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The re nement from an initial entity set into successive levels of entity subgroupings represents a top-down design process in which distinctions are made explicit The design process may also proceed in a bottom-up manner, in which multiple entity sets are synthesized into a higher-level entity set on the basis of common features The database designer may have rst identi ed a customer entity set with the attributes name, street, city, and customer-id, and an employee entity set with the attributes name, street, city, employee-id, and salary There are similarities between the customer entity set and the employee entity set in the sense that they have several attributes in common This commonality can be expressed by generalization, which is a containment relationship that exists between a higher-level entity set and one or more lower-level entity sets In our example, person is the higher-level entity set and customer and employee are lower-level entity sets Higher- and lower-level entity sets also may be designated by the terms superclass and subclass, respectively The person entity set is the superclass of the customer and employee subclasses For all practical purposes, generalization is a simple inversion of specialization We will apply both processes, in combination, in the course of designing the E-R

The McGraw Hill Companies, 2001

schema for an enterprise In terms of the E-R diagram itself, we do not distinguish between specialization and generalization New levels of entity representation will be distinguished (specialization) or synthesized (generalization) as the design schema comes to express fully the database application and the user requirements of the database Differences in the two approaches may be characterized by their starting point and overall goal Specialization stems from a single entity set; it emphasizes differences among entities within the set by creating distinct lower-level entity sets These lower-level entity sets may have attributes, or may participate in relationships, that do not apply to all the entities in the higher-level entity set Indeed, the reason a designer applies specialization is to represent such distinctive features If customer and employee neither have attributes that person entities do not have nor participate in different relationships than those in which person entities participate, there would be no need to specialize the person entity set Generalization proceeds from the recognition that a number of entity sets share some common features (namely, they are described by the same attributes and participate in the same relationship sets) On the basis of their commonalities, generaliza-

CHAPTER 2:

EXAMPLE 6-4 Suppose that the current owing through a 2 F capacitor is i(t) = 2e 3t Find the energy in the capacitor for 0 t 2 s The initial voltage across the capacitor is 1 V SOLUTION First we nd the voltage as a function of time v(t) = 1 + 1 2

The McGraw Hill Companies, 2001

2

tion synthesizes these entity sets into a single, higher-level entity set Generalization is used to emphasize the similarities among lower-level entity sets and to hide the differences; it also permits an economy of representation in that shared attributes are not repeated

FIGURE 2-7

.

We call a circuit consisting of a resistor and capacitor an RC circuit Initially, the capacitor is connected to a voltage source by a switch This allows the capacitor to charge up and attain an initial voltage When the switch is thrown, the connection between the capacitor and the voltage source is broken and the capacitor is connected to the resistor When this happens, the elements in the RC circuit start off with initial voltages and currents that decay rapidly to zero as the capacitor discharges through the resistor In fact, the voltages and currents decay exponentially We call such rapidly decaying voltages and currents transients The initial circuit is shown in Fig 6-6, where we see the capacitor connected to a voltage source There is an open circuit between the capacitor and the resistor so nothing is happening to the resistor Initially, it is trivial to see that applying KVL to the closed loop containing the voltage source and the capacitor puts a voltage V across the capacitor This will be the initial condition when the switch is thrown to the right, disconnecting the voltage source and connecting the capacitor to the resistor When this is done, we are left with the circuit shown in Fig 6-7 To solve this circuit, we can apply KCL Take a node at the top of the resistor and suppose that the current is owing in the clockwise direction If we take +