A method due to Fay and Walls for associating a factorization system with a radical is examined for associative rings. It is shown that a factorization system results if and only if the radical is strict and supernilpotent. For groups and non-associative rings, no radical defines a factorization system.

Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing the structure and complexity of strings, but their combinatorial structure is very different. In this paper, we establish the first direct connection between the two by showing that while the Lyndon factorization can be bigger than the non-overlapping LZ factorization (which we demonstrate by describin...

In this article the notion of quasi right factorization structure in a category X is given. The main result is a one to one correspondence between certain classes of quasi right factorization structures and 2-reflective subobjects of a predefined object in Lax(PrOrdX op ). Also a characterization of quasi right factorization structures in terms of images is given. As an application, the closure...

A well-known result from linear system theory states that the minimal inner size of a factorization of the Hankel matrix H of a system gives the minimal order of a realization. In this brief it is shown that when dealing with positive linear systems, the existence of a factorization of the Hankel matrix into two nonnegative matrices is only a necessary condition for the existence of a positive ...

The output behavior of a nonlinear control system depends not only on its input but also on its initial conditions. These two factors have to be considered simultaneously in nonlinear systems design. This paper presents a new definition, called dynamic right factorization, for nonlinear dynamic control systems. This factorization takes the initial conditions as well as the system input into acc...

The problem of projective reconstruction for multiple views is considered using a factorization method. A common difficulty of existing formulations of the factorization problem is that they do not adequately constrain the depth parameters thus allowing the algorithm to converge to view-deficient solutions with entire views being suppressed. We propose to include a variance measure with an adap...

Since its introduction in 2012, the factorization theory for rational motions quickly evolved and found applications in theoretical and applied mechanism science. We provide an accessible introduction to motion factorization with many examples, summarize recent developments and hint at some new applications. In particular, we provide pseudo-code for the generic factorization algorithm, demonstr...

In a recent paper, we investigated factorization properties of Hermite subdivision schemes by means of the so–called Taylor factorization. This decomposition is based on a spectral condition which is satisfied for example by all interpolatory Hermite schemes. Nevertheless, there exist examples of Hermite schemes, especially some based on cardinal splines, which fail the spectral condition. For ...

We present a counter example which shows the violation of the S-matrix factorization in the massive Thirring model. This is done by solving the PBC equations of the massive Thirring model exactly but numerically. The violation of the S-matrix factorization is related to the fact that the crossing symmetry and the factorization do not commute with each other. This confirms that the soliton antis...

Matrix factorization is one of the best approaches for collaborative filtering, because of its high accuracy in presenting users and items latent factors. The main disadvantages of matrix factorization are its complexity, and being very hard to be parallelized, specially with very large matrices. In this paper, we introduce a new method for collaborative filtering based on Matrix Factorization ...