Temporal intervals

In figure 3 the dependence pA(t) in log-log coordinates, corresponding to the relationship (4), for the reesterification reaction in TBT presence is adduced. As can be seen, this dependence breaks down into two linear parts with different slopes. For the first part (/<90 min.) the slope is equal to -0,75, i.e., corresponded to the equation (6) for reaction proceeding in three-dimensional Euclidean space (d= 3). For the second part (/>90 min.) the slope is equal to 3, i.e., not corresponded to possible value of this exponent for recombination reaction or other analogous reactions, for which the value a is limited from above by the value 1,5 [2-4, 9], This means, that for the considered reesterification reaction times smaller of 90 min. it s necessary to identify as short times, i.e., on this temporal interval reactive particles concentration decay controls by local fluctuations of TBT distribution, and times equal or... 

This intermediate asymptotic exponent is useful to demonstrate the formation in time of a new asymptotic law shown in Fig. 6.3. In a given temporal interval a(t) approaches its asymptotic value close to a = d/2. 

Figure 3.14. Log-log plot of the DFA function vs. the temporal interval At (in months) for detrended and deseasonalized C02 concentrations, during 1958-2004.

Thus, from the said above it follows, that thermooxidative degradation process of PAr and PAASO melts proceeds in the fractal space with dimension A In such space degradation process can be presented schematically as devil s staircase [33]. Its horizontal sections correspond to temporal intervals, where the reaction does not proceed. In this case the degradation process is described with fractal time t using, which belongs to Cantor s setpoints [34]. If the reaction is considered in Euclidean space, then time belongs to real numbers sets. 

Devalues, obtained for PAr and PUAr poly condensation process, showed, that the indicated processes were realized by aggre tion cluster-cluster mechanism [49], i.e., by small macromolecular coils joining in larger ones [23], Thus, polycondensation process is a fractal object with dimension D. reaction. Such reaction can be presented schematically in a form of devil s staircase [80], Its horizontal parts correspond to temporal intervals, in which reaction is not realized. In this case polycondensation process is described with irsing fractal time t, which belongs to Kantor s set points [81], If polycondensation process is considered in Euclidean space, then time belongs to a real number set. 

Accordingly, the so-called spatial-temporal interval (quadratic) Minkowski can be formed,... 

Perhaps the best argument for time quantization (at least in the empirical spirit of quantum mechanics) is that we perceive temporal intervals of finite duration rather than durationless instants and it is dangerous to assume that the world has properties that can never be observed. But this psychological argument, as developed for example by Bergson, provides no quantitative justification for a division of physical time into chronons of the order of lO" " s. (Brush, 1982)... 

According to the fluctuation of reservoir water level in the Three Gorges Reservoir, the range of September 28, 2008 to June 10, 2009 is selected as the inversion temporal interval. This interval shows a whole process for the variation of reservoir water level and precipitation in one year. 

Hence, a solid-phase polymers deformation process is realized in fractal space with the dimension, which is equal to structure dimension d. In such space the deformation process can be presented schematically as the devil s staircase [39]. Its horizontal sections correspond to temporal intervals, where deformation is absent. In this case deformation process is described with using of fractal time t, which belongs to the points of Cantor s set [30]. If Euclidean object deformation is considered then time belongs to real numbers set. 

Figure 6.20 shows such a t3q>ical collision event of two drops with different viscosities. The temporal interval between two frames was 100 ps. The brighter lower viscous droplet is an aqueous solution of PVP K30 at a mass fraction of 5 %, while the higher viscous droplet was a K30 solution of 25 % mass fraction. It is noticeable that the two drops did not coalesce right upcni contact, rather about 584 ps later, which is called delayed coalescence. 

Needham, 1981] P. Needham. Temporal Intervals and Temporal Order, Logique et Analyse, 93, 49-64, 1981. 

Moreover, from all plots of Figure 1.6 there can be concluded that the reversible reactions do not definitely flows to the product formation, imtil considerable high temporal intervals are leaved behind. Also important, the reaction (1.97) delivers the late but suddenly almost entirely dissociation of the errzyme-substrate complex since all the curves of Figure 1.6 behaves closely with step kind functions. 

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