On an Instance of the Small Cohen-Macaulay Conjecture

We provide a simplified proof of a theorem proved by Tavanfar and Shimomoto which states that a quasi-Gorenstein deformation of a $3$-dimensional quasi-Gorenstein local ring $(A,m,k)$ with $H^2_m(A)=k$ admits a small Cohen-Macaulay module.Comment: 5 pages; Expanded Introduction; To appear in J. Pure Appl. Algebr

Proofs of McIntosh's Conjecture on Franel Integrals and Two Generalizations

We provide a proof of a conjecture made by Richard McIntosh in 1996 on the values of the Franel integrals, $$\int_0^1((ax))((bx))((cx))((ex))\,dx,$$ where $((x))$ is the first periodic Bernoulli function. Secondly, we extend our ideas to prove a similar theorem for $$\int_0^1((a_1x))((a_2x))\cdots ((a_{n}x))\,dx.$$ Lastly, we prove a further generalization in which $((x))$ is replaced by any particular Bernoulli function with odd index.Comment: Typos correcte

Proposed clinical phases for the improvement of personalized treatment of checkpoint inhibitor–related pneumonitis

BackgroundCheckpoint inhibitor–related pneumonitis (CIP) is a lethal immune-related adverse event. However, the development process of CIP, which may provide insight into more effective management, has not been extensively examined.MethodsWe conducted a multicenter retrospective analysis of 56 patients who developed CIP. Clinical characteristics, radiological features, histologic features, and laboratory tests were analyzed. After a comprehensive analysis, we proposed acute, subacute, and chronic phases of CIP and summarized each phase’s characteristics.ResultsThere were 51 patients in the acute phase, 22 in the subacute phase, and 11 in the chronic phase. The median interval time from the beginning of CIP to the different phases was calculated (acute phase: ≤4.9 weeks; subacute phase: 4.9~13.1 weeks; and chronic phase: ≥13.1 weeks). The symptoms relieved from the acute phase to the chronic phase, and the CIP grade and Performance Status score decreased (P<0.05). The main change in radiologic features was the absorption of the lesions, and 3 (3/11) patients in the chronic phase had persistent traction bronchiectasis. For histologic features, most patients had acute fibrinous pneumonitis in the acute phase (5/8), and most had organizing pneumonia in the subacute phase (5/6). Other histologic changes advanced over time, with the lesions entering a state of fibrosis. Moreover, the levels of interleukin-6, interleukin-10 and high-sensitivity C-reactive protein (hsCRP) increased in the acute phase and decreased as CIP progressed (IL-6: 17.9 vs. 9.8 vs. 5.7, P=0.018; IL-10: 4.6 vs 3.0 vs. 2.0, P=0.041; hsCRP: 88.2 vs. 19.4 vs. 14.4, P=0.005).ConclusionsThe general development process of CIP can be divided into acute, subacute, and chronic phases, upon which a better management strategy might be based devised

A Thermodynamics-Oriented and Neural Network-Based Hybrid Model for Military Turbofan Engines

Traditional thermodynamic models for military turbofans suffer from non-convergence and inaccuracy due to inaccuracy of the component maps and the instability of the iterative process. To address these problems, a thermodynamically oriented and neural network-based hybrid model for military turbofans is proposed. Different from iteration-based thermodynamic models, the proposed hybrid model transforms the iteration process into a multi-objective optimization and training process for a component-level neural network in order to improve convergence and modeling accuracy. The experiment shows that the accuracy of the proposed hybrid model can reach about 7%, 5% better than the map-fitting-based thermodynamic model and 8% better than the purely data-driven method, with a similar number of network neutrons, verifying its effectiveness. The contributions of this work mainly lie in the following aspects: a new component-level neural network structure is proposed to improve convergence and computational efficiency; a multi-objective loss function based on component co-working is proposed to direct the model to converge toward the physical thermodynamic process; a fusion training method of multiple data sources is established to train the model with good convergence and high computational accuracy

Kinetics of sulphuric acid leaching of titanium from refractory anatase under atmospheric pressure

Anatase, as an important titanium resource, is attracting more and more attention in research and application. In this study, an efficient process of comprehensively extracting the titanium and other valuable elements from the anatase mineral was proposed. The effect of particle size, stirring speed, initial sulphuric acid concentration, solid-to-liquid ratio, and reaction temperature on the leaching rate of titanium from anatase was investigated. Under appropriate two-stage countercurrent leaching conditions, with the first stage of the liquid-to-solid ratio of 1/3 g/cm3, reaction temperature of 120 °C, initial acid concentration of 11 mol/dm3, residence time of 30 min, stirring speed of 200 rpm, and the second stage of the liquid-to-solid ratio of 1/3 g/cm3, reaction temperature of 200 °C, initial acid concentration of 13 mol/dm3, residence time of 30 min, and stirring speed of 200 rpm, over 99% TiO2, 99% Al2O3, and 97% Sc2O3 were extracted respectively with quartz still remained in the residue. X-ray diffraction, X-ray fluorescence spectrometer, and scanning electron microscopy/energy-dispersive spectroscopy were used to characterize the anatase samples before and after the leaching. Additionally, the leaching kinetics analysis indicated that both acid concentration and temperature were the most significant parameters for the leaching process. And, the titanium leaching reaction rate was controlled by the diffusion of reactants through the residual layer

Transcriptome Analyses Indicate Significant Association of Increased Non-Additive and Allele-Specific Gene Expression with Hybrid Weakness in Rice (Oryza sativa L.)

The heterosis in hybrid rice is highly affected by the environment and hybrid weakness occurs frequently depending on the genotypes of the hybrid and its parents. Hybrid weakness was also observed in our field experiments on nine rice hybrids produced by 3 × 3 incomplete diallel crosses. Among the nine hybrids, five displayed mid-parent heterosis (MPH) for grain yield per plant, while four showed mid-parent hybrid weakness (MPHW). A sequencing analysis of transcriptomes in panicles at the seed-filling stage revealed a significant association between enhanced non-additive gene expression (NAE) and allele-specific gene expression (ASE) with hybrid weakness. High proportions of ASE genes, with most being of mono-allele expression, were detected in the four MPHW hybrids, ranging from 22.65% to 45.97%; whereas only 4.80% to 5.69% of ASE genes were found in the five MPH hybrids. Moreover, an independence test indicated that the enhancements of NAE and ASE in the MPHW hybrids were significantly correlated. Based on the results of our study, we speculated that an unfavorable environment might cause hybrid weakness by enhancing ASE and NAE at the transcriptome level

Nanocomposite of N‑Doped TiO₂ Nanorods and Graphene as an Effective Electrocatalyst for the Oxygen Reduction Reaction

Developing an effective electrocatalyst for the oxygen reduction reaction is a momentous issue in fuel cells. In this paper, we successfully synthesized the N-doped TiO₂ nanorods/graphene (N-TiO₂/NG) nanocomposite, which comprise the N-doped TiO₂ (N-TiO₂) nanorods (40–60 nm diameter and 90–300 nm length) and self-assembled nitrogen-doped graphene (NG) networks. We found that the nanocomposite exhibits great oxygen reduction reaction (ORR) electrocatalytic performance and also shows long durability and methanol tolerance than that of the commercial 20% Pt/C catalyst. This new nanocomposite may also have potential applications in other fields, which are related to energy storage, gas sensors, photocatalysis, and so on