In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

As an essential synthetic material used in continuous casting of steels, mold fluxes improve the surface quality of steel slabs. In this study, a CaO-SiO₂-Na₂O based low-fluorine mold flux was solidified by an improved water-cooled copper probe with different temperatures of molten flux and different probe immersion times. The heat flux through solid films and the film structures were calculated and inspected, respectively. The results indicate: large internal cracks (formed in the glassy layer of films during solidification) were observed, the formation and evolution of those cracks contributed to the the unstable heat flux density. The roughness of the surface in contacted with the water-cooled copper probe formed as films were still glassy and the roughness have no causal relationship with crystallization or devitrification. Combeite with columnar and faceted dendritic shapes is the main crystal in the film.

Sweet sorghum is an important bioenergy grass and valuable forage with a strong adaptability to saline environments. However, little is known about the mechanisms of sweet sorghum coping with ion toxicity under salt stresses. Here, we first evaluated the salt tolerance of a sweet sorghum cultivar “Lvjuren” and determined its ion accumulation traits under NaCl treatments; then explored key genes involved in Na+, Cl−, K+ and NO3− transport using transcriptome profiling and qRT-PCR method. The results showed that the growth and photosynthesis of sweet sorghum were unaffected by 50 and 100 mM NaCl treatments, indicative of a strong tolerance of this species to salt stresses. Under NaCl treatments, sweet sorghum could efficiently exclude Na+ from shoots and accumulate Cl− in leaf sheaths to avoid their overaccumulation in leaf blades; meanwhile, it possessed a prominent ability to sustain NO3− homeostasis in leaf blades. Transcriptome profiling identified several differentially expressed genes associated with Na+, Cl−, K+ and NO3− transport in roots, leaf sheaths and leaf blades of sweet sorghum after 200 mM NaCl treatment for 6 and 48 h. Moreover, transcriptome data and qRT-PCR results indicated that HKT1;5, CLCc and NPF7.3-1 should be key genes involved in Na+ retention in roots, Cl− accumulation in leaf sheaths and maintenance of NO3− homeostasis in leaf blades, respectively. Many TFs were also identified after NaCl treatment, which should play important regulatory roles in salt tolerance of sweet sorghum. This work lays a preliminary foundation for clarifying the molecular basis underlying the adaptation of sweet sorghum to adverse environments.

As a critical transmitter, the compact 532 nm lasers operating on high repetition and narrow pulse widths have been used widely for airborne or space-borne laser active remote sensing. We developed a free space pumped TEM₀₀ mode sub-nanosecond 532 nm laser that occupied a volume of less than 125 mm × 50 mm × 40 mm (0.25 liters). The fundamental 1064 nm laser consists of a passively Q-switched composite crystal microchip laser and an off-axis, two-pass power amplifier. The pump sources were two single-emitter semiconductor laser diodes (LD) of 808 nm with a maximum continuous wave (CW) power of 10 W each. The average power of fundamental 1064 nm laser was 1.26 W with the laser operating at 16 kHz repetition rates, and 857ps pulse widths. Since the beam distortion would be severe in microchip lasers in terms of the increase in heat load, for obtaining a high beam quality of 532 nm, the beam distortion was compensated by adjusting the distribution of pumping beam in our experiment of fundamental amplification. Furthermore, better than 0.6 W average power, 770 ps, beam quality of M² ＜1.2, and 16 kHz pulse output at 532 nm was obtained by a Type I LiB₃O₅ (LBO) crystal in the critical phase matching (CPM) regime for second harmonic generation (SHG).

