par]G, which

factorizes partial representations by morphisms of algebras, was made in purely algebraic terms.

Factorizes X into the non-negative m x k matrix U and the non-negative k x n matrix [V.

Unlike typical matrix factorization methods, such as QR and SVD, which seek for exact factorization of original matrix, nonnegative matrix factorization (NMF) approximately

factorizes the original matrix into two low-dimensional nonnegative submatrixes.

Since E is a discrete [GAMMA]-module, the inclusion E [right arrow] E

factorizes via [E.

This work describes a unified approach to two problems previously addressed separately in Intelligent Tutoring Systems: (i) Cognitive Modeling, which

factorizes problem solving steps into the latent set of skills required to perform them; and (ii) Student Modeling, which infers students' learning by observing student performance.

In case of a complex scalar field we have to double the number of degrees of freedom, the amplitude then

factorizes into a product and becomes Z = det[([D.

The types of contributions to the PV NN-meson vertex were identified in this work as (a) the "factorization" process in which the vertex

factorizes into a product of a vector (axial vector) N-N current and an axial vector (vector) vacuum-meson current, (b) PV admixtures of the initial and final nucleon states, and (c) contributions from sea quarks.

This scheme

factorizes the common functions of calculation of land tax and build tax.

The factorization algorithm

factorizes out code containing branches, allows macros to be defined in terms of other macros, and permits the use of two bytes for defining a macro instruction code.

One finds also build_Poisson which assembles the Poisson operator on the defined domain,

factorize_Poisson which

factorizes the Poisson matrix, and solve_Poisson which returns the solution.

We found in Section III that the joint density function

factorizes into a "duration" part and an "application" part.

Then any homomorphism of A-algebras C [right arrow] B, with C finitely generated over A,

factorizes through a finitely generated A-algebra D, such that the homomorphism A [right arrow] D is regular.