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.

Regular almost periodicity in compact minimal abelian flows was characterized for the case of discrete acting group by W. Gottschalk and G. Hedlund and for the case of 0-dimensional phase space by W. Gottschalk a few decades ago. In 1995 J. Egawa gave characterizations for the case when the acting group is R. We extend Egawa’s results to the case of an arbitrary abelian acting group and a not n...

In this paper we solve positive and contractive multiblock problems in the Wiener algebra of almost periodic functions of several variables. We thus generalize the classical four block problem that appears in robust control in many ways. The necessary and sufficient conditions are in terms of appropriate Toeplitz (positive case) and Hankel operators (contractive case) on Besikovitch space. In a...

In this paper, we investigate the dynamics of a class of the so-called semi-ratio-dependent predator–prey interaction models with functional responses based on systems of nonautonomous differential equations with time-dependent parameters. The functional responses are classified into five types and typical examples of each type are provided. Then we establish sufficient criteria for the bounded...

By identifying functions whose difference has zero norm, he proved that {^£{R), || ||) is actually a Banach space. The space had been studied by many authors in the theory of almost periodic functions and generalized harmonic analysis (e.g., Besicovitch [4], Bohr and Folner [6], Bertrandias [3] and Lau and Lee [10]). In [10], it was shown that the transformation defined in (1.1) can be extended...

We discuss the exact number of almost periodic solutions of certain ordinary differential equations of the second order. The class of equations under consideration is inspired by a well-known result in the area of elliptic boundary value problems.