Related papers: Dynamical Theory of Generalized Matrices
We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
A novel spin-extended so($d+1$,1) algebra is introduced and shown to provide an interesting framework for discussing the properties of a $d$-dimensional matrix Hamiltonian with spin 1/2 and so($d+1$) symmetry. With some $d+2$ additional…
We present a generic framework for describing interacting, spinning, active polar particles, aimed at modelling dense cell aggregates, where cells are treated as polar, rotating objects that interact mechanically with one another and their…
In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…
An algebraic characterization of the property of approximate controllability is given, for behaviours of spatially invariant dynamical systems, consisting of distributional solutions, that are periodic in the spatial variables, to a system…
This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this…
In analogy to Nambu's generalization of mechanics, we present a generalization of Poisson sigma models to higher dimensional world volumes. We find corresponding generalizations of string sigma models and open-closed string relations for…
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
The transfer matrix in lattice field theory connects the covariant and the initial data frameworks; in spin foam models, it can be written as a composition of elementary cellular amplitudes/propagators. We present a framework for discrete…
We present a derivation of the dynamical r-matrices of the Calogero-Moser models using the Hamiltonian reduction procedure to get general formulae. We describe the dynamical r-matrices thus found for spin Calogero-Moser models and…
We propose generalized Fermat's conjecture in the framework of arithmetic dynamics, and give evidences. The multi-indexed version is added.
We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known…
Aims To propose and analyze a general, dynamic, process-oriented theory of the area of distribution. Methods The area of distribution is modelled by combining (by multiplication) three matrices: one matrix represents movements, another…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…
It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear…
We obtain a generic closed system of equations on a brane that describes its inner evolution and give a method for extending solutions on the brane to the bulk. We also discuss the cosmological implications of the closed system of equations…
In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…
A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of…
It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be…