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Search Results (2,761)

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31 pages, 2064 KiB  
Article
A Technique for Image Encryption Using the Modular Multiplicative Inverse Property of Mersenne Primes
by Shanooja M. A. and Anil Kumar M. N.
Symmetry 2025, 17(2), 166; https://doi.org/10.3390/sym17020166 - 22 Jan 2025
Abstract
Mersenne prime numbers, expressed in the form (2n − 1), have long captivated researchers due to their unique properties. The presented work aims to develop a symmetric cryptographic algorithm using a novel technique based on the logical properties of Mersenne primes. Existing [...] Read more.
Mersenne prime numbers, expressed in the form (2n − 1), have long captivated researchers due to their unique properties. The presented work aims to develop a symmetric cryptographic algorithm using a novel technique based on the logical properties of Mersenne primes. Existing encryption algorithms exhibit certain challenges, such as scalability and design complexity. The proposed novel modular multiplicative inverse property over Mersenne primes simplifies the encryption/decryption process. The simplification is achieved by computing the multiplicative inverse using cyclic bit shift operation. The proposed image encryption/decryption scheme involves a series of exor, complement, bit shift, and modular multiplicative inversion operations. The image is segmented into blocks of 521 bits. Each of these blocks is encrypted using a 521-bit key, ensuring high entropy and low predictability. The inclusion of cyclic bit shifting and XOR operations in the encryption/decryption process enhances the diffusion properties and resistance against attacks. This approach was experimentally proven to secure the image data while preserving the image structure. The experimental results demonstrate significant improvements in security metrics, including key sensitivity and correlation coefficients, confirming the technique’s effectiveness against cryptographic attacks. Overall, this method offers a scalable and secure solution for encrypting high-resolution digital images without compromising computational efficiency. Full article
(This article belongs to the Section Computer)
20 pages, 5644 KiB  
Article
Microstructure and Mechanical Properties of TixNbMoTaW Refractory High-Entropy Alloy for Bolt Coating Applications
by Ruisheng Zhao, Yan Cao, Jinhu He, Jianjun Chen, Shiyuan Liu, Zhiqiang Yang, Jinbao Lin and Chao Chang
Coatings 2025, 15(2), 120; https://doi.org/10.3390/coatings15020120 - 21 Jan 2025
Viewed by 247
Abstract
High-strength bolts are prone to crack initiation from the threaded hole during fastening due to large loads, which can compromise their performance and reliability. To enhance the durability of these bolts, coatings are often employed to strengthen their surfaces. NbMoTaW refractory high-entropy alloy [...] Read more.
High-strength bolts are prone to crack initiation from the threaded hole during fastening due to large loads, which can compromise their performance and reliability. To enhance the durability of these bolts, coatings are often employed to strengthen their surfaces. NbMoTaW refractory high-entropy alloy coatings are widely used in hard coating applications due to their exceptional mechanical properties. However, the brittleness of this alloy at room temperature limits its performance in high-stress environments. To enhance the ductility of NbMoTaW alloys, this study systematically investigates the effect of varying titanium (Ti) content on the alloy’s properties. First-principles calculations were employed to analyze the elastic properties of TixNbMoTaW alloys, including elastic constants, the elastic modulus, the bulk modulus (B)-to-shear modulus (G) ratio (Pugh’s ratio), Poisson’s ratio (ν), and Cauchy pressure (C12–C44). The results indicate that the addition of Ti significantly improves the alloy’s plasticity. Specifically, when the Ti content is x = 2, the B/G ratio increases to 3.23, and Poisson’s ratio increases to 0.39, indicating enhanced deformability. At x = 0.75, the elastic modulus (E) increases to 273.78 GPa, compared to 244.99 GPa for the original alloy. The experimental results further validate the computational findings. X-ray diffraction (XRD) and scanning electron microscopy (SEM) analyses indicate that all alloys exhibit a single body-centered cubic (BCC) phase. Room-temperature compression tests show that as the Ti content increases, the yield strength, fracture strength, and plasticity of the alloys significantly improve. Specifically, for a Ti content of x = 0.75, the yield strength reaches 1551 MPa, the fracture strength is 1856 MPa, and the plastic strain increases to 14.6%. For Ti1.5NbMoTaW, the yield strength is 1506 MPa, the fracture strength is 1893 MPa, and the plastic strain is 17.3%. Overall, TixNbMoTaW refractory high-entropy alloys demonstrate significant improvements in both plasticity and strength, showing great potential for coating applications in high-stress environments. Full article
(This article belongs to the Special Issue Coatings for Advanced Devices)
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<p>Cell model of Ti<sub>x</sub>NbMoTaW high-entropy alloy: (<b>a</b>) NbMoTaW, (<b>b</b>) Ti<sub>0.25</sub>NbMoTaW, (<b>c</b>) Ti<sub>0.5</sub>NbMoTaW, (<b>d</b>) Ti<sub>0.75</sub>NbMoTaW, (<b>e</b>) TiNbMoTaW, (<b>f</b>) Ti<sub>1.5</sub>NbMoTaW, (<b>g</b>) Ti<sub>2</sub>NbMoTaW.</p>
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<p>Convergence curve of k-point grid and total energy of Ti<sub>x</sub>NbMoTaW high-entropy alloys.</p>
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<p>Ti<span class="html-italic">x</span>NbMoTaW refractory high-entropy alloy characterization sample.</p>
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<p>Phase structure parameters of Ti<span class="html-italic">x</span>NbMoTaW high-entropy alloy with different Ti contents.</p>
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<p>Elastic modulus of Ti<span class="html-italic">x</span>NbMoTaW high-entropy alloy with different Ti content.</p>
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<p>Density of states of Ti<span class="html-italic">x</span>NbMoTaW system high-entropy alloys with different Ti contents.</p>
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<p>X-ray diffraction patterns of Ti<sub>x</sub>NbMoTaW high-entropy alloys in the as-cast state.</p>
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<p>Backscattered electron image of as-cast TixNbMoTaW high-entropy alloys: (<b>a</b>) NbMoTaW, (<b>b</b>) Ti<sub>0.25</sub>NbMoTaW, (<b>c</b>) Ti<sub>0.5</sub>NbMoTaW, (<b>d</b>) Ti<sub>0.75</sub>NbMoTaW, (<b>e</b>) TiNbMoTaW, (<b>f</b>) Ti<sub>1.5</sub>NbMoTaW, (<b>g</b>) Ti<sub>2</sub>NbMoTaW.</p>
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<p>Scanning backscattered electron (SEM) map and energy spectrum of each element (EDS) for Ti<sub>x</sub>NbMoTaW high-entropy alloys in cast state.</p>
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<p>Scanning backscattered electron (SEM) map and energy spectrum of each element (EDS) for Ti<sub>x</sub>NbMoTaW high-entropy alloys in cast state.</p>
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<p>Scanning backscattered electron (SEM) map and energy spectrum of each element (EDS) for Ti<sub>x</sub>NbMoTaW high-entropy alloys in cast state.</p>
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<p>Compositional distribution of each element of Ti<sub>x</sub>NbMoTaW high-entropy alloys in dendritic (DR) (<b>a</b>) and intergranular (ID) regions (<b>b</b>).</p>
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<p>Engineering stress–strain curves for room-temperature compression of refractory high-entropy alloys of the Ti<sub>x</sub>NbMoTaW system in cast temper.</p>
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<p>Plastic strain in room-temperature compression of refractory high-entropy alloys of the Ti<sub>x</sub>NbMoTaW system in cast temper.</p>
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19 pages, 56055 KiB  
Article
Excellent Strength–Impact Toughness Combination of Heterostructured Metastable Fe-Rich Medium-Entropy Alloy
by Dmitrii Panov, Ruslan Chernichenko, Stanislav Naumov, Egor Kudryavtsev, Alexey Pertcev, Nikita Stepanov, Sergey Zherebtsov and Gennady Salishchev
Materials 2025, 18(3), 476; https://doi.org/10.3390/ma18030476 - 21 Jan 2025
Viewed by 308
Abstract
The effect of a heterogeneous structure obtained via cold rotary swaging (CRS) and post-deformation annealing (PDA) on the dynamic mechanical properties of a non-equiatomic 49.5Fe-30Mn-10Co-10Cr-0.5C (at.%) medium-entropy alloy at room and cryogenic temperatures was studied. CRS to a reduction of 92% and subsequent [...] Read more.
