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(after multiplying numerator and denominator of the rst fraction by z). But note, by eq. (574), that z n ! 0 as n becomes in nitely great. Thus the nal fraction above has the limiting value of z= z 1 , and hence the z-transform of the unit-step sequence is z 577 F z z 1 Problem 295 Verify, to your satisfaction, that the suggested operation on eq. (576) does lead to the nal result of eq. (577). Another useful DT sequence* is the linear rise of Fig. 334, where T is the constant time between samples, as usual. The z-transform can be found as follows. Note that Fig. 334 is the sampled form of the CT function v t t, so that here v nT nT as you can see from the gure. Thus, upon substituting nT in place of v nT in eq. (573) we have that (remembering that T is constant) F z T

578

} // Verify start URL. else if (verifyUrl(startUrl) == null) { errorList.add("Invalid Start URL."); }

The above in nite-series form of the answer can be put into closed form by carrying out the following algebraic manipulations.

If either of these checks fails, an error message is added to the error list. Next, the Max URLs to Crawl combo box value is validated:

* Notations such as v t ; x t , and so on denote continuous-time analog signals, while v nT ; x nT , and so on denote their sampled ( discrete ) form. For convenience we ll often abbreviate continuous time as CT and discrete time as DT.

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Let us suppose that, after some experimentation, we decide to try multiplying both sides of eq. (578) by z. Doing this, and noting that zz 1 z0 1, eq. (578) becomes zF z T 1 2z 1 3z 2 4z 3 5z 4 Now take the algebraic sum of the above equation and eq. (578), thus getting 1 z F z T 1 z 1 z 2 z 3 z 4 which, upon multiplying both sides by 1, becomes z 1 F z T 1 z 1 z 2 z 3 z 4 But note that, by eq. (576), the quantity inside the parentheses on the right-hand side is equal to the z-transform of the unit-step sequence, which, by eq. (577) equals z= z 1 . Thus, making this substitution into the last equation and then solving for F z , you can verify that the z-transform of the linear-rise sequence of Fig. 334 is equal to F z Tz z 1 2 579

// Validate that Max URLs is either empty or is a number. int maxUrls = -1; String max = ((String) maxComboBox.getSelectedItem()).trim(); if (max.length() > 0) { try { maxUrls = Integer.parseInt(max); } catch (NumberFormatException e) { } if (maxUrls < 1) { errorList.add("Invalid Max URLs value."); } }

Next consider the important continuous-time relationship v t bt , this being called the negative exponential function, where b is a constant. From Fig. 18-A (note 13 in Appendix), it follows that in discrete time the negative exponential function would appear in sampled form as in Fig. 335.

Thus the CT function v t bt becomes the DT sequence v nT bnT , and upon substituting this value into eq. (573) we have that F z

Validating the maximum number of URLs to crawl is a bit more involved than the other validations in this method. This is because the Max URLs to Crawl field can either contain a positive number that indicates the maximum number of URLs to crawl or can be left blank to indicate that no maximum should be used. Initially, maxUrls is defaulted to 1 to indicate no maximum. If the user enters something into the Max URLs to Crawl field, it is validated as being a valid numeric value with a call to Integer.parseInt( ). Integer.parseInt( ) converts a String representation of an integer into an int value. If the String representation cannot be converted to an integer, a NumberFormatException is thrown and the maxUrls value is not set. Next, maxUrls is checked to see if it is less than 1. If so, an error is added to the error list. Next, the Matches Log File and Search String fields are validated:

580

The reason our fat nation keeps getting fatter despite the lowest placement of fats and oils on the pyramid is that the pyramid fails to take into account the difference between good fats and bad ones. This is a major oversight. Before we even get to the fats and oils category at the very top of the pyramid, Americans, thanks to the generality of the government guidelines, will have consumed far too much saturated fat in the form of dairy and meat, as well as hydrogenated fats from most convenience foods; but they will not have eaten enough of the beneficial unsaturated fat found in fish (especially cold-water fish), whole grains, nuts, and seeds. The government s advice that fats be consumed sparingly is undermined by our heavy reliance on saturated fat laden meat, dairy, and convenience foods

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