Strong convergence of the modified Ishikawa iterative method for infinitely many nonexpansive mappings in Banach spaces

In this paper, we introduce a new modified Ishikawa iterative process for computing fixed points of an infinite family nonexpansive mapping in the framework of Banach spaces. Then, we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions which solves a variational inequality. The results obtained in this paper extend and improve on the recent results of Qin et al. [Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces, Journal of Computational and Applied Mathematics 230 (1) (2009) 121–127], Cho et al. [Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces, Computers and Mathematics with Applications 56 (2008) 2058–2064] and many others.     

The Investigation of the Fractional-View Dynamics of Helmholtz Equations Within Caputo Operator

It is eminent that partial differential equations are extensively meaningful in physics, mathematics and engineering. Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior. In the present research, mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives. First, the Helmholtz equations are presented in Caputo’s fractional derivative. Then Natural transformation, along with the decomposition method, is used to attain the series form solutions of the suggested problems. For justification of the proposed technique, it is applied to several numerical examples. The graphical representation of the solutions shows that the suggested technique is an accurate and effective technique with a high convergence rate than other methods. The less calculation and higher rate of convergence have confirmed the present technique’s reliability and applicability to solve partial differential equations and their systems in a fractional framework.     

COVID-19 Infected Lung Computed Tomography Segmentation and Supervised Classification Approach

The purpose of this research is the segmentation of lungs computed tomography (CT) scan for the diagnosis of COVID-19 by using machine learning methods. Our dataset contains data from patients who are prone to the epidemic. It contains three types of lungs CT images (Normal, Pneumonia, and COVID-19) collected from two different sources; the first one is the Radiology Department of Nishtar Hospital Multan and Civil Hospital Bahawalpur, Pakistan, and the second one is a publicly free available medical imaging database known as Radiopaedia. For the preprocessing, a novel fuzzy c-mean automated region-growing segmentation approach is deployed to take an automated region of interest (ROIs) and acquire 52 hybrid statistical features for each ROIs. Also, 12 optimized statistical features are selected via the chi-square feature reduction technique. For the classification, five machine learning classifiers named as deep learning J4, multilayer perceptron, support vector machine, random forest, and naive Bayes are deployed to optimize the hybrid statistical features dataset. It is observed that the deep learning J4 has promising results (sensitivity and specificity: 0.987; accuracy: 98.67%) among all the deployed classifiers. As a complementary study, a statistical work is devoted to the use of a new statistical model to fit the main datasets of COVID-19 collected in Pakistan.     

A Novel Multiple Dependent State Sampling Plan Based on Time Truncated Life Tests Using Mean Lifetime

The design of a new adaptive version of the multiple dependent state (AMDS) sampling plan is presented based on the time truncated life test under the Weibull distribution. We achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans. A warning sign for acceptance number was proposed to increase the probability of current lot acceptance. The optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk. A simulation study was presented to support the proposed sampling plan. A comparison between the proposed and existing sampling plans, namely multiple dependent state (MDS) sampling plans and a modified multiple dependent state (MMDS) sampling plan, was considered under the average sampling number and operating characteristic curve values. In addition, the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling plan. The results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.     

Experimental and numerical investigations of the shear behavior of binary particle blends

In this study, a Schulze ring shear tester and the discrete element method (DEM) are employed to investigate the effect of polydispersity on the binary shear flows. Both experimental results and DEM simulations show that the preshear stresses are greater for binary blends than for monodispersed particles. The flowability of these mixtures is strongly affected by the solid fraction, with minimal flow function values correlating to maximum packing fraction. However, minimum flow function values are not observed at the same packing fractions where the maximum preshear stress occurs. Using DEM, it is demonstrated that the decrease of angular velocity of larger particles due to the addition of small adhesive particles reduces and the fraction of large-small particle contact both make contributions to shear stress difference. A mechanism is proposed to quantify the effects of these two factors.     

