Loss of accuracy

The continuous line in Figure 16 shows results from fitting a single tie line in addition to the binary data. Only slight improvement is obtained in prediction of the two-phase region more important, however, prediction of solute distribution is improved. Incorporation of the single ternary tie line into the method of data reduction produces only a small loss of accuracy in the representation of VLE for the two binary systems. 

Figure 4-16. Representation of ternary liquid-liquid equilibria using the UNIQUAC equation is improved by incorporating ternary tie-line data into binary-parameter estimation. Representation of binary VLB shows small loss of accuracy. ---- Binary...

Figure 17 shows results for the acetonitrile-n-heptane-benzene system. Here, however, the two-phase region is somewhat smaller ternary equilibrium calculations using binary data alone considerably overestimate the two-phase region. Upon including a single ternary tie line, satisfactory ternary representation is obtained. Unfortunately, there is some loss of accuracy in the representation of the binary VLB (particularly for the acetonitrile-benzene system where the shift of the aceotrope is evident) but the loss is not severe. 

Heat exchanger cost laws often can be adjusted with little loss of accuracy such that the coefficient c is constant for different specifications, i.e.. Cl = Ca = c. In this case, Eq. (7.23) simplifies to ... 

Since and depend only on die valence charge densities, they can be detennined once the valence pseudo- wavefiinctions are known. Because the pseudo-wavefiinctions are nodeless, the resulting pseudopotential is well defined despite the last temi in equation Al.3.78. Once the pseudopotential has been constructed from the atom, it can be transferred to the condensed matter system of interest. For example, the ionic pseudopotential defined by equation Al.3.78 from an atomistic calculation can be transferred to condensed matter phases without any significant loss of accuracy. 

The conductor-like screening model (COSMO) is a continuum method designed to be fast and robust. This method uses a simpler, more approximate equation for the electrostatic interaction between the solvent and solute. Line the SMx methods, it is based on a solvent accessible surface. Because of this, COSMO calculations require less CPU time than PCM calculations and are less likely to fail to converge. COSMO can be used with a variety of semiempirical, ah initio, and DFT methods. There is also some loss of accuracy as a result of this approximation. 

The precision of a result is its reproducibility the accuracy is its nearness to the truth. A systematic error causes a loss of accuracy, and it may or may not impair the precision depending upon whether the error is constant or variable. Random errors cause a lowering of reproducibility, but by making sufficient observations it is possible to overcome the scatter within limits so that the accuracy may not necessarily be affected. Statistical treatment can properly be applied only to random errors. 

Positive-displacement meters are normally rated for a limited temperature range. Meters can be constmcted for high or low temperature use by adjusting the design clearance to allow for differences in the coefficient of thermal expansion of the parts. Owing to small operating clearances, filters are commonly installed before these meters to minimize seal wear and resulting loss of accuracy. 

Accuracies achieved by ECG are usually about 0.125 mm, although some claims have been made for accuracies an order of magnitude better. A drawback of ECG is the loss of accuracy when inside corners are ground. Because of the electric field effects, radii better than 0.25—0.375 mm can seldom be achieved. 

A substance is in the ideal gas state when the volume of its molecules is a zero fraction of the total volume taken up by the substance and when the individual molecules are far enough apart from each other so that there is no interaction between them. Although this only occurs at infinite volume and zero pressure, in practice, ideal gas properties can be used for gases up to a pressure of two atmospheres with little loss of accuracy. Thermal properties of ideal gas mixtures may be obtained by mole-fraction averaging the pure component values. 

The value of r can be estimated as that of saturated liquid at the same temperature or related to supercritical properties at temperatures above critical. Critoph [2] found that for the practical purposes of modelling ammonia - carbon adsorption cycles, using experimentally determined porosity data, that the complexity of estimating both r and p at sub and supercritical levels was not justified. The measured porosity data could be fitted to a much simpler version of the equation with no loss of accuracy, as follows ... 

Ultrasoft pseudopotentials have now been constructed for all elements for all elements from H to Bi [10]. It has been shown that without any loss of accuracy even for first-row and transition-elements small PW basis-sets comparable in size to those necessai y for soft normconserving pseudopotentials for A1 or Si can be used. For any further details, see [9,. 37]. 

Though in this paper we have used the relativistic KKR wave functions ets betsis functions, the present approach may be easUy realized within any existing method for calculating the electron states. This will allow the electronic properties of materials with complex magnetic structure to be readily calculated without loss of accuracy. The present technique, being most eflicient for the SDW-type systems, can be also used for helical magnetic structures. In the latter case, however, the spin-polarizing part of potential (18) should be appropriately re-defined. 

If the instrument is to be direct reading, the second (or cold ) junction must be kept at a constant reference temperature. If high temperatures are to be measured then the terminals of the detector can be used as the cold junction without an unacceptable loss of accuracy. 

Hie quasi steady state approximation can be conveniently applied to equations 19 to 21, without any significant loss of accuracy, due to tlie high reactivity of tlie reacting species in aqueous solution. Hms, the system of ordinary differential equations is readily reduced to a system of algebraic non linear equations. 

The second major hurdle to be minimized is the evaluation of the PES. Obviously from Eq. (52) there are two tasks, calculating the weights and the Taylor series. The total number of data points in the PES may be very large because of symmetry. For example, a PES for CH5 with 2,500 symmetry-distinct data points has 2,500 x 5 = 300,000 data points in total. In some circumstances, the size of the symmetry group could be reduced without loss of accuracy by employing only the subset of feasible permutations, the molecular symmetry group,68 rather than the CNP group. 

Bridge the gap between users and developers, without loss of accuracy, when specifying a software product with non-software users. 

Efficient computer programs rarely use this method. The numerical algorithms used to search for eigenvalues are countless and difficult to implement without a dramatic loss of accuracy. Use of the best canned routines saves time and produces better results. 

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