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and du dx = exp(u) + C. dx We note for the record that the exponential function is the only function (up to constant multiples) that is its own derivative. This fact will come up later in our applications of the exponential exp(u) EXAMPLE 6.9

As corporate communications volumes increased, organizations realized the cost of telephone service was escalating. Originally, all long distance service was charged on a per minute basis. AT&T introduced a volume discount outbound calling plan called Wide Area Telephone Service [ 1 ] (WATS). For a monthly fixed payment, the organization got 240 hours of service to one of five bands across the country. Each band was priced, based on the distance from the originator s location. A typical company usually had a band 5 line and a band 1 or 2 to cover adjacent state calls. It took some analysis to determine the most cost-effective solution for each company s particular calling pattern. Foreign Exchange (FX) service provided a fixed rate-calling plan if a company had a large call volume for in-state locations. This is essentially subscribing to telephone service at the foreign central office location and leasing an extension cord from the telephone company to the home location. Originally, there were no usage charges on this line so the more you used it, the less expensive it was. Of course, long distance calls made from the foreign exchange were billed at the long-distance rate. A FX line is needed to each high volume calling location. Alternatively, a company could use a leased telephone line between locations. These lines went by several names: Terminal Interface Equipment (TIE) line, dedicated line, and a data line, when used for data. These are essentially point-to-point telephone lines that are available in two-wire or four-wire configurations. Because the difference in cost between two and four-wire connections was small (relative to the cost of the line), the four-wire option was preferred unless the company needed many lines. The next logical step was to use these TIE lines to connect PBXs at the various locations. Here again, there were no usage charges on these dedicated lines. A company with locations in Seattle, Phoenix, Atlanta, and headquarters in Chicago might have a hub and spoke arrangement of TIE lines from their headquarters to each regional office. Each location then might have FX lines to adjacent cities; for example, a company based in Seattle might have a FX line to Tacoma, Kent, and Everett (see Figure 3-1 ).

with a hydraulic drive will require a powerful motor and expensive, high flow-rate valves and tubing. Some builders have experimented with using a large spring to power the hammer and a high-torque motor or linear actuator to crank the hammer back and latch it after firing. While this can give a powerful hammer action, the increased reload time makes the concept questionable. A hammer that takes more than 5 seconds between shots may never manage to hit its opponent more than once or twice in an entire match. For optimum results, increase the hammer velocity as much as possible. Remember that your hammer may strike its opponent only partway through its stroke, so design for it to do most of its acceleration at the beginning of its travel.

1. Insert the HAI Web-Link II compact disc into your CDor DVD-ROM drive. 2. Select the Run command from the Start menu. 3. In the Run dialog box, type <drive>:setup (where drive is the letter of your CD- or DVD-ROM drive). 4. Follow the instructions provided on the screen.

DS3 C-Bit parity and performance parameters. In-service error detection and performance monitoring of DS3 traditionally uses either Bipolar Violations in the B3ZS interface code or the conventional parity check on the DS3 frame. The drawback with these two measurements is that errors in parity and interface code normally are corrected at intermediate points in the network, so they are not readily usable for end-to-end path monitoring, only for the previous span. Because there are very few frame bits in the DS3 frame, however, frame errors give an unreliable indication of overall payload performance. Conventional DS3 framing is designated M23 in the standards. A new framing application has been defined, called C-bit parity. Initially proposed by AT&T, the new DS3 frame structure is defined in ANSI T1.107. The idea behind C-bit parity is to provide a parity measurement that will pass through existing DS3 transmission equipment transparently, so that error performance data will accumulate along the DS3 path. The C-bits are not reset at intermediate points. In the C-bit parity application, the C-bits no longer are used for stuffing control; asynchronous DS2 tributary operation is not allowed. When carrying direct DS3 services or 28 DS1s, the C-bits are free and can be used for other purposes. Table 7.4 shows the disposition of frame overhead bits in the DS3 M-frame, which comprises 7 subframes, each of 680 bits. Each square in the matrix of Table 7.4 represents the designated frame overhead bit followed by 84 payload bits. The C-bits are carried in columns 3, 5, and 7. The remaining columns are the same as for M23 applications. The two P-bits in subframes 3 and 4 provide the conventional parity check on the payload bits (set to 11 for even and 00 for odd parity).

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Digital data signals are carried over Radio Frequency (RF) carrier signals on a cable system. Digital data utilizes cable modems, devices that convert digital information into a modulated RF signal and convert RF signals back to digital information. The conversion is performed by a modem at the subscriber premises, and again by head-end equipment handling multiple subscribers. Look at Figure 14-5 for a block diagram of the cable modem.