Order subtraction

Step 5 To determine the bond order, subtract the number of electrons in antibonding orbitals from the number in bonding orbitals and divide the result by 2 (Eq. 3). 

Color order systems n. Systems used to describe an orderly three-dimensional arrangement of colors. Three bases can be used for ordering colors (1) an appearance basis, i.e., a psychological basis in terms of hue, saturation, and lightness - an example is the Munsell System (2) an orderly additive color mixture basis, i.e., a psychophysical basis - examples are the CIE System and the Ostwald System and (3) an orderly subtractive color mixture basis - an example is the Plochere Color System, based on an orderly mixture of inks. 

The second equality follows from die fact that gomg from Bto AB involves subtracting a c -niunber from B and that c -niunber can be taken outside the trace. The resulting trace is the trace of a conmuitator, which vanishes. The invariance of the trace to cyclic pennutations of the order of the operators is used in the third equality. It is straightforward to write... 

On subsciCuLlng (12.49) into uhe dynamical equations we may expand each term in powers of the perturbations and retain only terms of the zeroth and first orders. The terms of order zero can then be eliminated by subtracting the steady state equations, and what remains is a set of linear partial differential equations in the perturbations. Thus equations (12.46) and (12.47) yield the following pair of linearized perturbation equations... 

Alternative procedure Mathcad. Follow the procedure above except that where QMOBAS is indicated, use Mathcad instead. Enter the Huckel molecular orbital matrix, modified by subtracting xl, with some letter name. For example, call the modified matrix A. Type the command eigenvals(A) = with the name of the modified HMO matrix in parentheses. Mathcad prints the eigenvalues. The command eigenvecs(A) yields the eigenvectors, which are useful in ordering the energy spectrum. 

Detained Darnings. After the equity earnings are subtracted from the net after-tax earnings, the balance is called the retained earnings and represents an iacrease ia equity. The retained earnings can be visualized theoretically as the new cash generated beyond that needed to provide for a return to iavestors and an orderly retirement of the investment. 

Consider the first-order equation, Eq. (2-6). Writing this for concentrations Ci and C2 at times ti and t2 and subtracting gives Eq. (2-42). 

Correct the base energy for residual correlation effects (to countera known deficiencies of truncating perturbation theory at fourth order) 1 computing the QCISD(T)/6-311G(d,p) energy. Subtract E from th energy to produce AE ... 

The above method is applicable directly to all oils containing above 50 per cent, of cineol in oils containing lower proportions of cineol the precipitate is not solid enough to permit convenient handling and if the cineol-content drops below 25 per cent, the separation of cineol arsenate is not quantitative. It was found that the addition of an equal volume of eucalyptol to such oils (i.e. mixing 5 c.c. of the oil with 5 c.c. of eucalyptol) successfully overcomes this difficulty it then only becomes necessary to subtract from the volume of cineol, as observed in the neck of the flask, 5 c.c., and to multiply the difference by 10, in order to obtain the percentage of cineol in the oil. 

We recall, from our earlier discussion of the Fredkin construction in section 3.1.4., that an arbitrary CA evolution that is first-order in time - Oi t+l) = second-order in time by subtracting the value of the center site at time f —1 ... 

Margolus [marg84] points out that second-order reversible CA may also be constructed by using operations other than the subtraction modulok we used in our example. The actual operation could in fact be a function of the neighbor s values at time f . In the most general case, the neighborhood at time C can be used to choose a permutation on the set of allowed site values. The permutation is then applied to the site value at time t-V to obtain its next state. 

Consider an ionic crystal in which the anion is a molecular ion. The orientation of this anion in the crystal is completely determined, or determined to a large extent, by the crystal structure and furthermore, its freedom of libration is severely limited by the intense fields of the adjacent ions. When this ion goes into solution, it will have a greater number of possible orientations, and its freedom of libration will be greater. Hence the AS0 for a molecular anion will contain a considerable increment in entropy over and above the cratic term (which is all that we subtract in the case of an atomic ion). This additional increment in entropy is likely to be somewhat different for different species of anion. The best we can do at present is to subtract an amount that is of the right order of magnitude. The question is whether we can, by sub-... 

Taking the coefficient of cubical expansion of soda glass as about 0.000030 and of borosilicate glass about 0.000010 per 1 °C, Part A of Table 3.1 gives the correction to be added when the sign is +, or subtracted when the sign is —, to or from the capacity of a lOOOmL flask correct at 20 °C in order to obtain the capacity at other temperatures. 

In the use of graduated glassware for measurement of the volume of liquids, the expansion of the liquid must also be taken into consideration if temperature corrections are to be made. Part B of Table 3.1 gives the corrections to be added or subtracted in order to obtain the volume occupied at 20 °C by a volume of water which at the tabulated temperature is contained in an accurate lOOOmL flask having a standard temperature of 20 °C. It will be seen that the allowance for the expansion of water is considerably greater than that for the expansion... 

The titration error will increase with increasing dilution of the solution being titrated and is quite appreciable (ca 0.4 per cent) in dilute, say 0.01 M, solutions when the chromate concentration is of the order 0.003-0.005M. This is most simply allowed for by means of an indicator blank determination, e.g. by measuring the volume of standard silver nitrate solution required to give a perceptible coloration when added to distilled water containing the same quantity of indicator as is employed in the titration. This volume is subtracted from the volume of standard solution used. 

It is simplest to consider these factors as they are reflected in the entropy of the solution, because it is easy to subtract from the measured entropy of solution the configurational contribution. For the latter, one may use the ideal entropy of mixing, — In, since the correction arising from usual deviation of a solution (not a superlattice) from randomness is usually less than — 0.1 cal/deg-g atom. (In special cases, where the degree of short-range order is known from x-ray diffuse scattering, one may adequately calculate this correction from quasi-chemical theory.) Consequently, the excess entropy of solution, AS6, is a convenient measure of the sum of the nonconfigurational factors in the solution. 

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