Dual theoretical calculations

The dual-cycle mechanism, recently introduced by Svelle et al. afto confirmation by theoretical calculations [91], combines the features of both mechanistical approaches (Fig. 14) [29,92,93]. This mechanism represents the most recent state on olefins formation from methanol and allows the best fitting with the experimental data. 

At present, most PET scanners can acquire in both a two-dimensional as well as a three-dimensional mode, whereas SPECT cameras measure in a three-dimensional mode. The physical property of the dual-positron gamma-rays emission lends itself to mathematical reconstruction algorithms to produce three-dimensional images in which the calculations are much closer to exact theoretical ones than those of SPECT. This is, in part, due to the two-photon as opposed to single-photon approach. PET can now achieve resolutions, for example in animal-dedicated scanners, in the order of 1 or 2 mm. The resolution is inherently limited theoretically only by the mean free path or distance in which the positron travels before it annihilates with an electron, e.g. those in biological water 2-8 mm. SPECT, although achieving millimeter resolution with the appropriate instrumentation, cannot quite achieve these levels. 

For the SDP problems arising from the variational calculation, in which we are interested, the theoretical number of floating-point operations required by parallel Primal-Dual interior-point method-based software scales as... 

Section 8 summarizes separation factors obtainable in isotope exchange reactions and their temperature dependence. The latter is the key property in dual-temperature exchange processes. Section 9 develops equations to be used for calculating the number of theoretical stages needed in exchange separation towers. 

Theoretical and experimental approaches to understanding structure and properties of cyclophosphazenes have appeared. The most significant of these is a report of the observed (x-ray diffraction) and calculated (ab initio) deformation electron densities in the benzene solvate of hexa(aziridinyl)-cyclotriphosphazene. The electron densities in the phosphazene clearly show the classic island model pattern with nodes in the n system at nitrogen. The dual system is also clearly... 

The key feature is likely the dual nature of the U 5f-states, i.e., the presence of both localized and delocalized U 5f-electrons. The theoretical investigation proceeds in three steps. Firstly, band-structure calculations have been performed starting from the self-consistent LDA potentials but excluding the U 5f j = 5/2, = 5/2 and jz = 1/2 states from forming... 

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