Synthesis,XRD, spectral (IR,UV–Vis,NMR) characterization and quantum chemical exploration of benzoimidazole‐based hydrazones: A synergistic experimental‐computational analysis

Present study advocates the joint experimental and computational studies of two potent benzoimidazole‐based hydrazones with chemical formula C₂₃H₁₈F₂N₄O ( 5a ) and C₂₅H₂₂FN₅O₃ ( 5b ). Both 5a and 5b were synthesized and resolved into their crystal structures using SC‐XRD for the assessment of bond lengths, bond angles, unit cells and space groups. The structures of 5a and 5b were chemically characterized using infrared (FT‐IR), UV–Visible, nuclear magnetic resonance (¹H‐NMR and ¹³C‐NMR), EIMS and elemental analysis. DFT at M06‐2X/6‐31G(d,p) level of theory was performed to get optimized structures and countercheck the experimental findings. Overall, DFT findings show excellent concurrence with the experimental data which confirms the purity of both compounds. FMO, NBO analysis, MEP surfaces and nonlinear optical (NLO) properties were explored at same level of theory. UV–Vis analysis at TDDFT/M06‐2X/6‐31G(d,p) level of theory showed that 5b is red shifted with λ_max 331.69 nm as compared to 5a with λ_max 240.25 nm. Global reactivity parameters were estimated using energy of FMOs indicated the greater harness value than the softness values of 5a and 5b . NBO analysis confirmed that the presence of non‐covalent interactions, hydrogen bonding and hyper conjugative interactions are pivotal cause for the existence of 5a and 5b in the solid‐state. NLO results of 5a and 5b were observed better than standard molecule recommended the NLO activity of said molecules for optoelectronic applications.     

A general approach to specific second order ordinary differential equations using homotopy perturbation method

Homotopy perturbation method is used to solve specific second order ordinary differential equations and tested for different examples. The results obtained demonstrate efficiency of the proposed method.     

加权(C)eby(s)ev-Ostrowski型不等式

关于著名的Cebysev不等式，已有众多的研究成果．通过建立积分不等式，来建立全新的加权Cebysev型积分不等式．给予了独立的证明，并给出了此类不等式的新评价．     

Influence of nozzle area ratio on the gas-particle flow for single-hose dry ice blasting nozzle

Journal of Thermal Analysis and Calorimetry - In this paper, a numerical study was performed to examine the effect of divergent nozzle length of single-hose dry ice blasting on the development of...     

Multiscale characterization of antimicrobial poly(vinyl butyral)/titania nanofibrous composites

Titania nanofillers were used to reinforce nanofibers in composite mats produced by electrospinning of poly(vinyl butyral) with two different concentrations of polymers. The titania nanoparticles and titania nanotubes were added into an acetic acid/ethanol solution in different contents of 3 and 1 wt%, respectively. The effect of the processing system on the morphology of the produced fibers was analyzed. The antimicrobial poly(vinyl butyral) composite fibers with titanium dioxide nanoparticles and titanium dioxide nanotubes were produced by single and multineedle electrospinning systems. This study reports fabrication of composite nanofibrous mats with significant mechanical and antimicrobial properties at a high production speed, which is promising for commercial applications (health care, photocatalysis, protective clothing, etc.). The reported result revealed an outstanding correlation between values of elastic modulus derived from nanoindentation and dynamic mechanical techniques. Copyright © 2017 John Wiley & Sons, Ltd.