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The total spin is always a fixed multiple of the basic unit ℏ : 1/2 for quarks and leptons, 1 for photons and other ordinary gauge bosons, 2 for gravitons, and in theory 0 for Higgs particles. … For ordinary massive particles in d -dimensional space the group is Spin( d ), while for massless particles it is E ( d -1) (the Euclidean group).
Specially constructed transcendental numbers Numbers known to be transcendental include ones whose digit sequences contain 1's only at positions n!
1- and 2-connection [network] clusters Clusters with just one or two dangling connections can always in effect be thought of just as adding extra structure to single connections in a network.
Note that a rather different way to get a somewhat similar ground state is to consider a spin glass, in which the standard Ising model energy function is used, but multiplied by -1 or +1 at random for each spin.
The effective mass for massive particles increases by a factor 1/Sqrt[1 - v 2 /c 2 ] at speed v , making it take progressively more energy to increase v .
Networks representing possible sequences of black and white cells that can occur at successive steps in the evolution of several class 1 and 2 cellular automata.
The system generates a dark gray stripe on the left at all positions that correspond to any product of numbers other than 1.
In every picture both x and y run from 1 to 127. d[n] stands for IntegerDigits[n, 2, 7] .
Representations of notable systems in mathematics are: (1) semigroup theory, (2) commutative group theory, (3) basic logic, (4) commutative semigroup theory, (5) squag theory, (6) group theory, (7) junctional calculus, (8) equivalential calculus and (9) implicational calculus.
Frequencies of [cellular automaton] classes The pie charts below show results for 1D totalistic cellular automata with k colors and range r .
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