The effect of a heterogeneous structure obtained via cold rotary swaging (CRS) and post-deformation annealing (PDA) on the dynamic mechanical properties of a non-equiatomic 49.5Fe-30Mn-10Co-10Cr-0.5C (at.%) medium-entropy alloy at room and cryogenic temperatures was studied. CRS to a reduction of 92% and subsequent PDA at 500–600 °C developed a heterogeneous structure consisting of a twinned γ-matrix and dislocation-free γ-grains in the rod core and an ultrafine-grained microstructure of γ-phase at the rod edge. Therefore, the maximum stress (σm) value increased. Charpy V-notch impact toughness (KCV) decreased after CRS to a reduction of 18% and stabilized after further straining. However, the contribution of the crack initiation energy consumption (KCVi) increased, while the crack propagation energy consumption (KCVP) decreased. PDA resulted in increases in KCVi and KCVP. A ductile-to-brittle transition occurred from −90 °C to −190 °C. Cryogenic Charpy impact testing of the heterostructured material revealed inflections on impact load–deflection curves. The phenomenon contributed to an increase in KCVP, providing a longer crack propagation path. The heterostructured material possessed an excellent σm-KCV combination in the temperature range between −90 °C and +20 °C. Full article
(This article belongs to the Section Advanced Materials Characterization)
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<p>(<b>a</b>) IPF map and (<b>b</b>) pole figure of the 49.5Fe-30Mn-10Co-10Cr-0.5C alloy in the initial condition. RD—radius direction; AD—axial direction.</p>
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<p>Scheme of CRS processing. RD—radius direction; AD—axial direction.</p>
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<p>(<b>a</b>) Cutting scheme and dimensions of a Charpy V-notch specimen; (<b>b</b>) application of the CCR method.</p>
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<p>XRD patterns of the 49.5Fe-30Mn-10Co-10Cr-0.5C (at.%) alloy subjected to (<b>a</b>) CRS18, (<b>b</b>) CRS62, and (<b>c</b>) CRS92 and subsequent (<b>d</b>) ANN600 and (<b>e</b>) ANN700.</p>
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<p>SEM-EBSD characterization of the 49.5Fe-30Mn-10Co-10Cr-0.5C alloy subjected to CRS18: (<b>a</b>,<b>c</b>) IPF maps and (<b>b</b>,<b>d</b>) phase maps. Pole figures are inserted in (<b>a</b>,<b>c</b>).</p>
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<p>SEM-EBSD characterization of the 49.5Fe-30Mn-10Co-10Cr-0.5C alloy subjected to (<b>a</b>,<b>c</b>) CRS62 and (<b>b</b>,<b>d</b>) CRS92: IPF maps and pole figures (PFs).</p>
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<p>SEM-EBSD characterization of the 49.5Fe-30Mn-10Co-10Cr-0.5C alloy subjected to (<b>a</b>,<b>c</b>) ANN600 and (<b>b</b>,<b>d</b>) ANN700: IPF maps and pole figures (PFs).</p>
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<p>TEM characterization of the 49.5Fe-30Mn-10Co-10Cr-0.5C alloy subjected to (<b>a</b>,<b>d</b>) CRS18, (<b>b</b>,<b>e</b>) CRS62, and (<b>c</b>,<b>f</b>) CRS92.</p>
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<p>TEM characterization of the 49.5Fe-30Mn-10Co-10Cr-0.5C alloy subjected to (<b>a</b>,<b>c</b>) ANN600 and (<b>b</b>,<b>d</b>) ANN700.</p>
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<p>(<b>a</b>,<b>c</b>) Impact load–deflection curves and (<b>b</b>,<b>d</b>) dynamic mechanical properties (Charpy V-notch impact toughness (KCV) and maximum stress (σ<sub>m</sub>)) after CRS and post-deformation annealing. Dotted ellipses outline inflections in (<b>a</b>,<b>c</b>).</p>
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<p>Impact load–deflection curves of the material under study in (<b>a</b>) the initial condition and after (<b>b</b>) CRS92, (<b>c</b>) ANN600, and (<b>d</b>) ANN700.</p>
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<p>Charpy V-notch impact toughness (KCV) and maximum stress (σ<sub>m</sub>) of the material under study in (<b>a</b>) the initial condition and after (<b>b</b>) CRS92, (<b>c</b>) ANN600, and (<b>d</b>) ANN700 versus testing temperature.</p>
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<p>(<b>a<sub>1</sub></b>–<b>d<sub>1</sub></b>) SEM-overviews and (<b>a<sub>2</sub></b>–<b>d<sub>2</sub></b>,<b>a<sub>3</sub></b>–<b>d<sub>3</sub></b>,<b>a<sub>4</sub></b>–<b>d<sub>4</sub></b>) microfractography after Charpy impact testing at −20 °C.</p>
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<p>(<b>a<sub>1</sub></b>–<b>d<sub>1</sub></b>) SEM-overviews and (<b>a<sub>2</sub></b>–<b>d<sub>2</sub></b>,<b>a<sub>3</sub></b>–<b>d<sub>3</sub></b>,<b>a<sub>4</sub></b>–<b>d<sub>4</sub></b>) microfractography after Charpy impact testing at −190 °C.</p>
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<p>Maximum stress (σ<sub>m</sub>)–Charpy V-notch impact toughness (KCV) combination of the 49.5Fe-30Mn-10Co-10Cr-0.5C alloy.</p>
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8 pages, 2097 KiB  
Communication
Preparation of High Entropy Alloys Without Pre-Alloying, Using Laser Melt Deposition (LMD) Technique
by Ferenc Hareancz, Gergely Juhász, Márk Windisch, Anita Heczel and Ádám Vida
Coatings 2025, 15(2), 116; https://doi.org/10.3390/coatings15020116 - 21 Jan 2025
Viewed by 323
Abstract
This study explores the fabrication of an equimolar CoCrFeNi high-entropy alloy (HEA) using laser metal deposition (LMD) technique on a 316 L austenitic stainless steel substrate, without pre-alloying. Elemental metal powders were mixed in a planetary ball mill and directly deposited to investigate [...] Read more.
