天津工业大学

Let G be a multiplicatively written finite group of order n. The Gao constant of the group G, denoted E(G), is defined as the smallest positive integer & ell; with the following property: for any given sequence g1 & centerdot; ... & centerdot; ge over G, there exist n distinct integers i1,..., i, is an element of {1,. .. , & ell;} such that the product of gz1 ,..., gzn , in some order, is the identity element of G. This constant originates from the celebrated additive theorem proved by Erd & odblac;s, Ginzburg and Ziv in 1961, which amounts to proving E(G) <= 2G-1 holds in case that G is abelian. It is also wellknown that E(G) = 2 G-1 holds for all finite cyclic groups. In 2010, Gao and Li [J. Pure Appl. Algebra] conjectured that E(G) <= 3|G| 2 for every finite non-cyclic group G. In this paper, we confirm the conjecture for all non-cyclic groups G whose order is not divisible by four, and we also characterize the groups achieving the equality E(G) =3|G| 2 as those with a cyclic subgroup of index two. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Broad resonance dips limit the spectral resolution and figure of merit (FOM) of wavelength-interrogated fiber surface plasmon resonance (SPR) sensors. Here, silver-coated no-core fiber (NCF), multimode fiber (MMF), and hollow-core fiber (HCF) probes were compared under matched sensing conditions to clarify the influence of host-fiber waveguide structure on SPR linewidth. Experiments over a refractive-index range of 1.333–1.420 showed similar resonance-shift and sensitivity trends for all three probes, while the measured full width at half maximum consistently followed NCF > MMF > HCF. The HCF probe therefore achieved the highest FOM over most of the tested range. Finite-element analysis further showed that NCF supports SPR-active modes with more diverse field distributions and coupling strengths, whereas the annular silica waveguide of HCF constrains the spatial and polarization characteristics of the surface-sensitive modes. In particular, the radially divergent HCF mode exhibited the strongest resonance loss and the narrowest calculated modal peak. Taken together, these results indicate that the observed linewidth narrowing is closely associated with waveguide-structure-dependent regulation of the dominant modal ensemble, providing a potential route to improve fiber-SPR spectral characteristics without introducing additional multilayer films, gratings, or complex micro/nanostructures.

Biomass-derived hard carbon materials are promising anode candidates for sodium ion batteries (SIBs) due to their low cost, renewability, and excellent sodium storage performance. In this study, softwood pulp fibers are employed to fabricate hard carbon for SIBs, and the influence of pyrolysis temperature on the microcrystalline structure, pore architecture, and graphitization degree of the obtained hard carbon, and the correlation between these structural features and sodium storage performance are investigated. Results indicate that increasing carbonization temperature from 1300 degrees C to 1600 degrees C decreases the interlayer spacing () (from 0.374 nm to 0.358 nm) and defect density, while increasing closed pore volume from 0.044 to 0.249 cm(3) g(-1). Electrochemical analysis reveals an "adsorption-intercalation/filling" sodium storage mechanism: sloping capacity (>0.1 V) correlates with specific surface area, whereas plateau capacity (<0.1 V) correlates with closed pore volume, but is limited by a critical d(002) threshold (similar to 0.36 nm). Hard carbon synthesized at 1500 degrees C, with a d(002) of 0.363 nm and a closed pore volume of 0.215 cm(3) g(-1), demonstrates a high reversible capacity of 299.9 mAh g(-1) at 0.1C and 171.2 mAh g(-1) at 10C, as well as 86.4% capacity retention over 200 cycles at 2C. This research offers a promising pathway for developing high-capacity, low-cost anodes for SIBs

Against the backdrop of intensifying global climate change, traditional building envelopes are constrained by their lack of environmental perception and dynamic regulation capabilities, leading to thermal management shortcomings including heat accumulation, insufficient buffering against thermal shocks, and sluggish response to heat loss transients. Bio-inspired dynamic thermal response technologies offer a promising pathway toward adaptive building envelopes. This paper reviews recent advances in three bio-inspired thermal management strategies. The first involves radiative cooling techniques that mimic biological sensing of external stimuli to regulate spectral properties through molecular vibration and scattering mechanisms. Bio-inspired radiative materials achieved solar reflectance up to 99.6% and surface temperature reductions of 3-10 degrees C. The second covers thermal insulation and buffering techniques that replicate hierarchical porous architectures found in nature, with thermal conductivities as low as 0.008 W/(m & sdot;K) and thermal-resistance switching ratios exceeding threefold. The third focuses on thermal storage regulation techniques that leverage biological topological networks to enhance heat storage density and the dynamic charging/discharging response of phase-change materials, reducing melting times by 45.9%-96.0% while maintaining energy-storage densities of approximately 122158 kJ/kg. A quantitative multi-dimensional evaluation covering dynamic thermal response, environmental stability, and cost-effectiveness reveals that the synergistic integration of these three bio-inspired strategies enables buildings to achieve all-season, low-energy, adaptive performance gains. Finally, the challenges impeding large-scale fabrication and long-term stability are outlined, and an adaptive thermal management framework integrating artificial intelligence is envisioned, providing a systematic pathway from mechanistic understanding to engineering implementation for dynamically responsive energy-saving buildings.

Two dimensional nanomaterials have exhibit promising performance in membrane science, especially hexagonal boron nitride nanosheets (BNNSs) with inherent chemical inertness. Here, BNNSs membranes with compact and well-organized stacking texture were successfully prepared via vacuum-assisted filtration approach using chemo-mechanical exfoliated and functionalized BNNSs as matrix. The BNNSs with an average lateral dimension of ~100 nm have few layers structure and abundant hydroxyl and amino groups. The viscosity of the solvent and thickness of membrane are important factors affecting the permeability performance. Importantly, the BNNSs membranes exhibit fascinating filtration and separation performance for various pollutants in water, including abusive organic dyes, heavy metal ion and drugs. Specifically, the membrane with a typical thickness of 30 μm shows the water flux up to 2.1 L⋅m−2⋅min−1⋅bar−1 and 99.87% removal rate for tetracycline. These performances are not only caused by simple physical interception of BNNSs constructed nanochannels, but also by certain intermolecular chemical interactions between functional groups on BNNSs and pollutant molecules. This work would provide experimental foundation and analytical experience for the practical application of BNNSs membranes in the field of complex water purification.