According to the DSC data (Fig. 2), the mechanically mixed with vinylated silica polymer after elimination of the volatile products at 83 °C has phase transition in the interval 150 270 °C with maximum on the endotherm at 230 °C corresponding to the melting process, which is not accompanied by a weight loss on the TG curve.
Following [14], we fix a time step h > 0 and define N i j as N i j ( t ) = N ˜ i j ( t + h ) − N ˜ i j ( t ), that is, the number of i → j transitions occurring in the interval ( t, t + h ]. The net increments in the state-occupancy numbers N i are then given by Δ i ( t ) ≡ N i ( t + h ) − N i ( t ) = ∑ j ≠ i N j i ( t ) − N i j ( t ).
The electrolytes were chosen to have a phase transition in the temperature interval to be monitored, resulting in large conductivity variations and thereby an easily interpreted output.
Integration by parts of eq. (3) shows that the proportion of the population experiencing the transition in the time interval Δ t (i.e. the "incident proportion") is given by: If the hazard is constant, that is, if h(t) = h t0) = h, ∫d t = Δ t and the integral collapses.
First, assuming that the transition propensities α i j ( k ) do not change dramatically in an interval of length τ, we can approximate the number of transitions in each interval by a collection of independent Poisson processes.
An alternative assumption would be to assume a continuous-time Markov process, implying an exponential distribution of time of transition within the interval, but in intervals of 2 years, the difference between both assumptions is small [ 26].
As shown in Figure 9A, C and E, normal cell samples, treated with rapamycin, showed a delay to exit from the G1 arrest (panel A) and, thus a 4 hours delay to reach the S-phase peak (panel C, peaks indicated by asterisks) and consequently to execute the G2/M transition that was not observed in the interval of time choose for this specific experiment (panel E).
More precisely, we can determine a larger window by increasing the confidence of the interval in Eq. (10), i.e. by choosing the time step Δ such that for each m the maximal/minimal number of transitions of type R m lies in the interval with a certain confidence (e.g. with a confidence of 80%).
With a small genotype-based variation in developmental timing and duration of the PCW/SCW transition stage, the interval between 17 and 24 dpa represents the general frame for PCW/SCW transition stage.
In changing the magnetic field intensity H in the interval (32), the transition frequencies ħ Ω 1 H (30) and ħ Ω 2 H (31) vary smoothly, respectively, in the intervals (Fig. 2): ( 19.7 meV ≤ ħ Ω 1 ≤ 53.7 meV ) ; ( 4.65 meV ≤ ħ Ω 2 ≤ 12.7 meV ), (38 arranged in the infrared spectrum area.
