partial representations of groups on algebras, we describe the universal partial group algebra which

factorizes every partial representation by a morphism of algebras.

The general 2-factor NMF

factorizes the input non-negative speech data matrix into 2 non-negative matrices.

So, the volume [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] does not necessary always

factorize as V ([Q.

We propose to

factorize recurring instruction sequences into new instructions.

A poisson_1d_class object

factorizes the matrix and sends back the solution of the equation.

Since B is a domain, [beta]

factorizes through one of these algebras, and we can suppose that I is a prime ideal.

Is it worth arguing that twelve surpasses ten because it

factorizes in more ways, so that the reader -- contentedly factorizing -- perceives more structures and symmetries?

Using this relaxed supernode partition, the multifrontal method now

factorizes the extremely sparse electric power matrices faster than the general sparse algorithm.

Our third main result is a partial answer (a sufficient but not necessary condition) to this question: the numerator N(P)

factorizes if there is a chain disconnecting the Hasse diagram of P (see Theorem 3.

Is it worth arguing that twelve surpasses ten because it

factorizes in more ways, so that the reader--contentedly factorizing--perceives more structures and symmetries?

MATHEMATICAL EXPRESSION OMITTED]

factorizes through the integral (*)

Then [alpha]

factorizes through an epimorphism [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and a monomorphism [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of algebras.

so that its Mellin transform

factorizes, in the fundamental strip (-1, 0), as

dR](A) = R[[omega]] [congruent to] R

factorizes throughout an isomorphism [[?

factorizes in fact over [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].