* NIST Definition of ampere and μ < sub > 0 </ sub >

) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is

Some authors require in addition that μ ( C ) < ∞ for every compact set C. If a Borel measure μ is both inner regular and outer regular, it is called a regular Borel measure.

Note that a locally finite Borel measure automatically satisfies μ ( C ) < ∞ for every compact set C.

* If G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g ) dμ ( h ) for x, y in L < sup > 1 </ sup >( G ).

μ < sub > e </ sub > has been set equal to 2.

In 1930, Stoner derived the internal energy-density equation of state for a Fermi gas, and was then able to treat the mass-radius relationship in a fully relativistic manner, giving a limiting mass of approximately ( for μ < sub > e </ sub >= 2. 5 ) 2. 19 · 10 < sup > 30 </ sup > kg.

If there is a change in the potential energy of a system ; for example μ < sub > 1 </ sub >> μ < sub > 2 </ sub > ( μ is Chemical potential ) an energy flow will occur from S < sub > 1 </ sub > to S < sub > 2 </ sub >, because nature always prefers low energy and maximum entropy.

The bottom two rows ' columns contain electron neutrino ( ν sub e ) and electron ( e ), muon neutrino ( ν sub μ ) and muon ( μ ), and tau neutrino ( ν sub τ ) and tau ( τ ), and Z sup 0 and W sup ± weak force.

f whereas for the μ or ν indexes one has the non-trivial relativistic rules, corresponding e. g. to the signature (+---).

The number e is called an index or Gödel number for the function f. A consequence of this result is that any μ-recursive function can be defined using a single instance of the μ operator applied to a ( total ) primitive recursive function.

Here e < sub > a </ sup >< sup > μ </ sup > is the vierbein and D < sub > μ </ sub > is the covariant derivative for fermion fields, defined as follows

Once a probability measure μ on the phase space is specified, one can define the ensemble average of an observable, i. e. real-valued function f defined on via this measure by

From this we can notice that for an average particle mass of μ times the atomic mass constant m < sub > u </ sub > ( i. e., the mass is μ u )

Another useful representation is available by means of double Taylor expansion of e < sup >( ln x − μ )< sup > 2 </ sup >/( 2σ < sup > 2 </ sup >)</ sup >.

: μ < sub > i </ sub > = μ < sub > i </ sub >< sup > std </ sup > + RT ln < sub > e </ sub > a < sub > i </ sub >

: μ < sub > i </ sub > = μ < sub > i </ sub >< sup > std </ sup > + RT ln < sub > e </ sub > f < sub > i </ sub >

Perhaps the most important restriction on the ETC framework for quark mass generation is that ETC interactions are likely to induce flavor-changing neutral current processes such as μ → e γ, K < sub > L </ sub > → μ e, and &# 124 ; Δ S &# 124 ; &# 61 ; 2 and &# 124 ; Δ B &# 124 ; &# 61 ; 2 interactions that induce and mixing.

A highest weight module is a module generated by a weight vector v, subject to for all weights μ, and for all i. Similarly, a quantum group can have a lowest weight representation and lowest weight module, i. e. a module generated by a weight vector v, subject to for all weights λ, and for all i.

Considering the drag on the moving particles due to the viscosity of the dispersant, in the case of low Reynolds number and moderate electric field strength E, the velocity of a dispersed particle v is simply proportional to the applied field, which leaves the electrophoretic mobility μ < sub > e </ sub > defined as:

When the evolution map Φ < sup > t </ sup > ( or the vector field it is derived from ) depends on a parameter μ, the structure of the phase space will also depend on this parameter.

A notable opioid for the purpose of relief of diarrhoea is loperamide which is only an agonist of the μ opioid receptors in the large intestine and does not have opioid affects in the central nervous system as it doesn't cross the blood – brain barrier in significant amounts.

The symbol μ denotes a positive measure: that is, a real-valued positive set function defined on a σ-algebra which is countably additive.

Any measure μ defined on the σ-algebra of Borel sets is called a Borel measure.

If μ is both inner regular and locally finite, it is called a Radon measure.

In this case, is the smallest σ-algebra that contains the open intervals of R. While there are many Borel measures μ, the choice of Borel measure which assigns for every interval is sometimes called " the " Borel measure on R. In practice, even " the " Borel measure is not the most useful measure defined on the σ-algebra of Borel sets ; indeed, the Lebesgue measure is an extension of " the " Borel measure which possesses the crucial property that it is a complete measure ( unlike the Borel measure ).

