Related papers: The bidomain problem as a gradient system
The effect of induced Riemann geometry in nonlinear electrodynamics is considered. The possibility for description of real gravitation by this effect is discussed.
In this work some nonlinear integral equation is studied. This equation has arisen in the (super)string field theory and cosmology. In this work it is proved that some boundary problem for this equation has a solution.
The problem of bi-equivariant extension of continuous maps of binary $G$-spaces is considered. The concept of a structural map of distributive binary $G$-spaces is introduced, and a theorem on the bi-equivariant extension of structural maps…
In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for…
We present a semiclassical study of the spectrum of a few-body system consisting of two short-range interacting bosonic particles in one dimension, a particular case of a general class of integrable many-body systems where the energy…
It is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system.…
We generalize the concept "well-posed linear system" to stochastic linear control systems and study some basic properties of such kind systems. Under our generalized definition, we show the well-posedness of the stochastic heat equation and…
A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…
A previous knowledge of the domains of dependence of an Hamilton Jacobi equation can be useful in its study and approximation. Information of this nature are, in general, difficult to obtain directly from the data of the problem. In this…
We consider a dynamical system consisting of subsystems indexed by a lattice. Each subsystem has one conserved degree of freedom ("energy") the rest being uniformly hyperbolic. The subsystems are weakly coupled together so that the sum of…
We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of…
Understanding how systems built out of modular components can be jointly optimized is an important problem in biology, engineering, and machine learning. The backpropagation algorithm is one such solution and has been instrumental in the…
The energy system studies include a wide range of issues from short term (e.g. real-time, hourly, daily and weekly operating decisions) to long term horizons (e.g. planning or policy making). The decision making chain is fed by input…
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…
The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of…
The H\'enon-Heiles system, initially introduced as a simplified model of galactic dynamics, has become a paradigmatic example in the study of nonlinear systems. Despite its simplicity, it exhibits remarkably rich dynamical behavior,…
Multi-energy systems have been leaping forward for its various benefits, e.g., energy conservation and emission reduction. Coupling components are capable of transmitting energy from one time scale system to another time scale system, so…
Consider the quotient of a Hilbert space by a subgroup of its automorphisms. We study whether this orbit space can be embedded into a Hilbert space by a bilipschitz map, and we identify constraints on such embeddings.
A well-known generalisation of positional numeration systems is the case where the base is the residue class of $x$ modulo a given polynomial $f(x)$ with coefficients in (for example) the integers, and where we try to construct finite…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…