Home About us Contact
|
Home About us Contact | ||
|
|
||
Order P (order + p)
Selected AbstractsMechanisms of H2, H2C=CH2, and O=CH2 Insertion into Cp2Zr(,2 -SiMe2=NtBu)(PMe3)EUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 14 2007Siwei Bi Abstract In this paper, the mechanisms for the insertion of H2, H2C=CH2, and O=CH2 into the Zr,Si bond of Cp2Zr(,2 -SiMe2=NtBu)(PMe3) (R) are theoretically investigated with the aid of density functional theory (DFT) calculations. The structure of the H2 insertion product P is discussed on the basis of our calculations, and its bonding features are rationalized in terms of molecular orbital theory. The regiochemistry for insertion of O=CH2 has also been theoretically investigated. It is found that the relative stabilities of the three insertion products of R are in the order P < P, < P,. For the reactions of R with H2 and CH2=CH2, the rate-determining steps are the insertions of H2 and CH2=CH2 into the Zr,Si bond of Cp2Zr(,2 -SiMe2=NtBu) (Int1), whereas PMe3 dissociation is the rate-determining step for the reaction of R with O=CH2. Only the precursor Int2,, formed by the coordination of O=CH2 to the Zr atom, is located; those formed by the coordination of H2 and CH2=CH2 to Int1 are not found.(© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007) [source] Bond length features of linear carbon chains of finite to infinite size: Visual interpretation from Pauling bond ordersINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 3 2003Zexing Cao Abstract Schemes for Kekulé structure counting of linear carbon chains are suggested. Mathematical formulas, which calculate the Pauling bond order P(k, N) of a chemical bond numbered by k, are given for the carbon chain with N carbon atoms. By use of the least-squares fitting of a linearity, relationships between Pauling bond orders and bond lengths are obtained, and such correlation of the Pauling bond order,bond length can be qualitatively extended to the excited states. The relative magnitudes of Pauling bond orders in unsaturated carbon chains dominate C,C bond lengths a well as the bond length feature with the chain size increasing. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 144,149, 2003 [source] Semiparametric estimation by model selection for locally stationary processesJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 5 2006Sébastien Van Bellegem Summary., Over recent decades increasingly more attention has been paid to the problem of how to fit a parametric model of time series with time-varying parameters. A typical example is given by autoregressive models with time-varying parameters. We propose a procedure to fit such time-varying models to general non-stationary processes. The estimator is a maximum Whittle likelihood estimator on sieves. The results do not assume that the observed process belongs to a specific class of time-varying parametric models. We discuss in more detail the fitting of time-varying AR(p) processes for which we treat the problem of the selection of the order p, and we propose an iterative algorithm for the computation of the estimator. A comparison with model selection by Akaike's information criterion is provided through simulations. [source] Stability of nonlinear AR-GARCH modelsJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2008Mika Meitz Abstract., This article studies the stability of nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a nonlinear autoregression of order p [AR(p)] with the conditional variance specified as a nonlinear first-order generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. Conditions under which the model is stable in the sense that its Markov chain representation is geometrically ergodic are provided. This implies the existence of an initial distribution such that the process is strictly stationary and , -mixing. Conditions under which the stationary distribution has finite moments are also given. The results cover several nonlinear specifications recently proposed for both the conditional mean and conditional variance, and only require mild moment conditions. [source] Dynamics of Model Overfitting Measured in terms of Autoregressive RootsJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2006Clive W. J. Granger C32 Abstract., One method of describing the properties of a fitted autoregressive model of order p is to show the p roots that are implied by the lag operator. Considering autoregressive models fitted to 215 US macro series, with lags chosen by either the Bayesian or Schwarz information criteria or Akaike information criteria, the roots are found to constitute a distinctive pattern. Later analysis suggests that much of this pattern occurs because of overfitting of the models. An extension of the results shows that they have some practical multivariate time-series modelling implications. [source] The adjustment of prediction intervals to account for errors in parameter estimationJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2004Paul Kabaila Abstract., Standard approximate 1 , , prediction intervals (PIs) need to be adjusted to take account of the error in estimating the parameters. This adjustment may be aimed at setting the (unconditional) probability that the PI includes the value being predicted equal to 1 , ,. Alternatively, this adjustment may be aimed at setting the probability that the PI includes the value being predicted equal to 1 , ,, conditional on an appropriate statistic T. For an autoregressive process of order p, it has been suggested that T consist of the last p observations. We provide a new criterion by which both forms of adjustment can be compared on an equal footing. This new criterion of performance is the closeness of the coverage probability, conditional on all of the data, of the adjusted PI and 1 , ,. In this paper, we measure this closeness by the mean square of the difference between this conditional coverage probability and 1 , ,. We illustrate the application of this new criterion to a Gaussian zero-mean autoregressive process of order 1 and one-step-ahead prediction. For this example, this comparison shows that the adjustment which is aimed at setting the coverage probability equal to 1 , , conditional on the last observation is the better of the two adjustments. [source] Random vectors satisfying Khinchine,Kahane type inequalities for linear and quadratic formsMATHEMATISCHE NACHRICHTEN, Issue 9 2005Jesús Bastero Abstract We study the behaviour of moments of order p (1 < p < ,) of affine and quadratic forms with respect to non log-concave measures and we obtain an extension of Khinchine,Kahane inequality for new families of random vectors by using Pisier's inequalities for martingales. As a consequence, we get some estimates for the moments of affine and quadratic forms with respect to a tail volume of the unit ball of lnq (0 < q < 1). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||