Linear potential, piecewise

Fig. 12.23 Two simple scoring functions used in docking. On the left is the basic scoring scheme used by the DOCK program [Desjarlais et al. 1988], On the right is the piecewise linear potential [Cclhaar et al. 1995],...

In PLPscore, both the steric and hydrogen bonding terms are calculated from a piecewise linear potential function (see Fig. 1), instead of a smooth 6-12 Lennard-Jones potential energy function. The difference between the two terms is simply in the parameter values chosen for each term. 

Each of the terms in Equation (12.2) has been the subject of considerable discussion in the literature, and for some of them there may be a number of different approaches to their estimation. However, many of these methods are unsuitable for doddng, due to the calculation time required. Some very simple functions have been employed for docking, such as that originally used in the DOCK program (illustrated in Figure 12.23 together with another similar form, the piecewise linear potential [Gelhaar et al. 1995]). Despite tiieir apparent simplicity, such functions continue to rate well in comparisons of different functional... 

C V uses a piecewise linear potential waveform that is described for one cycle (anodic... 

Thus, to obtain the timescales d and Q( ) we need to find the solution Y(x, s) of Eq. (5.78) at appropriate boundary conditions and evaluate limits (5.82) and (5.83) for y - > 0. It is precisely that way by which the various timescales for piecewise-linear and piecewise-parabolic potential profiles were derived in Refs. 32 and 33. 

Circuitry for setting gradients for piecewise-linear characteristics utilize a three-input OP amplifier to set the gradients for piecewise-linear characteristic of the twilight sensor output. Since the three inputs are at the lowest transistor base potential, the sensor s characteristics are as shown in Fig. 7.13.14 when the inputs are VI, V2, and V3. 

Furthermore, Eqs. (2.21)-(2.23) can be added to model quantity discounts, i.e., price reductions offered by the suppliers to induce large orders. Certainly, the relationship between the discount factor offered by external supplier e for raw material r (DFerd) and the amount of raw material purchased can be modeled as a piecewise linear function (see Fig. 2.4). The inclusion of these constraints allows the potential benefits... 

In ref. 151 the author studies the piecewise perturbation methods to solve the Schrodinger equation and the two form of this approach, i.e. the LP and CP methods. On each stepsize the potential is numerically approximated by a constant (in the case of CP) or by a linear function (in the case of LP). After that the deviation of the true potential from this numerical approximation is obtained by the perturbation theory. The main idea of the author is that an LP algorithm can be made computationally more efficient if expressed in a CP-like form. The author produces a version of order 12 whose the two main parts are a new set of formulae for the computation of the zeroth-order solution which replaces the use of the Airy functions, and an efficient way of obtained the formulae for the perturbation corrections. The main remark for this paper is that from our experience for these methods the computational cost is considerably higher than for the finite difference methods. 

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