A numerical scheme for a class of nonlinear Fredholm integral equations of the second kind

In this paper an iterative approach for obtaining approximate solutions for a class of nonlinear Fredholm integral equations of the second kind is proposed. The approach contains two steps: at the first one, we define a discretized form of the integral equation and prove that by considering some conditions on the kernel of the integral equation, solution of the discretized form converges to the exact solution of the problem. Following that, in the next step, solution of the discretized form is approximated by an iterative approach. We finally on some examples show the efficiency of the proposed approach.     

Analytical solution in transient thermo‐elasticity of functionally graded thick hollow cylinders (Pseudo‐dynamic analysis)

This work studies transient thermal stresses in a thick hollow cylinder made of a functionally graded material (FGM). Material properties are considered to be nonlinear with a power law distribution through the thickness. The cylinder is assumed to be of infinite length, and the plane strain condition is supposed. The displacement and the distribution of stresses are obtained by analytical solution of governing differential equations of the Navier type. The transient dynamic behavior of thermal stresses is determined and discussed for various power law exponents appearing in functions determining mechanical properties of FGMs. Copyright © 2009 John Wiley & Sons, Ltd.     

On the average degree of some irreducible characters of a finite group

Let G be a finite group and N be a non-trivial normal subgroup of G, such that the average degree of irreducible characters in $\mathrm{Irr}(G|N)$ is less than or equal to 16/5. Then, we prove that N is solvable. Also, we prove the solvability of G, by assuming that the average degree of irreducible characters in $\mathrm{Irr}(G|N)$ is strictly less than 16/5. We show that the bounds are sharp.     

Antibacterial Nanomaterials: Mechanisms,Impacts on Antimicrobial Resistance and Design Principles

Antimicrobial resistance (AMR) is one of the biggest threats to the environment and health. AMR rapidly invalidates conventional antibiotics, and antimicrobial nanomaterials have been increasingly explored as alternatives. Interestingly, several antimicrobial nanomaterials show AMR-independent antimicrobial effects without detectable new resistance and have therefore been suggested to prevent AMR evolution. In contrast, some are found to trigger the evolution of AMR. Given these seemingly conflicting findings, a timely discussion of the two faces of antimicrobial nanomaterials is urgently needed. This review systematically compares the killing mechanisms and structure-activity relationships of antibiotics and antimicrobial nanomaterials. We then focus on nano-microbe interactions to elucidate the impacts of molecular initiating events on AMR evolution. Finally, we provide an outlook on future antimicrobial nanomaterials and propose design principles for the prevention of AMR evolution.