On the two classes of high‐order convergent methods of approximate inverse preconditioners for solving linear systems

Two classes of methods for approximate matrix inversion with convergence orders p =3?2^k +1 (Class 1) and p =5?2^k ?1 (Class 2), k ≥1 an integer, are given based on matrix multiplication and matrix addition. These methods perform less number of matrix multiplications compared to the known hyperpower method or p th‐order method for the same orders and can be used to construct approximate inverse preconditioners for solving linear systems. Convergence, error, and stability analyses of the proposed classes of methods are provided. Theoretical results are justified with numerical results obtained by using the proposed methods of orders p =7,13 from Class 1 and the methods with orders p =9,19 from Class 2 to obtain polynomial preconditioners for preconditioning the biconjugate gradient (BICG) method for solving well‐ and ill‐posed problems. From the literature, methods with orders p =8,16 belonging to a family developed by the effective representation of the p th‐order method for orders p =2^k , k is integer k ≥1, and other recently given high‐order convergent methods of orders p =6,7,8,12 for approximate matrix inversion are also used to construct polynomial preconditioners for preconditioning the BICG method to solve the considered problems. Numerical comparisons are given to show the applicability, stability, and computational complexity of the proposed methods by paying attention to the asymptotic convergence rates. It is shown that the BICG method converges very quickly when applied to solve the preconditioned system. Therefore, the cost of constructing these preconditioners is amortized if the preconditioner is to be reused over several systems of same coefficient matrix with different right sides.     

Universal sound absorption in amorphous solids: A theory of elastically coupled generic blocks

Glasses are known to exhibit quantitative universalities at low temperatures, the most striking of which is the ultrasonic attenuation coefficient Q^?1. In this work we develop a theory of coupled generic blocks with a certain randomness property to show that universality emerges essentially due to the interactions between elastic blocks, regardless of their microscopic nature.     

One‐pot three‐component synthesis of novel 2‐(3‐nitro‐phenyl)‐quinazoline‐4‐carboxylic acid derivatives

A simple and easy synthesis of 2‐(3‐nitro‐phenyl)‐quinazoline‐4‐carboxylic acid ( 3 ) has been successfully developed through a one‐pot three‐component condensation reaction of (2‐amino‐phenyl)‐oxo‐acetic acid sodium salt ( 1 ) obtained from the hydrolysis of isatin with ammonium acetate and 3‐nitrobenzaldehyde. Some novel quinazoline‐ester derivatives 4‐7 were then obtained by the reaction between the new compound 3 and various alcohols. Then, quinazoline‐amide derivatives 10‐14 were synthesized from the reaction of various amines and 2‐(3‐nitro‐phenyl)‐quinazoline‐4‐carbonyl chloride ( 8 ), obtained by the reaction of compound 3 with SOCl₂. Finally, some novel quinazoline‐azo derivatives 17‐19 were synthesized by the coupling reaction between β‐dicarbonyl compounds and the novel amino‐quinazoline derivative compound 15 , obtained by reduction of nitro‐quinazoline derivative compound 11 . Thus, a new series of quinazoline‐4‐carboxylic acid, ester, amide, and azo derivatives was synthesized and fully characterized by ¹H NMR, ¹³C NMR, IR, and mass spectrometry analysis.     

A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm

Swarm intelligence is a research branch that models the population of interacting agents or swarms that are able to self-organize. An ant colony, a flock of birds or an immune system is a typical example of a swarm system. Bees’ swarming around their hive is another example of swarm intelligence. Artificial Bee Colony (ABC) Algorithm is an optimization algorithm based on the intelligent behaviour of honey bee swarm. In this work, ABC algorithm is used for optimizing multivariable functions and the results produced by ABC, Genetic Algorithm (GA), Particle Swarm Algorithm (PSO) and Particle Swarm Inspired Evolutionary Algorithm (PS-EA) have been compared. The results showed that ABC outperforms the other algorithms.     

A comparative study of Artificial Bee Colony algorithm

Artificial Bee Colony (ABC) algorithm is one of the most recently introduced swarm-based algorithms. ABC simulates the intelligent foraging behaviour of a honeybee swarm. In this work, ABC is used for optimizing a large set of numerical test functions and the results produced by ABC algorithm are compared with the results obtained by genetic algorithm, particle swarm optimization algorithm, differential evolution algorithm and evolution strategies. Results show that the performance of the ABC is better than or similar to those of other population-based algorithms with the advantage of employing fewer control parameters.     

Green synthesis of silver nanoparticles by using eugenol and evaluation of antimicrobial potential

The importance of green synthesis was revealed with advantages such as: eliminating the use of expensive chemicals; consume less energy; and generate environmentally benign products. With this aim, silver nanoparticles (AgNPs) were synthesized by using isolated eugenol from clove extract. Its antimicrobial potential was determined on three different microorganisms. Clove was extracted and eugenol was isolated from this extract. Green synthesis was performed and an anti‐microbial study was performed. All extraction and isolation analyses were performed by high‐performance liquid chromatography (HPLC); identification and confirmation were achieved using liquid chromatography–mass spectrometry (LC–MS); and scanning electron microscopy was used for characterization. Both HPLC and LC–MS analyses showed that eugenol obtained purely synthesized AgNPs and 20‐25‐nm‐sized and homogeneous shaped particles seen in images. The antimicrobial effects of AgNPs at eight concentrations were determinated against Staphylococcus aureus, Escherichia coli and Candida albicans, and maximum inhibition zone diameters were found as 2.6 cm, 2.4 cm and 1.5 cm, respectively. The results of the antimicrobial study showed that eugenol as a biological material brought higher antimicrobial effect to AgNPs in comparison to the other materials found in the literature.