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Two-frequency beats of a non-dispersive transverse wave. Since the wave is non-dispersive, phase and group velocities are equal. For an ideal string, the dispersion relation can be written as =, where T is the tension force in the string, and μ is the string's mass per unit length. As for the case of electromagnetic waves in vacuum, ideal ...
He confirmed the distribution of the spacings between non-trivial zeros using detailed numerical calculations and demonstrated that Montgomery's conjecture would be true and that the distribution would agree with the distribution of spacings of GUE random matrix eigenvalues using Cray X-MP.
In graph theory, a branch of mathematics, an undirected graph is called an asymmetric graph if it has no nontrivial symmetries. Formally, an automorphism of a graph is a permutation p of its vertices with the property that any two vertices u and v are adjacent if and only if p ( u ) and p ( v ) are adjacent.
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In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems.
An asymmetric graph is an undirected graph with only the trivial automorphism. A vertex-transitive graph is an undirected graph in which every vertex may be mapped by an automorphism into any other vertex. An edge-transitive graph is an undirected graph in which every edge may be mapped by an automorphism into any other edge.
An alternative to adding the axiom is to refer to incidence structures that do not satisfy the axiom as being trivial and those that do as non-trivial. Each non-trivial linear space contains at least three points and three lines, so the simplest non-trivial linear space that can exist is a triangle.
A graph with three components. In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting ...