Time operators and shift representation of dynamical systems

We introduce and characterise time operators for unilateral shifts and exact endomorphisms. The associated shift representation of evolution is related to the spectral representation by a generalized Fourier transform. We illustrate the results for a simple exact system, namely the Renyi map.

An investigation of possible mechanisms of the water-gas shift reaction over a ZrO2-supported Pt catalyst

The present work investigates the reactivity of the surface species observable by in situ DRIFTS formed over a Pt/ZrO2 during the water-gas shift (WGS) reaction. A DRIFTS cell/mass spectrometer system was operated at the chemical steady state during isotopic transients to yield information about the true nature (i.e., main reaction intermediate or spectators) of adsorbates. Only carbonyl and formate species were observed by DRIFTS under reaction conditions; the surface coverage of carbonate species was negligible. Isotopic transient kinetic analyses revealed that formates exchanged uniformly according to a first-order law, suggesting that most formates observed by DRIFTS were of the same reactivity. In addition, the time scale of the exchange of the reaction product CO2 was significantly shorter than that of the surface formates. Therefore, a formate route based on the formates as detected by DRIFTS can be ruled out as the main reaction pathway in the present case. The number of precursors of the reaction product CO2 was smaller than the number of surface Pt atoms, suggesting that carbonyl species or some \

Quantitative DRIFTS investigation of possible reaction mechanisms for the water-gas shift reaction on high-activity Pt- and Au-based catalysts

The present work emphasizes the importance of including a full quantitative analysis when in situ operando methods are used to investigate reaction mechanisms and reaction intermediates. The fact that some surface species exchange at a similar rate to the reaction product during isotopic transients is a necessary but not sufficient criterion for participation as a key reaction intermediate. This is exemplified here in the case of highly active low-temperature water-gas shift (WGS) catalysts based on gold and platinum. Operando DRIFTS data, isotopic exchanges, and DRIFTS calibration curves relating the concentration of formate species to the corresponding DRIFTS band intensity were combined to obtain a quantitative measure of the specific rate of formate decomposition. Despite displaying a rapid isotopic exchange rate (sometimes as fast as that of the reaction product CO2), the concentration of formates seen by DRIFTS was found to account for at most only 10% of the CO2 produced under the experimental conditions reported herein. These new results obtained on Au/CeZrO4 and Pt/CeO2 preparations (which are among the most active low-temperature WGS catalysts reported to date), led to the same conclusions regarding the minor role of IR-observable formates as those obtained in the case of less active Au/Ce(La)O-2 and Pt/ZrO2 catalysts. (c) 2007 Elsevier Inc. All rights reserved.

On the complexity of the water-gas shift reaction mechanism over a Pt/CeO2 catalyst: Effect of the temperature on the reactivity of formate surface species studied by operando DRIFT during isotopic transient at chemical steady-state

The present report investigates the role of formate species as potential reaction intermediates for the WGS reaction (CO + H2O -> CO2 + H-2) over a Pt-CeO2 catalyst. A combination of operando techniques, i.e., in situ diffuse reflectance FT-IR (DRIFT) spectroscopy and mass spectrometry (MS) during steady-state isotopic transient kinetic analysis (SSITKA), was used to relate the exchange of the reaction product CO2 to that of surface formate species. The data presented here suggest that a switchover from a non-formate to a formate-based mechanism could take place over a very narrow temperature range (as low as 60 K) over our Pt-CeO2 catalyst. This observation clearly stresses the need to avoid extrapolating conclusions to the case of results obtained under even slightly different experimental conditions. The occurrence of a low-temperature mechanism, possibly redox or Mars van Krevelen-like, that deactivates above 473 K because of ceria over-reduction is suggested as a possible explanation for the switchover, similarly to the case of the CO-NO reaction over Cu, I'd and Rh-CeZrOx (see Kaspar and co-workers [1-3]). (c) 2006 Elsevier B.V. All rights reserved.

Negative apparent kinetic order in steady-state kinetics of the water-gas shift reaction over a Pt-CeO2 catalyst

The kinetics of the water-gas shift reaction Were Studied on a 0.2% Pt/CeO2 catalyst between 177 and 300 degrees C over a range of CO and steam pressures. A rate decrease with increasing partial pressure of CO was experimentally observed over this sample, confirming that a negative order in CO can occur under certain conditions at low temperatures. The apparent reaction order of CO measured at 197 degrees C was about -0.27. This value is significantly larger than that (i.e, -0.03) reported by Ribeiro and co-workers [A.A. Phatak, N. Koryabkina, S. Rai, J.L. Ratts, W. Ruettinger, R.J. Farrauto, G.E. Blau, W.N. Delgass, F.H. Ribeiro, Catal. Today 123 (2007) 224] at a similar temperature. A kinetic peculiarity was also evidenced, i.e. a maximum of the reaction rate as a function of the CO concentration or possibly a kinetic break, which is sometimes observed in the oxidation of simple molecules. These observations support the idea that competitive adsorption of CO and H2O play an essential role in the reaction mechanism. (C) 2008 Elsevier B.V. All rights reserved.

Object tracking using SIFT features and mean shift

A scale invariant feature transform (SIFT) based mean shift algorithm is presented for object tracking in real scenarios. SIFT features are used to correspond the region of interests across frames. Meanwhile, mean shift is applied to conduct similarity search via color histograms. The probability distributions from these two measurements are evaluated in an expectation–maximization scheme so as to achieve maximum likelihood estimation of similar regions. This mutual support mechanism can lead to consistent tracking performance if one of the two measurements becomes unstable. Experimental work demonstrates that the proposed mean shift/SIFT strategy improves the tracking performance of the classical mean shift and SIFT tracking algorithms in complicated real scenarios.