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In 2016 a team of astronomers from Italy, Poland, and the U.K. reported [8] [9] observations of the light emitted by a neutron star (pulsar RX J1856.5−3754). The star is surrounded by a very strong magnetic field (10 13 G), and birefringence is expected from the vacuum polarization described by the Euler–Heisenberg Lagrangian.
Examples include lasers, electron microscopes, magnetic resonance imaging (MRI) devices and the components used in computing hardware. The study of semiconductors led to the invention of the diode and the transistor, which are indispensable parts of modern electronics systems, computer and telecommunications devices.
For planar graphs, the properties of being Eulerian and bipartite are dual: a planar graph is Eulerian if and only if its dual graph is bipartite. As Welsh showed, this duality extends to binary matroids: a binary matroid is Eulerian if and only if its dual matroid is a bipartite matroid, a matroid in which every circuit has even cardinality.
Phasor notation (also known as angle notation) is a mathematical notation used in electronics engineering and electrical engineering.A vector whose polar coordinates are magnitude and angle is written . [13] can represent either the vector (, ) or the complex number + =, according to Euler's formula with =, both of which have magnitudes of 1.
For example, in electromagnetic theory, ordinary light is described as a superposition of plane waves (waves of fixed frequency, polarization, and direction). As long as the superposition principle holds (which is often but not always; see nonlinear optics ), the behavior of any light wave can be understood as a superposition of the behavior of ...
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. [1] [2] [3] In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. [2]
In the 19th century, luminiferous aether (or ether), meaning light-bearing aether, was a theorized medium for the propagation of light. James Clerk Maxwell developed a model to explain electric and magnetic phenomena using the aether, a model that led to what are now called Maxwell's equations and the understanding that light is an ...
An Eulerian trail, [note 1] or Euler walk, in an undirected graph is a walk that uses each edge exactly once. If such a walk exists, the graph is called traversable or semi-eulerian. [3] An Eulerian cycle, [note 1] also called an Eulerian circuit or Euler tour, in an undirected graph is a cycle that uses each edge exactly once