Best approximation of $(\mathcal{G}_{1},\mathcal{G}_{2})$-random operator inequality in matrix Menger Banach algebras with application of stochastic Mittag-Leffler and $\mathbb{H}$-Fox control functions

We stabilize pseudostochastic $(\mathcal{G}_{1},\mathcal{G}_{2})$ ( G 1 , G 2 ) -random operator inequality using a class of stochastic matrix control functions in matrix Menger Banach algebras. We get an approximation for stochastic $(\mathcal{G}_{1},\mathcal{G}_{2})$ ( G 1 , G 2 ) -random operator inequality by means of both direct and fixed point methods. As an application, we apply both stochastic Mittag-Leffler and $\mathbb{H}$ H -fox control functions to get a better approximation in a random operator inequality.

On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

In this paper we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in $\tau$-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show that the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

Best approximation of κ-random operator inequalities in matrix MB-algebras

We introduce a class of stochastic matrix control functions and apply them to stabilize pseudo stochastic κ-random operator inequalities in matrix MB-algebras. We obtain an approximation for stochastic κ-random operator inequalities and calculate the maximum error of the estimate.

A Hybrid k-Means Cuckoo Search Algorithm Applied to the Counterfort Retaining Walls Problem

The counterfort retaining wall is one of the most frequent structures used in civil engineering. In this structure, optimization of cost and CO2 emissions are important. The first is relevant in the competitiveness and efficiency of the company, the second in environmental impact. From the point of view of computational complexity, the problem is challenging due to the large number of possible combinations in the solution space. In this article, a k-means cuckoo search hybrid algorithm is proposed where the cuckoo search metaheuristic is used as an optimization mechanism in continuous spaces and the unsupervised k-means learning technique to discretize the solutions. A random operator is designed to determine the contribution of the k-means operator in the optimization process. The best values, the averages, and the interquartile ranges of the obtained distributions are compared. The hybrid algorithm was later compared to a version of harmony search that also solved the problem. The results show that the k-mean operator contributes significantly to the quality of the solutions and that our algorithm is highly competitive, surpassing the results obtained by harmony search.

Approximation of an Additive ϱ1,ϱ2-Random Operator Inequality

We solve the additive ϱ1,ϱ2-random operator inequality ξtTω,u+v−Tω,u−Tω,v≥κMξtϱ1Tω,u+v+Tω,u−v−2Tω,u,ξtϱ22Tω,u+v/2−Tω,u−Tω,v, in which ϱ1,ϱ2∈ℂ are fixed and max2ϱ1,ϱ2<1. Finally, we get an approximation of the mentioned additive ϱ1,ϱ2-random operator inequality by direct technique.

Towards standardized postprocessing of global longitudinal strain by feature tracking – OptiStrain CMR-FT study

Background Left ventricular global longitudinal strain (GLS) with cardiovascular magnetic resonance (CMR) is an important prognostic biomarker. Its everyday clinical use is limited due to methodological and postprocessing diversity among the users and vendors. Standardization of postprocessing approaches may reduce the random operator-dependent variability, allowing for comparability of measurements despite the systematic vendor-related differences. Methods We investigated the random component of variability in GLS measurements by optimization steps which incrementally improved observer reproducibility and agreement. Cine images in two-, three- and four-chamber-views were serially analysed by two independent observers using two different CMR-FT softwares. The disparity of outcomes after each series was systematically assessed after a number of stepwise adjustments which were shown to significantly reduce the inter-observer and intervendor bias, resulting standardized postprocessing approach. The final analysis was performed in 44 subjects (ischaemic heart disease n = 15, non-ischaemic dilated cardiomyopathy, n = 19, healthy controls, n = 10). All measurements were performed blind to the underlying group allocation and previous measurements. Inter- and intra-observer variability were tested using Bland-Altman analyses, intra-class correlation coefficients (ICCs) and coefficients of variation (CVs). Results Compared to controls, mean GLS was significantly lower in patients, as well as between the two subgroups (p < 0.01). These differences were accentuated by standardization procedures, with significant increase in Cohen’s D and AUCs. The benefit of standardization was also evident through improved CV and ICC agreements between observers and the two vendors. Initial intra-observer variability CVs for GLS parameters were 7.6 and 4.6%, inter-observer variability CVs were 11 and 4.7%, for the two vendors, respectively. After standardization, intra- and interobserver variability CVs were 3.1 and 4.3%, and 5.2 and 4.4%, respectively. Conclusion Standardization of GLS postprocessing helps to reduce the random component of variability, introduced by inconsistencies of and between observers, and also intervendor variability, but not the systematic inter-vendor bias due to differences in image processing algorithms. Standardization of GLS measurements is an essential step in ensuring the reliable quantification of myocardial deformation, and implementation of CMR-FT in clinical routine.

Random fixed point theorems in Banach spaces applied to a random nonlinear integral equation of the Hammerstein type

The purpose of this paper is to define a new random operator called the generalized ϕ-weakly contraction of the rational type. This new random operator includes those studied by Khan et al. (Filomat 31(12):3611–3626, 2017) and Zhang et al. (Appl. Math. Mech. 32(6):805–810, 2011) as special cases. We prove some convergence, existence, and stability results in separable Banach spaces. Moreover, we produce some numerical examples to demonstrate the applicability of our analytical results. Furthermore, we apply our results in proving the existence of a solution of a nonlinear integral equation of the Hammerstein type.