Strong convergence theorems for infinite family of relatively quasi nonexpansive mappings and systems of equilibrium problems

In this paper, we construct a new iterative scheme by hybrid method for approximation of common element of set of common fixed points of countably infinite family of relatively quasi-nonexpansive mappings and set of common solutions to a system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space using the properties of generalized f-projection operator. Then, we prove strong convergence of the scheme to a common element of the two sets. Furthermore, we apply our results to solve convex minimization problem. Our results extend important recent results.     

Atomistic simulation reveals structural mechanisms underlying D614G spike glycoprotein-enhanced fitness in SARS-COV-2

D614G spike glycoprotein (sgp) mutation in rapidly spreading severe acute respiratory syndrome coronavirus-2 (SARS-COV-2) is associated with enhanced fitness and higher transmissibility in new cases of COVID-19 but the underlying mechanism is unknown. Here, using atomistic simulation, a plausible mechanism has been delineated. In G614 sgp but not wild type, increased D(G)614-T859 Cα-distance within 65 ns is interpreted as S1/S2 protomer dissociation. Overall, ACE2-binding, post-fusion core, open-state and sub-optimal antibody-binding conformations were preferentially sampled by the G614 mutant, but not wild type. Furthermore, in the wild type, only one of the three sgp chains has optimal communication route between residue 614 and the receptor-binding domain (RBD); whereas, two of the three chains communicated directly in G614 mutant. These data provide evidence that D614G sgp mutant is more available for receptor binding, cellular invasion and reduced antibody interaction; thus, providing framework for enhanced fitness and higher transmissibility in D614G SARS-COV-2 mutant.     

Synthesis,NMR conformational studies and host–guest behaviour of new (+)-tartaric acid derivatives

A series of dimeric α,α,α′,α′-tetraaryl-1,3-dioxolane-4,5-dimethanol TADDOLs has been prepared and host–guest interactions of these structures have been characterized using a series of ¹H NMR studies. Enantioselective recognition of the chiral alcohols glycidol and menthol was observed for phenyl and 2-naphthyl derivatives. The influence of steric bulk on the dynamic fluxional behaviour of the TADDOL structures was demonstrated by dynamic NMR.     

An Iterative Algorithm for Approximating Solutions of Hammerstein Integral Equations

Suppose E is a uniformly smooth real Banach space and F, K: E → E are bounded accretive maps with D(K) = F(E) = E. Assume that the Hammerstein equation u + KFu = 0 has a solution u*. An explicit simple iteration process is shown to converge strongly to u*. No invertibility or continuity assumption is imposed on K. Our theorems are significant improvements on important recent results (e.g. [11 C. E. Chidume and N. Djitte ( 2012 ). Approximation of solutions of nonlinear integral equations of Hammerstein type. ISRN: Mathematical Article ID 963802.  [Google Scholar]]).     

Experiments with a Wire-Mesh Sensor for stratified and dispersed oil-brine pipe flow

Two-phase oil–water flow was studied in a 15 m long horizontal steel pipe, with 8.28 cm internal diameter, using mineral oil (having 830 kg/m³ density and 7.5 mPa s viscosity) and brine (1073 kg/m³ density and of 0.8 mPa s viscosity). Measurements of the holdup and of the cross-sectional phase fraction distribution were obtained for stratified flow and for highly dispersed oil–water flows, applying a capacitive Wire-Mesh Sensor specially designed for that purpose. The applicability of this measurement technique, which uses a circuit for capacitive measurements that is adapted to conductive measurements, where one of the fluids is water with high salinity (mimicking sea water), was assessed. Values for the phase fraction values were derived from the raw data obtained by the Wire-Mesh Sensor using several mixture permittivity models. Two gamma-ray densitometers allowed the accurate measurement of the holdups, which was used to validate the data acquired with the capacitive Wire-Mesh Sensor. The measured time-averaged distribution of the phase fraction over the cross-sectional area was used to investigate the details of the observed two-phase flow patterns, including the interface shape and water height. The experiments were conducted in the multiphase-flow test facility of Shell Global International B.V. in the Netherlands.     

Algorithms for a system of generalized mixed equilibrium problems and a countable family of some nonlinear multi-valued nonexpansive-type maps

In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halperntype that approximate a solution of a system of a generalized mixed equilibrium problem and a common fixed point of a countable family of totally quasi-φ-asymptotically nonexpansive multi-valued maps are constructed. Strong convergence of the sequence generated by these algorithms is proved in uniformly smooth and strictly convex real Banach spaces with KadecKlee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this class of nonlinear problems.     

MHD Stokes flow in a corrugated curved channel

Magnetohydrodynamic (MHD) flow through a corrugated curved channel is modelled. The flow is perpendicular to the corrugations and applied magnetic field. A boundary perturbation analysis for small corrugation amplitude is used to find the expressions for the stream function and the flow rate. It is found that the flow is inevitably decreased by the corrugations. For a given Hartmann number, the flow reduction varies with the channel radius of curvature. The effect of the phase difference between the corrugated walls is distinct, with minimum and maximum effects when the corrugated curved walls are in-phase and out-of-phase, respectively, for small corrugation wavenumber. However, when the corrugation wavenumber is large enough, the flow is independent of the phase difference. Generally, the study shows that the Hartmann number decreases the effect of the corrugations on the flow rate.     

Viscoelastic flow through a wavy curved channel

Time-dependent flow of a viscoelastic material through a wavy curved channel is studied. The flow traversing the wavy curved domain is modelled in the curvilinear coordinates. The viscoelastic fluid is described by the fluid relaxation and retardation times, and their variations are considered in relation to the flow characteristic time scale. The wavy walls of the curved channels are in sinusoidal form, with arbitrary phase difference. Using domain perturbation technique, the analytical solution of the model is obtained, including the velocity and the volumetric flow rate. The analytical solution is explained as a function of the flow domain structure, the viscoelastic fluid properties, and the flow generating force. Flow enhancement due to the flow domain is discussed; we have shown that the flow augmentation depends on the properties of the viscoelastic fluid. Furthermore, comparisons have been made with Newtonian fluid flow, and the prominent variations in the flow behaviours have been reported.