During this study, a rapid and simple method is presented for the green synthesis of the Ag/bentonite nanocomposite using Euphorbia larica extract as a stabilizing and reducing agent. The average size of biosynthesized Ag nanoparticles (NPs) was estimated less than 32 nm. The catalytic activity of Ag/bentonite nanocomposite was investigated in the reduction of 4‐nitrophenol (4‐NP) and some organic dyes including Congo red (CR), Methylene blue (MB) and Rhodamine B (RhB). According to the catalytic results, the biosynthesized Ag/bentonite nanocomposite can be used as an appropriate catalyst for an efficient, simple and economic strategy to degrade various organic dyes from wastewaters. Recyclability tests demonstrated catalyst stability and its capability in practical applications.

No abstract

In this article, we study the integrability and the non-existence of periodic orbits for the planar Kolmogorov differential systems of the form x ˙ = x ( R n - 1 ( x , y ) + P n ( x , y ) + S n + 1 ( x , y ) ) , y ˙ = y ( R n - 1 ( x , y ) + Q n ( x , y ) + S n + 1 ( x , y ) ) , \matrix{ {\dot x = x\left( {{R_{n - 1}}\left( {x,y} \right) + {P_n}\left( {x,y} \right) + {S_{n + 1}}\left( {x,y} \right)} \right),} \hfill \cr {\dot y = y\left( {{R_{n - 1}}\left( {x,y} \right) + {Q_n}\left( {x,y} \right) + {S_{n + 1}}\left( {x,y} \right)} \right),} \hfill \cr } where n is a positive integer, Rn−1 , Pn , Qn and Sn +1 are homogeneous polynomials of degree n − 1, n, n and n + 1, respectively. Applications of Kolmogorov systems can be found particularly in modeling population dynamics in biology and ecology.