Search Results (407)

Reliable fault diagnosis of rotating machinery is critical for averting serious failures in modern industrial systems. While data-driven deep learning has advanced condition monitoring, its success is fundamentally predicated on the availability of independent and identically distributed (I.I.D.) datasets. In realistic operational environments, machinery frequently experiences massive domain shifts induced by varying rotational speeds. Concurrently, acquiring high-fidelity fault instances is limited compared to abundant healthy baseline data, often resulting in a long-tailed distribution. Under such data-starved conditions, conventional few-shot domain adaptation (FSDA) methodologies often may be affected by distributional erasure; global alignment objectives are mainly driven by the healthy majority, causing sparse fault signatures to be erroneously absorbed as noise and leading to severe diagnostic performance degradation. To address this setting, this study develops a physics-guided dual-stream fusion framework for extreme few-shot cross-domain fault diagnosis. The method does not treat the Laplace wavelet, STFT, CNNs, or AdaBN as newly introduced techniques. Instead, it integrates these components into a unified diagnostic pipeline designed for long-tailed target support sets under large speed shifts. A learnable Laplace wavelet convolution is used in the temporal branch to emphasize transient impact responses, while STFT spectrograms provide a complementary time-frequency representation for the two-dimensional branch. The two feature streams are then fused for target fault classification. For domain adaptation, a Strict AdaBN strategy is applied using only the target support set, rather than the target test data or a large unlabeled target pool. Under the evaluated 50 healthy + 12 fault support condition, the healthy samples provide target-domain operating-background statistics for BN recalibration, while the limited fault samples are used for supervised classifier adjustment. Experiments on the HUSTbearing and Torino DIRG datasets show that the proposed integrated framework achieves stable performance under the evaluated few-shot cross-speed settings. These results suggest that combining physics-guided Laplace convolution, time-frequency representations, and support-set-restricted BN recalibration can be useful for bearing fault diagnosis when target fault samples are limited. Full article

Let L be a non-negative and self-adjoint operator that is bounded on $L^2({\mathbb{R}}^n)$. Under the generalized Muckenhoupt weights $A_p^{\rho ,\theta }$, we establish more refined quantitative weighted estimates for the Laplace-transform-type spectral multiplier $\mathfrak{M}(L)$: the weighted bound is improved from ${\left[w\right]}_{A_p^{\rho ,\theta }}^{max\{1,1/(p-1)\}}$ to ${\left[w\right]}_{A_p^{\rho ,\theta }}^{1/p}({\left[w\right]}_{A_{\infty }^{\rho ,\theta }}^{1/p^{\prime }}+{\left[w^{1-p^{\prime }}\right]}_{A_{\infty }^{\rho ,\theta }}^{1/p})$, and the weak-type endpoint estimate at $p=1$ is provided. For the composition $\mathfrak{M}(L_1)\mathfrak{M}(L_2)$, we obtain the strong-type and weak-type weighted estimates, revealing the dependence on ${\left[w\right]}_{A_p^{\rho ,\theta }}$, ${\left[w\right]}_{A_{\infty }^{\rho ,\theta }}$ and ${\left[w^{1-p^{\prime }}\right]}_{A_{\infty }^{\rho ,\theta }}$. These results refine the weight constant dependency and extend composition theory to spectral multipliers. Full article

This study develops an analytical and computational framework for coupled transient gas redistribution induced by simultaneous localized injection and withdrawal in transmission pipelines. The aim is to describe source–sink interactions within a single transmission system, unlike conventional approaches that treat inflow and outflow processes independently. The governing equations of one-dimensional non-stationary isothermal compressible gas flow are transformed into a diffusion-type formulation using Charny regularization. The pipeline is divided into three interacting regions connected through pressure-continuity and mass-flux coupling conditions. Closed-form Laplace-domain solutions are derived for the dimensionless pressure field, and a practical Laplace-domain approximation is used for computational evaluation of transient pressure profiles. The results reveal a characteristic balancing point separating injection-dominated and withdrawal-dominated regions and show rapid convergence toward a quasi-steady redistribution regime. A pressure-deviation-based objective function is introduced to evaluate hydraulic disturbance, and the optimization analysis shows that the minimum disturbance occurs under a near-balanced source–sink operating condition. The obtained pressure profiles, asymptotic behavior, and regional redistribution patterns confirm the physical consistency of the proposed model. The framework provides a mathematically interpretable basis for analyzing coupled redistribution dynamics, hydraulic stabilization, and asymptotic equilibrium in gas transmission systems. Full article

Federated data spaces, established through initiatives such as IDSA and GAIA-X, enable organizations to share and monetize datasets under contractual terms. However, enforcing these contracts—particularly detecting unauthorized reuse or modification of datasets—remains an open challenge. We present the Off-Platform Contract Inspector, a component of the PISTIS framework, that implements a modular similarity-detection pipeline combining path-value Jaccard similarity, field-aware type-specific comparisons, and sentence-embedding-based semantic analysis across structured, semi-structured, and unstructured datasets. This contributes as follows: (i) an Inverse Document Frequency (IDF)-weighted structural similarity mechanism that discounts common domain vocabulary via Inverse Document Frequency weighting over the data space catalog, combined with a schema-evidence-gated fusion that reduces false positives from domain vocabulary overlap; (ii) an adaptive threshold optimization mechanism that learns modality-specific fusion weights and decision thresholds via cross-validated grid search; and (iii) a privacy-preserving similarity layer based on MinHash Locality-Sensitive Hashing signatures, Bloom filters with OR folding alignment, and Laplace noise for differential privacy, enabling cross-organizational dataset comparison without exposing raw data. Further, we contribute a threat taxonomy of seven dataset modification types ordered by detection difficulty, and evaluate the system on dataset pairs derived from real-world datasets across three smart-city application domains (Mobility, Energy, Automotive), with controlled augmentations applied to model adversarial behaviors. The IDF-weighted pipeline achieves high precision on intra-domain hard negatives—pairs of different tables from the same data space that share domain vocabulary—where text-similarity baselines produce false positives. The adaptive scheme learns per-modality fusion weights via cross-validated grid search. The privacy-preserving mode operates without accessing raw data and runs noticeably faster than the full pipeline, enabling screening while preserving data confidentiality. Full article

