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This help topic contains 533 unique words. Using the Sort cmdlet is fast and simple, but it doesn t cover everything we said we wanted to do, because it doesn t give the frequency of use. Let s look at another approach: using the Foreach-Object cmdlet and a hashtable. Using hashtables to count unique words In the previous example, we used the -unique parameter to Sort-Object to generate a list of unique words. Now we ll take advantage of the set-like behavior of hashtables to do the same thing, but in addition we will be able to count the number of occurrences of each word.



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The gamma function can be de ned in terms of complex variable z provided that Re(z) > 0 as follows: ( z ) = t z 1e t dt





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In mathematics, a set is simply a collection of unique elements. This is how the keys work in a hashtable. Each key in a hashtable occurs exactly once. Attempting to add a key more than once will result in an error. In PowerShell, assigning a new value to an existing key simply replaces the old value associated with that key. The key itself remains unique. This turns out to be a powerful technique, because it s a way of building index tables for collections of objects based on arbitrary property values. These index tables let us run database-like operations on object collections. See section B.9 for an example of how you can use this technique to implement a SQL-like join operation on two collections of objects.

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FIGURE 18-1 Glycolic acid is an irritant that can result in keratinolysis In this gure, pink tender plaques occurred on the cheeks 1 day after a 30% glycolic acid peel processes That is, with each subsequent dose of a chemical the ability to remember that chemical for future interactions becomes more likely For example, with the hepatitis B vaccine, three shots are required for establishing long-lasting and effective immunity, or memory of that chemical; conversely, a tetanus vaccine must be boosted to guarantee memory Like the tetanus, the more potent chemicals may only require a single dose, such as poison ivy In most cases of ACD, however, the shots are mini-doses that taken sequentially over a given period of time result in the individual being sensitized to that chemical routinely exposed These chemicals usually have a molecular weight less than 500 Da allowing them to penetrate the skin or mucous membranes and activate an immunologic cascade2,3 Subsequent to entry into the skin these chemicals are taken up by epidermal immunologic cells (Langerhans cells) and further processed for presentation to na ve T lymphocytes This process of chemical capture and presentation is known as the induction phase of sensitization With induction there is clonal expansion of memory T cells, each inheriting the capability to mount an immune response upon reexposure to the allergenic chemical Upon reexposure, or challenge, the elicitation phase of sensitization ensues, which involves a complex interplay between immune cells (ie, Langerhans, lymphocytes, and keratinocytes) Each cell releases its respective cytokine repertoire leading

Once again, we split the document into a stream of words. Each word in the stream will be used as the hashtable key, and we ll keep the count of the words in the value. Here s the script:

(111)

PS (18) > $words | % {$h=@{}} {$h[$_] += 1}

It s not really much longer than the previous example. We re using the % alias for Foreach-Object to keep it short. In the begin clause in Foreach-Object, we re initializing the variable $h to hold the resulting hashtable. Then, in the process scriptblock, we increment the hashtable entry indexed by the word. We re taking advantage of the way arithmetic works in PowerShell. If the key doesn t exist yet, the hashtable returns $null. When $null is added to a number, it is treated as zero. This allows the expression

We can show that Eq (111) is convergent in the right-hand plane by examining its behavior at t = 0 and as t Using | z | Re z we have t z 1e t t Re z 1 This tells us that Eq (111) is nite at t = 0 As t , note that we have t z 1e t t Re z 1e t e t / 2 This shows that the integral is convergent for large t If n is a positive integer, then (n + 1) = n(n 1) 1 = n! (112)

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