<p>Energy consumption accounting and prediction in the medium and thick plate rolling process are crucial for controlling costs, improving production efficiency, optimizing equipment management, and enhancing the market competitiveness of enterprises. Starting from the perspective of integrating process mechanism and industrial big data, we overcame the difficulties brought by complex and highly nonlinear coupling of process variables, proposed a rolling power consumption accounting algorithm based on time slicing method, and gave a calculation method for the additional power consumption of the main motor for rough rolling and finishing rolling (auxiliary system power consumption, power loss, main motor power consumption deviation); with the help of SIMS model, forward recursion, and reverse recursion pass rolling force estimation strategies are proposed, and the rated power consumption of the main motor was predicted. Furthermore, a random forest regression model of additional power consumption based on data was established, and then a prediction algorithm for the comprehensive power consumption of billet rolling was given. Experiments showed the effectiveness of the proposed method.</p>

In order to obtain high-quality restoration outcomes, this paper proposed a new nonconvex variational model tailored for reconstructing blurred images corrupted by impulse noise. The newly designed optimization framework integrated nonconvex high-order total variation regularization with $ \ell_0 $ norm data fidelity. This combination aided in overcoming the staircase artifacts and maintaining sharp contours while tackling the poor performance of $ \ell_1 $ norm-based data fidelity in handling high-density impulse noise. To deal with the nonconvex optimization problem, we designed an efficient alternating direction method of multipliers by combining the variable splitting technique with the iteratively reweighted $ \ell_1 $ algorithm. Finally, numerous experiments demonstrated that the suggested scheme achieves competitive performance in terms of objective metrics and visual quality.

We relate various characterizations of sandpile dynamics arising in the literature referred to as 'Abelian sandpile models', and we rigorously establish the sense in which they are commutative and associative as algebraic structures. In particular, associativity is approached from different perspectives: directly for the addition of configurations followed by stabilization; as a property of homomorphic images of semigroups; via the composition of operators on configurations; and, more generally, from an asynchronous perspective. We show how the existing formulations all arise within a common framework as substructures or homomorphic images of a non-commutative semigroup of operators. The appendix gives results on the algebraic complexity of sandpile semigroups, with 1) two different proofs determining the Krohn–Rhodes complexity of the finite Abelian sandpile models and all finite Abelian semigroups, 2) exact values of the aperiodic complexity measure for directed non-Abelian sandpile semigroups, and 3) exhibits new kinds of non-Abelian sandpile semigroups of higher Krohn–Rhodes complexity.

This paper has studied a predator-prey model that incorporates a nonlocal fear effect and nonlinear cross-diffusion under homogeneous Neumann boundary conditions. We have derived necessary and sufficient conditions for Turing instability in the presence of both nonlocal fear and nonlinear cross-diffusion by means of linear stability analysis. Moreover, we have investigated steady-state bifurcations induced by the nonlocal fear effect using the Lyapunov-Schmidt reduction.

Typhoons cause significant damage to coastal and inland areas, making the accurate classification of typhoon cloud images essential for effective monitoring and forecasting. While integrating multimodal data from different satellites can improve classification accuracy, existing methods often rely on aligned images and fail to account for radiometric and structural differences, leading to performance degradation during image fusion. In registration methods designed to address this issue, two-stage approaches inaccurately estimate deformation fields, while one-stage methods typically overlook radiometric differences between typhoon cloud images. Additionally, fusion methods suffer from inherent noise accumulation and insufficient cross-modal feature utilization due to cascaded structures. To address these issues, this study proposed a coarse-to-fine registration and fusion network (CoReFuNet) that integrated a one-stage registration module with a cross-modal fusion module for multimodal typhoon cloud image classification. The registration module adopted a one-stage coarse-to-fine strategy, using cross-modal style alignment to address radiometric difference and global spatial registration by affine transformations to resolve positional differences. Bidirectional local feature refinement (BLFR) then ensured precise adjustments, facilitating fine registration by evaluating feature points in each image. Following registration, the fusion module employed a dual-branch alternating enhancement (DAE) approach, which reduced noise by learning cross-modal mapping relationships and applying feedback-based adjustments. Additionally, a cross-modal feature interaction (CMFI) module merged low-level, high-level, intra-modal, and intermodal features through a residual structure, minimizing modality differences and maximizing feature utilization. Experiments on the FY-HMW (Feng Yun-Himawari) dataset, constructed using data from the Feng Yun and Himawari satellites, showed that the CoReFuNet outperformed existing registration methods (VoxelMorph and SIFT) and fusion methods (IFCNN and DenseFuse), achieving 84.34% accuracy and 87.16% G-mean on the FY test dataset, and 82.88% accuracy and 85.54% G-mean on the HMW test dataset. These results showed significant improvements, particularly in unaligned data scenarios, highlighting the potential for real-world typhoon monitoring and forecasting.

In this paper, we propose a finite-time flocking particle model with nonlinear velocity coupling and inter-driving forces. Initially, we demonstrate that under specific initial conditions, the system achieves flocking within a finite timeframe, with all particles' velocities converging to the average of their initial velocities. Our results include some results in the literature. Furthermore, a special case of mutual driving is given. Finally, we validate the obtained results through numerical simulations to confirm their accuracy.

