We analyze the asymptotic behavior of infinite products non-linear operators which take a non-empty, closed subset complete metric space into space, taking account summable computational errors. Our results can be applied in methods for solving convex feasibility and optimization problems.

For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on Hennessy-Milner logic. The logic for characterising ...

We present several results for the periods of periodic points of sup-norm nonexpansive maps. In particular, we show that the period of each periodic point of a sup-norm non-expansive map f : M → M , where M ⊂ R, is at most maxk 2 ( n k ) . This upper bound is smaller than 3 and improves the previously known bounds. Further, we consider a special class of sup-norm non-expansive maps, namely topi...

The paper examines studies based on the theory of expansive learning, formulated in 1987. In recent years the theory has been used in a wide variety of studies and interventions. The theory builds on foundational ideas put forward by Vygotsky, Leont’ev, Il’enkov, and Davydov, key figures in the Russian school of cultural–historical activity theory. Studies based on the theory are reviewed in si...

In this paper, we obtain an explicit formula for the interior of the domain of a maximal monotone multifunction in terms of its Fitzpatrick function.

Threshold logic gates, up to now, generally have been presumed to provide a single function of the input variables. The threshold gates that have been integrated [I1]-4] were naturally double-sided and provided complementary outputs or, more specifically, complemented dual outputs. This paper shows that the inphase and out-of-phase outputs can, in fact, be designed to provide grossly different ...

In this paper, some fixed point theorems for nonexpansive mappings in partially ordered spherically complete ultrametric spaces are proved. In addition, we investigate the existence of fixed points for nonexpansive mappings in partially ordered non-Archimedean normed spaces. Finally, we give some examples to discuss the assumptions and support our results.

The classification of the grade of shrink and expansion for the expansive soils is very important work for constructions in expansive soil area. Accurate evaluation of the estate of expansive soil may provide scientific data and basis for the prevention of engineering design and construction. This paper brings forward the classification method for expansive soil based on fractal interpolation t...