Fullerenes with the maximum Clar number

The Clar number of a fullerene is the maximum number of independent resonant hexagons in the fullerene. It is known that the Clar number of a fullerene with n vertices is bounded above by [n/6]-2. We find that there are no fullerenes whose order n is congruent to 2 modulo 6 attaining this bound. In other words, the Clar number for a fullerene whose order n is congruent to 2 modulo 6 is bounded above by [n/6]-3. Moreover, we show that two experimentally produced fullerenes C80:1 (D5d) and C80:2 (D2) attain this bound. Finally, we present a graph-theoretical characterization for fullerenes, whose order n is congruent to 2 (respectively, 4) modulo 6, achieving the maximum Clar number [n/6]-3 (respectively, [n/6]-2)

The minimum degree of minimal kk-factor-critical claw-free graphs*

A graph $G$ of order $n$ is said to be $k$-factor-critical for integers $1\leq k< n$, if the removal of any $k$ vertices results in a graph with a perfect matching. A $k$-factor-critical graph is minimal if for every edge, the deletion of it results in a graph that is not $k$-factor-critical. In 1998, O. Favaron and M. Shi conjectured that every minimal $k$-factor-critical graph has minimum degree $k+1$. In this paper, we confirm the conjecture for minimal $k$-factor-critical claw-free graphs. Moreover, we show that every minimal $k$-factor-critical claw-free graph $G$ has at least $\frac{k-1}{2k}|V(G)|$ vertices of degree $k+1$ in the case of $(k+1)$-connected, yielding further evidence for S. Norine and R. Thomas' conjecture on the minimum degree of minimal bricks when $k=2$.Comment: 17 pages, 12 figure

Editorial: Seeing convergent margin processes through metamorphism

Plate convergence can induce large-scale metamorphism and magmatism, reshape large parts of continental margins, and subsequently change regional climate and biodiversity. Metamorphic rocks in orogenic belts commonly record different metamorphic evolutions and temporal-spatial distributions at the regional scale, which are strongly influenced by convergent processes through time. In some cases, ultrahigh-pressure (UHP) and ultrahigh-temperature (UHT) metamorphic rocks are observed at both ancient and young convergent plate margins, marking the operation of extreme tectonism in the regime of plate tectonics. This Research Topic aims to understand how regional metamorphism operated at convergent plate margins through the study of field and petrographic observations, geochemical and petrological analysis, high-pressure experiments, and thermodynamic modeling. The scope is to gather new ideas and interpretations on the structure and processes of convergent plate margins

Petrogenesis of the Northwest Africa 4734 basaltic lunar meteorite

We report the petrography, mineralogy, trace element abundance geochemistry, and Pb–Pb geochronology of the lunar meteorite Northwest Africa (NWA) 4734 and make a comparison with the LaPaz Icefield (LAP) 02205/02224 low-Ti lunar basaltic meteorites. NWA 4734 is an unbrecciated low-Ti mare basalt composed mainly of subophitic-textured pyroxene (60 vol%) and plagioclase (30%). Pyroxene, plagioclase, and olivine exhibit large compositional variations and intra-grain chemical zoning. Pyroxene and plagioclase in NWA 4734 have rare earth element (REE) concentrations and patterns similar to those of the LAPs. The crystallization age of NWA 4734, determined in situ in baddeleyite, is 3073 ± 15 Ma (2σ), nearly identical to that of the LAPs (3039 ± 12 Ma). NWA 4734 and the LAPs have similar textures, modal abundances, mineral chemistry, and crystallization ages, and are most likely source-crater paired on the Moon. One baddeleyite grain in LAP 02224 displays distinctively older and spatially variable ages, from 3349 ± 62 to 3611 ± 62 Ma (2σ), similar to another baddeleyite grain (3109 ± 29 to 3547 ± 21 Ma) reported by Zhang et al. (2010) for the same meteorite. Raman spectra, cathodoluminescence, and stoichiometric studies of the baddeleyite suggest that the two older grains were not endogenic but were trapped by the parental magma. Equilibrium partition calculation shows that the parental melt from which the NWA 4734 plagioclase crystallized has much lower REE contents than its whole rock, indicating an open system during magma evolution. NWA 4734 could have originated from a parental melt with REE concentrations similar to that of the Apollo 12 olivine basalt. The magma likely assimilated a small amount (∼4 wt%) of KREEP-rich material during its ascent through the lunar crust

