Limited sample data due to the difficulty in digital acquisition of Dunhuang murals renders existing deep learning-based inpainting approaches prone to overfitting, causing color deviation and texture distortion in inpainted images. To address these challenges, this paper proposes DR-IFMM, an inpainting approach based on a dynamic radius strategy and an improved Fast Marching Method (IFMM) architecture. DR-IFMM addresses these challenges by decomposing the inpainting process into several key stages. First, it adaptively computes two optimal radii based on the pixel density of damaged regions within the neighborhood of the target pixel, dynamically optimizing the inpainting of irregular and large-area defects. Second, the weight calculation rules of the FMM algorithm are refined to improve the accuracy of boundary and texture line inpainting. Finally, an image recomposition strategy integrates global structure and local details, yielding coherent textures and fine details. Experimental results on the Dunhuang mural dataset demonstrate that DR-IFMM outperforms competing approaches in terms of SSIM, PSNR, and LPIPS, effectively recovering the original appearance of damaged murals. This validates the practical value of DR-IFMM in Dunhuang mural inpainting, contributing to the digital preservation and inheritance of cultural heritage.
This paper establishes the existence of positive solutions to a singular p-Laplacian Schro & uml;dinger-type equation exhibiting infinite semipositone structure: -triangle(p)u+V(x)|u|(p-2)u = lambda f(u)/u(alpha) , x is an element of Omega, u = 0 on partial derivative Omega, where triangle(p)u = div(|del u|(p-2)del u) denotes the p-Laplacian operator (p > 1), lambda > 0 is a parameter, alpha is an element of (0,1), and Omega subset of R-N is a smooth bounded domain. The nonlinearity f is an element of C([0,infinity),R) satisfies f(0) < 0 and exhibits asymptotic behavior characterized by lim(s -> 0)(+) f(s)/s(alpha) = -infinity, inducing a strong singularity at the origin. The potential V is an element of L-infinity(Omega) is allowed to change sign, adding indefinite structure to the problem. By developing a refined sub-and supersolution method adapted to the degenerate nature of the p-Laplacian, we prove the existence of positive solutions u(lambda) is an element of W-0(1,p) (Omega) boolean AND C(Omega(-)) for sufficiently large lambda.
Diamond-like carbon (DLC) thin films have emerged as highly reliable ultra-thin targets for relativistic laser-matter interaction studies owing to their exceptional mechanical resilience, high sp(3) bonding fraction, and low impurity content. These properties allow DLC membranes only tens of nanometers thick to maintain structural integrity under the extreme thermal and mechanical conditions imposed by high-intensity, ultrashort laser pulses. In this work, we investigate free-standing DLC films fabricated by plasma-enhanced chemical vapor deposition (PECVD) and released through a controlled copper back-etching process. The structural, chemical, and morphological characteristics of the films are examined using X-ray photoelectron spectroscopy (XPS) and optical microscopy. Analysis of sp(2)/sp(3) hybridisation, surface oxygen functionality, and membrane uniformity demonstrates that the films meet the stringent requirements of petawatt-class laser facilities. These results confirm that PECVD-grown free-standing DLC membranes provide robust, reproducible, and high-quality targets suitable for advanced ion-acceleration regimes including TNSA, RPA, BOA, and relativistic transparency.
This paper demonstrates that the total mass process of a branching Markov process with a spatially constant branching mechanism behaves identically to that of its corresponding pure branching process: either a continuous time Galton-Watson process or a continuous-state branching (CB) process. The discrete time context is also treated. The study analyses extinction in discrete-time subcritical and supercritical regimes, derives evolution equations for non-local pure branching processes, and examines the one-dimensional CBprocess. Using potential theory and stochastic analysis, the research advances branching process theory and population dynamics.
The paper presents a higher magnetic saliency-with open rotor flux barriers solution for a four-pole reluctance synchronous machine with transversal laminations anisotropic rotor. The rotor structure is very close to the axially laminated anisotropic rotor, but the manufacturing costs are estimated lower. Key FEM characterization and results for the two proposed solutions are compared in order to evaluate the applicability for power trains.
