Related papers: Factorization in categories of systems of linear p…

This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler…

We demonstrate that the complete factorization of equations of motion into first-order differential equations can be obtained for real and complex scalar field theories with non-canonical dynamics.

The Jacobi system on a full-line lattice is considered when it contains additional weight factors. A factorization formula is derived expressing the scattering from such a generalized Jacobi system in terms of the scattering from its…

We study the problem of decomposition (non-commutative factorization) of linear ordinary differential operators near an irregular singular point. The solution (given in terms of the Newton diagram and the respective characteristic numbers)…

Here we give a complete group classification of the general case of linear systems of three second-order ordinary differential equations excluding the case of systems which are studied in the literature. This is given as the initial step in…

In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…

Our paper "Solving Third Order Linear Difference Equations in Terms of Second Order Equations" gave two algorithms for solving difference equations in terms of lower order equations: an algorithm for absolute factorization, and an algorithm…

The linearization of a quadratic form gives rise to a Clifford algebra structure, as seen in Dirac's factorization of the d'Alembert operator. A similar structure known as a generalized Clifford algebra arises from the continuation of this…

An algebraic framework for the investigation of linear dynamic output feedback is introduced. Pivotal in the present theory is the problem of causal factorization, i.e. the problem of factoring two systems over each other through a causal…

Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…

We apply general difference calculus in order to obtain solutions to the functional equations of the second order. We show that factorization method can be successfully applied to the functional case. This method is equivariant under the…

It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous $G$-algebras, are finite factorization domains (FFD for short). Utilizing this result, we contribute an algorithm to…

In this paper, we discuss a systematic and self consistent procedure to factorize a rather general class of coupled nonlinear ordinary differential equations (ODEs), namely coupled quadratic and mixed Li\'enard type equations, which include…

For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…

In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…

Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…

This is the first one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple linear groups.

Using a new definition of generalized divisors we prove that the lattice of such divisors for a given linear partial differential operator is modular and obtain analogues of the well-known theorems of the Loewy-Ore theory of factorization…

Generalizing Eisenbud's matrix factorizations, we define factorization categories. Following work of Positselski, we define their associated derived categories. We construct specific resolutions of factorizations built from a choice of…

In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.