On unicyclic graphs whose second largest eigenvalue dose not exceed 1

AbstractConnected graphs in which the number of edges equals the number of vertices are called unicyclic graphs. In this paper, all unicyclic graphs whose second largest eigenvalue does not exceed 1 have been determined

Feroxichthys yunnanensis gen. et sp. nov. (Colobodontidae, Neopterygii), a large durophagous predator from the Middle Triassic (Anisian) Luoping Biota, eastern Yunnan, China

Neopterygii is a large group of ray-finned fishes which underwent a rapid radiation in the Middle Triassic. Until recently, 11 stem neopterygians have been recovered from the early Middle Triassic Luoping Biota in eastern Yunnan, China, and they are small to medium-sized fishes. Here, I report the discovery of a new stem neopterygian, Feroxichthys yunnanensis gen. et sp. nov. from the Luoping Biota, which represents the first evidence of large-sized stem neopteygians in this biota with a total length of ~340 mm (290 mm in standard length). The skull of the new taxon is exceptionally well-preserved, showing some peculiar features rarely known in other stem neopterygians, for example fusion of paired premaxillae, fusion of lacrimal with maxilla, and a fused parieto-dermopterotic with a strong posterior process. Phylogenetic studies recover Feroxichthys as a basal colobodontid, and a revised diagnosis of this family is presented. The feeding apparatus indicates that Feroxichthys might have been predominantly durophagous, resembling other colobodontids. However, the anterior peg-like teeth in the jaws of Feroxichthys are much longer and stronger than other colobodontids, enabling a more powerful initial prey capture before food was passed posteriorly to molariform teeth for crushing in the oral cavity. As a mysterious large durophagous predator previously unknown from the Luoping Biota, the new finding is important not only for understanding the early diversification of neopterygians during this age but also for investigating the trophic structure in this marine ecosystem

Topological energy gaps in the [111]-oriented InAs/GaSb and GaSb/InAs core-shell nanowires

The [111]-oriented InAs/GaSb and GaSb/InAs core-shell nanowires have been studied by the $8\times 8$ Luttinger-Kohn $\vec{k}\cdot\vec{p}$ Hamiltonian to search for non-vanishing fundamental gaps between inverted electron and hole bands. We focus on the variations of the topologically nontrivial fundamental gap, the hybridization gap, and the effective gap with the core radius and shell thickness of the nanowires. The evolutions of all the energy gaps with the structural parameters are shown to be dominantly governed by quantum size effects. With a fixed core radius, a topologically nontrivial fundamental gap exists only at intermediate shell thicknesses. The maximum gap is $\sim 4.4$ meV for GaSb/InAs and $\sim 3.5$ meV for InAs/GaSb core-shell nanowires, and for the GaSb/InAs core-shell nanowires the gap persists over a wider range of geometrical parameters. The intrinsic reason for these differences between the two types of nanowires is that in the shell the electron-like states of InAs is more delocalized than the hole-like state of GaSb, while in the core the hole-like state of GaSb is more delocalized than the electron-like state of InAs, and both features favor stronger electron-hole hybridization. Since similar features of the electron- and hole-like states have been found in nanowires of other materials, it could serve as a common rule to put the hole-like state in the core while the electron-like state in the shell of a core-shell nanowire to achieve better topological properties.Comment: 10 pages, 10 figure

BCS-BEC crossover at finite temperature in spin-orbit coupled Fermi gases

By adopting a $T$-matrix-based method within the $G_0G$ approximation for the pair susceptibility, we study the effects of the pairing fluctuation on the three-dimensional spin-orbit coupled Fermi gases at finite temperature. The critical temperatures of the superfluid/normal phase transition are determined for three different types of spin-orbit coupling (SOC): (1) the extreme oblate (EO) or Rashba SOC, (2) the extreme prolate (EP) or equal Rashba-Dresselhaus SOC, and (3) the spherical (S) SOC. For EO- and S-type SOC, the SOC dependence of the critical temperature signals a crossover from BCS to BEC state; at strong SOC limit, the critical temperature recover those of ideal BEC of rashbons. The pairing fluctuation induces a pseudogap in the fermionic excitation spectrum in both superfluid and normal phases. We find that, for EO- and S-type SOC, even at weak coupling, sufficiently strong SOC can induce sizable pseudogap. Our research suggests that the spin-orbit coupled Fermi gases may open new means to the study of the pseudogap formation in fermionic systems.Comment: V2: 13 pages, 8 figures, more discussions added, matches published versio

catena-Poly[[aqua­(dipyrido[3,2-a:2′,3′-c]phenazine-κ2 N 4,N 5)iron(II)]-μ-pyrazine-2,3-dicarboxyl­ato-κ3 N 1,O 2:O 3]

In the title compound, [Fe(C6H2N2O4)(C18H10N4)(H2O)]n, the FeII ion adopts a slightly distorted octahedral mer-FeN3O3 geometry, arising from one N,N′-bidentate dipyrido[3,2-a:2′,3′-c]phenazine ligand, one N,O-chelating pyrazine-2,3-dicarboxyl­ate dianion and one water mol­ecule. An O-bonded symmetry-related dianion completes the coordination of the metal. The bridging dianion results in a one-dimensional polymeric chain. Aromatic π–π stacking inter­actions between ligands [centroid–centroid separations = 3.528 (2) and 3.741 (2) Å] and O—H⋯O and O—H⋯N hydrogen bonds link the chains together, leading to a three-dimensional supra­molecular network