Where Z is a normalization constant, " A " is a symmetric positive definite matrix ( inverse covariance matrix a . k . a . precision matrix ) and " b " is the shift vector.
22.
The function \ lambda ( \ phi ) \; plays the same role as the cosmological constant in GR . G _ N \; is a dimensionless normalization constant that fixes the present-day value of G \;.
23.
Where " z " is in the upper half-plane and the normalization constant " m " " k " & minus; 1 assures that the image of a form with integer Fourier coefficients has integer Fourier coefficients.
24.
Where w _ 0, w, R, and \ zeta ( z ) are the waist, spot size, radius of curvature, and Gouy phase shift as given for a Gaussian beam; E _ 0 is a normalization constant; and H _ k is the th physicist's Hermite polynomial.
25.
In the discriminative approach, probability for a context state k given context C _ l is modeled directly by the exponential of an affine function of the context account profile where C _ l ( j, a ) is the context count profile with a normalization constant Z ( C _ l ) normalizes the probability to 1.
26.
Here k = \ sqrt { 2m E } / \ hbar and \ delta _ s =-k \ cdot r _ 0 is the s-wave phase shift ( the phase difference between incoming and outgoing wave ), which is fixed by the boundary condition u ( r _ 0 ) = 0; A is an arbitrary normalization constant.
27.
To explain the relationship between body mass and temperature, building on earlier work showing that the effects of both body mass and temperature could be combined multiplicatively in a single equation, the two equations above can be combined to produce the primary equation of the MTE, where " b " o is a normalization constant that is independent of body size or temperature:
28.
Metabolic rate scales with the mass of an organism of a given species according to Kleiber's law where " B " is whole organism metabolic rate ( in watts or other unit of power ), " M " is organism mass ( in kg ), and " B " o is a mass-independent normalization constant ( given in a unit of power divided by a unit of mass.
29.
Where " s " is the dimension of \ boldsymbol \ eta and \ nu > 0 and \ boldsymbol \ chi are hyperparameters ( parameters controlling parameters ) . ? corresponds to the effective number of observations that the prior distribution contributes, and \ boldsymbol \ chi corresponds to the total amount that these pseudo-observations contribute to the sufficient statistic over all observations and pseudo-observations . f ( \ boldsymbol \ chi, \ nu ) is a normalization constant that is automatically determined by the remaining functions and serves to ensure that the given function is a probability density function ( i . e . it is normalized ).
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