Observation time shortest

For concreteness, let us suppose that the universe has a temporal depth of two to accommodate a Fi edkin-type reversibility i.e. the present and immediate past are used to determine the future, and from which the past can be recovered uniquely. The RUGA itself is deterministic, is applied synchronously at each site in the lattice, and is characterized by three basic dimensional units (1) digit transition, D, which represents the minimal informational change at a given site (2) the length, L, which is the shortest distance between neighboring sites and (3) an integer time, T, which, while locally similar to the time in physics, is not Lorentz invariant and is not to be confused with a macroscopic (or observed) time t. While there are no a priori constraints on any of these units - for example, they may be real or complex - because of the basic assumption of finite nature, they must all have finite representations. All other units of physics in DM are derived from D, L and T. 

For both polymers the switching is very fast, less than a millisecond close to the Sc -Sa transition. Also, copolymer 40 exhibits a clear bistable ferroelectric switching even at room temperature (albeit slow, I > 600 ms). For both polymers a pronounced electrolink effect in the S phase was observed. The shortest electrook switching time for the copolymer was less than 30 is at T-T -Sa lOK. Close to the Sc -Sa transition, a tilt angle of nearly 18 is induced for an applied field of 100 V across a 10-)im cell. 

The apparatus used for picosecond flash spectroscopy on these systems has been described before(8 10). Figure 3a and b show typical transient absorption data obtained on 2-hydroxybenzophenone and the copolymer. Summary of these spectral data are given in Table 3. The transient observed at the shortest delay time (7ps) is the first excited singlet in all systems. The spectral data (at delay times > 50ps) permit placement of upper limits on triplet yields in CH2CI2 for both 2-hydroxy benzophenone itself and the copolymerized chromophore. 

For the first time dimerisation via the Li-F bond is found in the following molecule (Figure 1, 2). The Li-F distance (177.1 pm) is the shortest Li-F bond observed in a covalent lithium compound so far. 

To perform a PO analysis of nonadiabatic quantum dynamics, we employ a quasi-classical approximation that expresses time-dependent quantities of a vibronically coupled system in terms of the vibronic POs of the system [123]. Considering the quasi-classical expression (16) for the time-dependent expectation value of an observable A, this approximation assumes that the integrable islands in phase space represent the most significant contributions to the dynamics of the observables considered [236]. As a consequence, the short-time dynamics of the system is determined by its shortest POs and can be approximated by a time average over these orbits. Denoting the A th PO with period 7 by qk t),Pk t) we obtain [123]... 

The nonexponential decays impose limits on the shortest value of r) that can be measured. If we assume that the relaxation function can be determined accurately from 2 x Hr6 s to 100 s, then the limit will be determined by the condition that the function 2(t) should have a value at least as large as 1/e2 of its intercept value at the shortest reliable sampling interval. The value of P strongly affects the value of (r), but for = 0.5, the average relaxation time is two times the value of r. A practical limit for the shortest value of r) is 10-5 s. The average relaxation time is determined by the longest time part of the relaxation function, so that it is probably safe to calculate (r) even when most of the relaxation function is not measureable, as long as the final approach to the baseline is clearly observed. 

In human tumors, both the labeling index (LI) and Ts can be calculated from a single observation (5). These two parameters can be used to calculate the potential doubling time (rpo,), which describes the shortest possible time a cell... 

These peroxyalkyl nitrates are thermochemically unstable at room temperature and readily undergo dissociation back to their radical precursors [27], thus, these compounds have to be produced at a detectable level in the shortest possible reaction time. The main radical-generation scheme employed for their observation involved the Cl-atom initiated oxidation of the corresponding hydrocarbon [56]. However, in the case of CH4, its concentration had to be adjusted upward by a factor of 1000 relative to those of... 

Trajectories initiated from the vicinity of acetone radical cation showed essentially equal loss of either methyl (branching ratio 1.01 0.01). In contrast, the branching ratio observed for methyl loss in trajectories originating the TS was 1.13 0.01, which is in qualitative agreement with the experimental values of 1-1,4.24 When the trajectories were divided into time courses, with a resolution of 5fs, a unique phenomenon appeared that the newly created methyl dissociated predominantly at very short reaction time intervals. It was found that the trajectories that would lose the newly formed methyl at very short times never entered the PES minimum of the acetone radical cation. The shortest duration trajectories simply took the exit without ever attaining the equilibrium geometry of the radical cation. 

---