Streaming operator method

It was therefore useful and interesting to compare explicitly the derivations of Bogolubov, Choh-Uhlenbeck, and Cohen (which we shall call the streaming operators method) and the results of Prigogine s theory. Part of this comparison has been made previously. 

V. EQUIVALENCE BETWEEN THE STREAMING OPERATORS METHOD AND PRIGOGINE S THEORY... 

The process can be operated in two modes co-fed and redox. The co-fed mode employs addition of O2 to the methane/natural gas feed and subsequent conversion over a metal oxide catalyst. The redox mode requires the oxidant to be from the lattice oxygen of a reducible metal oxide in the reactor bed. After methane oxidation has consumed nearly all the lattice oxygen, the reduced metal oxide is reoxidized using an air stream. Both methods have processing advantages and disadvantages. In all cases, however, the process is mn to maximize production of the more desired ethylene product. 

We have also studied the generalized Boltzmann operator for four particles in the Choh-Uhlenbeck formalism (see, for example, this expression in the work of Cohen8). Since the paper by Stecki and Taylor,29 it seems clear that the results of Bogolubov and those of Choh and Uhlenbeck (which are derived from them) must be equivalent to the Prigogine formalism. However, it is very difficult to show this equivalence explicitly in the concentration form that we have presented here. Indeed, in the Choh and Uhlenbeck method, the streaming operators appear with their Fourier components < k S(i n) k )and< k 0 S(i -n) k >, and the products of these operators are then expressed in terms of the Y(1 > for several complex variables. This renders the mathematical operations extremely complicated (see Eq. 111). 

Inspection of the energy available in the by-products indicates that there is ample energy available for operating the pyrolysis furnaces without the need to use any fuel oil (as the flow-sheet in Figure 7.1). This operational method degrades high value propylene and gasoline streams to fuel oil value. This may be justified for smaller operations, but for... 

Wang eta/. [19] investigated the effect of third metal on the WGS activity of Cu-Mn spinels. They synthesized Cu-Mn-M catalysts (M = Ce, Zr, Zn, Fe and Al) using urea-nitrate combustion method. The activity order is Zr>Fe >non-doped > Ce > Al > Zn. In addition, Zr-doped Cu-Mn catalyst with 5 wt% content showed the best catalytic performance and optimal stability exposed to oxygen-stream and on-stream operation. 

Distinguishing between toxicity tests and bioassays is not only of theoretical relevance. From toxicity tests, a clear dose-response graph could be drawn and effect concentrations (ECio, EC50 and EC90) as well as LOEC and NOEC could be calculated. The evaluation of bioassays should preferably be limited to the expression of inhibition values of the original sample and the calculation of dilution rates (G-values) at which a specific rate of inhibition, most commonly 10%, is reached. For example, the G-values derived from a wastewater treatment process should provide an estimation basis for the treatment plant operator regarding the possible inhibition effect of a certain wastewater stream (for methods see DIN-standards listed in Table 4.2). 

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