Roughness order

Figure 1. An unrooted phylogenetic tree of the myosins based on the amino acid sequence comparison of their head domains demonstrating the division of the myosin superfamily into nine classes. The lengths of the branches are proportional to the percent of amino acid sequence divergence and a calibration bar for 5% sequence divergence is shovk n. The different classes of myosins have been numbered using Roman numerals in rough order of their discovery and hypothetical models of the different myosin structures are shown. Question marks indicate either hypothetical or unknown structural features, and only a fraction of the known myosins are shown. (Taken, in modified form, from Cheney et al., 1993).

The absolute determination of coverage is much more difficult. The formalism is well known, i.e., it is possible to go from the intensity of a spectral ion to the concentration material on the surface, but this can only be worked out if the transition dipole moment is known. A very rough order of magnitude version of this can, however, usually be obtained by analogy (rather than by quantum mechanical calculation) so that somewhat better than an order of magnitude calculation of the coverage of the surface radicals can be given. 

All metals in the neighborhood of rhodium on the periodic table are known to be active in hydroformylation. Rhodium is by far the most active metal being used in concentrations of 10-100 mg/kg, usually at temperatures below 140 °C. Typical concentrations of cobalt-based catalysts are in the range of 1 -10 g/kg at temperatures up to 190 °C to get sufficient space-time yield. Apart from some specialized applications, other metals are only of scientific interest because of their low activity. A proper comparison of metal activity is difficult because of the different requirements on the reaction conditions. A generally accepted rough order of activity is given in Table 1. 

The initial cost estimate in early 1999 for the JACADS closure program was 70 million to 80 million. This estimate was labeled a rough, order-of-magnitude estimate that, because it did not include certain noncontractor charges, was rather optimistic. Another estimate given to the committee in September 1999 was 150 million (Bushman, 1999). The most current estimate is between 200 million and 400 million. Final cost estimates for each permit modification can be made only after EPA approval. 

Even for vanishing cycle times, the ParTAD method introduces an additional approximation into the dynamics compared to regular TAD because the subpatch has a fixed size, concerted processes larger than this size, if they exist, will be suppressed. In exchange, the method gives a very favorable computational scaling with system size, which appears to be roughly order log(AJ) as processors are added in proportion to N [34],... 

The synthesis of aluminum and gallium hydrazides succeeds by several methods, which were used as a rough ordering scheme in the first part of this article ... 

Funding can be raised from a variety of sources (in rough order of increasing cost and increasing loss of control) ... 

For this paper, process modification for the purpose of source reduction in a plating operation will be defined as changes in equipment which lead to reduced generation of wastes. Purposely excluded are separation and concentration technologies covered elsewhere in this conference. The intent of this section is to list options, in rough order of simplicity of implementation, and provide information about each... 

The scaling factors for the nondimensionalization have been chosen so that the dependent and independent variables are roughly order one. There are two parameters that remain in the equations the Reynolds number, Re, and the wedge angle, a. Depending on the magnitudes of the parameters, there can be further simplifications of the system. 

Qualitative comparisons can be made using rough order of magnitude contributions made to n(kT/K)Qf /QxQyz from translation, rotation and vibration, and such calculations again demonstrate the importance of the internal motions of the molecules in determining predicted A factors. 

In the case of regio- or stereoselective reactions of 9 —> 7 as well as in biphotochromic systems (24 -> 23), the kinetics become more complicated (see Refs. 30 and 33). The 11/2 values can be used as a rough order for a structure-fade rate relationship. Again, to analyze the data in a simple way, DHI 7 is divided into... 

Eor the runs on NaCl solutions, plot y versus the bulk concentration c expressed in mol cm As seen by Eq. (13) the ratio Tic can be determined from the slope of the straight line obtained. Calculate the effective empty-layer thickness a , in A for NaCl. Since the laws of ideal solutions do not hold at the NaCl concentrations studied, the results obtained with NaCl have only qualitative significance and the a , obtained represents only a rough order of magnitude value. 

From Table 5 a rough order of reactivity for the cycloalkenecarbenes can be deduced ... 

For the purposes of this review we are interested more in using the kinetic data in order to obtain a rough order of the labilizing power of ligands, and less in the details of the mechanism. But, in the absence of any real evidence to the contrary, it will be assumed in the discussion below that all the complexes react by an <5 1 mechanism and can be compared directly. For a fuller discussion of the kinetic data and possible mechanisms see the reviews by Basolo and Pearson (29, 31), Tobe (174, 175), and Chan and Miller (46). 

A second order of ligands has been built up in order to compare the cis effect of ligands such as corrin (Section IV, B, 2). The following very rough order of labilizing effect of four cis ligands was obtained ... 

By reference to the electronegativity scale, arrange the following binary compounds in rough order of their stability, placing those that you think would be especially stable at the top of the list, and the most unstable at the bottom of the list ... 

We shall now examine briefly the calculation of the vapour pressure on the basis of statistical models of the solid and liquid states. Debye s model of the solid state, which we have discussed briefly in chapter XII, 5, allows us to evaluate the vapour pressure of a solid, but the agreement with experiment is very poor. We obtain only a rough order of magnitude. ... 

Over the years numerous scales of percent ionic character have been proposed for both simple molecules and solids. They may depend on some physical property, such as dipole moments or refractive indices, or be extracted from some theoretical analysis. The various scales usually agree on a rough ordering but the actual numbers vary widely. It seems to be impossible to define exactly what is meant by percent ionic character . Therefore, the numbers in the various scales have meaning only in terms of the model from which they were derived. Each scale is useful for some experimental or theoretical property, but transfer to other properties is hazardous. 

Only a very rough order of magnitude estimate is obtained for tan 8 from equations 9.13 and 9.14, useful for qualitative comparisons but not as input into more quantitative calculations. 

An advantage of equations 15.14-15.17 is that they can be used to obtain a rough (order of magnitude) estimate of Pq2 for all polymers built from the elements (C, N, O, H, F, Si, S, Cl and Br) of interest in this work, without being limited by the lack of group contributions. 

The unperturbed y9(t)(N) is Z Vt exp -r pEN) which is already a small number. Hence it is quite possible for the perturbation in y0(N) to be of the same order of magnitude as the unperturbed W0 (N) itself. All other y/0,( ) s would be necessary in order to ascertain whether or not this is the case. The rough order of magnitude of l can be obtained however from... 

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