Investigation of PT-symmetric Hamiltonian systems from an alternative point of view

Two non-Hermitian PT-symmetric Hamiltonian systems are reconsidered by means of the algebraic method which was originally proposed for the pseudo-Hermitian Hamiltonian systems rather than for the PT-symmetric ones. Compared with the way converting a non-Hermitian Hamiltonian to its Hermitian counterpart, this method has the merit that keeps the Hilbert space of the non-Hermitian PT-symmetric Hamiltonian unchanged. In order to give the positive definite inner product for the PT-symmetric systems, a new operator V, instead of C, can be introduced. The operator V has the similar function to the operator C adopted normally in the PT-symmetric quantum mechanics, however, it can be constructed, as an advantage, directly in terms of Hamiltonians. The spectra of the two non-Hermitian PT-symmetric systems are obtained, which coincide with that given in literature, and in particular, the Hilbert spaces associated with positive definite inner products are worked out.Comment: 13 pages, no figures; v2: 14 pages, typos corrected, clarifications and references added, this version accepted for publication in Commun. Theor. Phy

Respuestas del δ13C foliar y características foliares a la precipitación y temperatura en un ecosistema árido del noroeste de China

El δ13C foliar es ampliamente usado para explicar estrategias relacionadas con la disponibilidad de recursos en diferentes ambientes. Sin embargo, la respuesta conjunta del δ13C foliar a la precipitación y temperatura así como la relación entre el δ13C foliar y las características foliares no están claras. El δ13C foliar y su relación con las características foliares [tamaño de hoja (LS), longitud foliar (LL), ancho foliar (LW), relación entre la longitud y el ancho foliar (L:W), área foliar específica (SLA) y concentración de N foliar (en una base de peso seco) (Nmass)] fueron investigadas en la especie de arbusto dominante Nitraria tangutorum Bobr en la región árida (Dengkou y Minqin) del noroeste de China. El estudio se efectuó bajo condiciones de varias cantidades de precipitación simuladas (PGS) y temperaturas ambientales (TGS) en las estaciones de crecimiento de 2008, 2009 y 2010. Los resultados mostraron que LS, LW, LL, SLA y Nmass se incrementaron significativamente cuando las cantidades de PGS se incrementaron, pero hubo tendencias de reducción en dichas características cuando las TGS aumentaron. Sin embargo, la mayoría de las relaciones negativas entre las características foliares y las TGS no fueron obvias en Minqin. En ambos sitios, L:W se incrementó cuando las PGS y TGS aumentaron. Hubo un cambio en la relación negativa entre el δ13C foliar-PGS a través de Minqin y Dengkou, lo cual condujo a la falta de efectos de la precipitación en el δ13C foliar a través de ambos sitios, y mayor δ13C foliar a menor precipitación en Minqin. A través de Minqin y Dengkou, PGS solo pudo explicar un 14% de la variación en el δ13C foliar. La combinación de PGS y TGS pudo explicar un 64% de la variación en el δ13C foliar. Las características foliares (LW y L:W) mejoraron aún más la estimación del δ13C foliar. Las combinaciones de PGS, TGS, LW y L:W pudieron explicar un 84% de la variación en el δ13C foliar. Nuestro estudio demostró la importancia de las características foliares en explorar las respuestas del δ13C foliar a cambios globales en ecosistemas áridos.Leaf δ13C is widely used to explain plant strategies related to resource availability in different environments. To understand the coupled response of leaf δ13C to precipitation, temperature and the relationship between leaf δ13C and leaf traits in arid ecosystems, the leaf δ13C and leaf traits (leaf size (LS), leaf length (LL), leaf width (LW), leaf length to width ratio (L:W), specific leaf area (SLA) and mass-based leaf nitrogen concentration (Nmass)) of Nitraria tangutorum Bobr. under simulated increasing precipitation (PGS) and ambient temperature (TGS) in plant growing season from 2008 to 2010 and the relationships between leaf δ13C and leaf traits were investigated in the arid region (Dengkou and Minqin) of northwestern China. Our results showed that LS, LW, LL, SLA and Nmass significantly increased with increasing PGS, but had downward tendencies with increasing TGS although the majority of the negative relationships between leaf traits and TGS were not obvious in Minqin. At the two study sites, L:W increased simultaneously with increasing PGS and TGS. There was a shift in the negative leaf δ13C-PGS relationship across Minqin and Dengkou, which conduce to the lacking effect of precipitation on leaf δ13C across the two sites and higher leaf δ13C in lower precipitation fields in Minqin. Across Minqin and Dengkou, PGS could only explain 14% of the variation in leaf δ13C. The combinations of PGS and TGS could explain 64% of the variation in leaf δ13C. Leaf traits (LW and L:W) could be used to further improve the estimation of leaf δ13C. The combinations of PGS, TGS, LW and L:W could explain 84 % of the variation in leaf δ13C. Our study demonstrated the importance of leaf traits in exploring the responses of leaf δ13C to global changes in arid ecosystems.Fil: Xin, Z.M.. Chinese Academy of Forestry. Institute of Desertification Studies; China. Chinese Academy of Forestry. Experimental Center of Desert Forestry; ChinaFil: Liu, M.H.. Chinese Academy of Forestry. Experimental Center of Desert Forestry; ChinaFil: Lu, Q.. Chinese Academy of Forestry. Institute of Desertification Studies; China. State Forestry Administration. Kumtag Desert Ecosystem Research Station; ChinaFil: Busso, Carlos Alberto. Universidad Nacional del Sur. Departamento de Agronomía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; Argentina. State Forestry Administration. Kumtag Desert Ecosystem Research Station; ChinaFil: Zhu, Y.J.. State Forestry Administration. Kumtag Desert Ecosystem Research Station; China. Chinese Academy of Forestry. Institute of Desertification Studies; ChinaFil: Li, Z.. Chinese Academy of Forestry. Experimental Center of Desert Forestry; ChinaFil: Huang, Y.R.. Chinese Academy of Forestry. Experimental Center of Desert Forestry; ChinaFil: Li, X.L.. Chinese Academy of Forestry. Experimental Center of Desert Forestry; ChinaFil: Luo, F.M.. Chinese Academy of Forestry. Experimental Center of Desert Forestry; ChinaFil: Bao, F.. Chinese Academy of Forestry. Institute of Desertification Studies; ChinaFil: Qian, J.Q.. Henan Agricultural University. College of Forestry; ChinaFil: Li, Y.H.. Chinese Academy of Forestry. Institute of Desertification Studies; China. State Forestry Administration. Kumtag Desert Ecosystem Research Station; Chin

