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This time, we didn t get prompted, since we ve told the system that this certificate should always be trusted. So what exactly happened to the script It used to be one line long. Let s look at the beginning of the script. We ll use the Select-Object cmdlet to get the first 10 lines of the file:



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An important class of functions known as harmonic functions play an important role in many areas of applied mathematics, physics, and engineering We say that a function u( x , y) is a harmonic function if it satis es Laplace s equation in some domain of the x-y plane: 2u 2u + =0 x 2 y 2 (329)

FIGURE 11-2 A Normal desquamation of corneocytes leads to a smooth skin surface and radiance because of good light re ectance B Corneocytes in dry skin cling together leading to heaps and valleys that give skin a dull appearance and rough texture

PS (25) > gc test-script.ps1 | Select-Object -first 10 "Hello there" # # # # # # # # SIG # Begin signature block MIIEMwYJKoZIhvcNAQcCoIIEJDCCBCACAQExCzAJBgUrDgMCGgUAMGkGCisGAQQB gjcCAQSgWzBZMDQGCisGAQQBgjcCAR4wJgIDAQAABBAfzDtgWUsITrck0sYpfvNR AgEAAgEAAgEAAgEAAgEAMCEwCQYFKw4DAhoFAAQU0O2MiFZBx/X1iLwTml3Dg6o3 iOygggI9MIICOTCCAaagAwIBAgIQ0QlVf5hB+oZM3DApkhHZMTAJBgUrDgMCHQUA MCwxKjAoBgNVBAMTIVBvd2VyU2hlbGwgTG9jYWwgQ2VydGlmaWNhdGUgUm9vdDAe Fw0wNjA4MTMwMTM0MzFaFw0zOTEyMzEyMzU5NTlaMBoxGDAWBgNVBAMTD1Bvd2Vy U2hlbGwgVXNlcjCBnzANBgkqhkiG9w0BAQEFAAOBjQAwgYkCgYEAtB75pWZTD5Jo

How long is the file Let s check:





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Here, we have assumed that u( x , y) has continuous rst and second partial derivatives with respect to both x and y An important application of harmonic functions in physics and engineering is in the area of electrostatics, for example Harmonic functions also nd application in the study of temperature and uid ow It turns out that the Cauchy-Riemann equations can help us nd harmonic functions, as the next theorem illustrates THEOREM 34 Suppose that f ( z ) = u( x , y) + iv ( x , y) is an analytic function in a domain D If follows that u( x , y) and v ( x , y) are harmonic functions PROOF The proof is actually easy Since f (z) is analytic, then the Cauchy-Riemann equations are satis ed: u v = x y and v u = x y

Signing the file increased the size from one line to 27. As you can see, signing a file adds a lot of ugly comments to the end of the file. We can use the Get-AuthenticodeSignature to retrieve the signature information from the file:

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PS (28) > Get-AuthenticodeSignature test-script.ps1 | fl SignerCertificate : [Subject] CN=PowerShell User [Issuer] CN=PowerShell Local Certificate Root [Serial Number] D109557F9841FA864CDC30299211D931 [Not Before] 8/12/2006 6:34:31 PM

disruption in barrier function There are three rate-limiting enzymes involved in the synthesis of the main lipids of epidermal skin (Fig 11-4) They include 3-hydroxy-3-methylglutaryl coenzyme A (HMG-Co A) reductase (the rate-limiting enzyme in cholesterol synthesis), acetyl Co-A carboxylase (ACC), and the fatty acid synthase involved in the synthesis of free fatty acids and palmitoyl transferase (SPT), which is the regulatory enzyme for the synthesis of ceramides14,15 As expected, when skin barrier disruption occurs, the activity of these enzymes is enhanced in order to compensate for barrier dysfunction15 In addition, a group of transcription factors known as sterol regulatory element binding proteins (SREBPs) regulate cholesterol and fatty acid synthesis When decreased epidermal sterols are noted, the SREBPs are activated via proteolytic processes, enter the cell nucleus, and activate genes leading to increased

function method ([string]$name, [scriptblock] $script) { if (! $name) { elementSyntax "method name <value>" } new-object management.automation.PSScriptMethod ` $name,$script }

Taking the derivative of the second Cauchy-Riemann equation with respect to y gives 2u 2 v = y x y 2 Since partial derivatives commute (that is, their order does not matter) it is the case that 2 v 2 v = x y y x From which it follows that 2u 2u = 2 x 2 y 2u 2u + =0 x 2 y 2

We could continue to define keyword functions for all of the other member types, but to keep it simple, we ll stick with just these two. Having defined our keyword functions, we can look at the code that actually builds the object. First we need to create an empty PSObject with no methods or properties.

Next, execute the scriptblock that defines the body of this class. As mentioned previously, the result of that execution will be the set of members to attach to the new object we re creating.

So we ve shown that if a function is analytic, then the real part u( x , y) satis es Laplace s equation A similar procedure can be used to show that the imaginary part v ( x , y) is harmonic as well

Finally, attach the members to the object:

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