‎Let $(Sigma_P,sigma_P)$ be the space of a spacing shifts where $Psubset mathbb{N}_0=mathbb{N}cup{0}$ and $Sigma_P={sin{0,1}^{mathbb{N}_0}: ‎s_i=s_j=1 mbox{ if } |i-j|in P cup{0}}$ and $sigma_P$ the shift map‎. ‎We will show that $Sigma_P$ is mixing if and only if it has almost specification property with at least two periodic points‎. ‎Moreover‎, ‎we show that if $h(sigma_P)=0$‎, ‎then $Sigma_...

We study the planar problem of two satellites attracted by a center of force. Assuming that the center of mass of the two-satellite system is on a circular orbit around the center of force and using Levi-Civita regularization we prove the existence of an almost periodic orbit with an infinite number of collision between the satellites.

Let G be a locally compact group, and let A(G) and VN(G) be its Fourier algebra and group von Neumann algebra, respectively. In this paper we consider the similarity problem for A(G): Is every bounded representation of A(G) on a Hilbert space H similar to a ∗-representation? We show that the similarity problem for A(G) has a negative answer if and only if there is a bounded representation of A(...

It is sometimes claimed in the literature that subspace methods provide consistent estimates, also when the underlying observed signal has purely oscillatorymodes (or the generating system has uncontrollable eigenvalues on the unit circle) but a formal proof of this assertion does not seem to exist. In this paper, we prove consistency of subspacemethods with purely oscillatory modes. A well-kno...

Suppose that a sequence of numbers xn (a ‘signal’) is transmitted through a noisy channel. The receiver observes a noisy version of the signal with additive random fluctuations, xn + ξn, where ξn is a sequence of independent standard Gaussian random variables. Suppose further that the signal is known to come from some fixed space X of possible signals. Is it possible to fully recover the transm...

By utilizing the continuation theorem of coincidence degree theory, we shall prove that a Fox production harvesting model with delay has at least one positive almost periodic solution. Some preliminary assertions are provided prior to proving our main theorem. We construct a numerical example along with graphical representations to illustrate feasibility of the theoretical result.