Solidification of nitrogen-atomized Al(86)Ni(6)Y(4.5)Co(2)La(1.5) metallic glass

A comprehensive investigation has been made of the solidification of nitrogen-atomized AlNiYCo La, using focused ion beam, transmission electron microscopy, and other analytical means. Face-centered cubic Al2Y was identified to be the leading crystalline phase rather than crystalline Al. A new orthorhombic-structured phase was identified in partially or fully crystallized powder particles. Apart from oxygen, nitrogen was also found to be associated with the leading crystalline phase Al2Y in which nitrogen exists as substitutional N. These findings facilitate the basis for understanding the unique aspects of the AlNiY CoLa bulk metallic glass, including its powder preparation by gas atomization

Uncertainty Quantification for Traffic Forecasting:A Unified Approach

Uncertainty is an essential consideration for time series forecasting tasks. In this work, we specifically focus on quantifying the uncertainty of traffic forecasting. To achieve this, we develop Deep Spatio-Temporal Uncertainty Quantification (DeepSTUQ), which can estimate both aleatoric and epistemic uncertainty. We first leverage a spatio-temporal model to model the complex spatio-temporal correlations of traffic data. Subsequently, two independent sub-neural networks maximizing the heterogeneous log-likelihood are developed to estimate aleatoric uncertainty. For estimating epistemic uncertainty, we combine the merits of variational inference and deep ensembling by integrating the Monte Carlo dropout and the Adaptive Weight Averaging re-training methods, respectively. Finally, we propose a post-processing calibration approach based on Temperature Scaling, which improves the model's generalization ability to estimate uncertainty. Extensive experiments are conducted on four public datasets, and the empirical results suggest that the proposed method outperforms state-of-the-art methods in terms of both point prediction and uncertainty quantification.</p

Micrometer-sized quasicrystals in the Al 85Ni 5Y 6Co 2Fe 2 metallic glass: a TEM study and a brief discussion on the formability of quasicrystals in bulk and marginal glass-forming alloys

Large quasicrystals up to ∼10 μm in size with a volume fraction of ∼30% have been identified in a nitrogen gas-atomized marginal glass-forming alloy Al85Ni5Y6Co2Fe2 by detailed transmission electron microscopy. The formation of the large quasicrystal (Q) phase is discussed through the configuration of the valence electrons of its constituent elements, and the thermodynamic and kinetic factors associated with the solidification of this marginal glass-forming alloy during gas atomization. The finding leads to an important inference that marginal glass-forming alloys could be ideal systems for the formation of bulk quasicrystals under appropriate kinetic conditions. The Q phase is stable up to ∼500 °C and decomposes thereafter. The activation energy for the decomposition of the Q phase is similar to the self-diffusion of Al. Two new intermetallic phases associated with the formation and decomposition of the Q phase have also been identified and characterized