Predictability of nonstationary time series using wavelet and EMD based ARMA models

Research has been undertaken to ascertain the predictability of non-stationary time series using wavelet and Empirical Mode Decomposition (EMD) based time series models. Methods have been developed in the past to decompose a time series into components. Forecasting of these components combined with random component could yield predictions. Using this ideology, wavelet and EMD analyses have been incorporated separately which decomposes a time series into independent orthogonal components with both time and frequency localizations. The component series are fit with specific auto-regressive models to obtain forecasts which are later combined to obtain the actual predictions. Four non-stationary streamflow sites (USGS data resources) of monthly total volumes and two non-stationary gridded rainfall sites (IMD) of monthly total rainfall are considered for the study. The predictability is checked for six and twelve months ahead forecasts across both the methodologies. Based on performance measures, it is observed that wavelet based method has better prediction capabilities over EMD based method despite some of the limitations of time series methods and the manner in which decomposition takes place. Finally, the study concludes that the wavelet based time series algorithm can be used to model events such as droughts with reasonable accuracy. Also, some modifications that can be made in the model have been discussed that could extend the scope of applicability to other areas in the field of hydrology. (C) 2013 Elesvier B.V. All rights reserved.

Vapor phase oxidation of p-xylene

The kinetics of the vapor phase oxidation of p-xylene over ferric molybdate catalyst were studied in an isothermal, differential, tubular flow reactor in the temperature range of 360 to 420° C. The major product obtained was p-tolualdehyde with small amounts of maleic anhydride and p-toluic acid. No terephthalic acid or CO2 were observed. The reaction rate data collected fit the redox model given by Equation 1. The values of activation energies Ex, Eo and frequency factors Ax, Ao obtained are 72, 63 kJ/mol and 0.64, 2.89 m3/kg catalyst s respectively. The reaction mechanism was established by studying the oxidation of p-tolualdehyde, toluic and terephthalic acids. It is concluded that the reaction follows a parallel-consecutive scheme. On a étudié la cinétique de l'oxydation, en phase gazeuse, du para-xylène sur un catalyseur consistant en molybdate ferrique; cette oxydation s'est faite dans un réacteur à écoulement tubulaire, isothermique et différentiel, dans une échelle de températures comprises entre 360°C et 420°C. Le produit principal obtenu a été le para-tolualdéhyde; on a aussi trouvé de faibles quantités d'anhydride maléique et d'acide para-toluique, mais on n'a pas noté la présence d'acide téréphtalique ni d'anhydride carbonique (CO2). Les résultats obtenus en ce qui a trait à la vitesse de réaction concordent bien avec les données du modèle redox indiquées par l'équation 1. Les valeurs des énergies d'activation Ex et Eo ainsi que des facteurs de fréquence Ax et Ao obtenus sont respectivement 72 et 63 kilojoules/mol. et 0.64 × 103 et 2.89 m3/kg de catalyseur. On a établi le mécanisme de la réaction en étudiant l'oxydation du para-tolualdéhyde et des acides toluique et téréphtalique. On conclut que la réaction se fait d'une manière parallèle et consécutive.

A generalised cole-hopf transformation for nonlinear parabolic and hyperbolic equations

The Cole-Hopf transformation has been generalized to generate a large class of nonlinear parabolic and hyperbolic equations which are exactly linearizable. These include model equations of exchange processes and turbulence. The methods to solve the corresponding linear equations have also been indicated.La transformation de Cole et de Hopf a été généralisée en vue d'engendrer une classe d'équations nonlinéaires paraboliques et hyperboliques qui peuvent être rendues linéaires de façon exacte. Elles comprennent des équations modèles de procédés d'échange et de turbulence. Les méthodes pour résoudre les équations linéaires correspondantes ont également été indiquées.