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7 Barrandon Y, Green H Cell migration is essential for sustained growth of keratinocyte colonies: the roles of transforming growth factor-alpha and epidermal growth factor Cell 1987;50:1131 8 Ando Y, Jensen PJ Epidermal growth factor and insulin-like growth factor I enhance keratinocyte migration J Invest Dermatol 1993;100:633 9 Blay J, Brown KD Epidermal growth factor promotes the chemotactic migration of cultured rat intestinal epithelial cells J Cell Physiol 1985;124:107 10 Carpenter G, Cohen S Human epidermal growth factor and the proliferation of human fibroblasts J Cell Physiol 1976;88:227 11 Reenstra WR, Yaar M, Gilchrest BA Effect of donor age on epidermal growth factor processing in man Exp Cell Res 1993;209:118 12 Ye J, Garg A, Calhoun C, et al Alterations in cytokine regulation in aged epidermis: implications for permeability barrier homeostasis and inflammation I IL-1 gene family Exp Dermatol 2002;11: 209 13 Colige A, Nusgens B, Lapiere CM Response to epidermal growth factor of skin fibroblasts from donors of varying age is modulated by the extracellular matrix J Cell Physiol 1990;145:450 14 Sporn MB The transforming growth factors-b In: Peptide Growth Factors and Their Receptors (Handbook of Experimental Pharmacology), edited by AB Roberts New York, NY: Springer-Verlag; 1990:419 15 Edwards DR, Murphy G, Reynolds JJ, et al Transforming growth factor beta modulates the expression of collagenase and metalloproteinase inhibitor EMBO J 1987;6:1899 16 Roberts AB, Sporn MB, Assoian RK, et al Transforming growth factor type beta: rapid induction of fibrosis and angiogenesis in vivo and stimulation of collagen formation in vitro Proc Natl Acad Sci U S A 1986;83:4167 17 Beck LS, DeGuzman L, Lee WP, et al One systemic administration of transforming growth factor-beta 1 reverses age- or glucocorticoid-impaired wound healing J Clin Invest 1993;92:2841 18 Mustoe TA, Pierce GF, Thomason A, et al Accelerated healing of incisional wounds in rats induced by transforming growth factor-beta Science 1987;237: 1333 19 Quaglino D Jr, Nanney LB, Kennedy R, et al Transforming growth factor-beta stimulates wound healing and modulates extracellular matrix gene expression in pig skin I Excisional wound model Lab Invest 1990;63:307 20 Hebda PA Stimulatory effects of transforming growth factor-beta and epidermal growth factor on epidermal cell outgrowth from porcine skin explant cultures J Invest Dermatol 1988;91:440 21 Quan T, He T, Kang S, et al Solar ultraviolet irradiation reduces collagen in photoaged human skin by blocking transforming growth factor-beta type II receptor/Smad signaling Am J Pathol 2004;165:741 22 Quan T, He T, Voorhees JJ, et al Ultraviolet irradiation induces Smad7 via induction of transcription factor AP-1 in.



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Now let s consider differentiation with respect to s That is: d d [ F( s)] = f (t ) e st dt ds ds The integration is with respect to t, so it seems fair enough that we can slide the derivative with respect to s on inside the integral This gives

PS >> >> >> >> PS 6 (5) > function fact ($x) { if ($x -lt 2) {return 1} $x * (fact ($x-1)) } (6) > fact 3

This is a simple function that returns a single value with no side-effects. In this case, it makes sense to use the return statement with value.

d d d [ F ( s)] = [ f (t ) e st ] dt = f (t ) ( e st )dt = t f (t )e st dt ds ds ds





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The factorial of a number x is the product of all positive numbers less than or equal to x. Therefore the factorial of 6 is 6*5*4*3*2*1 which is really 6 * (fact 5) which, in turn, is 6 * 5 * (fact 4) and so on down to 1. Factorials are useful in calculating permutations. Understanding permutations is useful if you re playing poker. This should not be construed as an endorsement for poker it s just kind of cool. Bill Gates plays bridge.

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So far we ve only talked about using functions as standalone statements. But what about using functions in pipelines After all, PowerShell is all about pipelines, so shouldn t you be able to use functions in pipelines Of course, the answer is yes with some considerations that need to be taken into account. The nature of a function is to take a set of inputs, process it, and produce a result. So how do we make the stream of objects from the pipeline available in a function This is accomplished through the $input variable. When a function is used in a pipeline, a special variable $input is available that contains an enumerator that allows you to process through the input collection. Let s see how this works:

28 29

PS >> >> >> >> >> (1) > function sum { $total=0; foreach ($n in $input) { $total += $n } $total }

We can move the minus sign to the other side, that is:

Here we ve defined a function sum that takes no arguments but has one implied argument, which is $input. It will add each of the elements in $input to $total

and then return $total. In other words, it will return the sum of all the input objects. Let s try this on a collection of numbers:

(810)

Clearly it works as intended. We said that $input is an enumerator. You may remember our discussion of enumerators from chapter 6 when we talked about the $foreach and $switch variables. The same principles apply here. You move the enumerator to the next element using the MoveNext() method and get the current element using the Current property. Here s the sum function rewritten using the enumerator members directly.

35 36

PS >> >> >> >> >> >> >> >> (3) > function sum2 { $total=0 while ($input.movenext()) { $total += $input.Current } $total }

L {cos tu(t )} =

Let s write a variation of this that works with something other than numbers. This time we ll write a function that has a formal parameter and also processes input. The parameter will be the name of the property on the input object to sum up. Here s the function definition:

PS >> >> >> >> >> >> >> >> >> (7) > function sum3 ($p) { $total=0 while ($input.MoveNext()) { $total += $input.current.$p } $total }

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