Method, defined

The more recently developed methods define an energy expression for the combined calculation and then use that expression to compute gradients for a geometry optimization. Some of the earlier methods would use a simpler level of theory for the geometry optimization and then add additional energy corrections to a final single point calculation. The current generation is considered to be the superior technique. 

Toffoli [toff7,5] showed that it is possible to realize such conserved landscape permutations in CA systems of arbitrary dimensionality and site value space size I 1= k. In each case, as in the above example, the method defines the inverse along with the forward map. 

The first order (i.c. ]> 1) approximation of the CML system defined by equation 8.44 (using either of the two methods defined above) is given by an elementary fc = 2, r = 1 CA. Since there are only 32 such rules, the particular CA rule corresponding to a CML system with parameters e and s may be found directly by calculating the outcome of each of the five possible local states. Looking at the first-order step function fi x) in equation 8.47, we can identify the absorbing state X = X with the CA state ct = 0, and x = 1/2 with a = 1. 

In Fig. 11 results are given for sulfosuccinate surfactants of different molecular structure tested according to the Draize skin irritation procedure. The test method defines test scores verbally as described in Table 21. The data in Fig. 11 prove the nonirritant character of sulfosuccinates tested at 10% concentration. Similar results were found for another group of sulfosuccinates [103]... 

It is important to distinguish between the concept of method and the concept of technique . Method defines the aggregative state of the original material (e.g., liquid or gaseous state) from which crystals form directly. Each method is employed by means of several techniques. ... 

For the special case for which n = 2, it can be shown that the linearization method defined above becomes identical to the Newton-Raphson method. The result may be generalized to apply to any homogeneous function of degree n. 

When evaluating uncertainty, it is important to understand the distinction between empirical and non-empirical methods, as this influences how the uncertainty is evaluated. In the case of non-empirical methods, any bias in the results which is due to the method of analysis or, for example, a particular sample type, needs to be considered as part of the uncertainty evaluation process. For example, if a method was intended to determine the total amount of cadmium present in a soil sample, but for some reason only 90% of the cadmium present was extracted from the sample, then this 10% bias would need to be accounted for in the uncertainty estimate. One approach would be to correct results to take account of the bias. However, there would be an uncertainty associated with the correction as there will be some uncertainty about the estimate of the bias. For empirical methods, the method bias is, by definition, equal to zero (the method defines the result obtained). However, when evaluating the uncertainty associated with results obtained from an empirical method, we still need to consider the uncertainty associated with any bias introduced by the laboratory during its application of the method. One approach is to analyse a reference material that has been characterized by using the same empirical method. If no suitable reference material is available, then any bias associated with carrying out the individual stages of the method in a particular laboratory will need to be evaluated. 

For pipe fittings, valves, and other flow obstructions the traditional method has been to use an equivalent pipe length Lequiv in Equation 4-30. The problem with this method is that the specified length is coupled to the friction factor. An improved approach is to use the 2-K method,s-6 which uses the actual flow path length in Equation 4-30 — equivalent lengths are not used — and provides a more detailed approach for pipe fittings, inlets, and outlets. The 2-K method defines the excess head loss in terms of two constants, the Reynolds number and the pipe internal diameter ... 

Lichtarge, O., Bourne, H. R., and Cohen, F. E. (1996) An evolutionary trace method defines binding surfaces common to protein families. J. Mol. Biol. 257, 342-358. 

The semiempirical calculation of thermochemical properties has been reviewed recently [32], The present chapter is a condensed and updated version of this previous review. It outlines the theoretical background of semiempirical methods, defines specific conventions, provides statistical evaluations, and discusses the performance with regard to thermochemical properties. 

This method (EPA 1664) is a liquid-liquid extraction gravimetric procedure that employs n-hexane as the extraction solvent, in place of 1,1,2-trichloroethane (CFC-113) and/or 1,2,2-trifluoroethane (Freon-113), for determination of the conventional pollutant oil and grease. Because the nature and amount of material determined are defined by the solvent and by the details of the method used for extraction, oil and grease method-defined analytes are used. The method may be modified to reduce interferences and take advantage of advances in instrumentation provided that all method equivalency and performance criteria are met. However, n-hexane is a poor solvent for high-molecular-weight petroleum constituents (Speight, 1999, 2001). Thus, the method will produce erroneous data for samples contaminated with heavy oils. 

The transformation of the residual into a bba follows the method defined in section 3.1 with the operator p described by equation (15) ... 

Along with the complete QMMCC(2,6) method, defined by eqs (38)- (41), we decided to test the approximate QMMCC schemes, in which the high-order terms involving the most expensive hextuply or pentuply and hextuply excited moments of the CCSD equations are ignored. For example, we can neglect the term in eq (40) by reducing the summation over and we... 

There is no natural way to generalize the one-dimensional bisection method to solve this multidimensional problem. But it is possible to generalize Newton s method to this situation. The one-dimensional Newton method was derived using a Taylor expansion, and the multidimensional problem can be approached in the same way. The result involves a 3/V x 3/V matrix of derivatives, J, with elements 7y = dg, /dxj. Note that the elements of this matrix are the second partial derivatives of the function we are really interested in, E(x). Newton s method defines a series of iterates by... 

Only a minority of methods defined an internal standard biocide. 

Let us suppose that we are interested in implementing this procedure in our laboratory and we fix the time of agitation at 10 min. So, we want to look for the RC (Xi) and pH (X2) values that provide the largest percentage lead recovery (Y), and we will use the simplex method defined by Spendley etal [16]. 

Two methods are commonly used to determine the endpoint of an acidity titration. The potentiometric method titrates to a predetermined pH and the colorimetric method uses an indicator that changes color at a particular pH to determine the endpoint. Other methods define the endpoint as the inflection of a titration curve, i.e., plots of pH value versus milliliter of NaOH used (Sadler and Murphy, 1998 Hand et al., 1993). However, the increased precision... 

Template Method Define the skeleton of an algorithm in an operation, deferring some steps to subclasses. The Template Method lets subclasses redefine certain steps of an algorithm without changing the algorithm s structure. 

The CompoundMapper defines specific data access logic for the Compound object. Its findStatementPrimaryO method defines how to query the compound table using its primary key. The findByCorpIdPrimary() defines how to query the compound table using its corporate id and so on. 

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