In deep coal mining, the stability of coal roadways is critically governed by its immediate roof and floor strata. This study investigated the evolution characteristics of mechanical behaviors of coal-rock composites, aiming to elucidate its failure mechanism. Results demonstrated that, compared to sandy mudstone-coal-sandy mudstone (SCS) composites, the red sandstone-coal-red sandstone (RCR) composites exhibited more pronounced fracturing, greater stress fluctuations, and significantly higher acoustic emission (AE) activities, characterized by markedly higher AE ringing counts. For SCS composites, AE ringing counts surged at the initial stress drop point, and peaked twice near its ultimate failure point. Notably, between these two points, a distinct quiescent phase of AE activities was identified, serving as a precursor for imminent failure. Furthermore, the generation of tensile and shear cracks exhibited both a spatiotemporal concentration and a distinct stage-dependent evolution pattern. Specifically, AE events in SCS composites were concentrated vertically with higher density within the central coal layer, while in RCR composites, the high-energy AE events clustered predominantly at the mid-height region. Ultimately, both SCS and RCR composites failed through transverse dilatancy, characterized by the localization of macroscopic fractures within the central coal block. These findings provide crucial insights for the early-warning strategies of coalbursts hazards in deep coal mines.
Accurate coagulant dosing prediction in water treatment plants is challenging due to nonlinear, multivariable, and time-varying water-quality dynamics, while purely mechanistic or purely data-driven models often suffer from limited adaptability or interpretability. To address this, this study proposes BAT-Net(BiLSTM-Attention-Transformer Network with Wavelet Enhancement), a prior knowledge-driven dosing prediction framework that integrates an expert mechanistic model with data-driven residual correction. Specifically, wavelet transform is used to extract multiscale features from fluctuating inputs, a BiLSTM(Bidirectional Long Short-Term Memory)-Transformer backbone captures both short-term variations and long-range dependencies, and a weighted attention mechanism embeds expert-guided feature weighting to improve interpretability and robustness. Evaluations on two real-world datasets (Shanghai Xinghuo Water and Suzhou China-France Water) demonstrate consistent improvements over mainstream baselines (XGBoost, BP, LSTM, and BiLSTM), achieving test performance of R-2 = 0.976/MAE= 0.078/RMSE= 0.108 and R-2 = 0.971/MAE= 0.088/RMSE= 0.124, respectively. These results indicate that BATNet provides accurate and reliable dosing prediction for practical water treatment operations.
This paper aims to apply the dual-reduciton technique and derive integrable reductions of matrix modified Korteweg-de Vries (mKdV) models. Using the Lax pair formulation, the study employs two group reductions as the main analytical tool. Two illustrative examples of reduced Ablowitz-Kaup-Newell-Segur matrix spectral problems are presented, showcasing explicit examples of reduced matrix mKdV integrable models generated through these two distinct group reductions.
By means of two known combinatorial identities involving polynomials, recurrence relations, and the telescoping technique, we obtain new explicit expressions for Genocchi, Bernoulli and Euler numbers/polynomials, along with some other interesting transformation formulas and explicit double sum combinatorial identities.
This study addresses common issues in parallel mechanisms, such as input/output coupling, difficulty in obtaining closed-form solutions, and excessive singular configurations, by designing a spatial parallel mechanism with analytical solutions. The mechanism comprises two CRR kinematic limbs and one UPS kinematic limb. The motion screw systems and constraint screw systems of each limb are analyzed using screw theory, and the DOFs of the mechanism are calculated via the modified Kutzbach-Gr & uuml;bler formula. By establishing the input-output position relationships, closed-form expressions between the inputs and outputs are derived. The position equations are differentiated to obtain the velocity mapping and the velocity Jacobian matrix. Analysis of the velocity Jacobian matrix confirms that no singular configurations exist within the mechanism's normal motion range. Based on the structural parameters of the mechanism, the workspace of the moving platform's center point is calculated. Within this workspace, a global performance evaluation index integrating isotropy and manipulability is proposed, and a global performance atlas of the moving platform is obtained, revealing the mapping relationship between mechanism parameters and motion performance. A parallel mechanism analysis system is developed, and a prototype is manufactured to verify the DOFs and position accuracy of the moving platform. The results demonstrate that the mechanism features three translational DOFs and closed-form input-output solutions, and exhibits superior control simplicity and practical applicability relative to traditional coupled parallel mechanisms..
