Matches function

Colorimeters. Also known as tristimulus colorimeters, these are instniments that do not measure spectral data but typically use four broad-band filters to approximate the jy, and the two peaks of the x color-matching functions of the standard observer curves of Figure 7. They may have lower accuracy and be less expensive, but they can serve adequately for most industrial color control functions. Examples of colorimeters are the BYK-Gardner Co. XL-835 the Hunter Lab D25 series the Minolta CA, CL, CS, CT, and CR series (the last of these is portable with an interface) and the portable X-Rite 918. 

The C1E color coordinates are obtained by a similar procedure, repeating the convolution for each of the tabulated color matching functions that describe the response of the ideal observer s blue, green, and red cones (b, rA). 

In Eqs. (7)—(10), 5(A) is the spectral power distribution of the illuminant, and R A) is the spectral reflectance factor of the object. Jc(A), y(A), and 5(A) are the color-matching functions of the observer. In the usual practice, k is defined so that the tristimulus value, Y, for a perfect reflecting diffusor (the reference for R A)) equals 100. Using the functions proposed by the CIE in 1931, y(A) was made identical to the spectral photopic luminous efficiency function, and consequently its tristimulus value, Y, is a measure of the brightness of objects. The X and Z values describe aspects of color that permit identification with various spectral regions. 

The A(A), y(A), and z(A) terms were derived by the CIE from data obtained in visual experiments where observers matched colors obtained by the mixing of the blue, green, and red primary colors. The average result for human observers were defined as the CIE 1931 2° standard observer, and the wavelength dependencies of these color-matching functions are illustrated in Fig. 6. 

Fig. 6 Color-matching functions Jc(A), and z(A) of the CIE 1931 2° standard observer. (Data adapted from Ref. 40.)...

Baker, J. P., and Titus, M. A. (1998). Myosins Matching functions with motors. Cun. Opin. Cell Biol. 10, 80-86. 

Tristimulus values X, Y, and Z are computed for a primary light source with power spectrum L(X) from the color-matching functions x, y, and z as follows ... 

As discussed by Andersen [9, 10] for muffin-tin orbitals, the locally regular components y defined in each muffin-tin sphere are cancelled exactly if expansion coefficients satisfy the MST equations (the tail-cancellation condition) [9, 384], The standard MST equations for space-filling cells can be derived by shrinking the interstitial volume to a honeycomb lattice surface that forms a common boundary for all cells. The wave function and its normal gradient evaluated on this honeycomb interface define a global matching function %(cr). 

The coefficients ft = Sy are the expansion coefficients of the global matching function (cr) = Jft, l nl (G ) l - Defining t = —SiSUjy Sft which reduces to t = —SC l for square matrices [281], EIIV takes the standard MST form I — tg, without implying inversion of a rectangular matrix. Using these closed forms, the coefficients ft and y are related by... 

For an exact solution, the external function ijrv would be identical to the global matching function on each interface. An alternative algorithm can be based on fitting a linear combination of basis functions in each cell to %, which is uniquely determined. The VCM equations for an orbital basis at fixed energy reduce to [282]... 

At first sight, adsorption and reaction are well-matched functionalities for integrated chemical processes. Their compatibility extends over a wide temperature range, and their respective kinetics are usually rapid enough so as not to constrain either process, whereas the permeation rate in membrane reactors commonly lags behind that of the catalytic reaction [9]. The phase slippage observed in extractive processes [10], for example, is absent and the choice of the adsorbent offers a powerful degree of freedom in the selective manipulation of concentration profiles that lies at the heart of all multifunctional reactor operation [11]. Furthermore, in contrast to reactive distillation, the effective independence of concentration and temperature profiles... 

The "tristimulus" variables X, Y, Z are defined by color-matching functions x(l), y(l), and z(l) (Fig. 10.4) that roughly correspond to the color sensitivity of the three types of human retina rods. For any "primary" color, with intensity 1(1), the tristimulus values X, Y, and Z are defined by... 

Dendrimers have various useful properties. The number of branches increases with the step munber (the dendrimer generation). The branches are crowded at the outer surface while the inner part of the dendrimer has more empty space. Therefore, the dendrimer can behave like a capsule. Size-matched functional guest molecules become entrapped in this nanometer-scale capsule. 

The INDEX and MATCH functions are, in a sense, mirror images. The function INDEX(array, row num, column num, area num) returns a single value from within a one- or two-dimensional range of cells, based on a specified position in the array. Non-adjacent selections are permitted they are handled by area num. See Appendix B for details. 

You can use wildcard characters with the MATCH function. If your lookup values are text and match type is set to 0, lookup value can contain the asterisk ( ) and question mark ( ) wildcard characters. A question mark matches any single character, an asterisk matches any sequence of characters. 

This formula works fine as long as the table does not contain duplicate values of the sortkey. However, in this example there are many sets of duplicate melting point values, the first occurring in rows 5, 6 and 7. The MATCH function then returns the first occurrence of a match and as a result, all rows having duplicate sortkeys will display the same information in the associated cells, as illustrated in Figure 4-13. 

When you use VLOOKUP, you must always "look up" in the first column of the defined database and retrieve associated information from a column to the right in the same row you cannot VLOOKUP to the left, for example. In the table shown in Figure 9-2, you cannot use VLOOKUP to return the element name corresponding to symbol. If you want to perform a lookup to the left of, or above, the lookup value, you can either construct your own lookup-type function using the MATCH function (see later in this chapter) or use the LOOKUP function. 

You can use the MATCH and INDEX worksheet functions in a formula to perform linear interpolation in a table. The syntax of the MATCH function is MATCH lookup value,lookup array,match type). If match type = 1, MATCH returns the position of the largest array value that is less than or equal to... 

If the X values in the data table are in descending order, the match type argument in the MATCH function must be changed to -1. 

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