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In network science, the Configuration Model is a family of random graph models designed to generate networks from a given degree sequence. Unlike simpler models such as the ErdÅ‘s–Rényi model, Configuration Models preserve the degree of each vertex as a pre-defined property. This flexibility allows the modeler to construct networks with ...
To convert the standard form to factored form, one needs only the quadratic formula to determine the two roots r 1 and r 2. To convert the standard form to vertex form, one needs a process called completing the square. To convert the factored form (or vertex form) to standard form, one needs to multiply, expand and/or distribute the factors.
A vertex configuration can also be represented as a polygonal vertex figure showing the faces around the vertex. This vertex figure has a 3-dimensional structure since the faces are not in the same plane for polyhedra, but for vertex-uniform polyhedra all the neighboring vertices are in the same plane and so this plane projection can be used to visually represent the vertex configuration.
The relations can be made apparent by examining the vertex figures obtained by listing the faces adjacent to each vertex (remember that for uniform polyhedra all vertices are the same, that is vertex-transitive). For example, the cube has vertex figure 4.4.4, which is to say, three adjacent square faces.
This is the generating function for partitions, and is also written as q 1/24 times the weight −1/2 modular form 1/η (the reciprocal of the Dedekind eta function). The rank n free boson then has an n parameter family of Virasoro vectors, and when those parameters are zero, the character is q n/24 times the weight −n/2 modular form η −n.
PDFCreator is an application for converting documents into Portable Document Format format on Microsoft Windows operating systems. It works by creating a virtual printer that prints to PDF files, and thereby allows practically any application to create PDF files by choosing to print from within the application and then printing to the PDFCreator printer.
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