Doubting

An apparent systematic error may be due to an erroneous value of one or both of the pure-component vapor pressures as discussed by several authors (Van Ness et al., 1973 Fabries and Renon, 1975 Abbott and Van Ness, 1977). In some cases, highly inaccurate estimates of binary parameters may occur. Fabries and Renon recommend that when no pure-component vapor-pressure data are given, or if the given values appear to be of doubtful validity, then the unknown vapor pressure should be included as one of the adjustable parameters. If, after making these corrections, the residuals again display a nonrandom pattern, then it is likely that there is systematic error present in the measurements. ... 

The presence of thiophene and its derivatives in crude oils was detected in 1899, but until 1953, the date at which the methyl-thiophenes were identified in kerosene from Agha Jari, Iran crude oil, it was believed that they came from the degradation of sulfides during refining operations. Finally, their presence was no longer doubted after the identification of benzothiophenes and their derivatives (Table 8.9), and lately of naphthenobenzothiophenes in heavy cuts. 

The increase in the oil-change interval has already been a strong incentive for improving lubricant formulations. The increase in engine operating temperatures and the development of catalytic converters are without doubt two orientations that will have consequences on lubricant additives. 

Sampling saturated reservoirs with this technique requires special care to attempt to obtain a representative sample, and in any case when the flowing bottom hole pressure is lower than the bubble point, the validity of the sample remains doubtful. Multiple subsurface samples are usually taken by running sample bombs in tandem or performing repeat runs. The samples are checked for consistency by measuring their bubble point pressure at surface temperature. Samples whose bubble point lie within 2% of each other may be sent to the laboratory for PVT analysis. 

Although the presented results prove the efficiency of radioscopy, this system have certain characteristics which justify to develop and employ further process integrated testing systems. One of this characteristics is that the integration of radioscopy in industrial applications is doubtful because of reasons of radiation protection. This means, that the results from radioscopy should rather be used to fit other systems (acoustic emission analysis or temperature analysis) for industrial applications. 

It was pointed out, that the periodical inspection of the steam drums has been become an absolute must especially under the circumstance, that the economical pressure results in smaller wall thickness, higher steam pressure and higher rotation speed. The conventional periodical inspection (hydrotest and visual inside inspection) is on one hand time consuming and therefore expensive and on the other hand the results of the hydrotest are doubtful and can result in a seriously damage of the roundness and balance of the steam drum. 

Although the present Good Workmanship approach actually gives conventional NDT methods the credit they deserve (their capabilities are well-used), there should nevertheless be a certainty beyond reasonable doubt that an accepted weld is fit for service. Many years of industrial experience have demonstrated that this certainty statistically exists. We are not doing things totally wrong. 

The recent evidence of workmanship-related defects to major structures in extreme environments leaves a nagging doubt about weather the real issues behind the problems have really been understood, acknowledged and dealt with at all levels. 

In the case of solids, there is no doubt that a lateral tension (which may be anisotropic) can exist between molecules on the surface and can be related to actual stretching or compression of the surface region. This is possible because of the immobility of solid surfaces. Similarly, with thin soap films, whose thickness can be as little as 100 A, stretching or extension of the film may involve a corresponding variation in intermolecular distances and an actual tension between molecules. 

It is because of these complications, both theoretical and practical, that it is doubtful that calculated surface energies for solids will ever serve as more than a guide as to what to expect experimentally. Corollaries are that different preparations of the same substance may give different values and that widely different experimental methods may yield different apparent values for a given preparation. In this last connection, see Section VII-5 especially. 

The coefficient of friction between two unlubricated solids is generally in the range of 0.5-1.0, and it has therefore been a matter of considerable interest that very low values, around 0.03, pertain to objects sliding on ice or snow. The first explanation, proposed by Reynolds in 1901, was that the local pressure caused melting, so that a thin film of water was present. Qualitatively, this explanation is supported by the observation that the coefficient of friction rises rapidly as the remperarure falls, especially below about -10°C, if the sliding speed is small. Moreover, there is little doubt that formation of a water film is actually involved [3,4]. 

There has been considerable elaboration of the simple Girifalco and Good relationship, Eq. XII-22. As noted in Sections IV-2A and X-6B, the surface ftee energies that appear under the square root sign may be supposed to be expressible as a sum of dispersion, polar, and so on, components. This type of approach has been developed by Dann [70] and Kaelble [71] as well as by Schonhom and co-workers (see Ref. 72). Good (see Ref. 73) has preferred to introduce polar interactions into a detailed analysis of the meaning of in Eq. IV-7. While there is no doubt that polar interactions are important, these are orientation dependent and hence structure sensitive. 

These authors doubt that such interactions can be estimated other than empirically without fairly accurate knowledge of the structure in the interfacial region. Sophisticated scattering, surface force, and force microscopy measurements are contributing to this knowledge however, a complete understanding is still a long way off. Even submonolayer amounts of adsorbed species can affect adhesion as found in metals and oxides [74]. 

