Magic constant

The correction term in Eq. (9) shows that the basic assumption of additivity of the fragmental constants obviously does not hold true here. Correction has to be appHed, e.g., for structural features such as resonance interactions, condensation in aromatics or even hydrogen atoms bound to electronegative groups. Astonishingly, the correction applied for each feature is always a multiple of the constant Cu, which is therefore often called the magic constant . For example, the correction for a resonance interaction is +2 Cj, or per triple bond it is -1 A detailed treatment of the Ef system approach is given by Mannhold and Rekker [5]. 

Regression analyses revealed systematic differences between experimental log P and log P calculations based on the summation of fragment values. These differences could be attributed to chemical characteristics of the molecules, which in turn allowed the definition of correction rules such as chain conjugation, electronegativity facing bulk or the proximity effect, which describes the presence of electronegative centers in a molecule separated by one or two carbons. Correction values needed for log P calculation were shown to represent multiples of a constant value of 0.289, which is known as the magic constant (CM). 

A magic square in which all the broken diagonals as well as the main diagonals add up to the magic constant, pandigital... 

A salient feature of Rekker s approach is that all constitutive terms (correction factors) appear proportional to a constant, the so-called magic constant , As a result, correction factors can be described as follows ... 

Although the magic constant bears an unfortunate name, Rekker suggested that it originates from a fundamental property of water in the first solvation shell, namely a so-called quantum displacement of water molecules. A discussion of the relevance of the magic constant along with the related hydration factor, co, proposed by van de Waterbeemd and Testa, is outside the scope of this chapter. Table 3 summarizes the correction factors used in Rek-ker s revised fragmental method." ... 

Madclung constant, 63 magic number, 704 magnesium, 593 burning, F2... 

The close-packed-spheron theory of nuclear structure may be described as a refinement of the shell model and the liquid-drop model in which the geometric consequences of the effectively constant volumes of nucleons (aggregated into spherons) are taken into consideration. The spherons are assigned to concentric layers (mantle, outer core, inner core, innermost core) with use of a packing equation (Eq. I), and the assignment is related to the principal quantum number of the shell model. The theory has been applied in the discussion of the sequence of subsubshells, magic numbers, the proton-neutron ratio, prolate deformation of nuclei, and symmetric and asymmetric fission. 

You will notice how remarkably arbitrary this process is. The constant value 6.0 was not chosen because it has some magical properties in the GA, but because it seemed to be a value that would be "pretty good" in this particular application. The lack of sensitivity in the operation of the GA to the precise way in which the calculation is set up and run can seem unsettling at first, but this tolerance of the way that the user decides to use the algorithm is one of its important attractions, giving even novice users every chance of achieving good results. 

Normally, everything is balanced, C02 and bicarbonate are removed at exactly the same rate that they re formed, and the pH of the serum remains very close to 7.4. If for some reason the lungs blow off too much C02 by hyperventilating (breathing too fast), the numerator of the magic equation (pC02) decreases, and, as long as [HCO 3] remains constant, the [H+] must decrease (pH increases). 

Hypoventilating (breathing too slowly) increases the pC02 (numerator of the magic equation), and, as long as [HCO 3] remains constant, the [H+] must increase (pH decreases). 

The concept of magic-angle spinning arises from the understanding of the shielding constant, cr (Eq. 4). This constant is a tensor quantity and, thus, can be related to three principal axes ... 

The values for k+ and k were compared for temperature jump and stopped-flow conditions for DNA concentrations where the decay followed a mono-exponential function and no migration between DNA molecules occurred (see below).94 This report shows the importance of detecting fluorescence signals at the magic angle, which eliminated the fast components in the kinetics due to artifacts. The values for the association and dissociation rate constants obtained by both techniques are similar. 

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