Let $\mathcal{T}_{\frac{k}{r}}$ denote the set of trees $T$ such that $i(T-S)\leq\frac{k}{r}|S|$ for any $S\subset V(T)$ and for any $e\in E(T)$ there exists a set $S^{*}\subset V(T)$ with $i((T-e)-S^{*})>\frac{k}{r}|S^{*}|$, where $r k$ are two positive integers. A $\{C_{2i+1},T:1\leq i \frac{r}{k-r},T\in\mathcal{T}_{\frac{k}{r}}\}$-factor of a graph $G$ is a spanning subgraph of $G$, in which every component is isomorphic to an element in $\{C_{2i+1},T:1\leq i \frac{r}{k-r},T\in\mathcal{T}_{\frac{k}{r}}\}$. Let $A(G)$ and $Q(G)$ denote the adjacency matrix and the signless Laplacian matrix of $G$, respectively. The adjacency spectral radius and the signless Laplacian spectral radius of $G$, denoted by $\rho(G)$ and $q(G)$, are the largest eigenvalues of $A(G)$ and $Q(G)$, respectively. In this paper, we study the connections between the spectral radius and the existence of a $\{C_{2i+1},T:1\leq i \frac{r}{k-r},T\in\mathcal{T}_{\frac{k}{r}}\}$-factor in a graph. We first establish a tight sufficient condition involving the adjacency spectral radius to guarantee the existence of a $\{C_{2i+1},T:1\leq i \frac{r}{k-r},T\in\mathcal{T}_{\frac{k}{r}}\}$-factor in a graph. Then we propose a tight signless Laplacian spectral radius condition for the existence of a $\{C_{2i+1},T:1\leq i \frac{r}{k-r},T\in\mathcal{T}_{\frac{k}{r}}\}$-factor in a graph.
Let G be a graph and T be a spanning tree of G. We use Q(G) = D(G) +A(G) to denote the signless Laplacian matrix of G, where D(G) is the diagonal degree matrix of G and A(G) is the adjacency matrix of G. The signless Laplacian spectral radius of G is denoted by q(G). A necessary and sufficient condition for a connected bipartite graph G with bipartition (A, B) to have a spanning tree T with d(T)(v) >= k for every v is an element of A was independently obtained by Frank and Gyarfas (A. Frank, E. Gyarfas, How to orient the edges of a graph?, Colloq. Math. Soc. Janos Bolyai 18 (1976) 353-364), Kaneko and Yoshimoto (A. Kaneko, K. Yoshimoto, On spanning trees with restricted degrees, Inform. Process. Lett. 73 (2000) 163-165). Based on the above result, we establish a lower bound on the signless Laplacian spectral radius q(G) of a connected bipartite graph G with bipartition (A, B), in which the bound guarantees that G has a spanning tree T with d(T)(v) >= k for every v is an element of A.
This paper shows that the equation in the title has no solutions in the positive integers if (i) $n$ has prime factor congruent to $3$ (modulo $4$); or (ii) $8|n$; or $8|n-1$. Case (i) follows from an elementary argument. Case (ii) follows from the previous works of E. Dofs and the second author. Case (iii) follows from a standard Brauer-Manin obstruction argument.
The paper focuses on the comparative analysis of two magnetorheological clutches with different geometric configurations. One magnetorheological clutch corresponds to cylindrical geometry (MRC-CG) while the second is selected with disk geometry (MRC-DG). Both experimental and numerical investigations are performed to determine magnetorheological clutch performances. The constructive solution is detailed for each magnetorheological clutch type. The numerical simulations are carried out to determine the distribution of the magnetic field. The magnetorheological clutch performances are investigated experimentally over a range of variable speeds between shafts from 50 rpm to 500 rpm. The torque for both geometric configurations is determined using the same magnetorheological fluid (MRF-132DG). The torque control range of the MRC-CG is limited by the response of the MRF to the variation of the magnetic field induced by the coil. MRC-DG covers a wider range of the torque control than MRC-CG due to the additional contribution of the gap geometry. MRC-DG provides twice the torque density of MRC-CG proving more compact solutions. The conclusions are drawn in last section.
A P->= d-factor of a graph G is a spanning subgraph F of G such that every component of F is a path of order at least d (d >= 2). A graph G is called a (P->= d, k)-factor critical graph if after deleting any k vertices of G the remaining graph of G contains a P->= d-factor. Let rho (G) denote the spectral radius of G. In this paper, we first provide a characterization for a graph to be (P->= 2, k)-factor critical; then we prove that an n-vertex connected graph G is a (P->= 2, k)-factor critical graph unless G = K-k boolean OR (Kn-k-1 boolean OR K-1) if rho (G) >= rho (K-k boolean OR (Kn-k-1 boolean OR K-1)), where k and n are two positive integers with n >= k+2.
