摘要 : Recently, Andrews and Paule introduced a partition function P D N 1 ( N ) which denotes the number of partition diamonds with ( n + 1 ) copies of n where summing the parts at the links gives N . They also presented the generating function for P D N 1 ( n ) and proved several congruences modulo 5, 7, 25, 49 for P D N 1 ( n ) . At the end of their paper, Andrews and Paule asked for determining infinite families of congruences similar to Ramanujan's classical p ( 5 k n + d k ) ≡ 0 ( mod 5 k ), where 24 d k ≡ 1 ( mod 5 k ) and k ≥ 1 . In this paper, we give an answer of Andrews and Paule's open problem by proving three congruences modulo arbitrary powers of 5 for P D N 1 ( n ) . In addition, we prove two congruences modulo arbitrary powers of 7 for P D N 1 ( n ), which are analogous to Watson's congruences for p ( n ) .

摘要 : Transfer learning has become one of the most effective techniques to reduce the supervision cost of learning tasks, and has been applied in various domains. However, how to accurately and efficiently transfer knowledge between different domains is a challenging issue. Some previous pilot work can evaluate the transfer performance of different domains, but the practical performance of its application cannot be guaranteed when it is applied to the engineering domain. To tackle this issue, we focused on the task of surface defect detection in industrial engineering. The proposed method Defect-deepscore (D-deepscore) could quickly and accurately evaluate models from different source domains on a target domain, and then select the source domain model without any fine-tuning process. D-deepscore takes the parameters from deeper layers in the convolutional neural network, which are further processed by dimensionality reduction and information correlation analysis. In the experiments we demonstrate that finetuning the commonly used ImageNet pre-trained model is not necessarily the best choice and transfer learning from defect dataset will be more effective. Then, we evaluate the multiple pretrained models which were trained on multiple surface defect datasets, the results show that there is a strong correlation between D-deepscore's model evaluation scores and the classification accuracy. By comparing with existing SOTA (State-of-the-art) methods that focus on model transfer learning performance, D-deepscore improves the evaluation accuracy by 49.9 % over the best previous work. The proposed D-deepscore could provide a fast selection of the best pre-trained model for industrial defect detection tasks, which ultimately leads to improved detection performance.

摘要 : The metal–carbon dioxide batteries, emerging as high-energy–density energy storage devices, enable direct CO2 utilization, offering promising prospects for CO2 capture and utilization, energy conversion, and storage. However, the electrochemical performance of M-CO2 batteries faces significant challenges, particularly at extreme temperatures. Issues such as high overpotential, poor charge reversibility, and cycling capacity decay arise from complex reaction interfaces, sluggish oxidation kinetics, inefficient catalysts, dendrite growth, and unstable electrolytes. Despite significant advancements at room temperature, limited research has focused on the performance of M-CO2 batteries across a wide-temperature range. This review examines the effects of low and high temperatures on M-CO2 battery components and their reaction mechanism, as well as the advancements made in extending operational ranges from room temperature to extremely low and high temperatures. It discusses strategies to enhance electrochemical performance at extreme temperatures and outlines opportunities, challenges, and future directions for the development of M-CO2 batteries.

摘要 : The electrochemical nitrogen reduction reaction (eNRR) is a sustainable pathway for ammonia synthesis, yet it faces challenges in selectivity and efficiency. Herein, we report a catalyst characterized by the uniform anchoring of Pt single-atom centers within a nitrogen, phosphorus, sulfur, and carbon (NPSC) multiligand framework, thereby maximizing the advantages of the Pt noble metal and significantly enhancing the eNRR performance. In this catalyst, sulfur-modulated anchoring of the Pt center induces ligand-to-metal charge transfer (LMCT), primarily leveraging the strong interaction between the Pt 4f band and the S 2p orbitals to activate and protonate N 2 effectively. Key findings include an ammonia yield rate (R NH3 ) of 93.97μg h −1 mgcat −1 and a Faradaic efficiency (FE) of 46.64 % at − 0.30 V vs RHE. Furthermore, advanced flow cell technology improves material transfer efficiency, achieving an R NH3 of 326.87μg h −1 mgcat −1, outperforming many previously reported materials. Moreover, coupling eNRR with the oxidation of 5-hydroxymethylfurfural (HMFOR) enables the concurrent production of green ammonia and high-value chemicals. In situ Raman spectroscopy identifies the –NH group as a crucial intermediate, while Density functional theory (DFT) calculations reveal that the Pt-NPSC catalyst lowers the activation energy for N 2 adsorption and activation. These findings highlight the critical role of innovative catalyst design and device optimization in advancing sustainable ammonia synthesis and provide valuable insights for improving eNRR performance.