This study explores the fabrication of an equimolar CoCrFeNi high-entropy alloy (HEA) using laser metal deposition (LMD) technique on a 316 L austenitic stainless steel substrate, without pre-alloying. Elemental metal powders were mixed in a planetary ball mill and directly deposited to investigate the effect of layer number on alloy composition and substrate intermixing. Experimental results revealed significant dilution in the first four layers, with substrate intermixing affecting composition. The coarse-grained crystal structure observed in the initial layers persisted in subsequent layers, and hardness measurements indicated the cumulative thermal effects of sequential deposition. From an industrial perspective, this approach offers a cost-effective and flexible manufacturing strategy, eliminating the need for pre-alloying. Moreover, gradient compositional layers can be achieved, enabling tailored material properties. This work demonstrates the feasibility of producing multi-layer HEAs directly from elemental powders while addressing the challenges of compositional stability. Full article
(This article belongs to the Special Issue Research and Application of High Entropy Alloys)
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<p>The scanning strategy.</p>
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<p>Optical microscope image of ground and polished samples (<b>a</b>) 1 layer; (<b>b</b>) 10 layers.</p>
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<p>EDS measurement results (<b>a</b>) for 1 layer; (<b>b</b>) for 10 layers.</p>
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<p>EBSD-based orientation images (<b>a</b>) of 1 layer; (<b>b</b>) of 10 layers; (<b>c</b>) of melted zone border between substrate and first layer.</p>
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<p>Hardness measurements (<b>a</b>) for 1 layer; (<b>b</b>) for 10 layers.</p>
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20 pages, 3380 KiB  
Article
Application Layer Protocol Identification Method Based on ResNet
by Zhijian Fang, Xiang Gao, Huaxiong Zhang, Jingpeng Tang and Qiang Gao
Algorithms 2025, 18(1), 52; https://doi.org/10.3390/a18010052 - 18 Jan 2025
Viewed by 267
Abstract
Most network attacks occur at the application layer, where many application layer protocols exist. These protocols have different structures and functionalities, posing feature extraction challenges and resulting in low identification accuracy. This significantly affects application layer protocol recognition, analysis, and detection. We propose [...] Read more.
Most network attacks occur at the application layer, where many application layer protocols exist. These protocols have different structures and functionalities, posing feature extraction challenges and resulting in low identification accuracy. This significantly affects application layer protocol recognition, analysis, and detection. We propose a data protocol identification method based on a Residual Network (ResNet) to address this issue. The method involves the following steps: (1) utilizing a delimiter determination algorithm based on information entropy proposed in this paper to determine an optimal set of delimiters; (2) segmenting the original data using the optimal set of delimiters and constructing a feature data block frequency table based on the frequency of segmented data blocks; (3) employing a composite-feature-based RGB image generation algorithm proposed in this paper to generate feature images by combining feature data blocks and original data; and (4) training the ResNet model with the generated feature images to automatically learn protocol features and achieve classification recognition of application layer protocols. Experimental results demonstrate that this method achieves over 98% accuracy, precision, recall, and F1 score across these four metrics. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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<p>This image introduces the data preprocessing phase, feature separator algorithm, image generation algorithm, and overall structure of the training in this paper.</p>
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<p>This image introduces the pseudo-logic of the separator determination algorithm based on information entropy.</p>
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<p>This image primarily illustrates the implementation principle of the composite feature RGB image generation algorithm.</p>
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<p>These three images primarily showcase the pictures generated using the RGB image generation algorithm, where (<b>a</b>) represents the DNS protocol, (<b>b</b>) represents the SMTP protocol, and (<b>c</b>) represents the HTTP protocol.</p>
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<p>This image primarily introduces the ResNet18 network model.</p>
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<p>This image mainly displays the dataset used in this paper’s experiments and the data distribution ratios, where (<b>a</b>) represents the CIC-IDS2017 dataset and (<b>b</b>) represents the Shodan dataset.</p>
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<p>These six images show pictures generated from the same protocol using different algorithms. The first row displays images generated directly from the raw data, while the second row uses the algorithm proposed in this paper. (<b>a</b>) represents the BGP protocol, (<b>b</b>) represents SMB, and (<b>c</b>) represents HTTP.</p>
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<p>These images show the loss values and accuracy of five datasets in ResNet models with different depths, where (<b>a</b>) uses ResNet18, (<b>b</b>) uses ResNet34, and (<b>c</b>) uses ResNet50.</p>
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<p>This image displays the confusion matrix of the test set on ResNet50.</p>
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21 pages, 9000 KiB  
Article
An Investigation of Infrared Small Target Detection by Using the SPT–YOLO Technique
by Yongjun Qi, Shaohua Yang, Zhengzheng Jia, Yuanmeng Song, Jie Zhu, Xin Liu and Hongxing Zheng
Technologies 2025, 13(1), 40; https://doi.org/10.3390/technologies13010040 - 17 Jan 2025
Viewed by 544
Abstract
To detect and recognize small-size and submerged complex background targets in infrared images, we combine a dynamic receptive field fusion strategy and a multi-scale feature fusion mechanism to improve the detection performance of small targets significantly. The space-to-depth convolution module is introduced as [...] Read more.
To detect and recognize small-size and submerged complex background targets in infrared images, we combine a dynamic receptive field fusion strategy and a multi-scale feature fusion mechanism to improve the detection performance of small targets significantly. The space-to-depth convolution module is introduced as a downsampling layer in the backbone first and achieves the same sampling effect. More detailed information is retained at the same time. Thus, the model’s detection capability for small targets has been enhanced. Then, the pyramid level 2 feature map with minimum receptive field and maximum resolution is added to the neck, which reduces the loss of positional information during feature sampling. Furthermore, x-small detection heads are added, the understanding of the overall characteristics and structure of the target is enhanced much more, and the representation and localization of small targets have been improved. Finally, the cross-entropy loss function in the original network model is replaced by an adaptive threshold focal loss function, forcing the model to allocate more attention to target features. The above methods are based on a public tool, the eighth version of You Only Look Once (YOLO) improved, it is named SPT–YOLO (SPDConv + P2 + Adaptive Threshold + YOLOV8s) in this paper. Some experiments on datasets such as infrared small object detection (IR-SOD) and infrared small target detection 1K(IRSTD-1K), etc. have been executed to verify the proposed algorithm; and the mean average precision of 94.0% and 69% under the condition of threshold at 0.5 and over a range from 0.5 to 0.95 is obtained, respectively. The results show that the proposed method achieves the best performance of infrared small target detection compared to existing methods. Full article
(This article belongs to the Section Information and Communication Technologies)
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<p>A lightweight deep-learning model consisting of the backbone, neck, and head networks, and the YOLOv8 network architecture depicted in detail.</p>
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<p>The architecture of the SPT–YOLO detection model, highlights the improvements made to the original YOLOv8s. The red boxes in the backbone network represent the integration of SPDConv (labeled as SPD). In the neck network, the red-highlighted section corresponds to the addition of the P2 feature layer. Similarly, in the detection head, the red box denotes the inclusion of an x-small detection head.</p>
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<p>Conventional maximum pooling and strided convolution schematic; (<b>a</b>) several equal-sized rectangular regions called pooling windows; (<b>b</b>) SPDConv Module.</p>
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<p>Feature fusion process of the network after adding P2. The process from F3 to F2 is detailed in the purple box on the left, which includes the upsampling and fusion modules. F3 is the first upsampling to match the size of P2, after which it is fused with the P2 feature map.</p>
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<p>Imbalance between target and background. The left panel shows the original image with the target of interest highlighted within the red dashed border. The right panel shows the background of the image after target removal, with the green dashed border marking where the target was previously located.</p>
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<p>Visualization of model evaluation metrics during training (precision, recall, and mAP@0.5).</p>
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<p>Comparison of PR of different methods on IR-SOD dataset.</p>
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<p>Comparison of multiple target detection in a scene, where the blue bounding boxes represent cars, and the indigo boxes represent ships. In the ground truth annotations, green boxes denote cars and blue boxes denote ships, while the yellow bounding boxes highlight the missed detections.</p>
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<p>Presentation of a comparative analysis of various models in complex scenes.</p>
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<p>Presentation of a comparative analysis of various models in complex scenes.</p>
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<p>Illustration of a comparative analysis of target detection in scenes with few targets, where the purple bounding boxes indicate missed detections.</p>
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<p>Illustration of a comparative analysis of target detection in scenes with few targets, where the purple bounding boxes indicate missed detections.</p>
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<p>Comparison of feature maps for the output by the third convolutional module of the network.</p>
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<p>Comparison of detection performance with 3 and 4 detection heads.</p>
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22 pages, 7843 KiB  
Article
The Optimization of the Rear Guide Vane of a Bulb Tubular Pump Based on Orthogonal Tests
by Kuilin Wang, Xiaomin Meng, Tao Wang, Rongrong Jiang, Wang Yao, Mengru Zhang, Wentong Wang and Wenjie Wang
Processes 2025, 13(1), 264; https://doi.org/10.3390/pr13010264 - 17 Jan 2025
Viewed by 414
Abstract
Bulb tubular pumps have been widely used in hydraulic engineering because of their compact structure, easy maintenance, high adaptability, and other characteristics. In this paper, the performance optimization of the bulb tubular pump in the South-to-North water diversion project is studied, as well [...] Read more.
