Numeric constraint

There are numerous constraints and factors that affect procedures for design of multiproduct and multipurpose plants ... 

Coello Coello, C.A. (2002) Theoretical and numerical constraint handling techniques used with evolutionary algorithms A survey of the state of the art. Computer Methods in Applied Mechanics and Engineering, 191 (11—12), 1245-1287. 

Optimizing the operation of the blast furnace is important in every large-scale steel mill. A relatively large number of important variables (several of which cannot be measured) interact in this process in a highly complex manner, numerous constraints must be taken into account, and the age and efficiency of the plant significantly affect the optimum... 

Peacock S. M. (1983) Numerical constraints on rates of metamorphism, fluid production, and fluid flux during regional metamorphism. Geol Soc. Am. Bull 101,476-485. 

This graphical technique is adequate for the two variables investigated in this problem. This problem can also be solved using optimization techniques such as linear programming, a technique that can handle numerous constraints and variables... 

It is also possible to define other constraints on data in tables. For example, molecular weight might be stored as a numeric value. While the standard SQL numeric constraint applies, it might be desirable to also constrain molecular weight values to be positive values. This can be readily done after the column is defined using the following SQL. 

Philo JS (2000) Sedimentation equilibrium analysis of mixed associations using numerical constraints to impose mass or signal conservation. Methods Enzymol 321 100-120... 

This procedure yields values for the fundamental constants included in Z. These values are available on the web and in [3, Table XXVI, p. 63]. Through this method, for instance, the proton radius is determined to a precision of about 1%, mainly through numerical constraints set by transitions in hydrogen, as shown in Figure 13.1. 

When we have a constrained optimization problem and numerous constraint equations whereas the difference between the number of variables and the number of equations is relatively very small (see Chapter 14). 

Mote, Philip, and Alan O Neill, eds. Numerical Modeling of the Global Atmosphere in the Climate System. Boston Kluwer Academic, 2000. Meant for those actively creating climate models, this work explains the uses of numerical constraints to define climate... 

Z) is a Cartesian productof intervals 7jX...x/ (a box), where each 7 is the domain of variable x,-and C is a set of numerical constraints (equations or inequalities) on subsets of the variables in X. A solution of the CCSP is a value assignment toall variables satisfying all the constraints in C. The feasible space T is the set of all CCSP solutions within D. 

Some local controls are assumed to be in place, such as anti-surge control for the compressors. In addition, some valves are fiilly open or fixed, as shown in Fig. 35.1. The selection of controlled variables is strongly related to the goals that are set for operation of the fluid catalytic cracker. There are numerous constraints that all have to be met. Moreover, two main objectives should be met maximization of the total feed rate and dismtbance rejection. 

Either way, numerical constraints are unnecessary when sufficient data are available. Because there is a huge amount of reference data available for simple organic systems, numerical constraints in these systems are unnecessary. 

When the number of available data is small, a case can be made for using chemically meaningful constraints on the values of parameters. Under such circumstances the artificially imposed constraints or rules provide valid, useful information that would otherwise be missing. This situation occurs when elements for which there is a paucity of data (e.g., scandium) are parameterized. Numerical constraints are then likely to be necessary. 

Rule generation begins with a set of user-defined substructures, the reference compounds containing each of them, and an automatically created inverted file of reference compounds giving rise to each of the separate spectral features identified in the database. The resulting output is a spectral-feature - substructure array. In a step which is essentially a search of the feature-combination space, feature combinations for each of the substructures are generated. Numerous constraints limit the size of the search space to reveal those feature combinations that are highest in reliability and recall. 

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