Criterion incomplete

The extension of this scheme to dominance conditions requires us to deal with the problem of incomplete tree structure. When certain objective and lower-bound values are unavailable, due to nodes being terminated before full expansion, we cannot be certain that the (jc, y) pair satisfies the criterion for dominance. To solve this problem, we have to extend and relax the syntactic criteria. Such extensions are beyond the scope of this chapter, and for more details, the reader is referred to Realff, (1992). 

Equation (3.30) may be used as a criterion for completeness. If an eigenfunction tpn with a non-vanishing coefficient an were missing from the summation in equation (3.27), then the series would still converge, but it would be incomplete and would therefore not converge to /. The corresponding coefficient a would be missing from the left-hand side of equation (3.30). Since each term in the summation in equation (3.30) is positive, the sum without a would be less than unity. Only if the expansion set ipf in equation (3.27) is complete will (3.30) be satisfied. 

Incompleteness of the reaction this is the chief criterion of chemical equilibria. A reversible reaction is never complete in any direction provided none of the products is allowed to escape from the system. Stated differently, in the equilibrium condition, the reactants and the products are all present simultaneously in the reaction vessel. If any of the substances were to vanish, its concentration would become zero and the value of the equilib-... 

Another alternative to the 3 full factorial is the Box-Behnken design (Box and Behnken [19]). These designs are a class of incomplete three-level factorial designs that either meet, or approximately meet, the criterion of rotatability. A Box-Behnken design for p=3 variables is shown in Table 2.7. This design will estimate the ten coefficients of the second-order... 

Constipation is a complaint commonly seen in clinical practice. Because of the wide range of normal bowel habits, constipation is difficult to define precisely. Most persons have at least three bowel movements per week, and constipation has been commonly defined as a frequency of defecation of less than three times per week. However, stool frequency alone is not a sufficient criterion to use because many constipated patients describe a normal frequency of defecation but subjective complaints of excessive straining, hard stools, lower abdominal fullness, and a sense of incomplete evacuation. Thus, a combination of objective and subjective criteria must be used to define constipation. 

It is well known that the presence of water on an oxide catalyst surface effectively reduces the catalytic activity versus a wide variety of reactions. On the other hand, promotional effects have also been observed, so that criterion h (Section II.C.l) is invalidated. Water can be held by incompletely coordinated... 

The interesting point is that this is a mathematical version of the problem that we face in embryonic development. The fertilised egg contains far less information than the adult organism (whatever criterion is used to measure information in biological systems), and embryonic development can be described therefore as a process that is reconstructing a structure from incomplete information. This is another way of saying that embryonic development is a process that increases the complexity of a living system. The reconstruction of structures from incomplete information, in short, is a model that could help us understand how it is possible for a system to obtain a convergent increase of complexity. 

Another important criterion is to determine whether the nodular transformation in the liver is complete or incomplete. This morphological characteristic can be found both in progressive and stationary cirrhoses. In complete cirrhosis, the parenchyma is completely partitioned by connective tissue septa. The collapse of fibres (due to portocentral bridging necroses) results in the development of portocentral septa (= passive septa). Due to the spreading of the inflammation to the periportal parenchyma, septa develop and branch out from the portal fields (= active septa). Generally, they lead to capillarization of the sinusoidal walls as well. (s. fig. 35.7) Incomplete cirrhosis only displays the formation of short septa (= subsepta), so that there are areas of incomplete (partial) subdivision of the parenchyma. 

We shall now review some of these techniques, more or less in order of increasing complexity. Regarding the ycosa methods frequent reference will be made to chapter 1. Strictly speaking, a measurement is incomplete unless both the advancing and receding angle are obtained. By this strict criterion, the literature does not contain many complete measurements. According to Marmur (see below), the drop volume is also an Important parameter. 

Some recommended procedures that may be tried are described below. Regardless of the method used, the important criterion for success is the quantitative recovery of those amino acids or derivatives in which one is interested. For example, if one has made a radiolabeled derivative of cysteine in a protein, all of the radioactivity must be demonstrated to elute in the position of this derivative after complete enzymic hydrolysis if it does not, it is not certain whether the enzymic hydrolysis was incomplete or if other residues have also been modified. 

Reactions (d)-(0 represent idealized cases this type of reaction is incomplete and produces nitrides containing appreciable amounts of C and O the reaction is driven toward completion at high N2 overpressures. These processess can be carried out on a commerical scale because of the ready availability of many metal oxides, as long as high purity is not an important criterion. Reaction temperatures are in the range of 1200-1400°C. 

Any formal definition of a gel has been avoided, because its formulation would be difficult on the basis of external properties. By any criterion, a 1 % aqueous solution of agar does form a gel when it is cooled from 95 to 20°, whereas a 1 % solution of sucrose does not but properties may be so continuous between these extremes that any dividing line would be arbitrary. Most of this Chapter is concerned with fairly permanent network structures formed from polymer solutions. As a definition of gels, this description is incomplete. Some cellulose gels, and pastes of gelatinized, starch granules, would be excluded, because they are formed by limited dispersion of solids. In other words, an arbitrary choice will be made to focus on those gels that are dilute with respect to polymer, because the information available about them at the molecular level is more precise than for others. 

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