Very small

Large confidence regions are obtained for the parameters because of the random error in the data. For a "correct" model, the regions become vanishingly small as the random error becomes very small or as the number of experimental measurements becomes very large. 

On the other hand, if Ki is very small (Douglas has suggested a value less than 0.1) in Eq. (4.9), then... 

Table 5.4 gives the specific energies of selected organic liquid compounds. Compared with the isooctane chosen as the base reference, the variations from one compound to another are relatively small, on the order of 1 to 5%, with the exception of some particular chemical structures such as those of the short chain nitroparaffins (nitromethane, nitroethane, nitropropane) that are found to be energetic . That is why nitromethane, for example, is recommended for very small motors such as model airplanes it was also used in the past for competitive auto racing, for example in the Formula 1 at Le Mans before being forbidden for safety reasons. 

With regard to mass spectrometry, accuracy is not as high with an average error of 2.8 points, but on the other hand, the sample required is very small, being around 2 jl1. 

Paraffins consist mainly of straight chain alkanes, with a very small proportion of isoalkanes and cycloalkanes. Their freezing point is generally between 30°C and 70°C, the average molecular weight being around 350. When present, aromatics appear only in trace quantities. 

Crude oils contain, in very small quantities, water, sediments and mineral salts most of which are dissolved in the water, the remainder found as very fine crystals. 

Regardless of their presence in very small amounts, on the order of a few dozen ppm (Table 8.14), mineral salts cause serious problems during crude oil treatment. 

These products have molecular weights between 2000 and 10,000, well below those of additives improving the viscosity index (100,000). They are added in very small concentrations (0.01 to 0.3 weight percent) and at these concentrations they can lower the pour point 30°C. 

To detect surface anomalies caused by hydrocarbon accumulations often very small amounts of petroleum compounds have leaked into the overlying strata and to the surface. On land, these compounds, mostly gases, may be detectable in soil samples. 

In many cases faults will only restrict fluid flow, or they may be open i.e. non-sealing. Despite considerable efforts to predict the probability of fault sealing potential, a reliable method to do so has not yet emerged. Fault seal modelling is further complicated by the fact that some faults may leak fluids or pressures at a very small rate, thus effectively acting as seal on a production time scale of only a couple of years. As a result, the simulation of reservoir behaviour in densely faulted fields is difficult and predictions should be regarded as crude approximations only. 

The most common contaminants in produced gas are carbon dioxide (COj) and hydrogen sulphide (HjS). Both can combine with free water to cause corrosion and H2S is extremely toxic even in very small amounts (less than 0.01% volume can be fatal if inhaled). Because of the equipment required, extraction is performed onshore whenever possible, and providing gas is dehydrated, most pipeline corrosion problems can be avoided. However, if third party pipelines are used it may be necessary to perform some extraction on site prior to evacuation to meet pipeline owner specifications. Extraction of CO2 and H2S is normally performed by absorption in contact towers like those used for dehydration, though other solvents are used instead of glycol. 

Breakdown and subsequent repair is clearly non-scheduled, but gives rise to nonavailability of the item. Some non-critical items may actually be maintained on a breakdown basis, as discussed in Section 11.3. Flowever, an item which is critical to keeping the production system operating will be designed and maintained to make the probability of breakdown very small, or may be backed up by a stand-by unit. 

Generally, it has been shown that the NSC is capable of detecting very small disbonds (larger than 25% of the sensor area) and correctly identifying their position in the structure (identifying the defect joint). 

Evaluation data taken from the more than 8 thousand reports of the laboratory and field wire ropes inspections show that the visual methods and life time criteria are non adequate to real durability of the ropes in service [4]. The data show that only a very small percentage of all ropes was replaced in a proper time, when one has used a visual inspection. 

The physics of X-ray refraction are analogous to the well known refraction of light by optical lenses and prisms, governed by Snell s law. The special feature is the deflection at very small angles of few minutes of arc, as the refractive index of X-rays in matter is nearly one. Due to the density differences at inner surfaces most of the incident X-rays are deflected [1]. As the scattered intensity of refraction is proportional to the specific surface of a sample, a reference standard gives a quantitative measure for analytical determinations. 

Note that this relationship is in conPadiction to the well known equation for the calculation of the thickness resolving power given by Halmshaw in 111. The relationship in 111 requires explicit knowledge about built-up factors for scatter correction and the film contrast factory (depending on D) and is only valid for very small wall thickness changes compared to the nominal wall thickness. 

The case considered above corresponds to R < H. The calculation using formula (1) gives the next results. For example, consider the thickness of dry developer layer h = 20 pm. In the absence of sedimentation process our product family (penetrant and developer indicated above) could not detect the cracks with the depth lo < 1,33 mm of any widths. Nevertheless due to the sedimentation one can get the decrease of developer s thickness from h = 20 pm till h s 5 pm. As a result, our product family can ensure the detection of the cracks with H > 2,3 pm even with very small length lo = 0,4 mm. At the same time if lo = 1 mm, then the cracks with extremely small width H > 0,25 will be revealed. 

The performances of ultrasound generated and detected by lasers offer a wide field of applications in industry, so that we will pursue research for the testing of very small strucmres which could only be examined by a contactless technique. 

The pulser/receiver is completely shielded and therefore receives no noise coming from the PC components. The input connector is a Lemo 00 coupler. The extremely low noise amplifier with a maximum amplification of about 90 dB accommodates very small signals. A precise gain setting is possible up to 106 dB. 

It has been found that the contrast in film density caused by very small local variations in mass density of the concrete is considerable, e g. S D = 0.12 for a 6 mm diameter hole in a 250 mm thick concrete beam. The image quality provided by fine-grained films (Agfa Gaevert D7) was sufficient to distinguish the thin walls of a pre-stressing duct in a 750 mm thick concrete bridge slab. 

The methodology and the pigging tool have proven to be capable of identifying very small leaks. In oil pipelines like the Danish carrying 1500 m /h leakages down to 1 litre per hour can be detected without injection of large quantities of tracer. Leakages can be positioned with an accuracy of less than 1 metre. 

Very small sessile drops have a shape that depends on the line tension along the circular contact line if large enough it induces a dewetting transition detaching the drop from the surface [84]. 

This effect assumes importance only at very small radii, but it has some applications in the treatment of nucleation theory where the excess surface energy of small clusters is involved (see Section IX-2). An intrinsic difficulty with equations such as 111-20 is that the treatment, if not modelistic and hence partly empirical, assumes a continuous medium, yet the effect does not become important until curvature comparable to molecular dimensions is reached. Fisher and Israelachvili [24] measured the force due to the Laplace pressure for a pendular ring of liquid between crossed mica cylinders and concluded that for several organic liquids the effective surface tension remained unchanged... 

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

It might be noted that only for particles smaller than about 1 /ig or of surface area greater than a few square meters per gram does the surface energy become significant. Only for very small particles does the edge energy become important, at least with the assumption of perfect cubes. 

Many of the adsorbents used have rough surfaces they may consist of clusters of very small particles, for example. It appears that the concept of self-similarity or fractal geometry (see Section VII-4C) may be applicable [210,211]. In the case of quenching of emission by a coadsorbed species, Q, some fraction of Q may be hidden from the emitter if Q is a small molecule that can fit into surface regions not accessible to the emitter [211]. 

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