# half-integral

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## half-in·te·gral

(hăf′ĭn′tĭ-grəl, häf′-)
Having an odd integer as a numerator and 2 as a denominator. Used of a fraction.
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The sequence of these integers--for arbitrary integer or half-integer values of [alpha]--is found in the On-Line Encyclopedia of Integer Sequences [https://oeis.org/ol.html] as A004523 ["two even followed by one odd"] and as A232007 ["maximal number of moves needed to reach every square by a knight from a fixed position on an n x n chessboard, or -1 if it is not possible to reach every square"].)
All the Q(k, [alpha]) formulas we have (Appendix E), for nonnegative half-integer and integer values of [alpha], have roots (in unit steps) from k = -[alpha] - 1 downwards to k = -(1/4)[(-1).sup.[alpha]]([(-1).sup.[alpha]](10[alpha] + 1) - 1).
interpretation of moving particles with the integer or half-integer
a half-integer ray system  by means of which it is possible to
Another class of examples that use half-integer edge sequences appears in .
It is also shown that any half-integer point in I, as the additional sampling point, is optimal.
He explains the action approach, including its relation to Maxwell's equation and Dirac fields, then examines continuous symmetries and conservation laws, magnetostatics, multivalued fields in superfluids and superconductors, magnetic monopoles, electric charge confinement, multivalued mapping from ideal crystals to crystals with defects, defect melting, relativistic mechanics in curvilinear coordinates, torsion and curvature from defects and embedding, mutivalued mapping, field equations of gravitation, fields of integer spin, particles with half-integer spins, covariant conservation gravitation of spinning matter as a gauge theory, evanescent properties of torsion in gravity, the teleparallel theory of gravitation embedding, and emerging gravity.
at the half-integer points may not be averaged but computed.
The interpolation procedure must also take into account that the velocities are only solved for at two of the four surrounding half-integer nodes.
When the well width is approximately equal to an integer or half-integer multiple of the electron wavelength, a resonance condition occurs.
However, his progress was blocked by conventional wisdom, which assumed that neutron- and proton-like particles called baryons had to have half-integer values of isotopic spin, e.g.
Making a left half-shift transformation and summing an over the positive half-integers 1/2, 3/2, 5/2, ...

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