reaction of the Mn(III) complexes with two equivalents of 4-PPNO leads to a hexacoordinated compound, in which the manganese atom is octahedrally coordinated by four oxygen/nitrogen atoms of the salen ligand at an average distance of approximately 1.90 A and two additional, axially bonded oxygen atoms of the 4-PPNO at 2.25 A. The oxidation state of this complex was determined as approximately +IV by a comparative study of Mn(III) and Mn(V) reference compounds. The green intermediate obtained in reactions of MCPBA and solutions of 1 or 2 in acetonitrile was investigated with XANES, EXAFS, UV/Vis, and Raman spectroscopy, and an increase of the coordination number of the manganese atoms from 4 to 5 and the complete abstraction of the halide was observed. A formal oxidation state of IV was deduced from the relative position of the pre-edge 1s-->3d feature of the X-ray absorption spectrum of the complex. The broad UV/Vis band of this complex in acetonitrile with lambda(max)=648 nm was consistent with a radical cation structure, in which a MCPBA molecule was bound to the Mn(IV) central atom. An oxomanganese(V) or a dimeric manganese(IV) species was not detected.     

Unusual and unexpected reactivity of t-butyl dicarbonate (Boc2O) with alcohols in the presence of magnesium perchlorate. A new and general route to t-butyl ethers

[reaction: see text] A new mild method for protecting alcohols as t-butyl ethers is reported. The reaction proceeds with Mg(ClO4)2 and Boc2O and shows general applicability. The deprotection of t-butyl ethers has also been revisited. Preliminary results indicate the CeCl3 x 7H2O/NaI system is a very suitable catalyst for their removal.     

Method validation for detection and quantification of cocoa butter equivalents in cocoa butter and plain chocolate

A European interlaboratory study was conducted to validate an analytical procedure for the detection and quantification of cocoa butter equivalents in cocoa butter and plain chocolate. In principle, the fat obtained from plain chocolate according to the Soxhlet principle is separated by high-resolution capillary gas chromatography into triacylglycerol fractions according to their acyl-C-numbers, and within a given number, also according to unsaturation. The presence of cocoa butter equivalents is detected by linear regression analysis applied to the relative proportions of the 3 main triacylglycerol fractions of the fat analyzed. The amount of the cocoa butter equivalent admixture is estimated by partial least-squares regression analysis applied to the relative proportions of the 5 main triacylglycerols. Cocoa butter equivalent admixtures were detected down to a level of 2% related to the fat phase, corresponding to 0.6% in chocolate (assumed fat content of chocolate, 30%), without false-positive or -negative results. By using a quantification model based on partial least-squares regression analysis, the predicted cocoa butter equivalent amounts were in close agreement with the actual values. The applied model performed well at the level of the statutory limit of 5% cocoa butter equivalent addition to chocolate with a prediction error of 0.6%, assuming a chocolate fat content of 30%.     

Detection and quantification of cocoa butter equivalents in cocoa butter and plain chocolate by gas liquid chromatography of triacylglycerols

The development and in-house testing of a method for the detection and quantification of cocoa butter equivalents in cocoa butter and plain chocolate is described. A database consisting of the triacylglycerol profile of 74 genuine cocoa butter and 75 cocoa butter equivalent samples obtained by high-resolution capillary gas liquid chromatography was created, using a certified cocoa butter reference material (IRMM-801) for calibration purposes. Based on these data, a large number of cocoa butter/cocoa butter equivalent mixtures were arithmetically simulated. By subjecting the data set to various statistical tools, reliable models for both detection (univariate regression model) and quantification (multivariate model) were elaborated. Validation data sets consisting of a large number of samples (n = 4050 for detection, n = 1050 for quantification) were used to test the models. Excluding pure illipé fat samples from the data set, the detection limit was determined between 1 and 3% foreign fat in cocoa butter. Recalculated for a chocolate with a fat content of 30%, these figures are equal to 0.3-0.9% cocoa butter equivalent. For quantification, the average error for prediction was estimated to be 1.1% cocoa butter equivalent in cocoa butter, without prior knowledge of the materials used in the blend corresponding to 0.3% in chocolate (fat content 30%). The advantage of the approach is that by using IRMM-801 for calibration, the established mathematical decision rules can be transferred to every testing laboratory.     

Spectroscopic and photochemical properties of the lichen compound lobaric acid

Lichens synthesize and accumulate photoprotective compounds against possible damage induced by UV radiation in the photobiont. A biological model has been recently formulated that allows the use of lichens to evaluate changes at different UV radiation levels. The thermodynamics, photophysical and photochemical properties of lobaric acid were studied in acetonitrile, ethanol and Brij 35(3%) micelles at different pH values. Also the sun protector factor (SPF) was determined by in vitro methods. Lobaric acid was extracted from Stereoculon alpinum Laur. and characterized by means of standard procedures. Solutions were irradiated in oxygen and under nitrogen conditions with a UV medium pressure lamp. Lobaric acid absorbs at 287, 303 nm, and no fluorescence emission was observed. The maximum value of the molar extinction coefficient (5479.6 M(-1) cm(-1)) was obtained in Brij 35 at pH 12. Solubility is pH dependant and is highest in Brij 35 at pH 12 (4.45 x 10(-4) M). Photoconsumption quantum yields ranged between 10(-4) and 10(-5) in aerobic and anaerobic experimental conditions. Lobaric acid SPF was very low (0.5) compared with homosalate (4.0), (reference solar filter). Two pKa values, 5.05 (carboxylic acid group deprotonation) and 9.75 (phenolic OH deprotonation), were determined.     

Polyhydroxy pregnanes from Dregea volubilis

Three new polyhydroxy pregnanes named dregealol (1), volubilogenone (2) and volubilol (3) were isolated from the flowers of Dregea volubilis, and their structures elucidated from extensive 2D NMR analysis. The structure of volubilol (3) was confirmed by X-ray crystallographic studies. The known pregnane derivatives drevogenin D, iso-drevogenin P and 17α-marsdenin were also isolated.