This paper deals with the oscillatory properties of a class of nonlinear neutralparabolic partial differential equations with several delays. Sufficient criteria for the equa-tion to be oscillatory are obtained by mak...This paper deals with the oscillatory properties of a class of nonlinear neutralparabolic partial differential equations with several delays. Sufficient criteria for the equa-tion to be oscillatory are obtained by making use of some results of first-order functionaldifferential inequalities. These results fully reveal the essential difference between this typeand that without delays.展开更多
Weak intermolecular interactions in aniline-pyrrole dimer clusters have been studied by the dispersion-corrected density functional theory(DFT) calculations. Two distinct types of hydrogen bonds are demonstrated with ...Weak intermolecular interactions in aniline-pyrrole dimer clusters have been studied by the dispersion-corrected density functional theory(DFT) calculations. Two distinct types of hydrogen bonds are demonstrated with optimized geometric structures and largest interaction energy moduli. Comprehensive spectroscopic analysis is also addressed revealing the orientation-dependent interactions by noting the altered red-shifts of the infrared and Raman activities. Then we employ natural bond orbital(NBO)analysis and atom in molecules(AIM) theory to have determined the origin and relative energetic contributions of the weak interactions in these systems. NBO and AIM calculations confirm the V-shaped dimer cluster is dominated by N.H···N and C.H···π hydrogen bonds, while the J-aggregated isomer is stabilized by N.H···π, n→π* and weak π···π* stacking interactions.The noncovalent interactions are also demonstrated via energy decomposition analysis associated with electrostatic and dispersion contributions.展开更多
基金Supported by the National Natural Science Foundation of China(40373003, 40372121)Supported by the Youth Foundation of Cina University of Geosciences(CUGQNL0517)
文摘This paper deals with the oscillatory properties of a class of nonlinear neutralparabolic partial differential equations with several delays. Sufficient criteria for the equa-tion to be oscillatory are obtained by making use of some results of first-order functionaldifferential inequalities. These results fully reveal the essential difference between this typeand that without delays.
基金supported by the National Project“Development of Advanced Scientific Instruments Based on Deep Ultraviolet Laser Source”(Y31M0112C1)the National Basic Research Program of China(2011CB808402)Z.Luo acknowledges the Young Professionals Programme in Institute of Chemistry,Chinese Academy of Sciences(ICCAS-Y3297B1261)
文摘Weak intermolecular interactions in aniline-pyrrole dimer clusters have been studied by the dispersion-corrected density functional theory(DFT) calculations. Two distinct types of hydrogen bonds are demonstrated with optimized geometric structures and largest interaction energy moduli. Comprehensive spectroscopic analysis is also addressed revealing the orientation-dependent interactions by noting the altered red-shifts of the infrared and Raman activities. Then we employ natural bond orbital(NBO)analysis and atom in molecules(AIM) theory to have determined the origin and relative energetic contributions of the weak interactions in these systems. NBO and AIM calculations confirm the V-shaped dimer cluster is dominated by N.H···N and C.H···π hydrogen bonds, while the J-aggregated isomer is stabilized by N.H···π, n→π* and weak π···π* stacking interactions.The noncovalent interactions are also demonstrated via energy decomposition analysis associated with electrostatic and dispersion contributions.
