In this paper, we show the followings: (i) If a volume preserving diffeomorphism f belongs to the C-interior of the set of all volume preserving diffeomorphims having the ergodic shadowing property then it is transitive Anosov. Moreover, (ii) if a C-generic volume-preserving diffeomorphism f has the ergodic shadowing property then it is transitive Anosov. M.S.C. 2010: 37C50, 37D20.

A result on bi-shadowing for continuous single-valued contractions satisfying certain conditions has been given by AlBadarneh (2015). In this paper, we continue the discussion of asymptotic properties of trajectories for mappings belonging to more subclasses of almost contractions. In particular, we prove that Zamfirescu Mappings, QuasiContractions, Generalised Contractions, and Hardy-Rogers Co...

A method of deductive learning is developed to control deductive inference Our goal is to im prove problem solving time by experience when that experience monotonically adds knowledge to the knowledge base In particular for deductive reasoning systems where partial results are saved dur ing a derivation and at least some partial results are themselves deduction rules we suggest ways of taking m...

Accurate representation of the physical layer is required for analysis and simulation of multi-hop networking in sensor, ad hoc, and mesh networks. This paper investigates, models, and analyzes the correlations that exist in shadow fading between links in multi-hop networks. In the last few years, several studies have analyzed the performance of flooding and random walks as querying mechanisms ...

Sonography is being considered for the screening of women at high risk for breast cancer. We are developing computerized detection methods to aid in the localization of lesions on breast ultrasound images. The detection scheme presented here is based on the analysis of posterior acoustic shadowing, since posterior acoustic shadowing is observed for many malignant lesions. The method uses a nonl...

We calculate nuclear shadowing and Q 2 dependence of gluon densities within the framework of the Gribov theory of nuclear shadowing using as input recent HERA data on diffractive dijet and charm production in deep inelastic ep scattering. We explain that in the case of the deuteron and of the light nuclei (A ≤ 12) theoretical uncertainties in the calculations of shadowing are small. For the hea...

Shadowing is a task where the subject is required to repeat the presented speech as s/he hears it. Although shadowing is cognitively a challenging task, it is considered as an efficient way of language training since it includes processes of listening, speaking and comprehension simultaneously. Our previous study realized automatic assessment of shadowing speech using the average of Goodness of...

This paper presents methods using algebraic topology for showing that pseudo-trajectories are close to trajectories of a dynamical system. Our emphasis is the case where the trajectories are unstable in two or more dimensions. We develop the algebraic topology for guaranteeing the existence of such trajectories.

We show that if a diffeomorphism has the periodic shadowing property on the chain recurrent set, then the closure of the periodic set is the chain recurrent set. Mathematics Subject Classification: 37C50

Rigorous Shadowing of Numerical Solutions of Ordinary Di erential Equations by Containment Wayne Brian Hayes Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2001 An exact trajectory of a dynamical system lying close to a numerical trajectory is called a shadow. We present a general-purpose method for proving the existence of nite-time shadows of numerical ODE ...