Two Families of Multipoint Root-Solvers Using Inverse Interpolation with Memory

In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only one evaluation of its derivative are constructed by the inverse interpolation with the memory on the previous step for solving the simple root of a nonlinear equation. The order and order of convergence of them are proved respectively. Finally, the proposed methods and the basins of attraction are demonstrated by the numerical examples.

Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs

In this paper, a group of Gauss-Legendre iterative methods with cubic convergence for solving nonlinear systems are proposed. We construct the iterative schemes based on Gauss-Legendre quadrature formula. The cubic convergence and error equation are proved theoretically, and demonstrated numerically. Several numerical examples for solving the system of nonlinear equations and boundary-value problems of nonlinear ordinary differential equations (ODEs) are provided to illustrate the efficiency and performance of the suggested iterative methods.

The Study on the (L,M)-Fuzzy Independent Set Systems

Independent sets play an important role in matroid theory. In this paper, the definitions of pre-independent fuzzy set system and independent fuzzy set system in L-fuzzy setting are presented. Independent M-fuzzifying set system is introduced and some of its properties are discussed. Further independent (L,M)-fuzzy set system is given and some of its properties are obtained. The relations of these independent set systems in the setting of fuzzy vector spaces and fuzzy graphs are showed.

Multi-Objective Optimization for Active Disturbance Rejection Control for the ALSTOM Benchmark Problem

Based on a thing that it is difficult to choose the parameters of active disturbance rejection control for the non-linear ALSTOM gasifier, multi-objective optimization algorithm is applied in the choose of parameters. Simulation results show that performance tests in load change and coal quality change achieve better dynamic responses and larger scales of rejecting coal quality disturbances. The study provides an alternative to choose parameters for other control schemes of the ALSTOM gasifier.

A New Newton-Type Method with Third-Order for Solving Systems of Nonlinear Equations

In this paper, a new two-step Newton-type method with third-order convergence for solving systems of nonlinear equations is proposed. We construct the new method based on the integral interpolation of Newton’s method. Its cubic convergence and error equation are proved theoretically, and demonstrated numerically. Its application to systems of nonlinear equations and boundary-value problems of nonlinear ODEs are shown as well in the numerical examples.

Steffensen-Type Method of Super Third-Order Convergence for Solving Nonlinear Equations

In this paper, a one-step Steffensen-type method with super-cubic convergence for solving nonlinear equations is suggested. The convergence order 3.383 is proved theoretically and demonstrated numerically. This super-cubic convergence is obtained by self-accelerating second-order Steffensen’s method twice with memory, but without any new function evaluations. The proposed method is very efficient and convenient, since it is still a derivative-free two-point method. Its theoretical results and high computational efficiency is confirmed by Numerical examples.

Seaweed pattern formation in the non-axially directional solidification of 2D-like and 3D Al-3 wt.% Mg single crystal

1.Introduction Microstructures are at the centre of materials science and engineering and play an essential role in determining the in-service mechanical properties of metallic alloys[1–4].Extensive theoretical and experimental investigations have been undertaken to describe and determine solidification microstructures as a function of solidification conditions.The seaweed pattern is one of the most important classes of microstructural patterns[5–7].The characteristic of this pattern is that its extending tips—unlike the behaviour observed in needle-like dendrites—split repeatedly into two or more parts.

Inhibition of free radical induced oxidative hemolysis of red blood cells by green tea polyphenols

The in vitro oxidative hemolysis of human red blood cells (RBC) was used as a model to study the free radical induced damage of biological membranes and the inhibitory effect of natural antioxidants. The hemolysis was induced by a water-soluble free radical initiator 2,2’-azo(2-asmidinopropane)dihydrochloride (AAPH) and inhibited by the principal polyphenolic components extracted from green tea leaves, i.e. (-)-epicatechin (EC), (-)-epigallocatechin (EGC), (-)-epicat-echin gallate (ECG), (-)-epigallocatechin gallate (EGCG) and gallic acid (GA). Addition of AAPH at 37℃ caused fast hemolysis after a short period of inhibition period, while addition of the green tea polyphenols efficiently suppressed the hemolysis in the activity sequence of EGCG 】 EGC】 ECG ≈EC】GA, demonstrating that these green tea polyphenols are effective antioxidants which could protect biological membranes from free radical induced oxidative damage.

First Total Synthesis of （±）-Latifolin and Its Antioxidant Mechanism

The first total synthesis of （±）-latifolin has been accomplished in six steps and 47.8% overall yield. To understand the relative importance of phenolic O-H and benzhydryl C-H hydrogen on the antioxidant activity of latifolin, 2,2-diphenyl-1-picrylhydrazyl （DPPH） radical scavenging assay and density functional theory （DFT） studies were carried out. On scavenging DPPH radical in ethanol, the activity of latifolin （1） bearing phenolic hydrogen is remarkably higher than analogue 10 bearing no phenolic hydrogen. Therefore, Phenolic hydrogen is responsible for latifolin＇s antioxidant activity rather than benzhydryl C-H hydrogen. Furthermore, the 5-OH BDE is lower than 2＇-OH and 7-CH BDEs by a DFT calculation, respectively. Based on theoretical results it is definitely concluded that the phenolic 5-OH plays a major role in the antioxidant activity of latifolin.