We consider the operator H = d 4 dt4 + d dtp d dt + q with 1-periodic coefficients on the real line. The spectrum of H is absolutely continuous and consists of intervals separated by gaps. We describe the spectrum of this operator in terms of the Lyapunov function, which is analytic on a two-sheeted Riemann surface. On each sheet the Lyapunov function has the standard properties of the Lyapunov...

The general quasi-linear autonomous fourth order diffusion equation ut = −[G(u)uxxx + h(u, ux, uxx)]x with positive variable diffusivity G(u) and lower-order flux component h is considered on the real line. A direct algorithm produces a general class of equations for which the Shannon entropy density obeys a reaction-diffusion equation with a positive irreducible source term. Such equations may...

A. description In recent years several mathematical models in uid dynamics, materials science and plasticity have lead to fourth order nonlinear degenerate parabolic equations. We mention for example the lubrication approximation for thin viscous lms (cf. and models that describe dislocation densities in plasticity (cf. Gr un (1995)). Although there has been a considerable eeort to understand d...

In this paper we shall reduce the problem of the oscillation of all solutions of certain nonlinear fourth-order dynamic equations to the problem of oscillation of two second-order dynamic equations, which are discussed intensively in the literature. Further oscillation criteria of fourth-order equations are given and proved using integration and Taylor’s formula on time scales. Some conditions ...

We propose a new multiway filtering based on fourth-order cumulants for the denoising of noisy data tensor with correlated Gaussian noise. The classical multiway filtering is based on the TUCKALS3 algorithm that computes a lower-rank tensor approximation. The presented method relies on the statistics of the analyzed multicomponent signal. We first recall how the well-known lower-rank-(K1, . . ....

The algorithm proposed aims to identify moving average coefficient matrices of an MA process, not necessarily minimum-phase, driven by an unobserved non-gaussian input. It is assumed that the observation available is of limited duration, and coefficients are estimated from the set of fourth order output cumulants. It is shown that much more equations than unknowns are available, and that robust...