An important property of high altitude platform station (HAPS) Universal Mobile Telecommunications Systems (UMTS) is that unlike terrestrial tower based systems. interference is dependent on the antenna characteristics of HAPS rather than the terrain features (i.e., shadowing) in the service area. In this paper. we exploit this unique HAPS property to propose simple and effective adaptive softe...

We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.

— We give a survey of the entropy theory of interval maps as it can be analyzed using ergodic theory, especially measures of maximum entropy and periodic points. The main tools are (i) a suitable version of Hofbauer’s Markov diagram, (ii) the shadowing property and the implied entropy bound and weak rank one property, (iii) strongly positively recurrent countable state Markov shifts. Proofs are...

We study the properties of $ \Phi $-irregular sets (sets points for which Birkhoff average diverges) in dynamical systems with shadowing property. estimate topological entropy set terms on chain recurrent classes and prove that full are typical. also consider $-level whose is a specified interval), relating they carry some ergodic measures. Finally, we problem large deviations considering level...

A number of measures on paths or clusters on two-dimensional lattices arising from critical statistical mechanical models are believed to exhibit some kind of conformal invariance in the scaling limit. Schramm introduced a one-parameter family of such processes, now called the (chordal) Schramm-Loewner evolution with parameter κ (SLEκ), and showed that these give the only possible limits for co...

Unlike evolutionary dynamics, co-evolutionary dynamics can exhibit a wide variety of complex regimes. This has been confirmed by numerical studies e.g. in the context of Evolutionary Game Theory (EGT) and population dynamics of simple two-strategy games with various types of replication and selection mechanisms. Using the framework of shadowing lemma we study to what degree can such infinite po...