Serous cavity effusions provide valuable information for both cancer diagnosis and therapy. Conventional analysis relies on cytological examination, when nuclear/cytoplasmic morphology and coloration are evaluated under brightfield microscopy. In this study, we examined malignant and benign cells from serous cavity effusions using high-content hyperspectral microscopy. We propose several criteria for cells and cellular subcomponents segmentation based on spectral profiles. Differences were found between biophysical descriptors computed for the cytoplasm and nuclei of malign/benign cells. We demonstrate the possibility to extract quantitative information on bio-optical properties of cytology specimens, to be used further for an automate classification based on hyperspectral microscopy images.
For the buck converter facing the issue of nonlinear disturbance interference due to sudden output load changes, a robust anti-disturbance method based on finite-time sliding mode control and Radial Basis Function (RBF) neural network has been proposed. A new sliding mode control strategy has been crafted to accelerate the system's transient response while minimizing controller oscillations by dynamically adjusting the convergence rate of system states. The buck converter's unknown load parameters are adeptly estimated via a neural network, with its weights being refined through an adaptive mechanism. Finally, the rigorous convergence analysis of the system was conducted using Lyapunov's stability theory, and the effectiveness of the proposed method was validated through simulation and experimental verification.
Outage probability (OP) is a critical parameter for evaluating the performance of wireless networks. This paper introduces a novel and effective Rime-Support Vector Regression (RIME-SVR) algorithm for predicting the outage probability of dual hop mixed RF/underwater wireless optical communication (RF/UWOC) systems. The primary objective of proposing RIME-SVR is to enhance overall analytical efficiency while reducing the complexity of system evaluation. However, the mathematical representation of the outage probability of system is quite intricate, and the analysis of channel parameters is also complex, complicating accurate estimation. To facilitate precise predictions of the outage probability for RF/UWOC systems, the expression for system outage probability was derived using the Meijer-G function, and the reliability of this outage probability was validated through the Monte Carlo method. Additionally, the RIME algorithm is employed to optimize the parameters of SVR using a soft-rime search strategy, ahard-rime puncture mechanism, and apositive greedy selection mechanism, thereby improving the accuracy of outage probability predictions. Finally, the fitness levels of support vector regression, grey wolf optimized support vector regression (GWO-SVR), and RIME-SVR prediction models were compared. The results indicated that RIME-SVR exhibited the highest fitness, with a determination coefficient of 0.95205, a root mean square error of 3.131%, and a fitting degree of 98.48%. The RIME-SVR prediction model offers a more accurate and reliable approach for predicting the reliability of collaborative wireless communication systems.
Underwater images often suffer from non-uniform degradation caused by spectral attenuation, particle scattering, and depth-dependent absorption. Different regions within the same image may simultaneously exhibit low contrast, blurred details, and color distortion, leading to inadequate global modeling and inaccurate or excessive local adjustments in existing Underwater Image Enhancement (UIE) approaches. To address these challenges, this paper presents Aquatic Generative Adversarial Network (AquaticGAN), a novel UIE framework. Firstly, a Multi-scale Frequency-Spatial Attention (MFSA) module is designed within the generator, which integrates frequency channel attention, global spatial attention, and cross-domain attention interaction. MFSA enables bi-directional guidance and fusion between frequency and spatial features, thereby enhancing the response to salient textures while preserving structural consistency. Secondly, a composite padding strategy is developed as a bottleneck layer of the generator, which combines replication and reflection padding to introduce diverse feature distributions, enhancing the local continuity and global consistency between the padding and non-padding regions of underwater feature maps. Thirdly, an encoder-decoder structure composed of multiple triple-output residual units is constructed to aggregate hierarchical features, thereby further improving contrast and texture fidelity of underwater images. Lastly, a lightweight discriminator is proposed to balance performance and computational efficiency. AquaticGAN is evaluated on the UIEB and U45 benchmark datasets and demonstrates superior performance over state-of-the-art (SOTA) approaches, such as FUnIE-GAN, HAAM-GAN, WF-Diff, and FD-LDM. Specifically, on UIEB, the obtained SSIM, PSNR, UIQM, and UCIQE are 0.90, 24.59, 3.26, and 0.61, respectively.
By studying the welding process, it was determined that most formulae do not provide accurate results for the preheating temperature and critical cooling rate. The process of calculating the preheating temperature based on the critical cooling rate has proven to be unreliable, since in most cases it leads to deviations. This has motivated the authors to introduce the cooling rate into the procedure of welding design. That is why the mathematical procedure determines the accuracy of the general formula for the cooling rate, based on which we can precisely determine the value of the preheating temperature. The authors' intention is to mathematically present the thermal processes as much as possible, to support the assumption that this leads to a better analysis and a better understanding of the physical process and optimization of the welding process.
