The main difficulty with DFT is that the Hohenberg-Kohn theorem shows that the ground-state values of T,, V, etc. are all unique functionals of the ground-state p (i.e.. [Pg.499]

Two difficulties with this idea were overcome in unconventional ways [Pg.276]

The difficulties with approximations used in theoretical derivations and with the experimental techniques have been pointed out (8), and a series of tutorials have been pubHshed in which the deviations from paraboHc behavior are explained and the correct interpretations of cake filtration data, with many numerical examples, are laid down (8,9). [Pg.392]

The principal difficulty with steepest descent is that the successive direction s of search, g,., . .. arc ri ot conjugate direction s. [Pg.304]

Serviceability. ServiceabiUty is defined as the degree of ease (or difficulty) with which a system can be repaired. This measure specifically considers fault detection, isolation, and repair. RepairabiUty considers only the actual repair time, and is defined as the probabiUty that a failed system is restored to operation in a specified interval of active repair time. Access covers, plug-in modules, or other features to allow easy removal and replacement of failed components improve the repairabihty and serviceabihty (see also Electrical connectors). [Pg.5]

T. Bishop, R. D. Skeel, and K. Schulten. Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics. J. Comput. Chem., 18 1785-1791, 1997. [Pg.329]

HyperChem provides two forms of parameter sets — an ASCII text form and the database form consistent with dBASEIV and a large number of other database packages. Since the principal difficulty with using molecular mechanics is having or obtaining appropriate parameters, you may want to explore parameter sets as a database in the. dbf form. [Pg.197]

This reaction sequence is much less prone to difficulties with isomerizations since the pyridine-like carbons of dipyrromethenes do not add protons. Yields are often low, however, since the intermediates do not survive the high temperatures. The more reactive, faster but less reliable system is certainly provided by the dipyrromethanes, in which the reactivity of the pyrrole units is comparable to activated benzene derivatives such as phenol or aniline. The situation is comparable with that found in peptide synthesis where the slow azide method gives cleaner products than the fast DCC-promoted condensations (see p. 234). [Pg.256]

Furthermore, Tests D-L need not necessarily be carried out in the order given. As elementary students often experience difficulty with the interpretation of Test D, it is often convenient to relegate it to a lower position in the order of Tests. [Pg.402]

The purpose of this paper is twofold (i) We summarize possible difficulties with the midpoint method (other than resonance instability, which has been treated extensively elsewhere) by looking at a simple (molecular) model problem, (ii) We investigate the suitability of some energy conserving methods. [Pg.283]

This effect assumes importance only at very small radii, but it has some applications in the treatment of nucleation theory where the excess surface energy of small clusters is involved (see Section IX-2). An intrinsic difficulty with equations such as 111-20 is that the treatment, if not modelistic and hence partly empirical, assumes a continuous medium, yet the effect does not become important until curvature comparable to molecular dimensions is reached. Fisher and Israelachvili [24] measured the force due to the Laplace pressure for a pendular ring of liquid between crossed mica cylinders and concluded that for several organic liquids the effective surface tension remained unchanged [Pg.54]

This type of contract requires the operator to pay a fixed amount to the contractor upon completion of the well, while the contractor furnishes all the material and labour and handles the drilling operations independently. The difficulty with this approach Is to ensure that a quality well Is delivered to the company since the drilling contractor will want to drill as quickly and cheaply as possible. The contractor therefore should guarantee an agreed measurable quality standard for each well. The guarantee should specify remedial actions which will be implemented should a substandard well be delivered. [Pg.62]

A careful analysis of the fundamentals of classical thermodynamics, using the Born-Caratheodory approach. Emphasis on constraints, chemical potentials. Discussion of difficulties with the third law. Few applications. [Pg.377]

Another option is a q,p) = p and b q,p) = VU q). This guarantees that we are discretizing a pure index-2 DAE for which A is well-defined. But for this choice we observed severe difficulties with Newton s method, where a step-size smaller even than what is required by explicit methods is needed to obtain convergence. In fact, it can be shown that when the linear harmonic oscillator is cast into such a projected DAE, the linearized problem can easily become unstable for k > . Another way is to check the conditions of the Newton-Kantorovich Theorem, which guarantees convergence of the Newton method. These conditions are also found to be satisfied only for a very small step size k, if is small. [Pg.285]

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