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We now give domain-relational-calculus queries for the examples that we considered earlier Note the similarity of these expressions and the corresponding tuplerelational-calculus expressions Find the loan number, branch name, and amount for loans of over $1200: {< l, b, a > | < l, b, a > loan a > 1200} Find all loan numbers for loans with an amount greater than $1200: {< l > | b, a (< l, b, a > loan a > 1200)} Although the second query appears similar to the one that we wrote for the tuple relational calculus, there is an important difference In the tuple calculus, when we write s for some tuple variable s, we bind it immediately to a relation by writing s r However, when we write b in the domain calculus, b refers not to a tuple, but rather to a domain value Thus, the domain of variable b is unconstrained until the subformula < l, b, a > loan constrains b to branch names that appear in the loan relation For example, Find the names of all customers who have a loan from the Perryridge branch and nd the loan amount:

The McGraw Hill Companies, 2001

3

SOLUTION The function has a multiple pole at s = 2 Hence, we can see that it will be stable The inverse Laplace transform of the function is given by h(t) = 3te 2t A plot of the function is shown in Fig 14-5 We see that the function steeply rises to a maximum (behavior due to the monomial term) and then it quickly decays when the exponential becomes dominant It s easy to see that the maximum occurs at t = 05 since dh = 3e 2t 6te 2t = 0 dt t = 05 Next we consider sinusoidal functions Clearly sinusoidal waveforms are bounded and so (141) is satis ed The poles in the case of a sinusoidal transfer function will be complex Let s consider the following function H (s) = 1 (s 2)(s + 2) (146)

window) to move to the section of the Pinnacle Expression window shown in Figure 11-2

{< c, a > | l (< c, l > borrower b (< l, b, a > loan b = Perryridge ))} Find the names of all customers who have a loan, an account, or both at the Perryridge branch: {< c > | l (< c, l > borrower b, a (< l, b, a > loan b = Perryridge )) a (< c, a > depositor b, n (< a, b, n > account b = Perryridge ))} Find the names of all customers who have an account at all the branches located in Brooklyn: {< c > | n (< c, n > customer ) x, y, z (< x, y, z > branch y = Brooklyn a, b (< a, x, b > account < c, a > depositor ))} In English, we interpret this expression as The set of all (customer-name) tuples c such that, for all (branch-name, branch-city, assets) tuples, x, y, z, if the branch city is Brooklyn, then the following is true : There exists a tuple in the relation account with account number a and branch name x There exists a tuple in the relation depositor with customer c and account number a