Bulb tubular pumps have been widely used in hydraulic engineering because of their compact structure, easy maintenance, high adaptability, and other characteristics. In this paper, the performance optimization of the bulb tubular pump in the South-to-North water diversion project is studied, as well as the influence of the design of the rear guide vane structure on the hydraulic efficiency of the pump. This study takes a certain type of bulb tubular pump as its research object, optimizing the rear guide vane. Firstly, the accuracy of the numerical simulation method is verified using grid convergence analysis and model experimentation. The orthogonal experimental design method is used to optimize the design, and the range analysis results show that the blade wrap angle has the most significant influence on the hydraulic efficiency and head. Finally, the optimization results under a 0° impeller setting angle were verified by numerical analysis, and the hydraulic efficiency of the optimized pump was increased by 0.7%, 0.88%, and 1.1% under low flow, design flow, and high flow, respectively. By introducing entropy generation theory for inflow analysis, the reduction in energy loss in the pump is proven, thus verifying the effectiveness of the optimization. Through the optimization, the separation fluid phenomenon on the guide vane surface is improved, the vortex scale is reduced, and the flow field in the pump is improved to a certain extent. Full article
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<p>A schematic diagram of the post positional bulb tubular pump system. (1) Ribs. (2) Impeller. (3) Diffuser (4) Bulb body. (5) Support body.</p>
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<p>The layout of the bulb tubular pump. (1) Inlet channel. (2) Impeller. (3) Guide vane. (4) Support body. (5) Bulb body. (6) Outlet channel. (7) Water barrier pier.</p>
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<p>Flow passage component mesh.</p>
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<p>Grid convergence curve.</p>
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<p>Bulb tubular pump hydraulic model test. (1) Impeller. (2) Diffuser.</p>
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<p>External characteristics comparison.</p>
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<p>Overall streamline diagram.</p>
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<p>Diagram of leaf expansion.</p>
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<p>Impeller guide vane blade height expansion.</p>
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<p>Relationship between head and factor levels.</p>
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<p>Relationship between hydraulic efficiency and factor levels.</p>
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<p>Pressure contour of guide vane before and after optimization.</p>
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<p>Velocity streamlines at different blade heights.</p>
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<p>Entropy production chart at different blade heights.</p>
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17 pages, 821 KiB  
Article
Measuring the Risk Spillover Effect of RCEP Stock Markets: Evidence from the TVP-VAR Model and Transfer Entropy
by Yijiang Zou, Qinghua Chen, Jihui Han and Mingzhong Xiao
Entropy 2025, 27(1), 81; https://doi.org/10.3390/e27010081 - 17 Jan 2025
Viewed by 304
Abstract
This paper selects daily stock market trading data of RCEP member countries from 3 December 2007 to 9 December 2024 and employs the Time-Varying Parameter Vector Autoregression (TVP-VAR) model and transfer entropy to measure the time-varying volatility spillover effects among the stock markets [...] Read more.
This paper selects daily stock market trading data of RCEP member countries from 3 December 2007 to 9 December 2024 and employs the Time-Varying Parameter Vector Autoregression (TVP-VAR) model and transfer entropy to measure the time-varying volatility spillover effects among the stock markets of the sampled countries. The results indicate that the signing of the RCEP has strengthened the interconnectedness of member countries’ stock markets, with an overall upward trend in volatility spillover effects, which become even more pronounced during periods of financial turbulence. Within the structure of RCEP member stock markets, China is identified as a net risk receiver, while countries like Japan and South Korea act as net risk spillover contributors. This highlights the current “fragility” of China’s stock market, making it susceptible to risk shocks from the stock markets of economically developed RCEP member countries. This analysis suggests that significant changes in bidirectional risk spillover relationships between China’s stock market and those of other RCEP members coincided with the signing and implementation of the RCEP agreement. Full article
(This article belongs to the Special Issue Risk Spillover and Transfer Entropy in Complex Financial Networks)
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<p>Dynamic total connectedness. Note: This figure shows the time-varying total dependency across RCEP stock markets using TVP-VAR model.</p>
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<p>Net pairwise directional connectedness. Note: This figure only shows the directional spillover effect between China and other countries’ stock markets.</p>
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<p>Risk spillover network of RCEP member countries’ stock markets. Note: In this figure, blue nodes represent the main risk-exporting countries, and yellow nodes represent the risk-receiving countries, and the thickness of the links represents the intensity of risk spillovers. (<b>a</b>) Before the signing of the RCEP. (<b>b</b>) After the signing of the RCEP.</p>
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<p>Heat maps of transfer entropy between different sectors (<b>a</b>) before the singing of the RCEP and (<b>b</b>) after the signing of the RCEP. Note: 1–10 in this figure represent the stock markets of the following 10 countries: China, Vietnam, Singapore, Indonesia, Malaysia, South Korea, Japan, New Zealand, Thailand, and Australia (arranged in order).</p>
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<p>The stock market network constructed based on the transfer entropy matrix. This figure shows a directed network, and the arrows on the edges indicate the direction of information flow. (<b>a</b>) Before the singing of the RCEP. (<b>b</b>) After the signing of the RCEP.</p>
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15 pages, 2734 KiB  
Article
Engineering the Mechanics and Thermodynamics of Ti3AlC2, Hf3AlC2, Hf3GaC2, (ZrHf)3AlC2, and (ZrHf)4AlN3 MAX Phases via the Ab Initio Method
by Adel Bandar Alruqi
Crystals 2025, 15(1), 87; https://doi.org/10.3390/cryst15010087 - 17 Jan 2025
Viewed by 334
Abstract
When combined with ceramics, ternary carbides, nitrides, and borides form a class of materials known as MAX phases. These materials exhibit a multilayer hexagonal structure and are very strong, damage tolerant, and thermally stable. Further, they have a low thermal expansion and exhibit [...] Read more.
