Synthesis and ring-chain-ring tautomerism of bisoxazolidines, thiazolidinyloxazolidines, and spirothiazolidines

The synthesis of fused heterocycles such as thiazolidinyl-oxazolidine 3 is described starting from Tris·HCl. The mercaptomethyl bisoxazolidine 8 was found to convert to the corresponding thiazolidinyloxazolidine 3 and the spiro-heterocycle 4 by a ring-chain-ring tautomerism, depending on the electronic nature of the ring substituents as well as the reaction conditions. This equilibration pathway is absent in the hydroxymethyl bisoxazolidines 2. Computational studies confirm that both kinetic and thermodynamic control features play a role in the product distribution.     

Quantum chemical and conventional TST calculations of rate constants for the OH + alkane reaction

Reactions of OH with methane, ethane, propane, i-butane, and n-butane have been modeled using ab initio (MP2) and hybrid DFT (BHandHLYP) methods, and the 6-311G(d,p) basis set. Furthermore, single-point calculations at the CCSD(T) level were carried out at the optimized geometries. The rate constants have been calculated using the conventional transition-state theory (CTST). Arrhenius equations are proposed in the temperature range of 250–650 K. Hindered Internal Rotation partition functions calculations were explicitly carried out and included in the total partition functions. These corrections showed to be relevant in the determination of the pre-exponential parameters, although not so important as in the NO₃ + alkane reactions [G. Bravo-Pérez, J.R. Alvarez-Idaboy, A. Cruz-Torres, M.E. Ruíz, J. Phys. Chem. A 106 (2002) 4645]. The explicit participation of the tunnel effect has been taken into account. The calculated rate coefficients provide a very good agreement with the experimental data. The best agreement for the overall alkane + OH reactions seemed to occur when the BHandHLYP geometries and partition functions are used. For propane and i-butane, in addition to the respective secondary and tertiary H-abstraction channels, the primary one has been considered. These pathways are confirmed to be significant in spite of the large differences in activation energies between primary and secondary or primary and tertiary channels, respectively of propane and i-butane reactions and should not be disregarded.     

1,6‐ and 1,7‐naphthyridines III. 13C‐NMR analysis of some hydroxy derivatives

The ¹³C‐NMR spectra of some 1,6‐naphthyridines 2 and 1,7‐naphthyridines 3 , as well as those of N‐methyl derivatives 4 and 5 , were recorded and analyzed. Results in dimethyl‐d₆ sulfoxide and deuteriochlo‐roform provide useful data on intra and intermolecular hydrogen bonds.     

Some insight into characterizations of minimally nonideal matrices

Lehman (Polyhedral combinatorics 1 of DIMACS series in discrete math. and theoretical computer science, pp 101–105, 1990) described some conditions regular minimally nonideal (mni) matrices must satisfy. Although, there are few results on sufficient conditions for mni matrices. In most of these results, the covering polyhedron must have a unique fractional extreme point. This condition corresponds to ask the matrix to be the blocker of a near-ideal matrix, defined by the authors in a previous work (2006). In this paper we prove that, having the blocker of a near-ideal matrix, only a few very easy conditions have to be checked in order to decide if the matrix is regular mni. In doing so, we define the class of quasi mni matrices, containing regular mni matrices, and we find a generalization on the number of integer extreme points adjacent to the fractional extreme point in the covering polyhedron. We also give a relationship between the covering and stability number of regular mni matrices which allows to prove when a regular mni matrix can be a proper minor of a quasi mni. Partially supported by CONICET Grant PIP 2807/2000 (Argentina) and by CNPq/PROSUL Grant 490333/2004-4 (Brasil).     

Factorization of Hilbert port operators with poles on the imaginary axis

A factorization method is given to extract poles located on the imaginary axis for J-biexpansive meromorphic operator-valued functions acting on an infinite-dimensional Hilbert space. Decomposition of a real operator in terms of real factors, applicable to Hilbert ports, is also described, thus generalizing synthesis techniques originally developed for passive n-ports.     

Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter

This paper develops a robust profile estimation method for the parametric and nonparametric components of a single-index model when the errors have a strongly unimodal density with unknown nuisance parameter. We derive consistency results for the link function estimators as well as consistency and asymptotic distribution results for the single-index parameter estimators. Under a log-Gamma model, the sensitivity to anomalous observations is studied using the empirical influence curve. We also discuss a robust K-fold cross-validation procedure to select the smoothing parameters. A numerical study carried on with errors following a log-Gamma model and for contaminated schemes shows the good robustness properties of the proposed estimators and the advantages of considering a robust approach instead of the classical one. A real data set illustrates the use of our proposal.

     

On the asymptotic behavior of general projection-pursuit estimators under the common principal components model

The common principal components model for several groups of multivariate observations assumes equal principal axes among the groups. Robust estimators can be defined replacing the sample variance by a robust dispersion measure. This paper studies the asymptotic distribution of robust projection-pursuit estimators under a common principal components model.     

Ozonolysis of geraniol-trans, 6-methyl-5-hepten-2-one, and 6-hydroxy-4-methyl-4-hexenal: kinetics and mechanisms

A combined density functional theory and transition-state theory study of the mechanisms and reaction coefficients of gas-phase ozonolysis of geraniol-trans, 6-methyl-5-hepten-2-one, and 6-hydroxy-4-methyl-4-hexenal is presented. The geometries, energies, and harmonic vibrational frequencies of each stationary point were determined by B3LYP/6-31(d,p), MPW1K/cc-pVDZ, and BH&HLYP/cc-pVDZ methods. According to the calculations, the ozone 6-methyl-5-hepten-2-one reaction is faster than the ozone 6-hydroxy-4-methyl-4-hexenal reaction, but both are slower than the ozone geraniol-trans reaction. By using the BH&HLYP/cc-pVDZ data, a global rate coefficient of 5.9 x 10(-16) cm(3) molecule(-1) s(-1) was calculated, corresponding to the sum of geraniol-trans, 6-methyl-5-hepten-2-one, and 6-hydroxy-4-methyl-4-hexenal reactions with the ozone. These results are in good agreement with the experimental studies.     

Electronic structure, molecular interaction, and stability of the CH4-nH2O complex, for n = 1-21

Molecular calculations were carried out with four different methodologies to study the CH 4- nH 2O complex, for n = 1-21. The HF and MP2 methods used considered the O atom with pseudopotential to freeze the 1s shell. The other methodologies applied the Bhandhlyp and B3lyp exchange and correlation functionals. The optimized CH 4- nH 2O structures are reported, specifying the number and type of H 2O subunits (triangle, square, pentagon, etc.) that comprised the nH 2O counterpart cluster or cage, that interacted with the CH 4 molecule, and, in the latter case, that provided its confinement. Results are focused to understand the stability of the CH 4- nH 2O complex. The quality of the electron correlation effect, as well as the size of the nH 2O cage to confine the guest molecule, and the number and type of H 2O subunits comprising the nH 2O cluster or cage are the most important factors to provide the stability of the complex and also dictate the particular n value at which the CH 4 molecule confinement occurs. This number was 14 for the HF, Bhandhlyp, and B3Lyp methods and 16 for the MP2 method. The reported hydrate structures for n < 20 could be predictive for future experiments.