The rapid development of image deraining technology has made it possible to effectively restore images captured even in severe rainy weather, thereby alleviating the decline in image quality. However, existing image deraining solutions typically use overly deep neural networks, which are prone to gradient vanishing and explosion. This often results in the restored image losing essential background details. To address this important issue, this paper proposed an enhanced dual-encoder vision transformer UNet for single-image rain removal. First, a dual-branch heterogeneous encoding structure was formed by integrating two encoders with different architectures. These encoders extract rain streaks by leveraging their distinct characteristics. Specifically, the first encoder was based on a convolutional neural network, termed the residual encoder network, which utilizes the local receptive field capabilities of convolutional kernels to capture both rain streaks and corresponding background details. Concurrently, the second encoder, the parallel vision transformer encoder network, employs self-attention mechanisms to model long-range dependencies and establish global contextual relationships between rain streaks and background details. Subsequently, the rain streak information extracted by the two encoders was fused. The decoder then performs the rain removal task. To preserve spatial consistency and overall image integrity, high-frequency detail refinement was facilitated through residual connections between the encoders and the decoder. Evaluations on synthetic and real-world datasets confirm the algorithm's robustness in processing rain streaks of varied density. The restored images exhibit enhanced visual clarity, improving visibility for computer vision applications.

Deep learning has recently gained prominence in fluid dynamics due to advances in computational power, algorithm development, and data availability. While most applications have focused on modeling and control, its potential for design and optimization remains relatively unexplored. In this study, a conditional generative adversarial network (CGAN) was developed for inverse design of airfoils with flow control devices. This CGAN receives the characteristics of the flow (Reynolds number and angle of attack) and the desired aerodynamic characteristics (drag and lift coefficients). Based on those inputs, the CGAN generates an airfoil that fulfills the defined specifications. With this objective, numerical simulations of 4-digit NACA airfoils with variable flap configurations and flow conditions were conducted, in order to obtain the necessary aerodynamic data for training and testing the CGAN. The results demonstrate that the proposed CGAN generates airfoil geometries with high accuracy and efficiency, showing minor deviations from real geometries and achieving aerodynamic performances that approach the desired ones for all the flow conditions considered. Additionally, the model is able to generalize to extreme cases not seen during training, which significantly broadens its application range. This approach offers a significant reduction in computational time compared to traditional iterative optimization methods, making it suitable for rapid design exploration and real-time applications.

Feature selection is a crucial data processing method used to reduce dataset dimensionality while preserving key information. In this paper, we proposed a multi-strategy enhanced dung beetle optimization algorithm (mDBO) that integrates multiple strategies to effectively address the feature selection problem. First, a novel population initialization strategy based on a hybrid tent-sine map and random opposition-based learning was proposed to generate initial population. This strategy yielded a more uniform distribution of the initial population, significantly improving the quality of the population distribution within the search space. Second, a new differential evolution mutation strategy with a periodic retrospective adaptive mutation factor was proposed. This strategy effectively improved the algorithm's ability to jump out of the local optimal and explore potential candidate solutions. Third, based on Padé approximation technology and the novel adaptive evolutionary boundary constraint method, an innovative approximation strategy was proposed. The strategy was integrated into the framework of the dung beetle optimizer, significantly improving the solution accuracy and population quality of the algorithm. Finally, the binary version of the mDBO algorithm (bmDBO) was applied to feature selection tasks. Experiments entailing CEC2017 benchmark functions and 17 datasets showed that both mDBO and bmDBO outperformed other algorithms. The mDBO method outperformed other algorithms in 11 of the 29 benchmark functions, ranked second in 8 functions, and achieved an average rank of 1.62 in the Friedman ranking, securing the overall first place; the bmDBO method outperformed in 12 of 17 datasets, achieving an average ranking of 1.35 in the Friedman ranking, securing the first position.

We investigate Mahler's real $ T $-numbers through Cantor-type constructions inside $ \mathcal T\cap \mathbb{G} $, where $ \mathbb{G} $ is the middle-third Cantor set and $ \mathcal T $ is the set of real Mahler $ T $-numbers. We build explicit families $ \mathcal{T}^{(t)} $ which are homeomorphic to Cantor space and use them to analyze structural, combinatorial, and additive properties of $ \mathcal T $. Our results include the existence of descending chains of Cantor subsets of $ \mathcal T $ of length $ \mathfrak c $; a characterization of ternary expansions in $ \mathcal T^{(t)} $, showing non-normality but maximal block complexity under sparse forcing, linked to the Adamczewski–Bugeaud criterion; and a sumset theorem proving that for suitable parameters $ t_1, t_2 $ one has the interval identity $ \mathcal T^{(t_1)}+\mathcal T^{(t_2)} = [0, 1] $, which yields the global corollary $ \mathcal T+\mathcal T = \mathbb R $ (Erdős property) by integer translation invariance. We also discuss implications for cardinal invariants and entropy of the shift map, highlighting the interplay between thin Diophantine sets and large additive structure. To address a natural concern about existence, we include a non-emptiness lemma which shows that our scheduled deletion-and-witness procedure always leaves a non-empty perfect set $ \mathcal T^{(t)} $.