When combined with ceramics, ternary carbides, nitrides, and borides form a class of materials known as MAX phases. These materials exhibit a multilayer hexagonal structure and are very strong, damage tolerant, and thermally stable. Further, they have a low thermal expansion and exhibit outstanding resistance to corrosion and oxidation. However, despite the numerous MAX phases that have been identified, the search for better MAX phases is ongoing, including the recently discovered Zr3InC2 and Hf3InC2. The properties of MAX phases are still being tailored in order to lower their ductility. This study investigated Ti3AlC2 alloyed with nitrogen, gallium, hafnium, and zirconium with the aim of achieving better mechanical and thermal performances. Density functional theory within Quantum Espresso module was used in the computations. The Perdew–Burke–Ernzerhof generalised gradient approximation functionals were utilised. (ZrHf)4AlN3 exhibited an enhanced bulk and Young’s moduli, entropy, specific heat, and melting temperature. The best thermal conductivity was observed in the case of (ZrHf)3AlC2. Further, Ti3AlC2 exhibited the highest shear modulus, Debye temperature, and electrical conductivity. These samples can thus form part of the group of MAX phases that are used in areas wherein the above properties are crucial. These include structural components in aerospace and automotive engineering applications, turbine blades, and heat exchanges. However, the samples need to be synthesised and their properties require verification. Full article
(This article belongs to the Special Issue Modern Technologies in the Manufacturing of Metal Matrix Composites)
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<p>Original structure of Ti<sub>3</sub>AlC<sub>2</sub> as viewed in CrystalMaker software.</p>
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<p>Three-dimensional structures of the samples alloyed: (<b>a</b>) Hf<sub>3</sub>AlC<sub>2</sub>, (<b>b</b>) Hf<sub>3</sub>GaC<sub>2</sub>, (<b>c</b>) (ZrHf)<sub>3</sub>AlC<sub>2</sub>, and (<b>d</b>) (ZrHf)<sub>4</sub>AlN<sub>3</sub>.</p>
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<p>Total energy against standardised unit cell volumes for all the samples.</p>
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<p>Variation in pressure on the normalised unit cell volumes of the samples.</p>
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<p>Evolution of the computed mechanical properties with the materials in this study: (<b>a</b>) Bulk modulus, (<b>b</b>) Shear modulus, (<b>c</b>) Young’s modulus, (<b>d</b>) Poisson ratio, (<b>e</b>) Pugh’s ratio, and (<b>f</b>) Vickers hardness.</p>
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<p>Thermal properties of the samples: (<b>a</b>) Debye temperature, (<b>b</b>) Melting temperature, (<b>c</b>) Entropy, (<b>d</b>) Specific heat at constant volume, (<b>e</b>) Electrical conductivity, and (<b>f</b>) Electronic thermal conductivity.</p>
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<p>Plots of (<b>a</b>) entropy and (<b>b</b>) specific heat capacity with temperature for all the samples.</p>
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<p>Plots of (<b>a</b>) electrical conductivity and (<b>b</b>) thermal conductivity against energy for all the samples.</p>
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15 pages, 14739 KiB  
Article
Titanium Oxide Formation in TiCoCrFeMn High-Entropy Alloys
by Dominika Przygucka, Adelajda Polkowska, Wojciech Polkowski, Krzysztof Karczewski and Stanisław Jóźwiak
Materials 2025, 18(2), 412; https://doi.org/10.3390/ma18020412 - 17 Jan 2025
Viewed by 303
Abstract
High-entropy materials, characterized by complex chemical compositions, are difficult to identify and describe structurally. These problems are encountered at the composition design stage when choosing an effective method for predicting the final phase structure of the alloy, which affects its functional properties. In [...] Read more.
High-entropy materials, characterized by complex chemical compositions, are difficult to identify and describe structurally. These problems are encountered at the composition design stage when choosing an effective method for predicting the final phase structure of the alloy, which affects its functional properties. In this work, the effects of introducing oxide precipitates into the matrix of a high-entropy TiCoCrFeMn alloy to strengthen ceramic particles were studied. The particles were introduced by the ex situ method, such as TiO2 in the form of anatase, and by the in situ method, consisting of the reconstruction of CuO into TiO2. In both cases, it was assumed that after the homogenization process, carried out at 1000 °C, ceramic precipitates in the rutile phase, commonly considered a stable allotropic form of TiO2, would be obtained. However, the microscopic observations and XRD analyses, supported by EDS chemical composition microanalysis and EBSD backscattered electron diffraction, clearly revealed that, regardless of the method of introducing oxides, the final strengthening phase obtained was a mixture of TiO2 in the form of anatase with the Magnelli phase of Ti2O3. In this work, phase reconstruction in the Ti-O system was analyzed using changes in the Gibbs free energy of the identified oxide phases. Full article
(This article belongs to the Special Issue Advanced Science and Technology of High Entropy Materials)
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<p>Ti-O equilibrium system made on the basis [<a href="#B32-materials-18-00412" class="html-bibr">32</a>].</p>
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<p>View of the structures of the designed alloys based on TiCoCrFeMn and two alloys based on the addition of 5 vol.% CuO and TiO<sub>2</sub> after 1000 h of heating at 1273 K.</p>
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<p>View of the structures of the designed alloys based on TiCoCrFeMn and two alloys based on the addition of 5 vol.% CuO and TiO<sub>2</sub> after 1000 h of heating at 1273 K.</p>
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<p>Example of the analysis cycle of the oxide content in the structure of the TiCoCrFeMn alloy + vol. 5% TiO<sub>2</sub> heated for 100 h (original view of the structure—(<b>1</b>); binarized image—(<b>2</b>); outlining the of oxides (black precipitations on the original view)—(<b>3</b>)).</p>
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<p>Summary of the oxide fractions (<b>a</b>) and their corresponding equivalent diameters (<b>b</b>) for the two tested alloys as a function of homogenization time.</p>
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<p>X-ray diffraction phase analysis of samples of the CoCrFeMnTi base composition with CuO and TiO<sub>2</sub> additives in the as-sintered state subjected to homogenization annealing for 1, 10, 50, 100, and 1000 h, along with the positions of the planes for the following compounds: TiO<sub>2</sub> in the form of anatase and rutile, Ti<sub>2</sub>O<sub>3</sub>, Ti<sub>3</sub>O<sub>5</sub>, and CuO.</p>
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<p>Linear EDS analysis of the structure of the TiCoCrFeMn alloy with the addition of 5 vol.% TiO<sub>2</sub> in the area of titanium oxide precipitation.</p>
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<p>Identification of the phases forming the matrix of the tested materials, the BCC and HCP lattices, via EBSD.</p>
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<p>Linear EDS microanalysis of the chemical composition of the Ti oxide TiO<sub>2</sub> formed near the copper precipitate in the TiCoCr-FeMn alloy with the addition of CuO heated for 10 h.</p>
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<p>An attempt to fit anatase, rutile, and Ti<sub>2</sub>O<sub>3</sub> to the region of the ceramic precipitate is shown in <a href="#materials-18-00412-f006" class="html-fig">Figure 6</a>, together with an analysis of the CI fit factor.</p>
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<p>Comparison of EBSD diffraction tests aimed at identifying oxide phases for the TiCoCrFeMn + 5 vol.% TiO<sub>2</sub> alloy after 1000 h of annealing in the area of Laves phase occurrence. Changes in the CI coefficient values of the analyzed structure: (<b>a</b>) when fitting the crystal lattice of BCC, HCP, anatase, and rutile; (<b>b</b>) BCC, HCP, and anatase; (<b>c</b>) HCP and Ti<sub>2</sub>O<sub>3</sub>; (<b>d</b>) HCP and BCC; and (<b>e</b>) HCP, anatase, and Ti<sub>2</sub>O<sub>3</sub> (<b>f</b>).</p>
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<p>Gibbs free energy values for the oxides: TiO<sub>2</sub> (in the form of rutile and anatase), Ti<sub>2</sub>O<sub>3</sub>, Ti<sub>3</sub>O<sub>5</sub> and Ti<sub>4</sub>O<sub>7</sub>.</p>
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<p>Percentage changes in the content of the main phases (BCC, HCP and Oxides) in alloy with TiO<sub>2</sub> (<b>a</b>) and with CuO (<b>c</b>) and titanium oxide content changes in the phase composition of the alloy with TiO<sub>2</sub> (<b>b</b>) and with CuO (<b>d</b>) of the obtained sinters with increasing annealing time.</p>
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14 pages, 2687 KiB  
Article
Study on Evaluation and Dynamic Early Warning of Urban Water Resources Security
by Wenjie Xu, Hao Wang, Xiaolu Zhao, Dongxu Zhao, Xuepeng Ding, Yinghan Yin and Yuyu Liu
Water 2025, 17(2), 242; https://doi.org/10.3390/w17020242 - 16 Jan 2025
Viewed by 330
Abstract
Water resources security is crucial to the survival and development of human society. A water resources security assessment and dynamic early warning system was constructed. The weights of water resources evaluation indexes were calculated by the entropy weight method, and the water resources [...] Read more.
