Some remarks to multivariate regression model

Some remarks to problems of point and interval estimation, testing and problems of outliers are presented in the case of multivariate regression model. This work was supported by the Council of Czech Government J14/98:153100011.     

Confidence regions in a multivariate regression model with constraints II

The multivariate model, where not only parameters of the mean value of the observation matrix, but also some other parameters occur in constraints, is considered in the paper. Some basic inference is presented under the condition that the covariance matrix is either unknown, or partially unknown, or known. Supported by the grant of the Council of Czech Republic MSM 6 198 959 214.     

Problems of an additional experiment

In some situations estimates of unknown parameters must be corrected by additional measurements. It is in principle no problem to calculate the corrected estimates, however, it is of more interest to find formulae for correction itself. The formulae enable us to design an additional experiment and to judge its usefulness. The aim of the paper is to find such formulae for several situations. Supported by the grant of the Council of Czech Government MSM 6 198 959 214.     

Models of pesticides inside cavities of molecular dimensions. A role of the guest inclusion in the dechlorination process

The reduction mechanism of the pesticide vinclozoline (3-(3,5-dichlorophenyl)-5-methyl-5-vinyl-1,3-oxazolidine-2,4-dione) was studied in nonaqueous solvents in the confined environment of a cyclodextrin (CD) cavity. The effect of the cavity dimensions on the mechanism of the redox process was evaluated using glucose as a reference and using three cyclodextrin molecules of different cavity sizes, namely, alphaCD, betaCD, and gammaCD. In the absence of CD the main reduction product of vinclozoline in the first reduction step is dichloroaniline. An addition of glucose leads to a quantitative change of mechanism with 10 products in total. Addition of CD, however, leads exclusively to dechlorination of the phenyl ring. The degree of dechlorination depends strongly on the choice of cyclodextrin molecule. The importance of the complex formation equilibria in the change of the mechanism is supported by a series of semiempirical AM1 quantum-mechanical calculations. Very good correlation (correlation coefficient 0.995) was obtained between the complex stabilization energy of the inclusion complex and the degree of pesticide dechlorination. Additionally, we were able to show that the complexes are stabilized by the formation of intermolecular hydrogen bonds between the host and guest species. CD molecules do not simply act as proton donors in a nonaqueous environment, but also protect parts of the molecule included within the cavity and steer the degradation process toward fewer products.     

Elimination of the type B uncertainty

An uncertainty of an estimated parameter can be, in general, decomposed into two parts, i.e. an uncertainty caused by errors in the actual experiment (the type A uncertainty) and an uncertainty caused by errors in preceding experiment, where some wanted constants were estimated (the type B uncertainty). These constants are necessary for an estimation of the useful parameters. The aim of the paper is to find a condition for elimination of the type B uncertainty.     

A New Insight into the Stereoelectronic Control of the Pd0-Catalyzed Allylic Substitution: Application for the Synthesis of Multisubstituted Pyran-2-ones via an Unusual 1,3-Transposition

Pyran-2-ones 3 undergo a novel Pd⁰-catalyzed 1,3-rearrangement to afford isomers 6 . The reaction proceeds via an η²-Pd complex, the pyramidalization of which (confirmed by quantum chemistry calculations) offers a favorable antiperiplanar alignment of the Pd−C and allylic C−O bonds ( C ), thus allowing the formation of an η³-Pd intermediate. Subsequent rotation and rate-limiting recombination with the carboxylate arm then gives isomeric pyran-2-ones 6 . The calculated free energies reproduce the observed kinetics semi-quantitatively.     

Mechanistic Dichotomy in the Asymmetric Allylation of Aldehydes with Allyltrichlorosilanes Catalyzed by Chiral Pyridine N‐Oxides

Detailed kinetic and computational investigation of the enantio‐ and diastereoselective allylation of aldehydes 1 with allyltrichlorosilanes 5 , employing the pyridine N‐oxides METHOX ( 9 ) and QUINOX ( 10 ) as chiral organocatalysts, indicate that the reaction can proceed through a dissociative (cationic) or associative (neutral) mechanism: METHOX apparently favors a pentacoordinate cationic transition state, while the less sterically demanding QUINOX is likely to operate via a hexacoordinate neutral complex. In both pathways, only one molecule of the catalyst is involved in the rate‐ and selectivity‐determining step, which is supported by both experimental and computational data.     

