In this paper, d-dimensional (dD) quasi-periodically forced nonlinear Schrödinger equation with a general nonlinearity iut −∆u+Mξu+ εφ(t)(u+ h(|u| 2)u) = 0, x ∈ T, t ∈ R under periodic boundary conditions is studied, where Mξ is a real Fourier multiplier and ε is a small positive parameter, φ(t) is a real analytic quasi-periodic function in t with frequency vector ω = (ω1,ω2 . . . ,ωm), and h(|...

Although the spectrum of radially periodic images is often expressed in terms of finite or infinite series of Bessel functions, such expressions do not clearly reveal the exact impulsive structure of the spectrum. An alternative Fourier decomposition of radially periodic images, in terms of circular cosine functions, is presented, and its significant advantages are shown. It is shown that the F...

We show that the transmission through single and double -function potential barriers of strength P =VWb / vF in bilayer graphene is periodic in P with period . For a certain range of P values we find states that are bound to the potential barrier and that run along the potential barrier. Similar periodic behavior is found for the conductance. The spectrum of a periodic succession of -function b...

Denote x t x1 t , x2 t , . . . , xn t , xt x1t, x2t, . . . , xnt , xit s xi t s i 1, 2, . . . , n , s ∈ −τ, 0 , τ is a positive constant or τ ∞, the norm of a bounded continuous function space C −τ, 0 , R is defined as ‖φ‖ maxs∈ −τ,0 |φ s |, where |φ| max{|φi|, i 1, 2, . . . , n}, C −τ, 0 , R {φ ∈ C −τ, 0 , R : for all θ ∈ −τ, 0 , φ θ > 0}. We call an almost periodic function is positive if and...

A perfect sequence has the optimal periodic autocorrelation function where all out-of-phase values are zero, and an orthogonal set has orthogonality that the periodic correlation function for any pair of distinct sequences in the set takes zero at the zero shift. The real-valued perfect sequences of period N = 2 are derived from a real-valued Huffman sequence of length 2 + 1 with ν ≥ n whose ou...

The class of harmonizable processes is a natural extension of the class of stationary processes. This paper provides sufficient conditions for the sample paths of harmonizable processes to be almost periodic uniformly, Stepanov and Besicovitch.

We study conformally invariant nonlinear wave equations in four dimensions corresponding to multicomponent massless scalar elds with a quartic interaction. We prove that the scattering operator S on the space H of nite-Einstein-energy Cauchy data has innnitely many xed points, as well as periodic points of all orders. There are also 2 H such that S n is almost periodic but not periodic, and 2 H...

We exhibit examples of almost periodic Verblunsky coefficients for which Herman’s subharmonicity argument applies and yields that the associated Lyapunov exponents are uniformly bounded away from zero. As an immediate consequence of this result, we obtain examples of almost periodic Verblunsky coefficients for which the associated probability measure on the unit circle is pure point.