Let Λ be a complete metric space, and let {Sλ(·) : λ ∈ Λ} be a parametrised family of semigroups with global attractors Aλ. We assume that there exists a fixed bounded set D such that Aλ ⊂ D for every λ ∈ Λ. By viewing the attractors as the limit as t → ∞ of the sets Sλ(t)D, we give simple proofs of the equivalence of ‘equi-attraction’ to continuity (when this convergence is uniform in λ) and s...

In this paper, we present a semi-analytical model for determining the magnetic and electromagnetic characteristics of spoke-type permanent magnet (STPM) machine considering magnet segmentation and finite soft-material relative permeability. The proposed model is based on the resolution of the Laplace’s and Poisson’s equations in a Cartesian pseudo-coordinate system with respect to the relative ...

In this paper, the nonlinear dynamical behavior of an isotropic rectangular plate, simply supported on all edges under influence of a moving mass and as well as an equivalent concentrated force is studied. The governing nonlinear coupled PDEs of motion are derived by energy method using Hamilton’s principle based on the large deflection theory in conjuncture with the von-Karman strain-displacem...

This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear dynamic systems on time scales. Introducing the reasonable weak solution of nonlinear dynamic systems, the existence of the weak solution for the nonlinear dynamic systems on time scales and its properties are presented. Discussing L-strong-weak lower semicontinuity of integral functiona...

We report measurements of switching current distribution SWCD from a phase-diffusion branch PDB to a quasiparticle-tunneling branch QTB as a function of temperature in a cuprate-based intrinsic Josephson junction. Contrary to the thermal-activation model, the width of the SWCD increases and the corresponding switching rate shows a nonlinear behavior with a negative curvature in a semilogarithmi...

In this paper we introduce and explore conformal parabolic iterated function systems. We deene and study topological pressure, Perron-Frobenius type operators, semi-conformal and conformal measures and the Hausdorr dimension of the limit set. With every parabolic system we associate an innnite hyperbolic conformal iterated function system and we employ it to study geometric and dynamical featur...

In this paper we introduce and explore conformal parabolic iterated function systems. We deene and study topological pressure, Perron-Frobenius type operators, semi-conformal and conformal measures and the Hausdorr dimension of the limit set. With every parabolic system we associate an innnite hyperbolic conformal iterated function system and we employ it to study geometric and dynamical featur...

A new parameter of dynamical system predictability is introduced that measures the potential utility of predictions. It is shown that this parameter satisfies a generalized second law of thermodynamics in that for Markov processes utility declines monotonically to zero at very long forecast times. Expressions for the new parameter in the case of Gaussian prediction ensembles are derived and a u...