in this paper‎, ‎we determine the simple groups $g=ab$‎, ‎where $b$ is isomorphic to $l_{3}(4)$ and $a$ isomorphic to an alternating or a symmetric group on $ngeq5$‎, ‎letters‎.

Z[ √ −5] = {a+ b √ −5 : a, b ∈ Z}, because 2, 3, and 1± √ −5 are irreducible and nonassociate. These notes present a formula that in some sense measures the extent to which unique factorization fails in environments such as Z[ √ −5]. The large-scale methodology deserves immediate note, before the reader is immersed in a long succession of smaller attention-filling specifics: • algebra lets us d...

A question which was left open in [C-W] was the symplectic equivalence of the above (a, b, c)-surfaces. To this purpose, and for more general purposes, it is important to determine the braid monodromy factorization of the branch curve corresponding to a symplectic deformation of the 4-1 covering S → P × P possessed by an (a, b, c)-surface S (note that in [C-W] one key result was the determinati...

in this paper, we study the arens regularity properties of module actions and we extend some proposition from baker, dales, lau and others into general situations. we establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. in 1951 arens shows that the second dual of banach algebra endowed with the e...

We introduce a Bayesian extension of the tensor factorization problem to multiple coupled tensors. For a single tensor it reduces to standard PARAFAC-type Bayesian factorization, and for two tensors it is the first Bayesian Tensor Canonical Correlation Analysis method. It can also be seen to solve a tensorial extension of the recent Group Factor Analysis problem. The method decomposes the set o...

We present a method to factor a given matrix M into a short product of sparse matrices, provided M has a suitable “symmetry”. This sparse factorization represents a fast algorithm for the matrix-vector multiplication with M . The factorization method consists of two essential steps. First, a combinatorial search is used to compute a suitable symmetry of M in the form of a pair of group represen...

Community question answering (CQA) has become an important service due to the popularity of CQA archives on the web. A distinctive feature is that CQA services usually organize questions into a hierarchy of natural categories. In this paper, we focus on the problem of question retrieval and propose a novel approach, called group non-negative matrix factorization with natural categories (GNMFNC)...

Classes of‎ ‎Abaffy-Broyden-Spedicato (ABS) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎The algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎Here‎, ‎we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW‎ ‎factorizations of a nonsingular matrix as well as...