天津工业大学

Mechanical design today faces critical challenges in design efficiency and multidisciplinary optimization, often constrained by high computational costs and fragmented processes. To address these issues, this article proposes DesAgent, a multi-agent collaborative design methodology that integrates the semantic reasoning capabilities of large language models (LLMs) with the numerical prediction accuracy of reduced-order small models (ROSMs). The proposed approach constructs a semantic-numerical synergy loop, enabling a closed-loop, intelligent design process that bridges semantic interpretation and numerical validation. DesAgent features a hierarchical multi-agent system consisting of four specialized agents—requirements analyst, task planner, designer, and feedback evaluator—each responsible for a distinct phase of the design pipeline. The LLMs support natural language parsing and task planning, while the ROSMs ensure real-time simulation-level predictions through neural network-based surrogate models. To validate the proposed methodology, a case study on the structural optimization of a spinning frame wall plate is conducted. Experimental results show that DesAgent reduced material consumption by 21.2% while satisfying multiple constraints related to stress, deformation, and natural frequency avoidance. The entire design optimization process is completed in 232 s, consuming only 12,044 tokens of computational resources. This work presents an efficient, low-cost, and generalizable design framework that demonstrates the feasibility of LLM-augmented collaborative intelligence in complex mechanical design tasks.

Efficient separation of carbon dioxide (CO2) and acetylene (C2H2) is crucial because CO2 is a common impurity in C2H2 production. Here, we present a strategy for engineering the pore environment of RHO-type aluminosilicate zeolites by tuning extraframework cations to reverse the separation of CO2 and C2H2 and preadsorbing target molecules to accelerate adsorption kinetics. Na-RHO exhibited high CO2 selectivity via the "trapdoor" mechanism, achieving a selectivity of 105,515 and a static uptake of 4.39 mmol/g under ambient conditions, while Ag-RHO preferentially adsorbed C2H2 through equilibrium-driven interactions, with a selectivity of 10,872 and a static uptake of 4.16 mmol/g. Structural analyses by three-dimensional electron diffraction (3D ED) and Rietveld refinement revealed that the regulation of extraframework cations created distinct pore environments. Na-RHO also showed excellent cyclic stability and enabled one-step production of ultrahigh-purity C2H2 (>99.999%) from an equimolar CO2/C2H2 mixture. Notably, CO2 preadsorption on Na-RHO accelerated subsequent adsorption kinetics by 1.6-fold, making the first report of a preadsorption strategy that enhanced kinetics. Density functional theory (DFT) calculations revealed that CO2 preadsorption lowered the activation barrier associated with the "trapdoor" effect. These findings establish cation tuning and kinetic modulation as effective approaches for advancing zeolite-based gas separations. [GRAPHICS]

Schematic diagram of SHHEs and practical applications in flexible energy storage technologies.

In this paper, we apply the power-partible reduction to study arithmetic properties of sums involving Legendre polynomial [Formula: see text] and central Delannoy numbers [Formula: see text]. Let [Formula: see text] and [Formula: see text] be an odd prime. It is proved that, for any [Formula: see text], there exist [Formula: see text] and [Formula: see text], both free of [Formula: see text], such that [Formula: see text] if [Formula: see text] and [Formula: see text] if [Formula: see text], where [Formula: see text] is the Legendre symbol. When [Formula: see text] is a power of [Formula: see text], there exist odd integers [Formula: see text] and even integers [Formula: see text], both independent of [Formula: see text], such that [Formula: see text] and [Formula: see text] The case [Formula: see text] in the last congruence confirms a conjecture of Guo and Zeng [New congruences for sums involving Apéry numbers or central Delannoy numbers, Int. J. Number Theory 8 (2012) 2003–2016].

This paper introduces an adaptive inertial subgradient extragradient algorithm with extrapolations from the past for solving pseudo-monotone variational inequalities in real Hilbert spaces. The algorithm incorporates a dual inertial mechanism that combines Nesterov-type momentum with an additional extrapolation step, while employing a fully adaptive step-size rule that requires no prior knowledge of the Lipschitz constant. This design enhances stability and convergence speed while maintaining computational efficiency through adaptive step sizes and a single operator evaluation per iteration. Our theoretical contributions are twofold. First, we establish the weak convergence of the generated sequences to a solution under standard pseudo-monotonicity and Lipschitz assumptions, providing, to the best of our knowledge, the first such result for an algorithm with this dual-inertial structure. Second, under strong pseudo-monotonicity, we prove a linear convergence rate with an explicit bound, demonstrating fast convergence under stronger regularity conditions. Beyond the theoretical analysis, we demonstrate the practical superiority of the proposed algorithm through extensive numerical experiments on both finite and infinite-dimensional settings. The results show that our algorithm consistently outperforms several state-of-the-art methods in both convergence speed and stability, making it a compelling choice for large-scale optimization applications.