Influences of Soret and Dufour numbers on mixed convective and chemically reactive Casson fluids flow towards an inclined flat plate

The purpose of this study is to examine the magnetohydrodynamic mixed convection Casson fluid flow over an inclined flat plate along with the heat source/sink. The present flow problem is considered under the assumption of the chemical reaction and thermal radiation impacts along with heat and mass transport. The leading nonlinear partial differential equations of the flow problem were renovated into the nonlinear ordinary differential equations (ODEs) with the assistance of appropriate similarity transformations and then we solved these ODEs with the employment of the bvp4c technique using the computational software MATLAB. The consequences of numerous leading parameters such as thermophoretic parameter, local temperature Grashof number, solutal Grashof number, suction parameter, magnetic field parameter, Prandtl number, chemical reaction parameter, Dufour number, Soret number, angle of inclination, radiation parameter, heat source/sink, and Casson parameter on the fluid velocity, temperature, and concentration profiles are discoursed upon  and presented through different graphs. Some important key findings of the present investigation are that the temperature of the Casson fluid becomes lower for local temperature Grashof number and solutal Grashof number. It is initiated that the Casson fluid parameter increases the velocity of the fluid whereas the opposite effect is noticed in the temperature profile. Higher estimation of Prandtl number and magnetic parameter elevated the Casson fluid concentration. Finally, the skin friction coefficient, Nusselt number, and Sherwood number are calculated and tabulated. It is also examined that the Nusselt number is weakened for both the Dufour number and Soret number but the skin fraction coefficient is greater for both the Dufour number and Soret number.     

Perceptual depth synthesis in the visual system as revealed by selective adaptation.

Selective adaptation was used to determine the degree of interactions between channels processing relative depth from stereopsis, motion parallax, and texture. Monocular adaptations with motion parallax or binocular stationary adaptation caused test surfaces, viewed either stationary binocularly or monocularly with motion parallax, to appear to slant in the opposite direction compared with the slant initially adapted to. Monocular adaptations on frontoparallel surfaces covered with a pattern of texture gradients caused a subsequently viewed test surface, viewed either monocularly with motion parallax or stationary binocularly, to appear to slant in the opposite direction as the slant indicated by the texture in the adaptation condition. No aftereffect emerged in the monocular stationary test condition. A mechanism of independent channels for relative depth perception is dismissed in favor of a view of an asymmetrical interactive processing of different information sources. The results suggest asymmetrical inhibitory interactions among habituating slant detector units receiving inputs from static disparity, dynamic disparity, and texture gradients. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Entropy generation on MHD peristaltic flow of Cu‐water nanofluid with slip conditions

The current research explores entropy generation and effect of magnetic field on peristaltic flow of copper‐water nanofluid in an asymmetric configuration saturated with porous medium. Slip conditions are invoked for velocity and temperature. Governing flow problem is constructed under the long wave length assumption. Analytical result for the problem is computed by exploiting homotopy analysis methodology. The influences of involved physical parameters are investigated through plots.     

Magnetohydrodynamic mixed convective peristaltic slip transport of carbon nanotubes dispersed in water through an inclined channel with Joule heating

Carbon nanotubes are considered to be the latest nanotechnology innovation because of their remarkable physical and mechanical properties. Recently, researchers have shown great interest in the peristaltic transport of nanotube-based nanofluid as this process involves a wide range of uses in the bioengineering, biomechanics, and medical fields. In this investigation, influence of single-walled carbon nanotubes (SWCNTs) on magnetohydrodynamic mixed convective peristalsis through an inclined and asymmetric channel is analyzed. The additional physical mechanisms such as velocity slip, viscous dissipation, thermal slip, Joule heating, and heat consumption/injection are also encountered. The principal equations are formulated under the estimation of long wavelength and low Reynolds number. Perturbation method is operated to evaluate the solutions of subsequent nonlinear system of equations for small Brinkman number. To deeply analyze the characteristics of embedded parameters, graphs are presented and comprehensive interpretation is provided. Rate of heat transfer is augmented for higher proportion of SWCNTs in base fluid water. At the center of channel, increasing volume fraction of SWCNTs and strong Lorentz force retard the motion of fluid while flow is accelerated in more inclined channel. Volume fraction of SWCNTs, Grashof number, and inclination parameter encourage the pressure gradient at wider part of the channel. The size of bolus is contracted by strong Lorentz force and large volume fraction of SWCNTs. Three basic models named as Maxwell's, Hamilton-Crosser's, and Xue's model are utilized to forecast the thermal conductivity of nanofluid and succeeding numerical computations for heat transfer rate are presented through table. It is found that the Xue's model is most effective to anticipate the thermal conductivity of nanofluids. Moreover, the addition of a heat sink in the system significantly influences the heat transfer process and plays a supportive role to rapidly cool down the channel.