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Spectral layout is a class of algorithm for drawing graphs. The layout uses the eigenvectors of a matrix, such as the Laplace matrix of the graph, as Cartesian coordinates of the graph's vertices. The idea of the layout is to compute the two largest (or smallest) eigenvalues and corresponding eigenvectors of the Laplacian matrix of the graph ...
The same formula d 2 − r 2 may be extended to all points in the plane, regardless of whether they are inside or outside of C: points on C have zero power, and points inside C have negative power. [2] [3] [4] The power diagram of a set of n circles C i is a partition of the plane into n regions R i (called cells), such that a point P belongs ...
The circle diagram (also known as Heyland diagram or Heyland circle) is the graphical representation of the performance of the electrical machine [1] [2] [3] drawn in terms of the locus of the machine's input voltage and current. [4] It was first conceived by Alexander Heyland in 1894 and Bernhard Arthur Behrend in 1895.
Circular layouts are a good fit for communications network topologies such as star or ring networks, [1] and for the cyclic parts of metabolic networks. [2] For graphs with a known Hamiltonian cycle, a circular layout allows the cycle to be depicted as the circle, and in this way circular layouts form the basis of the LCF notation for Hamiltonian cubic graphs.
where A 1 and A 2 are the centers of the two circles and r 1 and r 2 are their radii. The power of a point arises in the special case that one of the radii is zero. If the two circles are orthogonal, the Darboux product vanishes. If the two circles intersect, then their Darboux product is
A diagram with four points, for example, represents a modulation scheme that can separately encode all 4 combinations of two bits: 00, 01, 10, and 11, and so can transmit two bits per symbol. Thus in general a modulation with N {\displaystyle N} constellation points transmits log 2 N {\displaystyle \log _{2}N} bits per symbol.
The radical axis of a pair of circles is defined as the set of points that have equal power h with respect to both circles. For example, for every point P on the radical axis of circles 1 and 2, the powers to each circle are equal: h 1 = h 2. Similarly, for every point on the radical axis of circles 2 and 3, the powers must be equal, h 2 = h 3.
In power engineering, a single-line diagram (SLD), also sometimes called one-line diagram, is a simplest symbolic representation of an electric power system. [1] [2] A single line in the diagram typically corresponds to more than one physical conductor: in a direct current system the line includes the supply and return paths, in a three-phase ...