A new predictor-corrector method for noncoercive mixed variational inequalities

In this paper, we use the auxiliary principle technique to suggest and analyze a class of predictor-corrector methods for solving noncoercive mixed variational inequalities. The convergence of the proposed method requires only the partially relaxed strongly monotonicity, which is even weaker than the co-coercivity. As special cases, we obtain a number of new and known results for classical variational inequalities.     

Strong convergence of the modified hybrid steepest-descent methods for general variational inequalities

In this paper, we consider the general variational inequality GVI(F, g, C), whereF andg are mappings from a Hilbert space into itself andC is the fixed point set of a nonexpansive mapping. We suggest and analyze a new modified hybrid steepest-descent method of type methodu _n+1=(1?α+θ _n+1)Tu _n +αu _n ?θ _n+1 g (Tu _n )?λ _n+1 μF(Tu _n ),n≥0. for solving the general variational inequalities. The sequencex _n is shown to converge in norm to the solutions of the general variational inequality GVI(F, g, C) under some mild conditions. Application to constrained generalized pseudo-inverse is included. Results proved in the paper can be viewed as an refinement and improvement of previously known results.     

Boundary Layer Flow over a Curved Surface Imbedded in Porous Medium

This research is made to visualize the boundary layer flow by a curved stretching sheet embedded in porous medium. The geometry is bended(curved), therefore the curvilinear coordinates are used to model the present problem.Fluid is electrically conducting with the presence of uniform magnetic field. The governing non-linear partial differential equation reduces to non-linear ordinary differential equations by using the dimensionless suitable transformations. The numerical solutions are obtained by using the method bvp4c from MATLAB. The effects of curvature parameter, nondimensional magnetic parameter, and porosity parameter on the velocity field and skin friction coefficient are examined.The skin friction profile enhances with enhancing the values of porosity and magnetic parameter. Comparison of the present results with the existing results in the literature for the flat surface is also given.     

Proximal Methods for Mixed Variational Inequalities

A proximal point method for solving mixed variational inequalities is suggested and analyzed by using the auxiliary principle technique. It is shown that the convergence of the proposed method requires only the pseudomonotonicity of the operator, which is a weaker condition than monotonicity. As special cases, we obtain various known and new results for solving variational inequalities and related problems. Our proof of convergence is very simple as compared with other methods.     

Unifying fourth-order family of iterative methods

In this work, we develop a new two-parameter family of iterative methods for solving nonlinear scalar equations. One of the parameters is defined through an infinite power series consisting of real coefficients while the other parameter is a real number. The methods of the family are fourth-order convergent and require only three evaluations during each iteration. It is shown that various fourth-order iterative methods in the published literature are special cases of the developed family. Convergence analysis shows that the methods of the family are fourth-order convergent which is also verified through the numerical work. Computations are performed to explore the efficiency of various methods of the family.     

An Edge-Supported Blockchain-Based Secure Authentication Method and a Cryptocurrency-Based Billing System for P2P Charging of Electric Vehicles

The popularity of electric vehicles (EVs) is constantly increasing, as they use relatively greener, sustainable energy. However, it is a fact that the charging stations for EVs are yet to meet the demand. It could be a great solution if a peer-to-peer (P2P) charging system could be initiated by anyone who wants to make their garage’s charge points publicly available for commercial purposes, named a home charging station (HCS). In this work, our idea is to bring interested charging stations under a network of nodes and a blockchain-based management system, where the blockchain is responsible for ensuring the authenticity of both the charging stations and charge receiver. A cryptocurrency-based payment system has also been proposed to ensure transactions’ security, integrity, transparency, and immutability. A reputation management system is applied to maintain the quality of service. Miners with high processing power are used to alleviate lagging during block creation, supported by edge servers. The proposed system has been implemented by using virtual machines. A theoretical analysis is presented to assess the compatibility and possible cost requirements to implement the system in a real-world scenario.     

Applications of Nanomaterials in Microbial Fuel Cells: A Review

Microbial fuel cells (MFCs) are an environmentally friendly technology and a source of renewable energy. It is used to generate electrical energy from organic waste using bacteria, which is an effective technology in wastewater treatment. The anode and the cathode electrodes and proton exchange membranes (PEM) are important components affecting the performance and operation of MFC. Conventional materials used in the manufacture of electrodes and membranes are insufficient to improve the efficiency of MFC. The use of nanomaterials in the manufacture of the anode had a prominent effect in improving the performance in terms of increasing the surface area, increasing the transfer of electrons from the anode to the cathode, biocompatibility, and biofilm formation and improving the oxidation reactions of organic waste using bacteria. The use of nanomaterials in the manufacture of the cathode also showed the improvement of cathode reactions or oxygen reduction reactions (ORR). The PEM has a prominent role in separating the anode and the cathode in the MFC, transferring protons from the anode chamber to the cathode chamber while preventing the transfer of oxygen. Nanomaterials have been used in the manufacture of membrane components, which led to improving the chemical and physical properties of the membranes and increasing the transfer rates of protons, thus improving the performance and efficiency of MFC in generating electrical energy and improving wastewater treatment.     

Global-local methodologies and their application to nonlinear analysis

An assessment is made of the potential of different global-local analysis strategies for predicting the nonlinear and postbuckling responses of structures. Two postbuckling problems of composite panels are used as benchmarks and the application of different global-local methodologies to these benchmarks is outlined. The key elements of each of the global-local strategies are discussed and future research areas needed to realize the full potential of global-local methodologies are identified.     

Well-posed variational inequalities

In this paper, we introduce the concept of well-posedness for general variational inequalities and obtain some results under pseudomonotonicity. It is well known that monotonicity implies pseudomonotonicity, but the converse is not true. In this respect, our results represent an improvement and refinement of the previous known results. Since the general variational inequalities include (quasi) variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems.