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Indeed, a graph has treewidth at most 2 if and only if it has branchwidth at most 2, if and only if every biconnected component is a series–parallel graph. [4] [5] The maximal series–parallel graphs, graphs to which no additional edges can be added without destroying their series–parallel structure, are exactly the 2-trees.
Graphical interpretation of the parallel operator with =.. The parallel operator ‖ (pronounced "parallel", [1] following the parallel lines notation from geometry; [2] [3] also known as reduced sum, parallel sum or parallel addition) is a binary operation which is used as a shorthand in electrical engineering, [4] [5] [6] [nb 1] but is also used in kinetics, fluid mechanics and financial ...
In electrochemistry, cell notation or cell representation is a shorthand method of expressing a reaction in an electrochemical cell.. In cell notation, the two half-cells are described by writing the formula of each individual chemical species involved in the redox reaction across the cell, with all other common ions and inert substances being ignored.
Cyclic reduction is a numerical method for solving large linear systems by repeatedly splitting the problem. Each step eliminates even or odd rows and columns of a matrix and remains in a similar form. The elimination step is relatively expensive but splitting the problem allows parallel computation.
This postulate does not specifically talk about parallel lines; [1] it is only a postulate related to parallelism. Euclid gave the definition of parallel lines in Book I, Definition 23 [2] just before the five postulates. [3] Euclidean geometry is the study of geometry that satisfies all of Euclid's axioms, including the parallel postulate.
The expression series-parallel can apply to different domains: Series and parallel circuits for electrical circuits and electronic circuits; Series-parallel partial order, in partial order theory; Series–parallel graph in graph theory; Series–parallel networks problem, a combinatorial problem about series–parallel graphs
A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of parallel (straight) lines. It can also be defined as a curve whose points are at a constant normal distance from a given curve. [1]
Any line not parallel to direction is mapped onto a line; any line parallel to is mapped onto a point. Parallel lines are mapped on parallel lines, or on a pair of points (if they are parallel to ). The ratio of the length of two line segments on a line stays unchanged. As a special case, midpoints are mapped on midpoints.