(M2 ) The torsion submodule is a direct summand : i . e ., there exists a complementary submodule P of M such that M = T \ oplus P.
32.
The rank-\ mu update of the covariance matrix, that is, the right most summand in the update equation of C _ k, maximizes a log-likelihood in that
33.
The function w is an auxiliary function defined via v up to a holomorphic summand, E is a real parameter corresponding to the energy level of the related 2-dimensional Schr�dinger equation
34.
Where " p " is a prime number that is perfect squares is divisible by such a " p " then each summand is divisible by " p ".
35.
From a pedestrian point of view, it seems that the denominator in the summand, [ ln ( m ) ln ( n-m ) ] flattens out as n tends to infinity.
36.
A direct summand of a serial module is not necessarily serial, as was proved by Puninski, but direct summands of " finite " direct sums of uniserial modules are serial modules.
37.
The notation allows moving boundary conditions of summations ( or integrals ) as a separate factor into the summand, freeing up space around the summation operator, but more importantly allowing it to be manipulated algebraically.
38.
As every *-representation is a direct sum of cyclic representations, it follows that every *-representation of " A " is a direct summand of some sum of copies of the universal representation.
39.
:where the value of the summand is taken to be zero when \ theta + 2 \ pi n-\ mu \ le 0, c is the scale factor and \ mu is the location parameter.
40.
Treating this system by means of time-dependent perturbation theory, one finds that the most likely transitions of the electron from one state to the other occur due to the summand of W ( t ) written as
