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To manipulate data, you need operators that can be applied to that data. Multiplication and addition are typical examples of operators in mathematics; you specify two numbers as input, and the operator produces one output value as a result. Multiplication and addition are examples of closed operators, because they produce things of the same type you provided as input (numbers). For example, for integers, addition is closed. Add any two integers, and you get another integer. Try it you can t find two integers that add up to a noninteger. However, division over the integers is not closed; for example, 1 divided by 2 is not an integer. Closure is a nice operator property, because it allows you to (re)use the operator results as input for a next operator. In a database environment, you need operators to derive information from the data stored in the database. In an RDBMS environment, all operators should operate at a high logical level. This means, among other things, that they should not operate on individual rows, but rather on tables, and that the results of these operators should be tables, too. Because tables are defined as sets of rows, relational operators should operate on sets. That s why some operators from the classical set theory such as the union, the difference, and the intersection also show up as relational operators. See Figure 1-1 for an illustration of these three set operators.

It should be noted that irritant-based reactions may also be seen at the 48-hour reading However, unlike the ACD-type reactions, these tend to be resolving at the delayed reading The sodium lauryl sulfate (SLS) test may be a useful adjuvant patch test, especially in the sensitive skin patient, as it may facilitate the differentiation between allergic and irritant reactions9 A reaction in the SLS application patch during patch testing indicates that macular erythema in the patch test sample on that patient more likely reflects an irritant etiology Conversely, if the SLS test fails to demonstrate a reaction upon patch testing, it is more likely that macular erythematous reactions may be allergic in nature While the SLS testing may be useful, it is important to note that clinical correlation of the presentation and exposure history are crucial for the correct diagnosis of allergic versus irritant contact dermatitis FIGURE 18-4 Contact dermatitis to avorings such as peppermint and cinnamon can lead to perioral dermatitis, which is a variant of contact dermatitis In this gure, the patient s dermatitis was caused by peppermint avoring in her toothpaste

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Along with these generic operators from set theory that can be applied to any sets, there are some additional relational operators specifically meant to operate on tables You can define as many relational operators as you like, but, in general, most of these operators can be reduced to (or built with) a limited number of basic relational operators The most common relational operators are the following: Restriction: This operator results in a subset of the rows of the input table, based on a specified restriction condition This operator is also referred to as selection Projection: This operator results in a table with fewer columns, based on a specified set of attributes you want to see in the result In other words, the result is a vertical subset of the input table.

FIGURE 10-15

Union: This operator merges the rows of two input tables into a single output table; the result contains all rows that occur in at least one of the input tables Intersection: This operator also accepts two input tables; the result consists of all rows that occur in both input tables Minus: Again, based on two input tables, this operator produces a result that consists of those rows that occur in the first table but do not occur in the second table Note that this operator is not symmetric; A MINUS B is not the same as B MINUS A This operator is also referred to as difference (Cartesian) product: From two input tables, all possible combinations are generated by concatenating a row from the first table with a row from the second table (Natural) Join: From two input tables, one result table is produced.

A full discussion of the wide range of sensitizing chemicals found in cosmeticbased products is beyond the scope of this chapter, but a list of the most common allergens is found in Table 18-1 Two categories deserve special attention, however, with regard to cosmetic-based contact allergies, most notably fragrances and preservatives

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