Continuous characters

It is not uncommon for a single molecule to have multiple populations. At non-zero temperatures, the population of different conformations will be dictated by Boltzmann statistics. If we make the approximation that we may neglect the continuous character of conformational space and simply work with discrete potential energy minima, we can replace a statistical mechanical probability integral with a discrete sum, and the equilibrium fraction F of any given conformer A at temperature T may be computed as... 

Some disadvantages are associated with this system. A first disadvantage is the disappearance of the continuous character of the sensor since a certain period of time elapses between the measurement of electrical current at the sensor surface and the moment in time when the sample to be analysed leaves the process bath. Whereas the developed sensor is intrinsically a continuous working system, it is clear that a basically discontinuous system can be considered as virtually continuous when the duration of the measurement is situated below a specific critical threshold, the dead time for every considered application. One of the tasks of the research is to keep the dead time as short as possible, and if necessary take this into account when the global process is directed by means of the output signal of the sensor expanded with a FIA system. 

In this limit, Eq. (3.86) is essentially a stationary mixture of projectors Eq)(Eq. ) Mote tliat a small degree of coherence between energy levels has been introduced. into Eq, (3.86) to account for the continuous character of E. 

In the real world, the following factors contribute to the continuous character of the devolatilization signal from the downgoing slab highly variable bulk compositions in the sedimentary and gabbroic layers as well as possibly different degrees of depletion (caused by different amounts... 

If you type a long VBA expression, it will not wrap to the next line but wiU simply disappear off the screen. You will have to insert a line-continuation character (a space followed by the underscore character followed by RETURN) to cause a line break in a line of VBA code, as in the following example ... 

The line-continuation character can t be used within a string. 

Df is usually an order of magnitude lower than I)]1. To avoid infinite gradients in the diffusion coefficient at the catalyst/backing layer interface and also to reflect the continuous character of the diffusion coefficient at the real interface, which is never sharp, A is approximated by... 

The interaction H12 can often be factored into electronic and vibrational parts, as in the case of predissociation, but here it is the electronic part that has the continuous character. In some cases, the vibrational part is simply an overlap factor and... 

Chaos can further be characterized by resorting to Poincare sections. By determining, for example, the value a of the substrate corresponding to the nth peak, /3 , of product Pi in the course of aperiodic oscillations, we may construct the one-dimensional return map giving a i as a function of a (Decroly, 1987a Decroly Goldbeter, 1987). The continuous character of the curve thus obtained (fig. 4.11) denotes the deterministic nature of the chaotic behaviour. 

Equation (16) may be regarded as the continuous generalization of the secular equation. In fact, in the past we already advocated an intrinsic continuous character of the Roothaan expansion (see Ref. [16b]). Then we may write... 

ArchaeaFEMS Microbiology Reviews 1998 18 225-236. Forterre, Patrick Institut Pasteur Paris France The universal tree of life an update. Front Microbiol 2015 6 717. Csurds, Miklos University Montreal Quebec Canada Ancestral reconstruction by asymmetric Wagner parsimony over continuous characters and squared parsimony over distributions (in print). 

Felsenstein, J., Maximum-likelihood estimation of evolutionary trees from continuous characters. Am. J. Hum. Genet, 15, 471-492, 1973. 

As an initial step it is necessary to predict the mean number of failures of all products sold in week s, which will occur in week w - [A ,s]. This value can be predicted using Equations (1), (2) or using other procedures. Equations (1) and (2) are vahd if the random variable (time elapsed fi om the product sale) has a continuous character. This fact is to be considered when predicting. The mean number of failures of all products sold in week s, which will occur in week w, is the difference between the predicted number of failures at the begirming and the end of week w. Given the warranty definition, the failures which will occur after the expiration of the warranty period ww are not taken into consideration, and for w-r > wiy theii[iV ,s] = 0. 

It follows from the above that the assumptions regarding weak coupling with the medium and at the same time with regard to the continuous character of the intramolecular vibrational energy spectrum of the reactants, which were made in some papers (see Refs. 3 and 8), to a certain degree contradict each other. 

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