We show that dynamical systems in inverse problems are sometimes foliated if the embedding dimension is greater than the dimension of the manifold on which the system resides. Under this condition, we end up reaching different leaves of the foliation if we start from different initial conditions. For some of these cases we have found a method by which we can asymptotically guide the system to a specific leaf even if we start from an initial condition which corresponds to some other leaf. We demonstrate the method by two examples. In the chosen cases of the harmonic oscillator and Duffing's oscillator we find an alternative set of equations which represent a collapsed foliation, such that no matter what initial conditions we choose, the system would asymptotically reach the same desired sub-manifold of the original system. This process can lead to cases for which a system begins in a chaotic region, but is guided to a periodic region and vice versa. It may also happen that we could move from an orbit of one period to an orbit of another period.
The article presents a numerical model of a coupled electro-magneto-mechanical system - an electromagnet exposed to vibration of a yoke. Operation of a multi-physical (an electro-magneto-mechanical) model is simulated under different working and excitation conditions and a response of the system is analyzed. Simscape, a tool of MATLAB programming environment, is used for numerical analysis of the problem. It is shown, that there exists a combination of operation parameters, which can lead to a substantial attenuation ot the yoke vibration. Furthermore, there exists a critical magnitude of the current, which corresponds to a permanent attraction of the yoke to the electromagnet. An analysis of electormagnet‘s initialization shows an induction of high voltages in electric circuit, which can damage the electromagnet and need to be avoided by a proper choice of parameters. and Obsahuje seznam literatury
A transit function $R$ on a set $V$ is a function $R\:V\times V\rightarrow 2^{V}$ satisfying the axioms $u\in R(u,v)$, $R(u,v)=R(v,u)$ and $R(u,u)=\lbrace u\rbrace $, for all $u,v \in V$. The all-paths transit function of a connected graph is characterized by transit axioms.
In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an n-normed space, we are interested in bounded multilinear n-functionals and n-dual spaces. The concept of bounded multilinear n-functionals on an n-normed space was initially intoduced by White (1969), and studied further by Batkunde et al., and Gozali et al. (2010). In this paper, we revisit the definition of bounded multilinear n-functionals, introduce the concept of n-dual spaces, and then determine the n-dual spaces of ℓ p spaces, when these spaces are not only equipped with the usual norm but also with some n-norms.