Related papers: The structure of rationally factorized Lax type fl…
Integro-differential methods, currently exploited in calculus, provide an inexhaustible source of tools to be applied to a wide class of problems, involving the theory of special functions and other subjects. The use of integral transforms…
Just as knowing some roots of a polynomial allows one to factor it, a well-known result provides a factorization of any scalar differential operator given a set of linearly independent functions in its kernel. This note provides a…
Let G be a block matrix function with one diagonal block A being positive definite and the off diagonal blocks complex conjugates of each other. Conditions are obtained for G to be factorable (in particular, with zero partial indices) in…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
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…
The paper investigates the Poisson structures associated with dynamical systems of the heavenly type, focusing on the Mikhalev-Pavlov and Pleba\'nski equation. The dynamical system is represented as a Hamiltonian system on a functional…
In this paper, we introduce a new concept of incorporating factorized flow maps as mid-level representations, for bridging the perception and the control modules in modular learning based robotic frameworks. To investigate the advantages of…
This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.
The structure of symplectic integrators up to fourth-order can be completely and analytical understood when the factorization (split) coefficents are related linearly but with a uniform nonlinear proportional factor. The analytic form of…
We translate effectively our earlier quantum constructions to the classical language and using Yang-Baxterisation of the Faddeev-Reshetikhin-Takhtajan algebra are able to construct Lax operators and associated $r$-matrices of classical…
We investigate solutions to the functional equation $f(f(x)) = e^x$, which can be interpreted as the problem of finding a half iterate of the exponential map. While no elementary solution exists, we construct and analyze non-elementary…
We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…
In this paper, we present a general scheme to construct integrable systems based on realization in the coboundary dynamical Poisson groupoids of Etingof and Varchenko. We also present a factorization method for solving the Hamiltonian…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles…
This paper presents the basic concepts of a systemic theory of interaction between non-deterministic open dynamics with varying temporalities, which includes three stages: the definition of these dynamics as lax-functors, the notion of…
We introduce the Delta-framework, LF-Delta, a dependent type theory based on the Edinburgh Logical Framework LF, extended with the strong proof-functional connectives, i.e. strong intersection, minimal relevant implication and strong union.…
In this article algebraic constructions are introduced in order to study the variety defined by a radical parametrization (a tuple of functions involving complex numbers, $n$ variables, the four field operations and radical extractions). We…