Time and storage requirements

EXECUTION TIME AND STORAGE REQUIREMENTS OF THERMODYNAMIC SUBROUTINES... 

This formulation contains P primal variables and 2P to (S + 1 )P — (S — 1)5 terms. Cheng and Mah (C8) evaluated this method and found both computing time and storage requirements to be quite excessive. A 14-oranch and 5-path problem, for instance, took 11.9 CPU seconds and occupied 9728 words of storage on a CDC 6400 computer. 

Discrete Merge Method Computing Time and Storage Requirements 1... 

Cluster-based and dissimilarity-based methods for compound selection were first discussed in the Eighties but it is only in the last few years that the area has attracted substantial attention as a result of the need to provide a rational basis for the design of combinatorial libraries. The four previous sections have provided an overview of the main types of selection method that are already available, with further approaches continuing to appear in the literature. Given this array of possible techniques, it is appropriate to consider ways in which the various methods can be evaluated, both in absolute terms and when compared with each other. A method can be evaluated in terms of its efficiency, /.< ., the computational costs associated with its use, and its effectiveness, /.< ., the extent to which it achieves its aims. As we shall see, it is not immediately obvious how effectiveness should be quantified and we shall thus consider the question of efficiency first, focusing upon the normal algorithmic criteria of CPU time and storage requirements. 

In practice, all 16 elements very often may not be independent. Some may be zero and some may be identical to others depending on symmetry and other physical properties of the studied object [7,8], A typical example is the deterministic class of objects which have less than seven independent elements. Hence, in measuring all 16 elements of the deterministic Mueller matrix, more than 50% are uni nformative measurements. This problem is relevant to imaging polarimetry, since time and storage requirements are important considerations. The number of independent elements of the Mueller matrix can be taken into account in developing a polarimeter. If one takes only three input polarizations, (4.9) can be stractured in the following way ... 

Efficiency Models can consume significant resources, both in their development and in their use. Modeling approaches differ in their requirements on the knowledge, sldll, and elapsed time required for development. Since most models will be implemented on a computer, such issues as running time and storage requirements can also be important. 

When the solute is relatively small, the number of surface tesserae is also small which makes direct matrix inversion of Eq. 10.7 feasible. The computational time and storage requirement for the direct inversion of matrix A is on the order of N, where N is the number of tesserae. For large solutes such as protein, the number of surface tesserae can be very large. Even the allocation for matrix A may cause memory overflow. Therefore iterative methods are required with on-the-fly calculations of the columns or rows of matrix A whenever necessary (Barrett et al., 1994). 

What are the costs that accompany the benefits of using symmetry in an electronic structure program It takes considerable effort to do the programming if a number of the types of computational synunetry use are put into a program. For calculations with synunetry, the benefits may be quite large in computation time and storage requirements. For calculations with no synunetry, there are no benefits and there are some costs in terms of unnecessary multiplications by I, etc., which are probably quite modest. 

The cure system must be slow at room temperature to prevent storage life and flow problems, but sufficiently rapid at elevated temperatures to permit reasonably short curing times. Even the most latent curing system in use today does not completely eliminate room temperature reaction thus shelf life and storage requirements must be critically controlled. 

A finite — and indeed a rather small — amount of computer time and storage is required to generate a tree of reactions the danger of an information explosion has been contained. Due to the formal character of the reaction generating process all conceivable reactions are obtained. This open-ended approach permits the discovery of completely novel synthetic reactions. 

In this paragraph the wall function concept is outlined. The wall functions are empirical parameterizations of the mean flow variable profiles within the inner part of the wall boundary layers, bridging the fully developed turbulent log-law flow quantities with the wall through the viscous and buffer sublayers where the two-equation turbulence model is strictly not valid. These empirical parameterizations thus allow the numerical flow simulation to be carried out with a finite resolution within the wall boundary layers, and one avoids accounting for viscous effects in the model equations. Therefore, in the numerical implementation of the k-e model one anticipates that the boundary layer flow is not fully resolved by the model resolution. The first grid point or node used at a wall boundary is thus placed within the fully turbulent log-law sub-layer, rather than on the wall itself [95]. In effect, the wall functions amount to a synthetic boundary condition for the k-e model. In addition, the limited boundary layer resolution required also provides savings on computer time and storage. 

Usually, p is chosen to be a number between 4 and 10. In this way the system moves in the best direction in a restricted subspace. For this subspace the second-derivative matrix is constructed by finite differences from the stored displacement and first-derivative vectors and the new positions are determined as in the Newton-Raphson method. This method is quite efficient in terms of the required computer time, and the matrix inversion is a very small fraction of the entire calculation. The adopted basis Newton-Raphson method is a combination of the best aspects of the first derivative methods, in terms of speed and storage requirements, and the more costly full Newton-Raphson technique, in terms of introducing the most important second-de-... 

Figure 5 shows the influence of harvest time and storage on total volatiles production. Since the production of many but not all of the aroma volatiles is linked to amino acid precursors it may be expected that the total volatiles behavior may reflect that of the amino acids especially those which supply many of the carbon skeletons for the esters found in melons. The pattern of behavior for the total volatiles is generally in accord with that of these amino acids and does very clearly illustrate the profound influence of harvest time on the generation of the aroma profile. Fruit harvested only two days before folly ripe develops only about one quarter of the total volatiles concentration shown a few days postharvest, by a folly ripe sample. This rather dramatic difference may reflect the inability of prematurely harvested fiuit to accumulate sufficient concentrations of required volatiles substrates because certain metabolic responses have not been activated. 

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