Distance between formula

Were we can give these equations for the heat transfer process along radius R. The other processes of heat transfer can be simulated analogously by changing formula for heat transfer area and distances between centers of cells. For Dirichlet cells, bordering a gas medium, an equation of heat balance can be written in the form ... 

Table 12.3 Formulae for various commonly used ways to compute the similarity or distance between molecules. For the binary data a is defined to be the number of bits on in molecule A, b is the number of bits on in molecule B and c is the number of bits that are on in both A and B. Table based on [Willett et al. 1998],...

Bismuthides. Many intermetaUic compounds of bismuth with alkafl metals and alkaline earth metals have the expected formulas M Bi and M Bi, respectively. These compounds ate not saltlike but have high coordination numbers, interatomic distances similar to those found in metals, and metallic electrical conductivities. They dissolve to some extent in molten salts (eg, NaCl—Nal) to form solutions that have been interpreted from cryoscopic data as containing some Bi . Both the alkafl and alkaline earth metals form another series of alloylike bismuth compounds that become superconducting at low temperatures (Table 1). The MBi compounds are particularly noteworthy as having extremely short bond distances between the alkafl metal atoms. 

The formula for this calculation is very simple and very accurate. It requires three factors (1) the difference in temperature of the machine housing between the feet and shaft bearings, (2) the distance between the shaft centerline and the feet, and (3) the coefficient of thermal expansion of the machine housing material. The thermal... 

Thus, in accordance with Equation (1.1) the mass Am(p) is subjected to the force dF(p) which is directly proportional to the product of both masses and inversely proportional to the square of the distance between them, and it has a direction opposite to hgp, (the presence of minus at the right hand side of Equation (1.1) illustrates this fact). This extremely simple formula describing the basic physical law of the gravimetry may need some comments. 

Here Lqp is the distance between points q and p. Note that G q, p) is called a Green s function. There are an infinite number of such functions and all of them have a singularity at the observation point p. Inasmuch as the second Green s formula has been derived assuming that singularities of the functions U and G are absent within volume V, we cannot directly use this function G in Equation (1.99). To avoid this obstacle, let us surround the point by a small spherical surface S and apply Equation (1.99) to the volume enclosed by surfaces S and S, as is shown in Fig. 1.9. Further we will be mainly interested by only cases, when masses are absent inside the volume V, that is. 

The TCNQ molecule in [TR(bzim)]2-TCNQ is sandwiched between two units of [ J,-N, C -bzimAu]3 in a face-to-face manner so that it is best represented by the formula (7t-[ J,-N, C -bzimAu]3)( j,-TCNQ)(7t-[p-N, C -bzimAu]3). The cyanide groups clearly are not coordinated to the gold atoms. The distance between the centroid of TCNQ to the centroid of the AU3 unit is 3.964 A. The packing of [TR(bzim)]2-TCNQ shows a stacked linear-chain structure with a repeat pattern of-(Au3)(Au3)(p-TCNQ) (Au3)(Au3)(p-TCNQ)- an ABBABB repeat The complex [TR(bzim)]2-TCNQ contains two very short intermolecular Au Au distances of 3.152 A (identical for the two aurophilic bonds). The intermolecular Au Au distance is even shorter than the intramolecular distances in the starting compound, which are 3.475, 3.471, and 3.534 A. The adjacent AU3 units in [TR(bzim)]2-TCNQ form a chair-type structure rather than the face-to-face (nearly eclipsed) pattern reported in Balch s studies of the nitro-9-fluorenones adducts with the trinuclear Au(I) alkyl-substituted carbeniate complexes. 

In compound 1, all interproton distances lie in a range which would be expected to give rise to an NOE, as the experiment confirmed. In 3, although the structural formula is very similar, only the distance between the CH proton and the neighbouring ortho protons lies clearly in the NOE range . The others are close to or above 5 A, so that only very small NOEs or none at all could be expected. 

In colorimetric terms, color differences are generally characterized by the distance between two colors in one of the color notation systems, most commonly the CIELAB system. The difference determined in this way represents the total color difference. Since a color is characterized by three quantities, a color difference can also be expressed in terms of three difference components (that is, differences in the color coordinates) and thus described in greater detail. Visually equal color differences between almost equal colors may, upon colorimetric measurement, be considered distinct if the colors of one pair differ strongly from those of the other pair. The formulas for color differences are further elaborated in order to remedy this defect. 

Takamatsu et al. studied the diffusion of water into the acid as well as mono-, di-, and trivalent salt forms of 1155 and 1200 EW samples."pj e gravimetric uptakes of membranes immersed in distilled liquid water versus time were determined. Three approximate diffusion formulas were applied to the data, and all yielded essentially the same result. The log D versus 1/7 plots, over the range 20—81 °C, yielded activation energies of 4.9 and 13.0 kcal/mol for the acid and K+ forms, respectively. Diffusion coefficients of various mineral cations that permeated from aqueous electrolytes were considerably smaller than that of water. Also, log Z7was seen to be proportional to the quantity q a, where q is the charge of the cation and a is the center-to-center distance between the cation and fixed anion in a contact ion pair. 

A close estimate of the dynamic correlation energy was obtained by a simple formula in terms of pair populations and correlation contributions within and between localized molecular orbitals. The orbital and orbital-pair correlation strengths rapidly decrease with the distance between the orbitals in a pair. For instance, the total valence correlation energy of diamond per carbon atom, estimated as 164 mh, is the result of 84 mh from intra-orbital contributions, 74.5 mh from inter-orbital closest neighbors contributions, and 6.1 mh from interorbital vicinal contributions. The rapid decay of the orbital correlation contributions with the distance between the localized orbitals explains the near-... 

The first effect is a change in the work function of the semiconductor. In Fig. 22 the work function is denoted by distance between the Fermi level and the level corresponding to the value of the potential outside the crystal. (We have in mind the thermoelectron work function which figures in Richardson s formula.) We have... 

In this formula, m and n are the number of ligand and receptor atoms, respectively r is the interatomic distance between atoms i and j the q s are the point charges on the atom, and A and B are adjustable van der Waals repulsion and attraction parameters, and D is the dielectric function. They assumed that this scoring function could account for hydrogen bond energies in the electrostatic term. 

The value of d, the perpendicular distance between adjacent planes in the set (hkl), may be calculated using the formulae ... 

Figure 8 shows the amplitude A (half the distance between top and bottom terrace, in units of layer spacing) of the surface profile as a function of t for a groove of wavelength L = 90a. The decay is slower than a simple exponential as in Mullins theory. From the function A t) one can estimate the lifetime of the top terrace t(t) using the formula,... 

The statistical similarity analysis was performed based on determination of Euclidean distance between hypothetical and catalyst profile according to the following formula ... 

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