Simultaneous definition

Consider an arbitrary observable A with a set of eigenfunctions, ipa, belonging to a series of eigenvalues denoted by o. According to the first assumption there is an element of reality corresponding to observable A in the system. Next, consider another observable B which does not commute with A, so that there exists no wave function for which A and B have simultaneously definite values. If every element of physical reality must have a counterpart in a complete physical theory, the previous conclusion implies that A and B cannot exist simultaneously. 

Therefore, an ITK experiment allows the simultaneous definition of the number of active sites on the catalyst and the specific rate of reaction over these active sites. A full description of the data analysis procedures used to interpret TTK data is beyond the scope of this article, but such details can be found in the literature (see eg [10]). 

Definition of Dust E losion A dust explosion is the rapid combustion of a dust cloud. In a confined or nearly confined space, the explosion is characterized by relatively rapid development of pressure with a flame propagation and the evolution of large quantities of heat and reaction products. The required oxygen for this combustion is mostly supphed oy the combustion air. The condition necessaiy for a dust explosion is a simultaneous presence of a dust cloud of proper concentration in air that will support combustion and a suitable ignition source. 

If separate blast sources are located close to one another, they may be initiated almost simultaneously. Coincidence of their blasts in the far field cannot be raled out, and their respective blasts should be superposed. The safe and most conservative approach to this issue is to assume a maximum initial blast strength of 10 and to sum the combustion energy from each source in question. Further definition of this important issue, for instance the determination of a minimum distance between potential blast sources so that their individual blasts may be considered separately, is a factor in present research. 

Interconversion between two tautomeric structures can occur via discrete cationic or anionic intermediates (scheme 24, where T is an anion capable of reacting with a proton at a minimum of two distinct sites). Alternatively, interconversion can occur by simultaneous loss and gain of different protons (scheme 25, w here T has the same definition as in scheme 24). These mechanisms are well established for acyclic compounds, but they have been much less thoroughly investigated for heteroaromatic systems. The rate of interconversion of two tautomers is greatest when both of the alternative atoms to which the mobile proton can be attached arc hetero atoms, and isolation of the separate isomers is usually impossible in this case. If one of the alternative atoms involved in the tautomerization is carbon, the rate of interconversion is somewhat slower, but still fast. When both of the atoms in question are carbon, however, interconversion is... 

If, for the purpose of comparison of substrate reactivities, we use the method of competitive reactions we are faced with the problem of whether the reactivities in a certain series of reactants (i.e. selectivities) should be characterized by the ratio of their rates measured separately [relations (12) and (13)], or whether they should be expressed by the rates measured during simultaneous transformation of two compounds which thus compete in adsorption for the free surface of the catalyst [relations (14) and (15)]. How these two definitions of reactivity may differ from one another will be shown later by the example of competitive hydrogenation of alkylphenols (Section IV.E, p. 42). This may also be demonstrated by the classical example of hydrogenation of aromatic hydrocarbons on Raney nickel (48). In this case, the constants obtained by separate measurements of reaction rates for individual compounds lead to the reactivity order which is different from the order found on the basis of factor S, determined by the method of competitive reactions (Table II). Other examples of the change of reactivity, which may even result in the selective reaction of a strongly adsorbed reactant in competitive reactions (49, 50) have already been discussed (see p. 12). 

In order to clarify these definitions, a geometrical interpretation of FXt0 t(x1,x2) is given in Pig. 3-7. It should be clear from this picture that is the fraction of the time that, simultaneously, X(t) 5... 

In the course of reactions of chromium(VI) with different substrates (inductors), depending on whether the inductor is 1- or 2-equivalent reagent, in the primary reaction formation of Cr(V) and Cr(IV), respectively, was assumed. However, no definite statement can be made as to whether the chromium species formed in the primary reaction or another chromium entity produced in a secondary step reacts with the acceptor. The possibility of simultaneous formation of both chromium species in the primary reaction can be excluded. 

The transfer of heat by radiation in general can be said to occur simultaneously with heat transfer by convection and conduction. Transfer by radiation tends to become more important than that by the other two mechanisms as the temperature increases. It is useful to gain an appreciation of the basic definitions of the energy flux terms, the surface property terms and their relationships while discussing radiative heat transfer. With this objective, reference may be made to Table 3.4 in which these are presented. 

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