Background: Recent researches have investigated the biological importance of RNA N1-methyladenosine (m1A) modifications in oncogenesis and progression of head and neck squamous cell carcinoma (HNSCC). However, whether m1A modifications also have latent effect in tumor microenvironment (TME) generation and immune regulation in HNSCC is unknown. Methods: We evaluated the m1A modification patterns and related to these modification patterns with TME cell infiltration features in 1041 HNSCC samples by bioinformatics approach. Results: The m1A score is an independent prognostic indicator. HNSCC patients with low m1A score group with poor overall survival (OS) was mainly characterized by stroma activation, lack of sufficient immune infiltration, and exhibited an immune- desert TME phenotype. Low m1A scores were also correlated with increased tumor mutation burden (TMB), and HNSCC patients with high TMB and low m1A scores had the worst OS. In addition, anti-CTLA-4 combined with anti-PD1 treatment was more effective in the high m1A score subgroup than in the low m1A score subgroup. Conclusions: This study revealed that m1A modifications play a non-negligible role in developing the TME versatility and complexity of HNSCC. Assessing m1A modification patterns in HNSCC helps improve our comprehension of its TME infiltration profile and guides more effective immunotherapeutic approaches.

The ongoing outbreak of the novel coronavirus pneumonia (also known as COVID-19) has triggered a series of stringent control measures in China, such as city closure, traffic restrictions, contact tracing and household quarantine. These containment efforts often lead to changes in the contact pattern among individuals of the population. Many existing compartmental epidemic models fail to account for the effects of contact structure. In this paper, we devised a pairwise epidemic model to analyze the COVID-19 outbreak in China based on confirmed cases reported during the period February 3rd--17th, 2020. By explicitly incorporating the effects of family clusters and contact tracing followed by household quarantine and isolation, our model provides a good fit to the trajectory of COVID-19 infections and is useful to predict the epidemic trend. We obtained the average of the reproduction number $R=1.494$ ($95\%$ CI: $1.483-1.507$) for Hubei province and $R=1.178$ ($95\%$ CI: $1.145-1.158$) for China (except Hubei), suggesting that some existing studies may have overestimated the reproduction number by neglecting the dynamical correlations and clustering effects. We forecasted that the COVID-19 epidemic would peak on February 13th ($95\%$ CI: February $9-17$th) in Hubei and 6 days eariler in the regions outside Hubei. Moreover the epidemic was expected to last until the middle of March in China (except Hubei) and late April in Hubei. The sensitivity analysis shows that ongoing exposure for the susceptible and population clustering play an important role in the disease propagation. With the enforcement of household quarantine measures, the reproduction number $R$ effectively reduces and epidemic quantities decrease accordingly. Furthermore, we gave an answer to the public concern on how long the stringent containment strategies should maintain. Through numerical analysis, we suggested that the time for the resumption of work and production in China (except Hubei) and Hubei would be the middle of March and the end of April, 2020, respectively. These constructive suggestions may bring some immeasurable social-economic benefits in the long run.

In tobacco plants, symbiont endophytic fungi are widely distributed in all tissues where they play important roles. It is therefore important to determine the species distribution and characteristics of endophytic fungi in tobacco. Here, two parasitic fungi Leptosphaerulina chartarum and Curvularia trifolii were isolated and identified from normal tobacco tissue. We sequenced the mitogenomes of these two species and analysed their features, gene content, and evolutionary histories. The L. chartarum and C. trifolii mitochondrial genomes were 68,926 bp and 59,100 bp long circular molecules with average GC contents of 28.60% and 29.31%, respectively. The L. chartarum mitogenome contained 36 protein coding genes, 26 tRNA genes, and 2 rRNA genes (rrnL and rrnS), which were located on both strands. The C. trifolii mitogenome contained 26 protein coding genes, 29 tRNA genes, and 2 rRNA genes (rrnL and rrnS). The L. chartarum 26 tRNAs ranged from 70 bp to 84 bp in length, whereas the 29 tRNAs in C. trifolii ranged from 71 bp to 85 bp. L. chartarum and C. trifolii mtDNAs had an identical mitochondrial gene order and orientation and were phylogenetically identified as sisters. These data therefore provide an understanding of the gene content and evolutionary history of species within Pleosporales.