The attempt to extend the Galois theory for commutative algebras, due to Chase, Harrison and Rosenberg , to the case of partial group actions (see reference ) spawned a new and unexpected development, namely the extension of the notion of partial actions to the realm of Hopf algebras.
These above mentioned articles were the starting point of the theory of partial actions of Hopf algebras.
Let u, v, x, y be partial words such that ux [up arrow] vy.
i) If [absolute value of u] [greater than or equal to] [absolute value of v], then there exist partial words w, z such that u = wz, v [up arrow] w, and y [up arrow] zx.
The Jacobian determinant is a combination of partial derivatives.
The partial derivatives of [PHI] can be found by differentiating (4), and then the following formulations are obtained :
Romaguera: Characterizations of partial metric completeness in terms of weakly contractive mappings having fixed point, Appl.
Simsek: Generalized contractions on partial metric spaces, Topology Appl.
Many people are not aware of the effect that partial
dentures can have on existing teeth," said Kletter.
A similar for the partial differentiations [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII](1 [less than or equal to] j [less than or equal to] n) and [partial [derivative].
Let D be the algebra of partial differential operators with variable coefficients on [R.
Crosland Moor Junior School, partial
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