For summations in which the summand is given ( or can be interpolated ) by an integrable function of the index, the summation can be interpreted as a Riemann sum occurring in the definition of the corresponding definite integral.
42.
Much later, it was discovered by Nesterenko and Suslin and by Totaro that Milnor " K "-theory is actually a direct summand of the true " K "-theory of the field.
43.
While pure projective modules have not found as many applications as pure injectives, they are more closely related to the original work : A module is pure projective if it is a direct summand of a direct sum of finitely presented modules.
44.
In general, the Lie algebra of a compact Lie group decomposes as the Lie algebra direct sum of a commutative summand ( for which the corresponding subgroup is a torus ) and a summand on which the Killing form is negative definite.
45.
In general, the Lie algebra of a compact Lie group decomposes as the Lie algebra direct sum of a commutative summand ( for which the corresponding subgroup is a torus ) and a summand on which the Killing form is negative definite.
46.
The concept of " minimal free resolution " is well-defined in a strong sense, in that such a resolution is unique ( up to isomorphism of chain complexes ) and occurs as a direct summand in any free resolution.
47.
:: : Yes, excluding the case where every summand are zero, however some summand ( s ) must be negative, if we are talking about a field of characteristic zero ( which, in this case, I believe we are ).
48.
:: : Yes, excluding the case where every summand are zero, however some summand ( s ) must be negative, if we are talking about a field of characteristic zero ( which, in this case, I believe we are ).
49.
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 . characteristic function of the L�vy distribution yields:
50.
If " G " is a finite group and " k " a field with characteristic 0, then one shows in the theory of group representations that any subrepresentation of a given one is already a direct summand of the given one.
