We consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the forcing term for the existence of quasi-periodic solutions which have the same frequency vector as the forcing.

We study the ordinary differential equation εẍ+ ẋ+ ε g(x) = εf(ωt), with f and g analytic and f quasi-periodic in t with frequency vector ω ∈ R. We show that if there exists c0 ∈ R such that g(c0) equals the average of f and the first non-zero derivative of g at c0 is of odd order n, then, for ε small enough and under very mild Diophantine conditions on ω, there exists a quasi-periodic solution...

Abstract This paper focuses on the study of multistage stochastic vector generalized quasi-variational inequalities with a variable ordering structure. The proposed problems are defined in suitable functional setting relative to finite set final possible states and certain information fields; these formulations multicriteria extension variational inequalities. A relevant aspect is presence nona...

OBJECTIVE While standard magnetoencephalographic systems record only one component of the biomagnetic field, novel vector-biomagnetometers enable measurement of all three components of the field at each sensing point. Because information content in standard one-component magnetoencephalography (MEG) is often not adequate to reconstruct quasi-radial dipolar activity, we tested the hypothesis tha...

A functional enzyme displays activity with at least one substrate and can be represented by a vector in substrate-activity space. Many enzymes, including GSTs (glutathione transferases), are promiscuous in the sense that they act on alternative substrates, and the corresponding vectors operate in multidimensional space. The direction of the vector is governed by the relative activities of the d...

In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the  assumption of normality we establish common fixed point theorems for the generalized quasi-contractions  with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$  in the set...