Tacit

In the linear approximation there is a direct Fourier relationship between the FID and the spectrum and, in the great majority of experunents, the spectrum is produced by Fourier transfonnation of the FID. It is a tacit assumption that everything behaves in a linear fashion with, for example, imifonn excitation (or effective RF field) across the spectrum. For many cases this situation is closely approximated but distortions may occur for some of the broad lines that may be encountered in solids. The power spectrum P(v) of a pulse applied at Vq is given by a smc fiinction 18]... 

The analysis of Manousiouthakis and Deem [75] mentioned above has demonstrated that it is also correct to choose atoms sequentially rather than randomly it has been tacitly assumed for many years that this violation of the Markovian restriction is acceptable, so a proof of tiiis kind is very welcome. 

We have tacitly assumed that the rate constants depend only on the last unit of the chain. In such a situation, the copolymerization is called a Markov copolymerization of first order. The special case (i), r r- = 1, is a Markov copolymerization of order zero. If reactivity also depends on the penultimate unit of the chain, the polymerization is a Markov copolymerization of second order. 

Equation (3.20) is conventionally termed the Kelvin equation. The tacit assumption is made at the integration stage that K is independent of pressure, i.e. that the liquid is incompressible. 

At the junction of the adsorbed film and the liquid meniscus the chemical potential of the adsorbate must be the resultant of the joint action of the wall and the curvature of the meniscus. As Derjaguin pointed out, the conventional treatment involves the tacit assumption that the curvature falls jumpwise from 2/r to zero at the junction, whereas the change must actually be a continuous one. Derjaguin put forward a corrected Kelvin equation to take this state of affairs into account but it contains a term which is difficult to evaluate numerically, and has aroused little practical interest. 

Like the analogous equation for capillary condensation (Equation (3.74) Equation (3.81) is based on the tacit assumption that the pore is of constant cross-section. Integration of Equation (3.81) over the range of the mercury penetration curve gives an expression for the surface area -4(Hg) of the walls of all the pores which have been penetrated by the mercury ... 

Mercury porosimetry is generally regarded as the best method available for the routine determination of pore size in the macropore and upper mesopore range. The apparatus is relatively simple in principle (though not inexpensive) and the experimental procedure is less demanding than gas adsorption measurements, in either time or skill. Perhaps on account of the simplicity of the method there is some temptation to overlook the assumptions, often tacit, that are involved, and also the potential sources of error. 

The microstructure/property relationships observed in shock-recovered samples have been often tacitly assumed to result solely from the shock compression, duration, and rarefaction due to the imposed uniaxial-strain shock. Recent shock-recovery studies have, however, shown that the degree of residual strain in the sample significantly influences the measured struc-... 

This formula, however, tacitly supposes that the instanton period depends monotonically on its amplitude so that the zero-amplitude vibrations in the upside-down barrier possess the smallest possible period 2nla>. This is obvious for sufficiently nonpathological one-dimensional potentials, but in two dimensions this is not necessarily the case. Benderskii et al. [1993] have found that there are certain cases of strongly bent two-dimensional PES when the instanton period has a minimum at a finite amplitude. Therefore, the cross-over temperature, formally defined as the lowest temperature at which the instanton still exists, turns out to be higher than that predicted by (4.7). At 7 > Tc the trivial solution Q= Q Q is the saddle-point coordinate) emerges instead of instanton, the action equals S = pV (where F " is the barrier height at the saddle point) and the Arrhenius dependence k oc exp( — F ") holds. 

The above discussion has tacitly assumed that it is only molecular interactions which lead to adhesion, and these have been assumed to occur across relatively smooth interfaces between materials in intimate contact. As described in typical textbooks, however, there are a number of disparate mechanisms that may be responsible for adhesion [9-11,32]. The list includes (1) the adsorption mechanism (2) the diffusion mechanism (3) the mechanical interlocking mechanism and (4) the electrostatic mechanism. These are pictured schematically in Fig. 6 and described briefly below, because the various semi-empirical prediction schemes apply differently depending on which mechanisms are relevant in a given case. Any given real case often entails a combination of mechanisms. 

The formation and decomposition of benzenediazoazide and phenylpentazole can be described by a mechanism alternative to the one discussed in Section III, A, 1 [Eq. (3)]. In contrast to the tacitly assumed independent formation and decomposition of phenylpentazole, e.g. one-step four-centered processes as described by 21 and 22,... 

Part of the answer may lie in the tacit assumption latent in the question itself how a child processes information is distinctly different from the way traditional... 