Water resources security is crucial to the survival and development of human society. A water resources security assessment and dynamic early warning system was constructed. The weights of water resources evaluation indexes were calculated by the entropy weight method, and the water resources security was evaluated with the comprehensive index method. The obstacle degree model was used to identify and analyze the main obstacle factors. The grey model was adopted to predict the future water resources security situation. The empirical study was carried out in Jinan. The results showed that the grade of water resources security in Jinan from 2008 to 2021 showed a gradually increasing trend. The obstacle factors were mainly concentrated in the pressure subsystem, indicating that the contradiction between supply and demand of water resources was the main problem affecting water resources security, which was accorded with the actual situation. The comprehensive index of water resources security from 2022 to 2026 shows a gradually increasing trend on the whole, and the warning situation develops towards a good trend, indicating that remarkable results in comprehensively building a water-saving society and vigorously promoting water pollution control have been achieved. The measures such as optimizing economic structure, improving water use structure, and improving water use efficiency will promote the further development of water resources security in Jinan. Full article
(This article belongs to the Section Urban Water Management)
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<p>The map of Jinan.</p>
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<p>The change trend of the comprehensive index of water resources security in Jinan from 2008 to 2021.</p>
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<p>The change trend for each subsystem index of water resources security in Jinan from 2008 to 2021.</p>
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<p>The change trend of obstacle degree of each factor for water resources security in Jinan from 2008 to 2021.</p>
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<p>The change trend of obstacle degree for each subsystem of water resources security in Jinan from 2008 to 2021.</p>
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<p>The fitting trend between the original value and the predicted value of the comprehensive index of water resources security in Jinan from 2008 to 2021.</p>
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26 pages, 26206 KiB  
Article
Unveiling the Influencing Factors of the Residual Life of Historical Buildings: A Study of the Wuhan Lutheran Missions Home and Agency Building
by Bo Huang, Xueqi Liu, Lanjun Liu, Zhiyong Li, Zhifeng Wu, Bin Huang and Zimo Jia
Buildings 2025, 15(2), 246; https://doi.org/10.3390/buildings15020246 - 16 Jan 2025
Viewed by 326
Abstract
The development of a city needs the accumulation of culture, and historical buildings are the most direct witness of the rise and fall of a city. Like the human body, historical buildings have a certain life cycle, but the acceleration of urbanization and [...] Read more.
The development of a city needs the accumulation of culture, and historical buildings are the most direct witness of the rise and fall of a city. Like the human body, historical buildings have a certain life cycle, but the acceleration of urbanization and unreasonable use cause an irreversible reduction in the remaining life of historical buildings. There is a notable lack of quantitative analysis regarding the residual life of historical buildings. Therefore, identifying the factors that influence their residual life is crucial for both preserving these buildings and sustaining urban culture. In order to obtain a more accurate correlation degree of influencing factors, a systematic-analysis model of influencing factors on the residual life of historical buildings based on the entropy weight method (EWM) and the grey relation analysis method (GRA) was established, so as to excavate the mechanism of the influencing factors on the residual life of historical buildings, accurately identify the main influencing factors on the residual life of historical buildings, and propose preventive measures. The results show that the structural system has the greatest influence on the residual life of historical buildings, followed by the enclosure system, and the equipment system. The research findings offer valuable insights for extending the residual life of historical buildings in the future. Full article
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<p>Analysis framework of factors affecting the residual life of historical buildings.</p>
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<p>Location and survey map of the Wuhan Lutheran Missions Home and Agency Building.</p>
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<p>The proportion of evaluation indicators.</p>
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<p>Numerical graphs of each sequence after standardization.</p>
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<p>Evaluation index deviation matrix.</p>
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<p>Correlation coefficient of evaluation indicators.</p>
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<p>Reference sequence association curve.</p>
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<p>Reference sequence association ranking diagram.</p>
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34 pages, 15315 KiB  
Review
Recent Advances in the Performance and Mechanisms of High-Entropy Alloys Under Low- and High-Temperature Conditions
by Rui Xi and Yanzhou Li
Coatings 2025, 15(1), 92; https://doi.org/10.3390/coatings15010092 - 15 Jan 2025
Viewed by 460
Abstract
High-entropy alloys, since their development, have demonstrated great potential for applications in extreme temperatures. This article reviews recent progress in their mechanical performance, microstructural evolution, and deformation mechanisms at low and high temperatures. Under low-temperature conditions, the focus is on alloys with face-centered [...] Read more.
