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Muons, a subatomic particle, travel at a speed such that they have a relatively high Lorentz factor and therefore experience extreme time dilation. Since muons have a mean lifetime of just 2.2 μs, muons generated from cosmic-ray collisions 10 km (6.2 mi) high in Earth's atmosphere should be nondetectable on the ground due to their decay rate ...
In his theory, the longitudinal mass = and the transverse mass =, where is the Lorentz factor and is the rest mass of the electron. [5] The concept of (transverse) electromagnetic mass m T {\displaystyle m_{T}} , which was based on specific models of the electron, was later transmuted into the purely kinematical concept of relativistic mass ...
Below are few ultrarelativistic approximations when .The rapidity is denoted : Motion with constant proper acceleration: d ≈ e aτ /(2a), where d is the distance traveled, a = dφ/dτ is proper acceleration (with aτ ≫ 1), τ is proper time, and travel starts at rest and without changing direction of acceleration (see proper acceleration for more details).
A k-factor of a graph is a spanning k-regular subgraph, and a k-factorization partitions the edges of the graph into disjoint k-factors. A graph G is said to be k-factorable if it admits a k-factorization. In particular, a 1-factor is a perfect matching, and a 1-factorization of a k-regular graph is a proper edge coloring with k colors.
In an inertial reference frame a free particle has a straight world line. In a non-inertial reference frame the world line of a free particle is curved. Take the example of the fall of an object dropped without initial velocity from a rocket. The rocket has a uniformly accelerated motion with respect to an inertial reference frame.
with a corresponding factor graph shown on the right. Observe that the factor graph has a cycle. If we merge (,) (,) into a single factor, the resulting factor graph will be a tree. This is an important distinction, as message passing algorithms are usually exact for trees, but only approximate for graphs with cycles.
In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz. For example, the following laws, equations, and theories respect Lorentz symmetry:
Reinhard Diestel (born 1959) [1] is a German mathematician specializing in graph theory, including the interplay among graph minors, matroid theory, tree decomposition, and infinite graphs. He holds the chair of discrete mathematics at the University of Hamburg .