Related papers: Flows of vector fields and the Kalman Theorem
We obtain limit theorems (Stable Laws and Central Limit Theorems, both Gaussian and non-Gaussian) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The proofs of the limit…
The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and, then, on more involved nonlocal theories (colored and non colored)…
We define a Tanaka's equation on an oriented graph with two edges and two vertices. This graph will be embedded in the unit circle. Extending this equation to flows of kernels, we show that the laws of the flows of kernels $K$ solution of…
We extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. As far as we consider a…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
It is investigated a possibility of physical interpretation of vector fields (dynamic flows) in Euclidean spaces of higher dimension. There are analyzed the methods of measurements of dynamic flows, the characteristics of dynamic flow and…
Mainstream flow matching methods typically focus on learning the local velocity field, which inherently requires multiple integration steps during generation. In contrast, Mean Velocity Flow models establish a relationship between the local…
Close insight into mathematical and conceptual structure of classical field theories shows serious inconsistencies in their common basis. In other words, we claim in this work to have come across two severe mathematical blunders in the very…
We prove some results concerning Alcuin number of graphs. First, we classify graphs which have unique minimum vertex cover. Then we present two necessary conditions for a graph to be of class two and show why one of them (condition on…
We study a class of discontinuous vector fields brought to our attention by multi-legged animal locomotion. Such vector fields arise not only in biomechanics, but also in robotics, neuroscience, and electrical engineering, to name a few…
Classical relativistic field theory is applied to perfect and magneto-hydrodynamic flows. The fields for Hamilton's principle are shown to be the Lagrangian coordinates of the fluid elements, which are potentials for the matter current…
Subject of research is complex networks and network systems. The network system is defined as a complex network in which flows are moved. Classification of flows in the network is carried out on the basis of ordering and continuity. It is…
This work is devoted to the control of the Fokker-Planck equation, posed on a smooth bounded domain of R^d, with a localized drift force. We prove that this equation is locally controllable to regular nonzero trajectories. Moreover, under…
We give a new proof of Brakke's partial regularity theorem up to C^{1,\varsigma} for weak varifold solutions of mean curvature flow by utilizing parabolic monotonicity formula, parabolic Lipschitz approximation and blow-up technique. The…
In this paper, we develop a notion of controllability for hypergraphs via tensor algebra and polynomial control theory. Inspired by uniform hypergraphs, we propose a new tensor-based multilinear dynamical system representation, and derive a…
The Fluctuation Theorem gives an analytical expression for the probability of observing second law violating dynamical fluctuations, in nonequilibrium systems. At equilibrium statistical mechanical fluctuations are known to be ensemble…
We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the…
Here we study the nonlinear hyperbolic equations of the type of equations from theory of flows on networks, for which we prove the solvability theorem under the appropriate conditions and also investigate the behaviour of the solution.
Subject of present paper is the review of results of authors on foliation theory and applications of foliation theory in control systems. The paper consists of two parts. In the first part the results of authors on foliation theory are…
A general organizing principle is proposed that can be used to derive the equations of motion describing the near-equilibrium dynamics of causal and thermodynamically stable relativistic systems. The latter are found to display some new…