In case of perfect similarity between two molecules A and B, one would find <7AB = 0, and the more the two density functions differ, the larger will be the value [Pg.232]

It can be seen that neither of these leads to a perfectly similar scaled system. [Pg.196]

According to this index, a perfect similarity is indicated by CAB=1, and lower values indicate decreasing similarity. [Pg.232]

These equations lead to fomis for the thermal rate constants that are perfectly similar to transition state theory, although the computations of the partition functions are different in detail. As described in figrne A3.4.7 various levels of the theory can be derived by successive approximations in this general state-selected fomr of the transition state theory in the framework of the statistical adiabatic chaimel model. We refer to the literature cited in the diagram for details. [Pg.783]

These C-class indices vary from 0 to 1, 1 denoting perfect similarity, which does not infer equality between the molecules involved. Maggiora, Petke [Pg.165]

When scaling a process, similarity between the various sizes and processes is sought. As a rule, a perfectly scalable prototype is one that is perfectly similar to its scaled system. A perfectly similar set of systems is one where all the dimensionless numbers or n-groups [Pg.192]

A different class of indices is the D indices, where similarity is expressed as a distance. With these indices, perfect similarity is characterized by a zero distance. The best known is the Euclidean distance, introduced in Equation 16.5. Again, different connections have been found to exist between C- and D-class indices [59-62]. [Pg.237]

This body as we perceive, offers but little interest in its properties but it is the more remarkable in its relation to hydrobenzdyl, from the fact, as analysk proves, that it has a perfectly similar composition, and is therefore an isomeric modification of the same, as is apparently shewn by its unintelligible origin from the oil, through the equally inexplicable action of potassa when air is excluded. [Pg.53]

A different class of indices are those that behave like a distance. With these indices, a perfect similarity corresponds to a value 0, and no strict upper limit exists. The best-known of these D-class indices is the Euclidean distance introduced previously in Eqs. [7]-[13]. This Euclidean distance index has been extended to give an index for any operator used by chemists in evaluating the MQSMs by using [Pg.167]

The relative potency, p, functions here much like a currency exchange rate functions. It converts concentration of one metal into the equivalent concentration of the other. If one were interested in detecting trends away from perfect similar joint action and toward independent action, the absolute difference between estimated slopes from Equations (1.6) and (1.7), i.e., SlopeM - Slope 2 could be used as a metric of deviation from similar mode of action. [Pg.16]

This generalized cosine index is often called the Carbo index. Naturally the Carbo index is limited to the range (0,1), where Cab = 1 means perfect similarity. Still more (dis)similarity measures have been introduced and will be discussed further in this chapter. The range of the Carbo index naturally agrees with the Schwartz integral inequality " [Pg.136]

If we wish to obtain standards of length, time and mass which shall be absolutely permanent, we must seek them not in the dimensions, or the motion, or the mass of our planet, but in the wave-length, the period of vibration, and the absolute mass of these imperishable and unalterable and perfectly similar molecules [Pg.446]

Still another variation of this interaction comes into play, when during the approach, a new type of i nthon appears, and the q nthons match afterwards. For sample in the Hodges superhelical structure (Fig. 13.16), only after formation of the a-helices does it turn out that the leucine and valine side chains of one helix match perfectly similar synthons of the second helix ( leudne-valine zipper ). [Pg.753]

Both these causes probably contribute to produce the excess of hydride of ethyl but the very small amount of gaseous products, compared with the solid ones, convinced me that the production of the former is only an accidental circumstance, which, however it may be interpreted, does not at all affect the principal reaction, viz. the formation of iodide of stanethylium. The gases, evolved by the action of light upon iodide of ethyl and tin, are perfectly similar to those obtained by the action of heat, [Pg.88]

It is necessary to pay careful attention to these last two expressions where H is considered in conventional length units, which corresponds to a Vj,= 1. For example if v = 1 cm/s, then the conventional unit (cu) is cm, therefore, in the relations, H would be expressed in cm. Another example shows that v = 0.02 m/s so a value of the conventional length unit of 1 cu = 0.02 m is requested to make v = 1 cu/s. If, in this case, the trajectory is 0.2 m, for example, then, for H, H = 0.2/0.02 = 10 is used which corresponds to a dimensionless value. For very large H values, relation (4.55) can be simplified as follows Tjn = 2a(H + 1) 2aH. This simplification can guide us towards various speculative conclusions with respect to the covered linear distance. Categorically, the result obtained can be explained by the perfect similarity of the final relationships with the well-known formulas used in mechanics. [Pg.215]

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