High-entropy alloys, since their development, have demonstrated great potential for applications in extreme temperatures. This article reviews recent progress in their mechanical performance, microstructural evolution, and deformation mechanisms at low and high temperatures. Under low-temperature conditions, the focus is on alloys with face-centered cubic, body-centered cubic, and multi-phase structures. Special attention is given to their strength, toughness, strain-hardening capacity, and plastic-toughening mechanisms in cold environments. The key roles of lattice distortion, nanoscale twin formation, and deformation-induced martensitic transformation in enhancing low-temperature performance are highlighted. Dynamic mechanical behavior, microstructural evolution, and deformation characteristics at various strain rates under cold conditions are also summarized. Research progress on transition metal-based and refractory high-entropy alloys is reviewed for high-temperature environments, emphasizing their thermal stability, oxidation resistance, and frictional properties. The discussion reveals the importance of precipitation strengthening and multi-phase microstructure design in improving high-temperature strength and elasticity. Advanced fabrication methods, including additive manufacturing and high-pressure torsion, are examined to optimize microstructures and improve service performance. Finally, this review suggests that future research should focus on understanding low-temperature toughening mechanisms and enhancing high-temperature creep resistance. Further work on cost-effective alloy design, dynamic mechanical behavior exploration, and innovative fabrication methods will be essential. These efforts will help meet engineering demands in extreme environments. Full article
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<p>Overview of the historical evolution and milestones in HEA research.</p>
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<p>Schematic diagram of lattice distortion in HEAs [<a href="#B90-coatings-15-00092" class="html-bibr">90</a>].</p>
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<p>Variations in (<b>a</b>) mechanical strength and (<b>b</b>) fracture strain across temperatures ranging from 113 K to 1273 K and different loading directions [<a href="#B135-coatings-15-00092" class="html-bibr">135</a>].</p>
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<p>Twin interactions in [111]-oriented CoCrFeMnNi HEA crystals subjected to 20% tensile deformation at 77 K are shown as: (<b>a</b>) a bright-field image, (<b>b</b>) a dark-field image, and (<b>c</b>) a diffraction pattern [<a href="#B136-coatings-15-00092" class="html-bibr">136</a>].</p>
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<p>(<b>a</b>) Elemental distributions of Cr, Fe, Ni, Co, and Cu in the FeNiCoCrCu0.5 HEA; (<b>b</b>) Composition variations between the FCC matrix and Cu-rich areas; (<b>c</b>) atom probe tomography reconstruction illustrating Cu distribution, enlarged cluster images, and a one-dimensional composition analysis [<a href="#B140-coatings-15-00092" class="html-bibr">140</a>].</p>
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<p>Fracture surface morphology of CrMnFeCoNi<sub>2</sub>Cu alloy under tensile deformation at various temperatures. (<b>a</b>) 300 K. (<b>b</b>) Partial enlarged view of (<b>a</b>). (<b>c</b>) 77 K. (<b>d</b>) Partial enlarged view of (<b>c</b>). (<b>e</b>) 10 K. (<b>f</b>) Partial enlarged view of (<b>e</b>). (<b>g</b>) 4.2 K. (<b>h</b>) Partial enlarged view of (<b>g</b>) [<a href="#B129-coatings-15-00092" class="html-bibr">129</a>].</p>
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<p>Tensile deformation structures of the alloy at 223 K. (<b>a</b>) Primary deformation twin formation; (<b>b</b>,<b>c</b>) secondary nanoscale twin development; (<b>d</b>) indexed results illustrating twin orientations and strain conditions [<a href="#B137-coatings-15-00092" class="html-bibr">137</a>].</p>
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<p>Fracture surface appearances under various conditions. (<b>a</b>) Entire fracture view at 293 K; (<b>b</b>) detailed fracture morphology at 293 K; (<b>c</b>) side view of the sample at 293 K; (<b>d</b>) entire fracture view at 77 K; (<b>e</b>) detailed fracture morphology at 77 K; (<b>f</b>) side view of the sample at 77 K [<a href="#B144-coatings-15-00092" class="html-bibr">144</a>].</p>
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<p>Surface morphology of the alloy post-machining. (<b>a</b>) Cutting speed (vc) = 2000 mm/min at RT; (<b>b</b>) vc = 2200 mm/min at RT; (<b>c</b>) vc = 2000 mm/min at low temperature; (<b>d</b>) vc = 2200 mm/min at low temperature [<a href="#B125-coatings-15-00092" class="html-bibr">125</a>].</p>
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<p>The microstructure of Fe<sub>28.2</sub>Ni<sub>7</sub>Co<sub>11</sub>Al<sub>2.5</sub>Ta<sub>0.04</sub>B HEA after tensile testing at 77 K. (<b>a</b>) Martensite forms mainly in fine grains at ~7% strain. (<b>b</b>) At ~12% strain, martensite spreads to fine and coarse grains. (<b>c</b>) TEM shows thin-plate martensite in coarse grains. (<b>d</b>) High-resolution TEM shows nanotwins in martensite. (<b>e</b>) TEM shows thin-plate martensite in fine grains. (<b>f</b>) Nanotwins in fine-grain martensite [<a href="#B147-coatings-15-00092" class="html-bibr">147</a>].</p>
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<p>(<b>a</b>) The AlCoCrFeNi2.1 alloy fractured in tension at 77 K, (<b>b</b>) a SAED pattern from the area indicated by a green marker, and (<b>c</b>) an SAED pattern from the region indicated by a red marker. At higher magnifications, dislocation arrangements are clearly visible in both the (<b>d</b>) FCC and (<b>e</b>) B2 domains [<a href="#B127-coatings-15-00092" class="html-bibr">127</a>].</p>
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<p>Stress–strain relationships for the HEA under varying thermal conditions at strain rates of (<b>a</b>) 10<sup>−1</sup> s<sup>−1</sup> and (<b>b</b>) 10<sup>−2</sup> s<sup>−1</sup> [<a href="#B135-coatings-15-00092" class="html-bibr">135</a>].</p>
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<p>(<b>a</b>) The AlCoCrFeNi<sub>2.1</sub> microstructure, (<b>b</b>) compositional mappings, and (<b>c</b>) its stress–strain curve at 973 K [<a href="#B135-coatings-15-00092" class="html-bibr">135</a>].</p>
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<p>(<b>a</b>) Tensile stress–strain curves at various temperatures. (<b>b</b>) YS, UTS, and fracture elongation versus temperature [<a href="#B160-coatings-15-00092" class="html-bibr">160</a>].</p>
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<p>TEM micrographs of the Nb<sub>40</sub>Ti<sub>25</sub>Al<sub>15</sub>V<sub>10</sub>Ta<sub>5</sub>Hf<sub>3</sub>W<sub>2</sub> alloy after 120 h of aging at 923 K (<b>a</b>), 1023 K (<b>b</b>), and 1123 K (<b>c</b>), illustrating APB development and Hf-enriched segregations [<a href="#B164-coatings-15-00092" class="html-bibr">164</a>].</p>
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28 pages, 20155 KiB  
Article
Vision-Based Damage Detection Method Using Multi-Scale Local Information Entropy and Data Fusion
by Yiming Zhang, Zili Xu, Guang Li and Cun Xin
Appl. Sci. 2025, 15(2), 803; https://doi.org/10.3390/app15020803 - 15 Jan 2025
Viewed by 386
Abstract
Low-spatial-resolution measurements from contact sensors and excessive measurement noise have impeded the implementation of vibration-based damage detection. To tackle these challenges, we propose a novel vision-based damage detection method combining multi-scale signal analysis theory and data fusion algorithm. For high-spatial-resolution vibration measurements, phase-based [...] Read more.
