Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.

Amino group stretching vibrations in primary aliphatic amines

Abstract: Primary aliphatic amines can be characterized by infrared spectroscopy as to the nature and degree of branching of the alkyl chain, using the fundamental antisymmetric and symmetric NH2 stretching frequencies measured in dilute C2Cl4 solution. Where steric and direct conjugation effects are absent both frequencies and the integrated intensity of the antisymmetric band increase linearly with decreasing inductive electron-donating power of the alkyl chain. The integrated intensity of the symmetric band, which is smaller than that for the antisymmetric band in all the 26 compounds studied, is independent of the inductive nature of the alkyl chain as a first approximation. These results indicate that the N-atom lone-pair orbital in RNH2 plays a negligibly small role in modifying the inductive effect of R on NH2 frequencies and intensities as long as the N-atom hybridization remains sp3.

Theoretical calculations of the nuclear magnetic shielding tensors for the ethylenic carbon atoms in cyclopropenes

Abstract: Theoretical calculations of the chemical shielding tensor using the coupled Hartree-Fock and localized orbital methods with different basis sets are compared for the ethylenic carbon atoms, which are expected to have a large antisymmetric component, in tetrachlorocyclopropene, tetrafluorocyclopropene, dichlorocyclopropene and cyclopropene at optimized geometries. Two modest attempts, made to extrapolate these results to the Hartree-Fock limit, demonstrate that the LORG method gives the most reliable calculated results but that there is still much room for improvement. Comparison of the calculated value of the antisymmetric component of the shielding tensor for tetrachlorocyclopropene agrees approximately with the experimental value.

Optical fiber couplers and methods of their manufacture

Abstract: Fiber optic couplers formed of at least two single mode optical fibers (10, 11), at least one of which is an input fiber, are shown, the fibers constructed and arranged in the manner that coupling between the input fiber and the other fibers limits antisymmetric modal energy to substantially less than 50 % of the input energy, the coupling region (20) of said coupler being fused and drawn to an extended length sufficient to cause cutoff of the antisymmetric mode energy, whereby the coupler exhibits coupling ratio stability over an extended range of wavelengths and an excess loss of substantially less than 50 %. Numerous fiber couplers of various construction, all employing cutoff of the antisymmetric mode to achieve wideband response or wavelength insensitivity are shown along with their method of manufacture.

Nonlinear breakup of thin liquid sheets

Abstract: The breakup of thin planar liquid sheets due to the nonlinear growth of disturbances is determined. Conservation equations are derived using a control volume method and solved using MacCormack's predictor-corrector scheme. It is found that the size and geometry of ligaments, formed during breakup, vary with the weber number. Antisymmetric waves, which spontaneously intensify at higher values of the Weber number, give rise to thin ligaments. At lower values of the Weber number antisymmetric waves formed initially get transformed into symmetric interfaces giving larger ligaments. The magnitude of the initial amplitude of the disturbances is shown to strongly influence the disintegration. The results are compared with experimental results obtained for thin water sheets and good agreement is demonstrated.