If two pure, immiscible liquids, such as benzene and water, are vigorously shaken together, they will form a dispersion, but it is doubtful that one phase or the other will be uniquely continuous or dispersed. On stopping the agitation, phase separation occurs so quickly that it is questionable whether the term emulsion really should be applied to the system. A surfactant component is generally needed to obtain a stable or reasonably stable emulsion. Thus, if a little soap is added to the benzene-water system, the result on shaking is a true emulsion that separates out only very slowly. Theories of... 

Equation XVII-70 bears a strong resemblance to the Langmuir equation (see Ref. 4)—to the point that it is doubtful whether the two could always be distinguished experimentally. An equivalent form obtained by Volmer [53] worked well for data on the adsorption of various organic vapors on mercury [54] (see Problem XVII-40). 

There is little doubt that, at least with type II isotherms, we can tell the approximate point at which multilayer adsorption sets in. The concept of a two-dimensional phase seems relatively sterile as applied to multilayer adsorption, except insofar as such isotherm equations may be used as empirically convenient, since the thickness of the adsorbed film is not easily allowed to become variable. 

Long-range forces are most conveniently expressed as a power series in Mr, the reciprocal of the intemiolecular distance. This series is called the multipole expansion. It is so connnon to use the multipole expansion that the electrostatic, mduction and dispersion energies are referred to as non-expanded if the expansion is not used. In early work it was noted that the multipole expansion did not converge in a conventional way and doubt was cast upon its use in the description of long-range electrostatic, induction and dispersion interactions. However, it is now established [8, 9, 10, H, 12 and 13] that the series is asymptotic in Poincare s sense. The interaction energy can be written as... 

A fiirther diflfieulty arises beeause the exaet wavefiinetions of the isolated moleeules are not known, exeept for one-eleetron systems. A eoimnon starting point is the Hartree-Foek wavefiinetions of the individual moleeules. It is then neeessary to inelude the eflfeets of intramoleeular eleetron eorrelation by eonsidering them as additional perturbations. Jeziorski and eoworkers [M] have developed and eomputationally implemented a triple perturbation theory of the syimnetry-adapted type. They have applied their method, dubbed SAPT, to many interaetions with more sueeess than might have been expeeted given the fiindamental doubts raised about the method. SAPT is eurrently both usefiil and praetieal. A reeent applieation [ ] to the CO2 dimer is illustrative of what ean be aehieved widi SAPT, and a rieh soiiree of referenees to previous SAPT work. 

No one doubts the correctness of either of these statements of the third law and they are universally accepted as equivalent. Flowever, there seems to have been no completely satisfactory proof of their equivalence some additional, but very plausible, assumption appears necessary in making the coimection. 

There is now consensus on some questions about which there had been lingering doubts. 

There is no reason to doubt that the inequalities of section A2.5.4.5(e) are other than equalities. The equalities are assumed in most of the theoretical calculations of exponents, but they are confmned (within experimental error) by the experiments. 

The vibrationally excited states of H2-OH have enough energy to decay either to H2 and OH or to cross the barrier to reaction. Time-dependent experiments have been carried out to monitor the non-reactive decay (to H2 + OH), which occurs on a timescale of microseconds for H2-OH but nanoseconds for D2-OH [52, 58]. Analogous experiments have also been carried out for complexes in which the H2 vibration is excited [59]. The reactive decay products have not yet been detected, but it is probably only a matter of time. Even if it proves impossible for H2-OH, there are plenty of other pre-reactive complexes that can be produced. There is little doubt that the spectroscopy of such species will be a rich source of infonnation on reactive potential energy surfaces in the fairly near future. 

The simplest condensed phase VER system is a dilute solution of a diatomic in an atomic (e.g. Ar or Xe) liquid or crystal. Other simple systems include neat diatomic liquids or crystals, or a diatomic molecule bound to a surface. A major step up in complexity occurs with poly atomics, with several vibrations on the same molecule. This feature guarantees enonnous qualitative differences between diatomic and polyatomic VER, and casts doubt on the likelihood of understanding poly atomics by studying diatomics alone. 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

Anhydrous titanium dioxide is only soluble with difficulty in hot concentrated sulphuric acid dilution allows the crystallisation of a sulphate of formula T10S04.H20, but it is doubtful if the titanyl cation TiO actually exists, either in solution or the solid. Certainly [TifHjOIn] does not exist, and solutions of titanyl salts may best be considered to contain ions [Ti(0H)2(H204)] . Titanium... 

There is no doubt that the coefficient of the third term on the right hand side of this equation is much larger than the coefficient of the second term at the bulk diffusion limit, and this justifies our original form (5,29). However, on constructing from and using equation (5,32) and its... 

Other measurements by Adzumi [36] are often quoted as further support for this statement. However, it is doubtful whether Adzumi s results extend to low enough pressures to be sure of this. 

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