Low-spatial-resolution measurements from contact sensors and excessive measurement noise have impeded the implementation of vibration-based damage detection. To tackle these challenges, we propose a novel vision-based damage detection method combining multi-scale signal analysis theory and data fusion algorithm. For high-spatial-resolution vibration measurements, phase-based optical flow estimation algorithm is adopted to deploy virtual sensors on the structure, yielding reliable mode shapes. We then introduce the concept of entropy into damage detection. A novel damage index, defined in Gaussian multi-scale space and named multi-scale local information entropy (MS-LIE), is proposed. The MS-LIE integrates the multi-scale analysis component and the entropy analysis component, addressing both the issue of detection sensitivity and noise immunity, thereby showcasing enhanced performance. Moreover, a data fusion technique for multi-scale damage information is developed to further mitigate the noise-induced uncertainty and pinpoint damage locations. A series of numerical and experimental scenarios are designed to validate the method, and the results indicate that the proposed method accurately detects single and multiple damages in noisy environments, obviating the need for baseline data as a reference. Full article
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<p>An overview of the workflow of the proposed damage detection method.</p>
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<p>Flow diagram for phase-based optical flow estimation.</p>
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<p>Complex Gabor filters in different orientations: (<b>a</b>) the real parts from <span class="html-italic">θ</span> = 0 to <span class="html-italic">θ</span> = 90°, (<b>b</b>) the imaginary parts from <span class="html-italic">θ</span> = 0 to <span class="html-italic">θ</span> = 90°.</p>
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<p>The process of calculating the local probability.</p>
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<p>Flow diagram for data fusion.</p>
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<p>Analytical model for numerical investigations: (<b>a</b>) a cracked cantilever beam, (<b>b</b>) the corresponding rational spring model.</p>
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<p>Evaluations on single damage with SNR = 90 dB: (<b>a</b>–<b>c</b>) the MS-LIE heat map obtained from the 1st, 2nd and 3rd mode shapes, (<b>d</b>–<b>f</b>) damage localization results of the 1st, 2nd and 3rd mode shapes.</p>
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<p>Evaluations on single damage with SNR = 60 dB: (<b>a</b>–<b>c</b>) the MS-LIE heat map obtained from the 1st, 2nd and 3rd mode shapes, (<b>d</b>–<b>f</b>) damage localization results of the 1st, 2nd and 3rd mode shapes.</p>
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<p>Evaluations on single damage with SNR = 60 dB: (<b>a</b>–<b>c</b>) the MS-LIE heat map obtained from the 1st, 2nd and 3rd mode shapes, (<b>d</b>–<b>f</b>) damage localization results of the 1st, 2nd and 3rd mode shapes.</p>
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<p>Evaluations on double damages with SNR = 90 dB: (<b>a</b>–<b>c</b>) the MS-LIE heat map obtained from the 1st, 2nd and 3rd mode shapes, (<b>d</b>–<b>f</b>) damage localization results of the 1st, 2nd and 3rd mode shapes.</p>
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<p>Evaluations on double damages with SNR = 90 dB: (<b>a</b>–<b>c</b>) the MS-LIE heat map obtained from the 1st, 2nd and 3rd mode shapes, (<b>d</b>–<b>f</b>) damage localization results of the 1st, 2nd and 3rd mode shapes.</p>
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<p>Evaluations on double damages with SNR = 60 dB: (<b>a</b>–<b>c</b>) the MS-LIE heat map obtained from the 1st, 2nd and 3rd mode shapes, (<b>d</b>–<b>f</b>) damage localization results of the 1st, 2nd and 3rd mode shapes.</p>
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<p>Compared with other methods on single damage with SNR = 60 dB: (<b>a</b>) the fractal dimension-based method, (<b>b</b>) the deep learning-based method, (<b>c</b>) the proposed method.</p>
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<p>Compared with other methods on double damages with SNR = 60 dB: (<b>a</b>) the fractal dimension-based method, (<b>b</b>) the deep learning-based method, (<b>c</b>) the proposed method.</p>
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<p>Monte Carlo experiments for comparison with other methods on different SNRs: (<b>a</b>) single damage case, (<b>b</b>) multiple damage case.</p>
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<p>Monte Carlo experiments for ablation study on different SNRs: (<b>a</b>) single damage case, (<b>b</b>) multiple damage case.</p>
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<p>Monte Carlo experiments for ablation study on different damage degrees: (<b>a</b>) single damage case, (<b>b</b>) multiple damage case.</p>
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<p>Computational complexity analysis: (<b>a</b>) impact of total number of scales, (<b>b</b>) impact of total number of measurement points.</p>
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<p>The experimental set-up: (<b>a</b>) the vision-based system, (<b>b</b>) the experimental platform, (<b>c</b>) a screenshot of the motion video.</p>
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<p>The comparison of displacement responses obtained from the vision-based system and laser vibrometer.</p>
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<p>The comparison of mode shapes: (<b>a</b>) the high-spatial-resolution mode shapes obtained by vision-based method, (<b>b</b>) the MAC results between the vision-based method and FEM.</p>
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<p>The specimen with single damage: (<b>a</b>) the model of the cracked beam, (<b>b</b>) the image of the specimen.</p>
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<p>The high-spatial-resolution mode shapes obtained via vision: (<b>a</b>) 1st mode shape, (<b>b</b>) 2nd mode shape, (<b>c</b>) 3rd mode shape.</p>
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<p>The MS-LIE results of single damage: (<b>a</b>,<b>c</b>,<b>e</b>) the MS-LIE heat map obtained from the 1st, 2nd and 3rd mode shapes, (<b>b</b>,<b>d</b>,<b>f</b>) the corresponding enlarged heatmaps at larger scales.</p>
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<p>The MS-LIE results of single damage: (<b>a</b>,<b>c</b>,<b>e</b>) the MS-LIE heat map obtained from the 1st, 2nd and 3rd mode shapes, (<b>b</b>,<b>d</b>,<b>f</b>) the corresponding enlarged heatmaps at larger scales.</p>
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<p>The damage localization results of single damage: (<b>a</b>) based on the 1st mode shape, (<b>b</b>) based on the 2nd mode shape, (<b>c</b>) based on the 3rd mode shape.</p>
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<p>The damage localization results of single damage: (<b>a</b>) based on the 1st mode shape, (<b>b</b>) based on the 2nd mode shape, (<b>c</b>) based on the 3rd mode shape.</p>
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<p>The specimen with multiple damages: (<b>a</b>) the model of the cracked beam, (<b>b</b>) the image of the specimen.</p>
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<p>The MS-LIE results of double damages: (<b>a</b>,<b>c</b>,<b>e</b>) the MS-LIE heat map obtained from the 1st, 2nd and 3rd mode shapes, (<b>b</b>,<b>d</b>,<b>f</b>) the corresponding enlarged heatmaps at larger scales.</p>
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<p>The damage localization results of multiple damages: (<b>a</b>) based on the 1st mode shape, (<b>b</b>) based on the 2nd mode shape, (<b>c</b>) based on the 3rd mode shape.</p>
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27 pages, 1428 KiB  
Article
Digital Economy, Green Innovation Efficiency, and New Quality Productive Forces: Empirical Evidence from Chinese Provincial Panel Data
by Yunsong Xu, Ruixun Wang and Shanfei Zhang
Sustainability 2025, 17(2), 633; https://doi.org/10.3390/su17020633 - 15 Jan 2025
Viewed by 440
Abstract
As a new economic form driven and empowered by digital technology, the development of the digital economy has become a crucial pathway for boosting the advancement of new quality productive forces. This study employs the entropy method to measure the comprehensive evaluation index [...] Read more.
As a new economic form driven and empowered by digital technology, the development of the digital economy has become a crucial pathway for boosting the advancement of new quality productive forces. This study employs the entropy method to measure the comprehensive evaluation index system for both the digital economy and new quality productive forces and further utilizes the unexpected output super-efficiency model to calculate the green innovation efficiency index. On this basis, panel data of 31 provinces in China from 2012 to 2022 are selected to conduct a quantitative analysis from a multidimensional perspective innovatively, examining the overall, heterogeneous, and spatial effects of the digital economy on new quality productive forces, as well as the mediating, moderated mediating, and threshold effects of green innovation efficiency. The research findings indicate that (1) the digital economy significantly promotes the development of new quality productive forces, and this conclusion is robust; (2) the impact of the digital economy on new quality productive forces exhibits regional heterogeneity; (3) there is a positive spatial spillover effect of the digital economy on new quality productive forces; (4) the digital economy can facilitate the development of new quality productive forces by enhancing green innovation efficiency; (5) industrial structure upgrading moderates the mediating effect of the digital economy on new quality productive forces, specifically regulating the promoting effect of green innovation efficiency on new quality productive forces; and (6) the impact of the digital economy on new quality productive forces exhibits a nonlinear characteristic of “increasing marginal effect”. Consequently, this study proposes targeted suggestions from four dimensions: accelerating the construction of digital infrastructure, vigorously enhancing green innovation efficiency, promoting the deep integration of digitalization and greenization, and facilitating industrial upgrading and coordinated development. These suggestions serve as valuable empirical insights into China’s transformation path selection and sustainable high-quality development in the new era. Full article
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<p>Theoretical mechanism of moderated mediation effects.</p>
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<p>Moran’s I scatterplot of new quality productive forces index. (<b>a</b>) Moran’s I scatterplot of urban-rural common wealth index in 2012; (<b>b</b>) Moran’s I scatterplot of urban-rural common wealth index in 2022.</p>
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<p>Threshold estimates and confidence intervals. (<b>a</b>) 1st threshold parameter; (<b>b</b>) 2nd threshold parameter.</p>
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