摘要 : In their seminal work, Andrews and Merca studied the truncated version of Euler's pentagonal number theorem and deduced an infinite family of linear inequalities for ordinary partition function. The work of Andrews and Merca opened up the study of truncated theta series and linear inequalities for certain restricted partition functions and many articles followed. Recently, Ballantine and Feigon, and Merca posed four conjectures on linear inequalities for partitions with odd parts. In this paper, we confirm those conjectures based on a classical result contributed to Pólya and Szegő.

摘要 : Nanotechnology leveraging natural materials offers sustainable and cost-effective solutions for therapeutic advancements. Lignin and gum Arabic (GA), as biocompatible natural polymers, possess significant bioactive properties; however, their synergistic potential in nanocomposite form remains underexplored. This study synthesized and characterized Lignin-GA nanocomposites (LGA-NPs) through ultrasonic-assisted laccase catalysis, a green synthesis method. The resulting nanocomposites exhibited an average size of 67 ± 18.9 nm and a zeta potential of −32 ± 0.3 mV. Structural analysis via XRD, FTIR, and XPS confirmed the introduction of new functional groups and enhanced oxygen functionalities driven by enzymatic oxidative coupling and ultrasonic treatments. LGA-NPs demonstrated potent antimicrobial activity, with MIC values of 156 μg/mL for S. aureus and C. albicans and 312 μg/mL for E. coli, significantly outperforming lignin, GA, and lignin nanoparticles. Mechanistic studies revealed that LGA-NPs interact with microbial surfaces, disrupting membranes, inhibiting respiratory chains, generating ROS, and reducing ATP and metabolic activity, ultimately impairing microbial growth. Antioxidant evaluations showed superior radical scavenging activity (IC50 at 50 μg/mL), while α-amylase inhibition assays confirmed antidiabetic potential (IC50 of 75.0 μg/mL). Hemolysis tests demonstrated biocompatibility, with hemolysis rates below 5 %, reflecting safety for biomedical applications. The incorporation of GA into lignin not only improved bioactivity but also enhanced safety, emphasizing the synergistic effects of composite formation. These nanocomposites present a novel, sustainable, and economically viable therapeutic platform, addressing complex conditions like diabetic septic foot that demand effective glycemic control, robust antimicrobial action, and potent antioxidant capabilities.

摘要 : Short-process recycling of lithium-ion batteries (LIBs) is of great importance for both valuable metals and environmental protection. In this study, a tandem electro-leaching and solvent extraction method was developed for the selective recovery of metals from spent LiNi x Co y Mn (1-x-y) O 2 . Using in-situ generated H 2 O 2 from the two-electron oxygen reduction reaction, the cathode waste black powder dismantled from spent LIBs was successfully leached with Li, Ni, Co, and Mn leaching rates of 97.4%, 85.9%, 81.1%, 67.6%, respectively. Owing to the easy passivation of the refractory oxide surface of spent LIBs, the leaching performance of in-situ generated H 2 O 2 was better than that with corresponding external H 2 O 2 addition. Subsequently, more than 98.0% of Ni, Co, and Mn were selectively separated from Li by solvent extraction, and finally, Li 3 PO 4 with a purity of up to 99.5% was obtained, meeting battery-grade requirements. Compared with other available recovery methods, the reactants and conditions required for this process are considerably milder, suggesting favorable cost-effectiveness and environmental sustainability. Therefore, this concise stepwise recovery method can be explored as a promising practical solution to overcome the bottlenecks in current metal recycling and solid waste treatment.

