Affinity maps

Fig. 9.11 Local-electron-affinity maps of < xTTF-oPPV3-C60 (top) and erTTF-oPPE3-C60 (bottom) as viewed with Tramp 1.Id...

Fig. 9.21 Local electron affinity maps of the exTTF-oPPE3-C6o trimer compared to the H2P/ ZnP-oPPE3-C60, 15c, triads, scaling high to low in red to blue...

Additionally, electron-affinity calculations confirm these findings. Especially with respect to the oPPV and oPPE molecular wires, local affinity mappings as... 

Fig. 9.50 Local electron affinity maps of the cjcTTF—oPPV3-C60, the exTTF-oFL3-C60 and the cxTTF-oPPEj-Qo trimer (left to right) scaring high to low in red to blue—displaying the differences between the three different molecular-systems...

GRID P. Goodford was the first to compute discontinuous atom affinity maps on a 3-D lattice around proteins to aid structure-based design. The use of precomputed affinity maps for atoms and charges increased the efficiency of docking and de novo design algorithms. 

Assume that the full spectrum of H (denoted by A(//)) is contained in [y,b]. Then, in order to approximate the eigensubspace associated with the lower end of the spectrum, say [y,a] with y < u < it is necessary to map [a,b] into [—1,1] before applying the Chebyshev polynomial. This can be easily realized by an affine mapping defined as... 

The dependency operator. If X is a variable, then X.f is the functional composition of X and the affine mapping /. This operator makes it possible to represent delays or spatial operations on variables. 

The reduction operator. red(-f,/,X) represents the S operator applied to expression X, where / is an affine mapping describing the range of summation [6]. 

PROOF Let t r — Af be an embedding of tori, t an induced mapping of universal coverings, and t C — C . Then the Jacobian matrix of t is a periodic holomorphic function on with a complete lattice of periods of rank 2p and is therefore constant. Consequently, t is an affine mapping, and we have come to the desired conclusion. 

Assume now that n = p, for some prime number p. Assume that the Evasiveness Conjecture is false for that value of n, and let Q denote a monotone, but nonevasive, graph property. Furthermore, let GF(n) denote a field with n elements, which exists because n is a prime power, and let GF(n) denote the multiplicative group of that field. Let F be a subgroup of [Pg.228]

An important observation about the EMM approach is that it is manifestly a scale-translation (affine map) invariant variational procedure, unlike other approaches, such as Rayleigh-Ritz. At each order, the variation with respect to the Cj s is actually optimizing over all possible affine map transforms of the polynomial sampling function. 

More explicitly, for an arbitrary polynomial, P, of degree N, its affine map transform is given by... 

Because moments are extensive, non-local, objects, their use in quantizing the energy and wavefunction will implicitly be of a multiscale nature, proceeding from large through small scales, as more moments are used. In addition, since moments transform linearly under affine maps, any moment based analysis will incorporate some degree of space-scale invariance, which can be an efficient feature for quantizing systems. 

Iso-lattice constant, iso-energy gap and iso-electron affinity maps can be constructed for such alloy systems according to the following procedure developed by Moon etal. Suppose that the values of lattice constant, energy gap and electron affinity are known for the particular ternary alloy represented by the point (x, y ) on the square shown in Fig. 10. Then the values of these parameters for alloys represented by a point (x,y) in the vicinity of (x, y )can be represented by a two-dimensional Taylor series around the point (x, y ) of the form... 

Catomic affinity map file. A.map A-atomlc affinity map file ,N map If K-atomic affinity map file... 

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