Algorithmic development

The data from Table 2 show that the algorithm developed in allows sizing of different cracks with complex cross-sections and unknown shapes for orientation angles not exceeding 45°. It is seen that the width 2a and the parameter c (or the surface density of charge m=4 r // e at the crack walls) are determined with 100% accuracy for all of the Case Symbols studied. The errors in the computation of the depths dj and di are less than 4% while the errors in the computation of d, dj, d, and d are less than 20% independent of the shape of the investigated crack and its orientation angle O <45°. 

Obviously, the theory outhned above can be applied to two- and three-dimensional systems. In the case of a two-dimensional system the Fourier transforms of the two-particle function coefficients are carried out by using an algorithm, developed by Lado [85], that preserves orthogonality. A monolayer of adsorbed colloidal particles, having a continuous distribution of diameters, has been investigated by Lado. Specific calculations have been carried out for the system with the Schulz distribution [86]... 

First-order horn clause logic is the representation that has been adopted by workers in the field of explanation-based learning (Minton et al., 1990). Hence, using this representation allows us take advantage of the results and algorithms developed in that field to carry out the machine learning task. 

The importance of the degree of esterification (%DE) to the gelation properties of pectins makes it desirable to obtain a fast and robust method to determine (predict) the %DE in pectin powders. Vibrational spectroscopy is a good candidate for the development of such fast methods as spectrometers and quantitative software algorithms (chemometric methods) becomes more reliable and sophisticated. Present poster is a preliminary report on the quantitative performance of different instrumentations, spectral regions, sampling techniques and software algorithms developed within the area of chemometrics. 

This is the principle of the pyramidal algorithm developed by Mallat [20], which is computationally more efficient. Continuing the calculations according to this algorithm, the four a components are input to a 4x4 level transformation matrix, giving the level-3 components ... 

Matlab - high-level technical computing language and interactive environment for algorithm development, data visualization, data analysis and numerical computation (http / /www. math works. com/)... 

Kendall, R. A., Friichtl, H. A., 1997, The Impact of the Resolution of the Identity Approximate Integral Method on Modern Ab Initio Algorithm Development , Theor. Chem. Acc., 97, 158. 

Since the values for p((p), p(surface-tension force could be distorted if the variation of V

very large, the thickness of the interface needs to be maintained uniformly, i.e. V = 1 (Sussman et al., 1998). In the algorithm developed, the general level set function 4>(x,t) is replaced by a... 

As a consequence, in a sensor space of dimension N the effective dimension of the sub-space occupied by the data is less than N. This dimension can be precisely evaluated using algorithms developed to describe dynamic systems. An example is the correlation distance that allows evaluating the fractional dimensionality of a data-set [16]. Correlation distance provides an independent way to evaluate the expected reduction of dimension. 

Predictions of high explosive detonation based on the new approach yield excellent results. A similar theory for ionic species model43 compares very well with MD simulations. Nevertheless, high explosive chemical equilibrium calculations that include ionization are beyond the current abilities of the Cheetah code, because of the presence of multiple minima in the free energy surface. Such calculations will require additional algorithmic developments. In addition, the possibility of partial ionization, suggested by first principles simulations of water discussed below, also needs to be added to the Cheetah code framework. 

The algorithms developed in this chapter can model any situation, e.g. they can serve to demonstrate the effects of initial concentrations and rate constants in kinetics and of total concentration and equilibrium constants in equilibrium situations. Very importantly, these algorithms further form the core of non-linear least-squares fitting programs for the determination of rate or equilibrium constants, introduced and developed in Chapter 3, Model-Based Analyses. 

An exact determination of the relative values of P for the BPTI and villin simulations is not possible, because some algorithmic developments reduce computational costs (particularly methods that allow one to increase the size of the time step and to efficiently treat long-range interactions), while others increase the costs (e.g., more detailed force fields and appropriate boundary conditions). But we can place reasonable bounds on the historical growth rate of P by using r=l and r=2 as lower and upper limits on the costs of calculating interatomic interactions. 

Least square fits were obtained by the gradient-expansion algorithm developed by Marquardt (30). The DC offset (i.e. EPR signal at 20 mtorr) was subtracted from each data point before performing the least squares fit. The inverse of the fitting parameter, k, is the pressure at which the EPR signal reaches half maximum and, presumably, is related to the number oxygen. In these studies, constant at 475 25 torr. 

We demonstrated that by the selection of a representation of the Dirac Hamiltonian in the spinor space one may strongly influence the performance of the variational principle. In a vast majority of implementations the standard Pauli representation has been used. Consequently, computational algorithms developed in relativistic theory of many-electron systems have been constructed so that they are applicable in this representation only. The conditions, under which the results of these implementations are reliable, are very well understood and efficient numerical codes are available for both atomic and molecular calculations (see e.g. [16]). However, the representation of Weyl, if the external potential is non-spherical, or the representation of Biedenharn, in spherically-symmetric cases, seem to be attractive and, so far, hardly explored options. 

Generally speaking, it can be said that the algorithms developed and tested here, give good approximations of the variances of the partition coefficients of compounds and of selectivities estimated with models obtained from mixture experimental designs. 

Evaluation of a number of irradiation scenarios and approaches to combining the Hp(lO) values from the two personal monitors indicates that an algorithm developed by the NCRP using the /fp(lO) values for the front and back personal monitors of the form ... 

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