Now, to be sure, McCulloch-Pitts neurons are unrealistically rendered versions of the real thing. For example, the assumption that neuronal firing occurs synchronously throughout the net at well defined discrete points in time is simply wrong. The tacit assumption that the structure of a neural net (i.e. its connectivity, as defined by the set of synaptic weights) remains constant over time is known be false as well. Moreover, while the input-output relationship for real neurons is nonlinear, real neurons are not the simple threshold devices the McCulloch-Pitts model assumes them to be. In fact, the output of a real neuron depends on its weighted input in a nonlinear but continuous manner. Despite their conceptual drawbacks, however, McCulloch-Pitts neurons are nontrivial devices. McCulloch-Pitts were able to show that for a suitably chosen set of synaptic weights wij, a synchronous net of their model neurons is capable of universal computation. This means that, in principle, McCulloch-Pitts nets possess the same raw computational power as a conventional computer (see section 6.4). 

Fredkiii s universe is a universe in which there is only a finite amount of information and, for want of a better or more suggestive metaphor, is thought to evolve according to some underlying local CA rule. While the information content of the universe is assumed to be finite, it is also tacitly assumed that all of that information resides on an underlying lattice, whose own existence comes, so to speak, free-of-charge. This underlying lattice supplies an arena for an informational dynamics to take place in, but, except for its role as dynamical mediator, it itself remains effectively uninvolved in that dynamics. Clusters of information may form and dissipate and all sorts of interactions may take place within it, but the lattice remains separate and fixed. 

P should also minimize distinction.s between conventionally distinct but atomic. primitives (such as space, mass, time, etc.). The vision is to take one more step along the metaphoric road remove jnan from the center of the universe —> remove all privileged frames of reference —> remove all absolutes —> remove all distinction between space and matter—r remove all distinction ( ) Start by eliminating the tacit assumption that whatever physics is self-organizing itself out of the soup of the current crop of physicists is the physics of this universe in short, go from a solipsistic phys-ics to a fundamentally relativistic physics, wherein even physics itself becomes a set (an infinite hierarchical set ) of self-consistent world-views rather than a prescribed set of exactly/uniquely prescribed laws operating independently of all observers. 

The receptor compartment is defined as the aqueous volume containing the receptor and cellular system. It is assumed that free diffusion leads to ready access to this compartment (i.e., that the concentration within this compartment is the free concentration of drug at the receptor). However, there are factors that can cause differences between the experimentally accessible liquid compartment and the actual receptor compartment. One obvious potential problem is limited solubility of the drug being added to the medium. The assumption is made tacitly that the dissolved drug in the stock solution, when added to the medium bathing the pharmacological preparation, will stay in solution. There are cases where this may not be a valid assumption. 

In the above consideration it has been tacitly assumed that the charge carrier mobility docs not depend on the electric field. This is a good approximation for molecular crystals yet not for disordered systems in which transport occurs via hopping. Abkowitz et al. [37] have solved that problem for a field dependence of ft of the form p-po (FIFU) and trap-free SCL conduction. Their treatment predicts... 

With its jockey theme, gentleman receptionist and drinking-cartoon Bar Room, the 21 Club, a former speakeasy on East 52nd Street, is a touchstone for the particularly metropolitan idea of a restaurant with a tacit membership—the only survivor of a saloon-society heyday that included the Stork Club and El Morocco. 

The existence of derivatives of sufficiently high order will be tacitly assumed throughout. 

This argument tacitly assumes that J"M h t) kdt < oo for all positive mtegers A more careful argument, based on Taylor s theorem with the remainder, shows that it is sufficient that this condition be fulfilled for k a= 1,2. 

The assumption tacitly introduced by Mayer was called into question by Joule, who pointed out that it certainly is not true if the expanding substance is a liquid, and who in 1845 subjected Mayer s hypothesis to the test of a direct experiment. The principle was the following ... 

In our discussion of the coexistence curve, we tacitly assumed that at least one liquid phase can exist for any composition. However, since component 2 is a supercritical gas, the physically allowable liquid compositions are limited by the solubility of the gas in the binary solvent mixture. As the pressure rises, the solubility of the gas increases, thereby enlarging the composition range which permits the existence of a liquid phase. 

Up to now it has been tacitly assumed that each molecular motion can be described by a single correlation time. On the other hand, it is well-known, e.g., from dielectric and mechanical relaxation studies as well as from photon correlation spectroscopy and NMR relaxation times that in polymers one often deals with a distribution of correlation times60 65), in particular in glassy systems. Although the phenomenon as such is well established, little is known about the nature of this distribution. In particular, most techniques employed in this area do not allow a distinction of a heterogeneous distribution, where spatially separed groups move with different time constants and a homogeneous distribution, where each monomer unit shows essentially the same non-exponential relaxation. Even worse, relaxation... 

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