摘要 : The development of non-noble metal oxide catalysts for oxygen evolution reaction (OER) under acidic conditions is critical to sustainable energy conversion and storage. However, achieving catalytic performance comparable to that of noble metals remains a significant challenge. Herein we leverage crystal field theory and the site occupancy preferences of magnetic ions to introduce magnetic sites in a half-selective manner into the conventional spinel-structured catalyst Co 3 O 4, thereby realizing alternating atomic hybridization within the crystal lattice. Drawing on the long-range exchange interaction in a half-ordered crystal field, bisymmetry breaking occurs thanks to the synergistic effect of the double magnetic sites, triggering a controllable spin-state transition at the active site. Meanwhile effective metal-adsorbate bonding induced by enhanced spin-orbit coupling leads to fast charge transfer and low rate-determining barrier. As a result, the spin-electron state modulated Co 4 Fe 2 MnO x delivers an OER overpotential drastically reduced by 240 mV compared to the conventional Co 3 O 4, while maintaining outstanding stability of over 300 h at a high current density of 200 mA cm −2 . This work provides a new insight into the design of high-performance non-noble metal oxide catalysts for acidic OER applications.

摘要 : This study successfully synthesized CuBi 2 O 4 /Bi 2 O 3 composite materials through a two-step hydrothermal process, and evaluated their catalytic performance by activating persulfate (PS) under visible light to degrade RhB and TCH. Notably, the CBB-20 % composite material exhibited the highest catalytic activity, with degradation rates of 97.1 % and 86.4 % for Rhodamine B (RhB) and tetracycline hydrochloride (TCH), respectively. In addition, the structure, morphology, optical and electrochemical properties of CuBi 2 O 4 /Bi 2 O 3 composite material were comprehensively characterized. Active species capture experiments revealed that SO 4 •-, •OH, •O 2 −, and h + all contributed to the degradation process, with •OH serving as the primary active species. Repeated cycling experiments revealed the good stability and reusability of the CuBi 2 O 4 /Bi 2 O 3 composite materials. The reaction mechanism of Z-type heterojunction was proposed through electron paramagnetic resonance (EPR) and free radical trapping experiments. In addition, three possible degradation pathways of TCH were proposed based on LC-MS analysis.

摘要 : Tandem catalysis reaction, which integrates two consecutive steps into a single one, can efficiently eliminate the separation of intermediate products, shortening the reaction time and decreasing energy expenditure. Therefore, the development of an efficient method for catalyzing tandem conversion of alkenes to prepare 1, 2-diols is extremely fascinating. In this work, we reported the hydrothermal synthesis of tin-tungsten oxide catalysts at different pH values and their application as bifunctional catalyst for the one-pot tandem catalysis of alkenes to 1, 2-diols. The SnWO 4 catalyst prepared at pH = 5 revealed the best tandem conversion performance and could attain a 95.4 % of cyclohexene conversion as well as a 77.2 % of 1, 2-cyclohexanediol selectivity within 4 h of reaction. A possible mechanism corresponding to the tandem catalytic conversion of cyclohexene into 1, 2-cyclohexanediol over SnWO 4 catalyst was proposed. Moreover, quenching experiments, density functional theory (DFT) calculations and in-situ infrared characterizations were further utilized to verify the reaction mechanism. Sn(II) could stabilize tungstate through the formation of W-O-Sn bonds and effectively reduced the energy of tungsten active centre binding to hydrogen peroxide, promoting the tandem catalysis reaction of cyclohexene to 1, 2-cyclohexanediol. In addition, the one-pot tandem catalysis system could be further extended to the majority of linear and cyclic alkene substrates. This work can give a basis for the development of more green and efficient tandem conversion reaction of alkenes into 1, 2-diols.