If X is Cauchy distributed with median μ and scale parameter γ, then the complex variable

Since μ is a function of x, we cannot simplify any further directly.

If the observed data X < sub > 1 </ sub >, ..., X < sub > n </ sub > are ( i ) uncorrelated, ( ii ) have a common mean μ, and ( iii ) have a common variance σ < sup > 2 </ sup >, then the sample average < span style =" text-decoration: overline "> X </ span > has mean μ and variance σ < sup > 2 </ sup > / n. If our null hypothesis is that the mean value of the population is a given number μ < sub > 0 </ sub >, we can use < span style =" text-decoration: overline "> X </ span > − μ < sub > 0 </ sub > as a test-statistic, rejecting the null hypothesis if < span style =" text-decoration: overline "> X </ span > − μ < sub > 0 </ sub > is large.

The constant μ < sub > 0 </ sub > is non-zero if you want to test whether the average of the difference is significantly different from μ < sub > 0 </ sub >.

Using the fact that μ is preserved by the Hamiltonian flow, we can show that indeed the time average exists for all observables.

The ensemble average is defined using μ.

However, when the temperature reaches the QCD energy scale ( T of order 10 < sup > 12 </ sup > kelvins ) or the density rises to the point where the average inter-quark separation is less than 1 fm ( quark chemical potential μ around 400 MeV ), the hadrons are melted into their constituent quarks, and the strong interaction becomes the dominant feature of the physics.

The traffic intensity, ρ, is the average arrival rate ( λ ) divided by the average service rate ( μ ):

A model is said to have a strict molecular clock if the expected number of substitutions per year μ is constant regardless of which species ' evolution is being examined.

If the coefficients of the basis functions in the molecular orbital are C < sub > μi </ sub > for the μ ' th basis function in the i ' th molecular orbital, the density matrix terms are:

If the highest weight is dominant and integral ( a weight μ is dominant and integral if μ satisfies the condition that is a non-negative integer for all i ), then the weight spectrum of the irreducible representation is invariant under the Weyl group for G, and the representation is integrable.

These terms apply to different operating conditions, but are related by common mechanical factors: input torque to the driving wheels, the wheel diameter, coefficient of friction ( μ ) between the driving wheels and supporting surface, and the weight applied to the driving wheels ( m ).

Left to right: Brain weight distributions in grams for Black women ( μ = 1158, σ = 119 ), White women ( μ = 1252, σ = 125 ), Black men ( μ = 1286, σ = 138 ), and White men ( μ = 1392, σ = 130 ).

where μ < sub > i </ sub > is the chemical potential per particle for an i-type particle, and N < sub > i </ sub > is the number of such particles.

The throughput can be analyzed mathematically by means of queueing theory, where the load in packets per time unit is denoted arrival rate λ, and the throughput in packets per time unit is denoted departure rate μ.

where the linear density μ is the mass per unit length of the string.

Proper motion may also be given by the angular changes per year in the right ascension ( μ < sub > α </ sub >) and declination ( μ < sub > δ </ sub >).

where f is the frequency, L is the length, T is the force and μ is the mass per unit length.

The total discharge, Q ( units of volume per time, e. g., m < sup > 3 </ sup >/ s ) is equal to the product of the permeability of the medium, k ( m < sup > 2 </ sup >), the cross-sectional area to flow, A ( units of area, e. g., m < sup > 2 </ sup >), and the pressure drop ( Pb-Pa ), all divided by the viscosity, μ ( Pa · s ) and the length over which the pressure drop is taking place.

where ρ is the density of water ( units of mass per volume ), v is the specific discharge ( not the pore velocity — with units of length per time ), d < sub > 30 </ sub > is a representative grain diameter for the porous media ( often taken as the 30 % passing size from a grain size analysis using sieves-with units of length ), and μ is the viscosity of the fluid.

where Q is the flowrate of the formation ( in units of volume per unit time ), k is the relative permeability of the formation ( typically in millidarcies ), A is the cross-sectional area of the formation, μ is the viscosity of the fluid ( typically in units of centipoise, and L is the length of the porous media the fluid will flow through.

The expected number of substitutions per site per year is often indicated with the Greek letter mu ( μ ).