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The compressed exponential function (with β > 1) has less practical importance, with the notable exceptions of β = 2, which gives the normal distribution, and of compressed exponential relaxation in the dynamics of amorphous solids. [1] In mathematics, the stretched exponential is also known as the complementary cumulative Weibull distribution.
In stretched tuning, two notes an octave apart, whose fundamental frequencies theoretically have an exact 2:1 ratio, are tuned slightly farther apart (a stretched octave). If the frequency ratios of octaves are greater than a factor of 2, the tuning is stretched ; if smaller than a factor of 2, it is compressed ."
Given the above, most texture compression algorithms involve some form of fixed-rate lossy vector quantization of small fixed-size blocks of pixels into small fixed-size blocks of coding bits, sometimes with additional extra pre-processing and post-processing steps. Block Truncation Coding is a very simple example of this family of algorithms.
Excel 2.0 was released a month before Windows 2.0, and the installed base of Windows was so low at that point in 1987 that Microsoft had to bundle a runtime version of Windows 1.0 with Excel 2.0. [129] Unlike Microsoft Word, there never was a DOS version of Excel.
Besides differences in the schema, there are several other differences between the earlier Office XML schema formats and Office Open XML. Whereas the data in Office Open XML documents is stored in multiple parts and compressed in a ZIP file conforming to the Open Packaging Conventions, Microsoft Office XML formats are stored as plain single monolithic XML files (making them quite large ...
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y = a x k {\displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the exponent corresponding to ...
An example graph, with the properties of being planar and being connected, and with order 6, size 7, diameter 3, girth 3, vertex connectivity 1, and degree sequence <3, 3, 3, 2, 2, 1> In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations such as ...
Together with F, this makes 2 N +1 files that all compress into one of the 2 N files of length N. But 2 N is smaller than 2 N +1, so by the pigeonhole principle there must be some file of length N that is simultaneously the output of the compression function on two different inputs. That file cannot be decompressed reliably (which of the two ...