Sentence examples for processes under suitable from inspiring English sources

The purpose of this paper is to propose the modified proximal point algorithm using the S-type iteration process for four asymptotically nonexpansive mappings in (operatorname{CAT}(0)) spaces and to prove some △- and strong convergence theorems of the proposed processes under suitable conditions.

It was followed by the anodization process, under suitable conditions calculated by the surface area of the samples.

The purpose of this paper is to prove that the PMH-iteration process converges to a fixed point of continuous function f on an arbitrary interval E, and compare the convergence speed of (1.5) with the other iteration processes under the suitable conditions and the same computational cost.

29– 33 The main challenge in the accomplishment of efficient DKR processes is finding racemization and kinetic-resolution processes that are mutually compatible under suitable reaction conditions.

These second-order models have been used in a constrained optimization study which showed that both high and selective yields of TiO2 may be obtained under suitable process conditions.

Based on such a probabilistic model and on the analysis of peculiar non-dimensional parameters, a spectral model for the modal force induced by pedestrian groups, modeled as a stationary random process, is analytically deduced under suitable simplifying assumptions.

These facts imply that the electrodeposition process was carried out under suitable conditions, and the filling of the template pores was practically total.

It is observed that, if the process (M) is convergent, then the process (I) with condition ((mathrm{I}_{1}^)) is also convergent under suitable conditions on (alpha_{n}) and (beta_{n}).

The proposed filament dissolution model has been deemed as self-accelerated due to the process of the rupture of filament accelerates by itself under suitable conditions.

They also obtained that a modified Mann iterative process {x n } converges weakly to a fixed point of T under suitable control conditions.

In fact, for the above implicit iterative processes, most researchers always considered weak convergence theorems, and few researchers considered strong convergence theorem under suitable conditions.