Color excess

Figurp 2. The absorption corrected combination of emitted and observed relative fluxes [eq. (7)] versus frequency. Lines corresponding to two choices of color excess are also shown. Results from our "fiducial model", as well as models in which only the parameter indicated has been varied, are shown.

Structural colors may be caused by the diffraction or interference of light by tiny, regularly-spaced structures within a substance. Many insects and bird feathers display structural color. Structural defects in a material s crystal lattice can also affect its color. Excess or missing ions act as color centers and may affect the way the substance absorbs light. 

In preparation to the definitions in the following we need to define the color excess or A value. It is the absolute magnitude of the difference between the numbers of black and white (or starred and unstarred) vertices. Here it is referred to the coloring (or starring) of vertices. It is known that the A value also is the absolute magnitude of the difference between the numbers of valleys and peaks. 

Another subdivision of benzenoids (apart from catacondensed/pericondensed) distinguishes between Kekulean and non-Kekulean systems. A Kekulean benzenoid system possesses Kekule structures (K > 0). A non-Kekulean benzenoid has no Kekule structure (K = 0). The shorter designations Kekuleans and non-Kekuleans are often used. All catacondensed benzenoids are Kekulean therefore all non-Kekuleans are pericondensed. Any Kekulean benzenoid has a vanishing color excess A = 0. 

A classification of the benzenoids according to the color excess (A) sorts out the obvious non-Kekuleans (A > 0) and the systems with vanishing color excess... 

All snowflakes have vanishing color excess A = 0. Therefore they can be either normal, essentially disconnected or concealed non-Kekulean (but not obvious non-Kekulean). 

Another important classification of benzenoids follows the A values [30]. Here A is the color excess, defined as the absolute magnitude of the difference between... 

It increases rapidly with decreasing wavelength. The extinction is measured in magnitudes. From optical observations of stars, it is easy to determine the relative extinction or color excess E = AB — A v, with AB and A v the total extinction at wavelengths B (= 4400 A) and V (= 5500 A). On the assumption that the extinction curve is similar in all directions in space, the total extinction in the visual is (Fig. 6b)... 

Benzenoid (chemical) isomers are, in a strict sense, the benzenoid systems compatible with a formula C H, = (n s). The cardinality of C HS, viz. C HS = n, s is the number of isomers pertaining to the particular formula. The generation of benzenoid isomers (aufbau) is treated and some fundamental principles are formulated in this connection. Several propositions are proved for special classes of benzenoids defined in relation to the place of their formulas in the Dias periodic table (for benzenoid hydrocarbons). Constant-isomer series for benzenoids are treated in particular. They are represented by certain C HS formulas for which n s = In Sjl = n2 52 =. .., where (nk sk) pertains to the k times circumscribed C HS isomers. General formulations for the constant-isomer series are reported in two schemes referred to as the Harary-Harborth picture and the Balaban picture. It is demonstrated how the cardinality n s for a constant-isomer series can be split into two parts, and explicit mathematical formulas are given for one of these parts. Computational results are reported for many benzenoid isomers, especially for the constant-isomer series, both collected from literature and original supplements. Most of the new results account for the classifications according to the symmetry groups of the benzenoids and their A values (color excess). 

The Kekulean and non-Kekulean systems are those which possess Kekule structures K > 0) oi do not possess Kekule structures K = 0), respectively. In an essentially disconnected system there are fixed bonds, viz. edges which correspond to double and/or single bonds in the same positions of all Kekule structures. Kekulean systems without fixed bonds are called normal Obvious- and concealed non—Kekulean systems have A > 0 and A = 0, respectively, where A is the color excess, viz. the absolute magnitude of the difference between the numbers of peaks and valleys (1-3.2.4). Finally, the catacondensed (unbranched or branched) and the pericondensed systems have n- = 0 and n-> 0, respectively, where n- designates the number of internal vertices (I-3.3.1). 

Table 2 shows the numbers of single coronoid isomers according to the neo classification (n normal e essentially disconnected o non—Kekulean). Furthermore, the non—Kekulean systems, o, are classified according to their color excess (A). The table is arranged in a way which was found suitable for benzenoid isomers (Brunvoll, Cyvin BN and Cyvin 1992b). All the numbers in this table, although they have not been given before explicitly, can be deduced firom the data of Volume I, Tables 1-9.1 to 1-9.8. 

Table 7.15. Numbers of single coronoids with different color excess (A), classified according to symmetry complete list for h = 15.

Among the proposed methods for quantification of LA, high-performance liquid chromatography (HPLC) coupled with UV detection has been the technique most applied to analysis of fermented dairy and beverage products [22-24]. With this strategy, it is possible to quantify LA in the presence of other organic acids with a similar structure however, there are some limitations and drawbacks, including problems associated with matrix color, excessive sample preparation and analysis time, separation efficiency, complexity, and cost. Some improvements in resolution and simplicity, reduction of consumption of chemicals, and reduction of sample preparation have been reported... 

It has been recognized for some time that infrared colors could be used to directly measure the extinction and its distribution through a molecular doud (e.g., Hyland 1980, Jones et d. 1981, Frerking, Langer and Wilson 1982). The line-of-sight extinction to an individual star can be directly determined from knowledge of its color excess and the extinction law. The color excess, E(H-K), cm be directly derived from observations provided the intrinsic color of the star is known ... 

The mean color excess is proportional to the extinction and colrunn density of dust at each point where it is determined. The color excess can be directly converted to an extinction at some specified wavelength via the reddening law. For example, the mean color excess can be scaled to a mean visual extinction using the normal reddening law (Rieke and Lebosfky 1985) ... 

Fig. 1. Schematic cartoon illustrating ihe binning method for determining Hhe mean color excess through a molecular cloud on angular scales on the order of US minutes of arc.

Fig. 2. Map of the equivalent mean visual extinction in the Northern Streamer cloud derived from H-K color excess measurements of more than 1200 stars observed in this field. The lowest contour corresponds to a visual extinction of 2 magnitudes and subsequent contours increase in steps of 2 magnitudes.

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