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It is shown that a general two-component feedback loop can be viewed as a deformed Hamiltonian system. Some of the implications of using ideas from theoretical physics to study biological processes are discussed.
In this paper we characterize all nilpotent orbits under the action by conjugation that intersect the nilpotent centralizer of a nilpotent matrix $B$ consisting of two Jordan blocks of the same size. We list all the possible Jordan…
The aim of this paper is to offer an overview of the most important applications of Jordan structures inside mathematics and also to physics, up-dated references being included. For a more detailed treatment of this topic see - especially -…
A generalization of the filled-in Julia set is presented using the multicomplex numbers and an algorithm is presented to visualize these sets in the tridimensional space. There are many ways to visualize these higher dimensional fractals…
Order three elements in the exceptional groups of type G2 are classified up to conjugation over arbitrary fields. Their centralizers are computed, and the associated classification of idempotents in symmetric composition algebras is…
In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory…
This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank $23$ decompositions for the $3\times 3$ matrix multiplication tensor $M_{\langle 3\rangle}$. All our decompositions…
A generalized two-component model with peakon solutions is proposed in this paper. It allows an arbitrary function to be involved in as well as including some existing integrable peakon equations as special reductions. The generalized…
We investigate the variety of commuting matrices. We classify its components for any number of matrices of size at most 7. We prove that starting from quadruples of size 8 matrices, this scheme has generically nonreduced components, while…
The paper is devoted to construction of some closed inductive sequence of models of the generalized second-order Dedekind theory of real numbers with exponentially increasing powers. These models are not isomorphic whereas all models of the…
Let $\Pi$ be a convex decomposition of a set $P$ of $n\geq 3$ points in general position in the plane. If $\Pi$ consists of more than one polygon, then either $\Pi$ contains a deletable edge or $\Pi$ contains a contractible edge.
An indecomposable decomposition of a torsion-free abelian group $G$ of rank $n$ is a decomposition $G=A_1\oplus\cdots\oplus A_t$ where $A_i$ is indecomposable of rank $r_i$ so that $\sum_i r_i=n$ is a partition of $n$. The group $G$ may…
Cycloids are particular Petri nets for modelling processes of actions and events, belonging to the fundaments of Petri's general systems theory. Defined by four parameters they provide an algebraic formalism to describe strongly…
Cycloids are particular Petri nets for modelling processes of actions and events, belonging to the fundaments of Petri's general systems theory. Defined by four parameters they provide an algebraic formalism to describe strongly…
We consider the degrees of the elements of a homogeneous system of parameters for the ring of invariants of a binary form, give a divisibility condition, and a complete classification for forms of degree at most 8.
Generalized parton distribution functions (GPDs) of spin-3/2 particles are defined for the first time in this paper. Eight unpolarized and eight polarized GPDs are found. In the forward limit of GPDs, the structure functions and parton…
We determine the structure of the graded ring of Siegel modular forms of degree 3. It is generated by 19 modular forms, among which we identify a homogeneous system of parameters with 7 forms of weights 4, 12, 12, 14, 18, 20 and 30. We also…
A general model for the fragmentation of a two-component system (e.g. protons and neutrons) is proposed and solved exactly. The extension of this model to any number of components is also shown to be exactly solvable. A connection between…
In this paper the analytic characterization of generalized poles of operator valued generalized Nevanlinna functions (including the length of Jordan chains of the representing relation) is completed. In particular, given a Jordan chain of…
A notion of open rank, related with generic power sum decompositions of forms, has recently been introduced in the literature. The main result here is that the maximum open rank for plane quartics is eight. In particular, this gives the…