Theoretical Aspects of Hydrolysis of Peptide Bonds by Zinc Metalloenzymes

Activation and reaction energies for four model systems capturing the essential physicochemical features of the hydrolysis of the peptide bond have been calculated at various level of theory, including the presumably accurate CCSD(T) calculations. The models studied covered a part of the spectrum encountered in biological systems: the hydrolysis in the absence of metal ions (represented by formamide and Ala–Ala) and the hydrolysis in the presence of one and two zinc(II) ions, mimicking the active sites of mono‐ and dizinc metallopeptidases, respectively (by using thermolysin and glutamate carboxypeptidase II as the model catalytic systems and formamide as the model substrate). The results obtained using CCSD(T)/def2‐TZVP and CCSD(T)/aug‐cc‐pVTZ calculations were used as the benchmark values to which the set of cheaper methods, such as (RI‐)DFT, (RI‐)MP2, and SCS‐MP2, were referenced. It was shown that deviations of 3–5 kcal mol^?1 (translating to 2–3 orders in reaction constants) with respect to the reference CCSD(T) barriers are frequently encountered for many correlated methods and most of studied DFT functionals. It has been concluded that from the set of wave‐function methods, both MP2 and SCS‐MP2 methods can be recommended for smaller models (measured by the mean absolute deviation of the activation barriers over the four systems studied), whereas among the popular DFT functionals, B3LYP and especially M06‐2X are likely to be reasonable choices for calculating the activation barriers of zinc metallopeptidases. Finally, with the model of glutamate carboxypeptidase II, issues related to the convergence of the calculated barriers with the size of the model system used as the representative of the enzyme active site were addressed. The intricacies related to system truncation are demonstrated, and suggest that the correlated wave‐function methods may suffer from problems, such as intramolecular BSSE, which make their usage for the larger system questionable. Altogether, the presented data should contribute to efforts to understand enzymatic catalysis more deeply and to gain control of the accuracy and deficiencies of the available theoretical methods and computational approaches.     

Fast choice of separation conditions for analyses by capillary zone electrophoresis using an information system Xemic

An information system Xemic applicable in analytical chemistry is described and its use in capillary electrophoresis for searching suitable separation conditions is demonstrated. This system is capable to provide suitable separation conditions even for analytes for which no electrophoretic experiments have been published so far. The system works with a database of components of anionic character the analyses of which have been performed, published in reviewed scientific journals, and included into a database created by an expert. Moreover, the system learned to search also in abstracts or complete scientific articles to find articles dealing with the determination of a substance in a given sample matrix. When no experiments have been published so far for a defined substance in a specific matrix, Xemic shows the separation conditions for determination of the substance regardless of the matrix. When no response can be found for the analyte of interest at all, the system Xemic works like an expert in the field and searches chemically similar substances and offers a series of substances the physicochemical properties of which are close to the followed analyte with respect to the behavior in the electric field, and shows working conditions for their analysis. Thus, the analyst puts only the order in the form of a given analyte in a given matrix and obtains a recommendation of a separation system that should enable to perform a successful separation. The system is not rigid and enables the operator to change the importance of individual attributes used in similarity search so as to obtain a broader or narrower group of similar components. With a certain probability the analyte of interest can be successfully analyzed under separation conditions that suited for the analysis of the most similar substances in the given matrix.     

The stability and reactivity of activated acryloylcarbamates as reagents for the synthesis of N‐1 substituted thymine and uracil – an NMR and DFT study

The mechanism of the decomposition of acryloylcarbamates 7a–b yielding highly reactive isocyanates 3a–b was proposed based on NMR measurements and quantum chemical calculations. A good agreement between the experimental kinetic data and DFT calculations allowed us to demonstrate that the stability of 7a–d depends on the presence of methyl in the acryloyl moiety and the position of the nitro group in the nitrophenolic part of the molecule. Furthermore, the reactivity of 7a–d with weakly nucleophilic and sterically hindered 2,4,6‐tri‐tert‐butylaniline was explored by ¹H NMR demonstrating the usefulness of reagents 7a–d offering access to a variety of 1‐N‐substituted uracils and thymines with potentially interesting biological properties. Copyright © 2010 John Wiley & Sons, Ltd.