This article demonstrates that third-order real symmetric tensors cannot be classified up to equivalence by their eigenvalues only, thereby resolving a question posed by Qi in 2006. Leveraging Harrison's center theory and characteristic polynomials, we construct explicit examples across all dimensions, specifically, pairs of tensors sharing identical eigenvalues yet belonging to distinct equivalence classes. (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The project management of high-voltage substation expansion project is facing greater construction safety risks. It is of great significance to ensure the safety of personnel and the reliable operation of power grid to do a good job in the safety risk management of high-voltage substation expansion project construction. The aim of this study is to establish a dynamic control system for safety risk system dynamics (SD) of high voltage substation expansion construction based on the combination of analytic hierarchy process and fuzzy comprehensive evaluation (AHP-FCE). Firstly, the weights and scores of risk indicators are determined based on AHP-FCE theory to carry out static risk assessment. Then, based on SD, a dynamic evaluation model is established to analyze the change trend of risk indicators over time and the most sensitive secondary risk indicators among the primary risk indicators through causality diagram and stock flow diagram. Finally, this study proposes three control strategies, and simulates the implementation effect through SD, which provides an effective reference for project managers to dynamically control the safety risks of high-voltage substation expansion construction.
A nonlinear shaft-plate coupled load transfer model is proposed for axially compressed helical piles. The novelty of the model lies in treating the helix plate as a discrete internal bearing interface embedded within a continuous shaft load transfer system, so that the axial-force jump, displacement compatibility, and nonlinear resistance mobilization are solved simultaneously within a single boundary value problem. Hyperbolic load-displacement relations are adopted for both the distributed shaft resistance and the localized plate bearing, with the initial stiffness parameters ks0 and Kb0 derived from the same elastic continuum solution to ensure internal consistency within a unified framework. Displacement compatibility and axial force jump at each plate location complete the nonlinear boundary value problem, which is solved through an iterative finite-difference scheme updating equivalent secant stiffness until convergence on both plate load and displacement field. The pile head response, axial force distribution, shaft friction mobilization, plate bearing ratio, and interface stiffness degradation are obtained. Parametric studies reveal that pile geometry, helix embedment depth, and soil stiffness gradient collectively govern the nonlinear load transfer characteristics. Within the investigated parameter range, increasing load promotes a progressive redistribution of axial resistance from the shaft toward the helix plate. The extent of this transition depends on the relative shaft-plate strength and stiffness, rather than being a fixed response mode. Both shaft friction mobilization and interface stiffness degradation exhibit a spatially non-monotonic distribution, peaking in a primary transfer zone above the helix plate and diminishing below. This depth-zoning pattern is induced by plate-mediated load diversion and is absent in conventional straight piles.
Abstract Accurate and efficient identification of pavement defects is crucial for reducing traffic accident rates and ensuring the safety of road users’ lives and property. To effectively address the multiscale issue in pavement defect detection and significantly improve the detection accuracy of pavement defects, this study takes the YOLOv8 model as the basic framework. A new detection model is designed through targeted improvements, which is named Enhanced Multiscale Attention-YOLO (EMSA-YOLO), which integrates multiscale attention mechanisms with large-target feature extraction capabilities. Firstly, to enhance the extraction of defect features across multiple spatial scales, the EMSA module is designed to expand the receptive field and incorporate multiscale contextual information through the application of a learned weight matrix. Secondly, DySample is employed to optimize the upsampling process in the neck network, yielding clearer fused feature images and enhancing the detection accuracy of small-sized potholes. Finally, we add a new P6 large target detection layer to expand the receptive field and capture multiscale features, which enables the model to capture deeper semantic features and improve the detection of longitudinal and transverse cracks. Experimental results on the RDD2022 dataset demonstrate that the EMSA-YOLO achieves 84.1% mAP@50 and 57.5% mAP@50-95, outperforming the baseline by 2.1% and 1.7%, respectively. Significant accuracy improvements are observed in three critical defect categories: transverse crack with a 2.4% increase, alligator crack with a 4.8% increase, and potholes with a 1.4% increase compared to the baseline performance.
For a simple graph G=(V,E), a proper total weighting is a mapping w: V∪ E→ℝ such that for every edge uv∈ E, w(u)+∑_e∋ uw(e)≠ w(v)+∑_e∋ vw(e). The graph G is said to be (2,2)-choosable if, for any list assignment L that assigns to each z in V∪ E a set L(z) of two real numbers, there exists a proper total weighting w with w(z)∈ L(z) for every z∈ V∪ E. Wong and Zhu, and independently Przybyło and Woźniak conjectured that every simple graph is (2,2)-choosable. This conjecture remains open. For a set {a,b}⊂ℝ, its span is defined as |b-a|. We call a graph G=(V,E) uniform-span (2,2)-choosable if, for any list assignment L that assigns to every z∈ V∪ E a two-element list of a common span, there exists a proper total weighting respecting the assignment. In this paper, we present a novel lemma and perform comprehensive enhancements to our previous algorithm. These contributions enable us to prove that every graph is uniform-span (2,2)-choosable, and thus admits a proper total weighting using any prescribed pair {a,b}⊂ℝ. This confirms the 1-2 conjecture in full generality.
