mathematics, a half-integer is a number of the form n + 1 2 , {\displaystyle n+{\tfrac {1}{2}},} where n {\displaystyle n} is an integer. For example,...

subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin ⁠1/2⁠, spin ⁠3/2⁠, etc.) and obey the Pauli exclusion principle...

Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (halves of odd integers; a mixture of integers and half-integers...

(n-k+1)}}\left(2z\right)^{-k}} . This allows for the Matérn covariance of half-integer values of ν {\displaystyle \nu } to be expressed as C p + 1 / 2 ( d )...

a half-integer, the wasted space is at least proportional to its square root. The precise asymptotic growth rate of the wasted space, even for half-integer...

exclusion principle: observations of exclusion imply half-integer spin, and observations of half-integer spin imply exclusion. Spin is described mathematically...

integer. Rounding a number x to the nearest integer requires some tie-breaking rule for those cases when x is exactly half-way between two integers –...

Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state...

an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have half odd-integer...

mathematics. Its particular values can be expressed in closed form for integer, half-integer, and some other rational arguments, but no simple expressions are...

statistics applies to identical and indistinguishable particles with half-integer spin (1/2, 3/2, etc.), called fermions, in thermodynamic equilibrium...

cases are when α {\displaystyle \alpha } is an integer or half-integer. Bessel functions for integer α {\displaystyle \alpha } are also known as cylinder...

elementary particles with integer spin (bosons) is symmetric under the exchange of any two particles, whereas for particles with half-integer spin (fermions),...

In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. For...

for every energy eigenstate of a time-reversal symmetric system with half-integer total spin, there is another eigenstate with the same energy related...

are classified according to their spin. Fermions have half-integer spin while bosons have integer spin. All the elementary particles of the Standard Model...

Hankinson, John; Sprinkle, Mike; Berger, Claire; de Heer, Walt A. (2009). "Half integer quantum Hall effect in high mobility single layer epitaxial graphene"...

conjecture, states that every nonnegative integer can be represented as a sum of four non-negative integer squares. That is, the squares form an additive...

statistics, which describes the behaviour of fermions, particles with half-integer spin. His 1930 monograph, The Principles of Quantum Mechanics, is one...

particles. Baryons are also classified as fermions because they have half-integer spin. The name "baryon", introduced by Abraham Pais,: 457  comes from...

The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems...

{\displaystyle l=m/2} , where l {\displaystyle l} is then either an integer or a half-integer, and the dimension is 2 l + 1 {\displaystyle 2l+1} . The representations...

{\displaystyle z} except non-positive integers, and Γ ( n ) = ( n − 1 ) ! {\displaystyle \Gamma (n)=(n-1)!} for every positive integer ⁠ n {\displaystyle n} ⁠. The...

which have integer values of spin. In contrast, particles that follow Fermi-Dirac statistics are called fermions and have half-integer spins. At low...

existence of a symmetry between particles with integer spin (bosons) and particles with half-integer spin (fermions). It proposes that for every known...

is differentiated via the spin–statistics theorem: it is half-integer for fermions, and integer for bosons. v t e Notes: [†] An anti-electron (e+ ) is conventionally...

\beta } onto the line through α {\displaystyle \alpha } is an integer or half-integer multiple of α {\displaystyle \alpha } . Equivalent ways of writing...

frequency and the audio carrier frequency a half-integer multiple of the line rate. The sum of these two half-integers implies that the distance between the...

leads to quantum numbers that take values in discrete sets of integers or half-integers; although they could approach infinity in some cases. The tally...

such as s = ⁠1/2⁠ for all electrons. It is an integer for all bosons, such as photons, and a half-odd-integer for all fermions, such as electrons and protons...