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关键词： local semirings   semirings   semiring of continuous functions C+(X)   semi-fields   weakly 1-absorbing prime ideals   weakly prime ideals  

摘要： In this paper, we introduce and investigate weakly 1-absorbing prime ideals, a generalization of weakly prime ideals in semirings. We establish several results, including the characterization that every proper ideal of a semiring R is a weakly 1-absorbing prime ideal if and only if R is either a local semiring with M-3=0 or R=F(1)xF(2), where F-1 and F-2 are semi-fields. We also explore weakly 1-absorbing prime ideals in the semiring of continuous non-negative functions C+(X) and examine their connections with z-ideals, prime z-filters, and weakly prime z-filters.

关键词： Fourier transform infrared spectroscopy  

摘要： Three new boron fluoride complexes were synthesized using azaazulene derivatives, and their optical properties were investigated. These complexes were identified using single-crystal X-ray structural analysis, nuclear magnetic resonance spectroscopy, and Fourier transform infrared spectroscopy. We investigated the optical properties of these complexes in dichloromethane solution, poly­(styrene) films, and the solid state. The addition of acid led to a hypsochromic shift of approximately 60–90 nm in the absorption and fluorescence wavelengths in the dichloromethane solution and poly­(styrene) film. Moreover, two boron fluoride complexes exhibited up to 28.7-fold increases in fluorescence intensity upon protonation, while the remaining one exhibited fluorescence quenching. Density functional theory calculations revealed that the excited-state intramolecular proton transfer (ESIPT) involving the nitro group and subsequent donor excited photoinduced electron transfer (d-PeT) are responsible for these differences.