Nonlocal beam theory for nonlinear vibrations of embedded multiwalled carbon nanotubes in thermal environment

A nonlocal elastic beam model is developed to investigate the small scale effects on the large-amplitude vibration analysis of embedded multiwalled carbon nanotubes (MWCNTs) at an elevated temperature. The nested slender nanotubes are coupled with each other through the van der Waals (vdW) interlayer interaction. The curvature-dependent vdW force employed incorporates not only pairwise nearest-neighbor but also nonneighbor interactions between nested nanotubes. The incremental harmonic balance method is adopted to analytically solve the nonlinear equations that are governed by the vibrations of nested nanotubes. The influences of small scale parameter, geometrical parameters, temperature rise, and the elastic medium are fully examined.     

Mo (CO)6‐assisted Pd‐supported magnetic graphene oxide‐catalyzed carbonylation‐cyclization as an efficient way for the synthesis of 4(3H)‐quinazolinones

In this paper, a novel catalyst is introduced based on the immobilization of palladium on modified magnetic graphene oxide nanoparticles. The catalyst is characterized by several methods, including transmission electron microscopy, scanning electron microscopy, X‐ray fluorescence, vibrating‐sample magnetometer, Fourier transform‐infrared and dynamic light scattering (DLS) analysis. The activity of the catalyst was investigated in the synthesis of 4(3H)‐quinazolinones via Pd‐catalyzed carbonylation‐cyclization of N‐(2‐bromoaryl) benzimidamides by Mo (CO)₆. The Mo (CO)₆ is used as a carbon monoxide source for performing the reaction under mild conditions. The catalyst showed good reusability, and no change in activity was observed after 10 cycles of recovery.     

Invariant Pseudolinearity with Applications

In this paper, we introduce the notion of invariant pseudolinearity for nondifferentiable and nonconvex functions by means of Dini directional derivatives. We present some characterizations of invariant pseudolinear functions. Some characterizations of the solution set of a nonconvex and nondifferentiable, but invariant, pseudolinear program are obtained. The results of this paper extend various results for pseudolinear functions, pseudoinvex functions, and η-pseudolinear functions, and also for pseudoinvex programs, pseudolinear programs, and η-pseudolinear programs.