Proton exchange membranes (PEMs) serve as essential elements in direct methanol fuel cells (DMFCs). Although sulfonated poly(ether ether ketone) (SPEEK) has shown competitive proton conductivity at high sulfonation levels, the elevated sulfonation inevitably induces excessive swelling. In this study, chitosan (CS) was modified to synthesize phosphorylated chitosan (PCS), which served as a dual-functional ionic crosslinker for SPEEK to fabricate SPEEK/PCS composite PEMs. Owing to the in-situ ionic crosslinking between the -NH2 groups of PCS and the -SO3H groups of SPEEK, the SPEEK/PCS-6 composite membrane achieves a tensile strength of 67.7 MPa and elongation at break of 203.3% in the hydrated state. Simultaneously, the phosphate groups of PCS provide extra proton-conducting pathways, yielding a high proton conductivity of 148.3 mS cm- 1 at 80 degrees C. Moreover, assembled DMFC achieves a low methanol crossover current density of 136 mA cm- 2 and high power density of 160.3 mW cm- 2, demonstrating promising potential for DMFCs.
Dillon-type Boolean functions are trace polynomial functions from F22n to F2, with all the exponents being multiples of 2n−1, often referred to as Dillon-type exponents. This paper investigates a class of bent functions within this family associated with trace rational functions. Specifically, we introduce a novel infinite family of trace rational functions and generalize a key bentness criterion established by Li et al. (2013) [22] for binary Dillon-type functions.Using our family of functions as structural components, we explicitly construct and characterize three distinct classes of bent functions, each derived via a different bridge function with a small number of variables. These characterizations are given either explicitly or in terms of the well-known binary Kloosterman sums. The choice of bridge functions proves to be crucial. We show that when the bridge function is the product of three variables, the resulting construction degenerates, yielding no new bent functions.Remarkably, our first two subclasses of Boolean bent functions can be naturally extended to vectorial bent functions. To the best of our knowledge, these constitute the first explicitly characterized classes of vectorial bent functions within the partial spread class. Moreover, our theoretical analysis and experimental results reveal that these constructions yield new bent functions that are not Extended-Affine equivalent to any previously known class of monomial functions.
Aromatic amines are one kind of crucial raw materials used to manufacture fine chemicals, biofuel, fuel additives, resins, polymers, pharmaceuticals and other biobased materials, which can be obtained by aminating lignin-valorized aromatic alcohols and aldehydes. In this study, a sustainable biosynthetic route for producing vanillylamine and related aromatic amines from lignin-derived alcohols was developed. First, the galactose oxidase gene from Fusarium NRRL 2903 was introduced into E. coli to construct recombinant strain GO for entirely oxidizing 100 mM vanillyl alcohol into vanillin in ethyl acetate:Triton X-114:water = 5:5:90 (vol/vol/vol) containing Cu2+ (1 mM) (25 °C, pH 7.5). In addition, the CV ω-transaminase gene from Chromobacterium violaceum was acquired to construct recombinant E. coli CV for efficiently converting vanillin-derived vanillin into vanillylamine through transamination (35 °C, pH 7.5) with amine donor L-alanine (L-alanine/vanillin molar ratio 10:1), achieving the mass yield of 1.0 g vanillylamine per g vanillyl alcohol. This established tandem biocatalysis process for converting vanillyl alcohol was an efficient and ecofriendly way for synthesizing vanillylamine, and lignin-derived aromatic aldehydes could be transformed into organic amines, rendering the high-value valorization of biomass and its derivatives. In addition, this study has expanded the efficient oxidation transformation of furfuryl alcohol and aromatic alcohol compounds (anisyl alcohol, cinnamyl alcohol, benzyl alcohol, veratryl alcohol, and syringic alcohol) that can be produced from lignocellulose, supplemented the substrate pedigree of the one-pot two-enzyme method, and provided a new idea for the high-value transformation of lignocellulose-derived compounds.
Let F-q be a finite field with q elements, where q is an odd prime power. Let D be a nonempty subset of F-q with cardinality |D|, and let k be an integer such that 1 <= k <= vertical bar D vertical bar. For m is an element of N and b = (b(1), ... , b(m)) is an element of F-q(m), define N-m(k, b, D) as the number of subsets D ' subset of D with cardinality k such that Sigma(x) (is an element of D), x(i) = b(i) for i = 1, 2, ... , m. The problem of determining whether N-m(k, b, D) > 0 is referred to as the m-th moment k-subset sum problem (m-th moment k-SSP). In this paper, we focus on the second moment k-SSP over finite fields in the case D = F-q and b = (b, b(2)) is an element of F-q(2) with q being an odd prime power. By applying the Li-Wan sieve [8], we derive new explicit combinatorial formulas for N-2(k, (b, b(2)), F-q), which correct and improve the previous results obtained by Nguyen [14]. Moreover, we establish two more precise estimates for N-2(k, (b, b(2)), F-q) than those presented by Li and Wan [8] in the case of odd prime power q. As applications, we construct two infinite families of almost-MDS codes with arbitrary dimensions over F-q for odd prime power q. Additionally, we determine the number of minimum-weight codewords of these codes. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Knowledge tracing aims to estimate students’ knowledge states from their historical interactions and predict future performance. Existing session-aware methods can model session structures in the learning process. However, they still suffer from cross-session context inconsistency during target session prediction. Historical evidence is often compressed and accessed through a fixed interaction pattern, which limits the model’s ability to adaptively activate heterogeneous historical dependency patterns under the current target-session context. Meanwhile, the long-term knowledge state aggregated from historical sessions is easily affected by session intervals and unobserved knowledge changes, leading to a mismatch with the target session. To address these issues, this paper proposes a Session-aware Diffusion Routed Knowledge Tracing (SDRKT) framework. The model first adopts a hierarchical session encoder to learn short-term representations within sessions and long-term representations across sessions. Then, a dynamic routing-based cross-session interaction mechanism is introduced to adaptively adjust the contributions of different historical interaction patterns according to the target session context. In addition, a causal prefix-conditioned diffusion refinement module is designed to progressively calibrate the long-term knowledge state using only the target-session concept prefix available up to the current prediction position, which improves its alignment with the current prediction scenario while avoiding future question or concept leakage. Experiments on four public datasets show that SDRKT consistently outperforms state-of-the-art methods across multiple metrics. The code is available at https://github.com/Zhangcantprogram/SDRKT.
