Value approximate

The generalized use of computers makes seemingly complex calculations quite easy to perform however, curves and tables are still invaluable when one needs to obtain approximate values or to take into account the sensitivity of a property to operating conditions or to a mixture s characteristics. 

In the first approximation, valuing DSM, it needs to take into account several feetors ... 

Benjamin Franklin s experiment is mentioned in the opening paragraphs of this chapter. Estimate, from his results, an approximate value for Avogadro s number make your calculation clear. The answer is a little off explain whether more accurate measurements on Franklin s part would have helped. 

Table VI-1 shows the approximate values for the Keesom Debye,...

For the steady-state case, Z should also give the forward rate of formation or flux of critical nuclei, except that the positive free energy of their formation amounts to a free energy of activation. If one correspondingly modifies the rate Z by the term an approximate value for I results ... 

For large Cl calculations, the frill matrix is not fonned and stored in the computer s memory or on disk rather, direct CF methods [ ] identify and compute non-zero and inunediately add up contributions to the sum jCj. Iterative methods [, in which approximate values for the Cj coefficients are refined tlirough sequential application of to the preceding estimate of the vector, are employed to solve... 

Widely used algorithms for calculating the molecular and accessible surfaces were developed by Connolly [Connolly 1983a, b], and others [e.g. Richmond 1984] have described formulae for the calculation of exact or approximate values of the surface area. There are many ways to represent surfaces, some of which are illustrated in Figure 1.7 (colour plate section). As shown, it may also be possible to endow a surface with a translucent quality, which enables the molecule inside the surface to be displayed. Clipping can also be used... 

Let be a well-defined finite element, i.e. its shape, size and the number and locations of its nodes are known. We seek to define the variations of a real valued continuous function, such as/, over this element in terms of appropriate geometrical functions. If it can be assumed that the values of /on the nodes of Oj, are known, then in any other point within this element we can find an approximate value for/using an interpolation method. For example, consider a one-dimensional two-node (linear) element of length I with its nodes located at points A(xa = 0) and B(a b = /) as is shown in Figure 2.2. 

Data taken from Ref 206, derived from a comparison of AGto (water —> solvent) for Ag with the mean of AGt,ro(water —> solvent) for Na and K. By definition. ° Only approximate values are reported. 

Approximate values relative to tetramethylsilane other groups within the molecule can cause a proton signal to appear outside of the range cited... 

During a molecular dynamics simulation, HyperChem stores the current positions, Tj (t), and the mid-step velocities, Vj (t - 1/2 At). Since the algorithm provides mid-step velocities, but not velocities, Vj (t), for the positions at time t, HyperChem calculates approximate values of Ej-qt (O- This results in slightly larger fluctuations in Ej-ot (t) than an algorithm that calculates exact values of... 

For thermometers containing organic liquids, it is sufficient to use the approximate value, K = 0.001. In such thermometers the value of K is practically independent of the kind of glass. 

Each of the f2 samples had a nominal weight of O.f g. Determine the approximate value for fQ, and the mass of sample needed to achieve a percent relative standard deviation of 2%. 

Other important areas of mass spectrometric investigation of isotope ratios need accurate, not approximate values. For example, for some investigations in archaeology, pharmaceuticals, and chemistry, very accurate precise ratios of isotope abundances are needed. 

Question. From the following separations of vibrational levels in the ground electronic state of CO obtain values of cOg and cOgXg and also an approximate value for the dissociation energy Dy. 

A vacuum system can be constmcted that includes a solar panel, ie, a leak-tight, instmmented vessel having a hole through which a gas vacuum pump operates. An approximate steady-state base pressure is estabUshed without test parts. It is assumed that the vessel with the test parts can be pumped down to the base pressure. The chamber is said to have an altitude potential corresponding to the height from the surface of the earth where the gas concentration is estimated to have the same approximate value as the base pressure of the clean, dry, and empty vacuum vessel. 

Downfield shifts positive. Chemical shifts from NH3 or MeN02 calculated using approximate values McN02 380 p.p.m., NOJ 376p.p.m., NH3 Op.p.m. (b-79mui70i). 

Numerical techniques therefore do not yield exact results in the sense of the mathematician. Since most numerical calculations are inexact, the concept of error is an important feature. The error associated with an approximate value is defined as... 

Table 1.9 Approximate values of efficiency and power factor at three-quarter and half loads corresponding to values at full load...

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