Unified Multi-Modal Image Synthesis for Missing Modality Imputation

Multi-modal medical images provide complementary soft-tissue characteristics that aid in the screening and diagnosis of diseases. However, limited scanning time, image corruption and various imaging protocols often result in incomplete multi-modal images, thus limiting the usage of multi-modal data for clinical purposes. To address this issue, in this paper, we propose a novel unified multi-modal image synthesis method for missing modality imputation. Our method overall takes a generative adversarial architecture, which aims to synthesize missing modalities from any combination of available ones with a single model. To this end, we specifically design a Commonality- and Discrepancy-Sensitive Encoder for the generator to exploit both modality-invariant and specific information contained in input modalities. The incorporation of both types of information facilitates the generation of images with consistent anatomy and realistic details of the desired distribution. Besides, we propose a Dynamic Feature Unification Module to integrate information from a varying number of available modalities, which enables the network to be robust to random missing modalities. The module performs both hard integration and soft integration, ensuring the effectiveness of feature combination while avoiding information loss. Verified on two public multi-modal magnetic resonance datasets, the proposed method is effective in handling various synthesis tasks and shows superior performance compared to previous methods.Comment: 10 pages, 9 figure

Cinnamaldehyde Exerts Its Antifungal Activity by Disrupting the Cell Wall Integrity of Geotrichum citri-aurantii

Our previous study showed that cinnamaldehyde (CA) significantly inhibited the mycelial growth of Geotrichum citri-aurantii, one of the main postharvest pathogens in citrus fruits. This study investigated the antifungal mechanism of CA against G. citri-aurantii. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) images showed that CA treatment led to clear morphological changes in the cell walls and membranes of G. citri-aurantii. However, the membrane integrity, total lipids and ergosterol contents were not apparently affected by CA treatment. Notably, the extracellular alkaline phosphatase (AKP) activity was increased after CA treatment, suggesting impairment in cell wall permeability. A weakened fluorescence in the cell wall, a decrease in the chitin contents, and changes of ten genes involved in cell wall integrity were also observed. These results suggested that CA may exhibit its antifungal activity against G. citri-aurantii by interfering the build of cell wall and therefore lead to the damage of cell wall permeability and integrity

Magma mingling in kimberlites: evidence from the groundmass cocrystallization of two spinel-group minerals

We present the results of a detailed petrographic study of fresh coherent samples of the Menominee kimberlite sampled at site 73, located in Menominee County, MI, USA. Our objective is to account for its unusual and complex paragenetic sequence. Several generations of olivine, ilmenite, and spinel-group minerals are described. Early olivine and ilmenite are xenocrystic and were replaced or overgrown by primary minerals. Zoned microcrysts of olivine have a xenocrystic core mantled by a first rim in which rutile, geikielite, and spinel s.s. (spinel sensu stricto) cocrystallized. The in situ U-Pb dating of a microcryst of primary rutile yielded 168.9 ± 4.4 Ma, which was interpreted as the age of emplacement. The groundmass consists of olivine, spinel s.s., a magnesian ulvöspinel-ulvöspinel-magnetite (MUM) spinel, calcite, and dolomite. An extremely low activity of Si is suggested by the crystallization of spinel s.s. instead of phlogopite in the groundmass. The presence of djerfisherite microcrysts indicates high activities of Cl and S during the late stages of melt crystallization. The occurrence of two distinct spinel-group minerals (spinel s.s. and qandilite-rich MUM) in the groundmass is interpreted as clear evidence of the mingling of a magnesiocarbonatitic melt with a dominant kimberlitic melt