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In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. The exponential of a variable is denoted or , with the two notations used interchangeably.
One of the reasons for the importance of the matrix exponential is that it can be used to solve systems of linear ordinary differential equations.The solution of = (), =, where A is a constant matrix and y is a column vector, is given by =.
Let Γ be the fundamental group corresponding to the spanning tree T.For every vertex x and edge y, G x and G y can be identified with their images in Γ.It is possible to define a graph with vertices and edges the disjoint union of all coset spaces Γ/G x and Γ/G y respectively.
The exact origins of the LTE lemma are unclear; the result, with its present name and form, has only come into focus within the last 10 to 20 years. [1] However, several key ideas used in its proof were known to Gauss and referenced in his Disquisitiones Arithmeticae. [2]
A graph with a loop having vertices labeled by degree. In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge. [1]
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). The opposite, a graph with only a few edges, is a sparse graph.
Denali is a granitic pluton, mostly pink quartz monzonite, lifted by tectonic pressure from the subduction of the Pacific Plate beneath the North American Plate; at the same time, the sedimentary material above and around the mountain was stripped away by erosion.