Solvable 3-Lie algebras with a maximal hypo-nilpotent ideal N

This paper obtains all solvable 3-Lie algebras with the m-dimensional filiform 3-Lie algebra N (m >= 5) as a maximal hypo-nilpotent ideal, and proves that the m-dimensional filiform 3-Lie algebra N can't be as the nilradical of solvable non-nilpotent 3-Lie algebras. By means of one dimensional extension of Lie algebras to the 3-Lie algebras, we get some classes of solvable Lie algebras directly

3-Lie algebras with an ideal N

AbstractWe define the hypo-nilpotent ideal in n-Lie algebras and obtain all solvable 3-Lie algebras with an m-dimensional simplest filiform 3-Lie algebra as a maximal hypo-nilpotent ideal. We prove that the dimension of such solvable 3-Lie algebras is at most m+2, and there is no solvable 3-Lie algebra with the simplest filiform 3-Lie algebra as the nilradical

Broad-line region in NGC 4151 monitored by two decades of reverberation mapping campaigns. I. Evolution of structure and kinematics

We report the results of long-term reverberation mapping (RM) campaigns of the nearby active galactic nuclei (AGN) NGC 4151, spanning from 1994 to 2022, based on archived observations of the FAST Spectrograph Publicly Archived Programs and our new observations with the 2.3m telescope at the Wyoming Infrared Observatory. We reduce and calibrate all the spectra in a consistent way, and derive light curves of the broad H$\beta$ line and 5100\,{\AA} continuum. Continuum light curves are also constructed using public archival photometric data to increase sampling cadences. We subtract the host galaxy contamination using {\it HST} imaging to correct fluxes of the calibrated light curves. Utilizing the long-term archival photometric data, we complete the absolute flux-calibration of the AGN continuum. We find that the H$\beta$ time delays are correlated with the 5100\,{\AA} luminosities as $\tau_{\rm H\beta}\propto L_{5100}^{0.46\pm0.16}$. This is remarkably consistent with Bentz et al. (2013)'s global size-luminosity relationship of AGNs. Moreover, the data sets for five of the seasons allow us to obtain the velocity-resolved delays of the H$\beta$ line, showing diverse structures (outflows, inflows and disks). Combining our results with previous independent measurements, we find the measured dynamics of the H$\beta$ broad-line region (BLR) are possibly related to the long-term trend of the luminosity. There is also a possible additional $\sim$1.86 years time lag between the variation in BLR radius and luminosity. These results suggest that dynamical changes in the BLR may be driven by the effects of radiation pressure.Comment: Accepted for publication in MNRAS; comments welcome

Metabolomics Profiling of Serum and Urine in Three Beef Cattle Breeds Revealed Different Levels of Tolerance to Heat Stress

This study was to determine differences in the global metabolic profiles of serum and urine of Xuanhan yellow cattle, Simmental crossbred cattle (Simmental × Xuanhan yellow cattle), and cattle-yaks (Jersey × Maiwa yak) under heat stress (temperature–humidity index remained above 80 for 1 week). A total of 55 different metabolites associated with the three breeds were identified in the serum and urine samples by gas chromatography–mass spectrometry. The metabolic adaptations to heat stress are heterogeneous. Cattle-yaks mobilize a greater amount of body protein to release glucogenic amino acids to supply energy, whereas the tricarboxylic acid cycle is inhibited. Simmental crossbred cattle mobilize a greater amount of body fat to use free fatty acids as an energy source. In comparison with Simmental crossbred cattle and cattle-yaks, Xuanhan yellow cattle have higher glycolytic activity and possess a stronger antioxidant defense system and are, in conclusion, more adapted to hot and humid environments