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e aX e bX = e (a + b)X; e X e −X = I; Using the above results, we can easily verify the following claims. If X is symmetric then e X is also symmetric, and if X is skew-symmetric then e X is orthogonal. If X is Hermitian then e X is also Hermitian, and if X is skew-Hermitian then e X is unitary.
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.
PDF/X-5pg: An extension of PDF/X-4p that enables the use of external graphical content in conjunction with a reference to an external ICC Profile for the output intent. PDF/X-5n: An extension of PDF/X-4p that allows the externally supplied ICC Profile for the output intent to use a color space other than Grayscale, RGB and CMYK.
In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y -axis which are half the maximum amplitude.
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Filters can be deleted by clicking the X next to "Edit." Create a filter. 1. Click Create filter. 2. Enter the parameters of your filter. 3. Click Save. Edit a filter. 1. Mouse over the filter's name. 2. Click Edit. 3. Enter the change you want to make. 4. Click Save.
For example, from the differential equation definition, e x e −x = 1 when x = 0 and its derivative using the product rule is e x e −x − e x e −x = 0 for all x, so e x e −x = 1 for all x. From any of these definitions it can be shown that the exponential function obeys the basic exponentiation identity.
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