This paper introduces novel recurrence relations that enable the systematic calculation of derivatives for five fundamental Bessel function ratios: $J_{p\pm 1}\left(z\right)/J_p\left(z\right)$, $I_{p\pm 1}\left(z\right)/I_p\left(z\right)$, and $J_p^{\prime }\left(z\right)/J_p\left(z\right)$. The recursive structure reduces the calculation of this derivatives to algebraic operations, allowing for the explicit derivation of formulas up to the sixth order. These results are applied to generate new infinite series based exclusively on Bessel function zeros, extending the classical Rayleigh function framework. The methodology’s practical utility is demonstrated through application to an inverse Laplace transform problem arising in fluid mechanics, namely water hammer analysis. Additionally, we systematically extend and generalize Pedersen’s series, providing closed-form expressions for previously missing cases. The recursive framework established herein transforms what were once cumbersome ad hoc calculations into tractable algebraic procedures, opening new avenues for both theoretical exploration and engineering applications. Full article

The governing reaction–diffusion model for carbohydrate oxidation catalyzed by an immobilized bienzyme system glucose dehydrogenase and laccase within a spherical porous microreactor is adapted from Baronas et al. and extended here to the non-steady-state regime. The model consists of coupled non-linear partial differential equations based on non-Michaelis–Menten kinetics. The principal novelty of this work lies in the derivation of closed-form semi-analytical expressions for transient and steady-state concentrations of the carbohydrate substrate, oxygen, and product, as well as for the effectiveness factor, using the Laplace Homotopy Perturbation Method (LHPM). The LHPM solutions are validated against MATLAB R2026a numerical simulations (maximum error $<0.009\%$) and demonstrate superior accuracy compared to previously reported Adomian Decomposition Method (ADM) and Taylor Series Method (TSM) solutions. Parametric analysis reveals that the Thiele modulus, saturation parameters, and dimensionless time strongly influence the internal concentration profiles and reactor effectiveness. These analytical results provide rapid, closed-form predictive tools for optimizing catalyst particle size, enzyme loading, and operating conditions in immobilized enzyme microreactor systems. Full article

Protein–ligand binding affinity prediction underpins structure-based drug discovery, yet random partitions of public benchmarks overestimate generalisation due to protein-family and ligand leakage, and the marginal value of explicit pocket-geometry descriptors over atom-level graph neural networks remains unclear. We computed a 59-dimensional discrete differential geometry descriptor on the ligand-aware solvent-excluded surface of 3285 PDBBind v2020 complexes, combining curvature distributions, the leading sixteen Laplace–Beltrami eigenvalues and a ten-point heat-kernel signature, and evaluated it in gradient-boosted tree pipelines across progressively stricter split regimes and two leak-proof external benchmarks, together with four mechanistically distinct injection strategies in a SchNet-style graph neural network. The descriptor lifted Pearson correlations by 0.111 on cluster-disjoint testing, 0.258 on LP-PDBBind DataSAIL S2 and 0.365 on CASF-2016, while in isolation reaching 0.456 to 0.594 on external benchmarks, on a par with X-Score and AutoDock Vina (version 1.2). TreeSHAP attribution localised the dominant signal to the heat-kernel signature. The four graph neural network injection strategies produced no statistically significant lift, indicating that distance-based message passing on atomic coordinates already captures much of the geometric content. Pocket-surface discrete differential geometry, therefore, offers an interpretable, leakage-robust and lightweight feature class for early-stage virtual screening, and motivates hybrid mesh-to-atom architectures. Full article

We develop a closed-form analysis of the joint distribution for cumulative shock reliability systems with phase-type inter-shock times. The analytical literature on shock-driven reliability has hitherto been split into two largely separate traditions: scalar fluctuation theory, which delivers closed-form joint distributions of pre-failure and failure-time observables but cannot accommodate matrix phase structure; and matrix-analytic methods, which handle phase-type dynamics naturally but focus on stationary indicators rather than first-passage distributions. We bridge these traditions by introducing a matrix-valued reliability functional ${\mathbf{\Phi }}_{\nu }(\xi ,u,v,\vartheta ,\theta )$ that encodes the joint distribution of the failure index, pre-failure damage and time, failure-time damage and time, and the operational phase at the moment of failure. We derive ${\mathbf{\Phi }}_{\nu }$ in closed form via Sherman–Morrison reduction of the matrix Laplace–Stieltjes transform together with the Dshalalow $\mathfrak{D}$-operator, and establish a span-reduction theorem showing that ${\mathbf{\Phi }}_{\nu }$ lies in a three-dimensional matrix subspace generated by the identity and two matrix LSTs. The functional simultaneously generalizes the scalar fluctuation functional of Dshalalow and White and the phase-tagged first excess functional of Tadj, recovering both as projections. We extract twelve closed-form reliability indices, including the reliability function, mean time to failure, mean overshoot, joint pre-failure and failure transforms, and, new to the cumulative shock literature, the phase distribution at failure and the phase-resolved failure-time distribution. Two structural identities of Wald type emerge as corollaries. The framework reduces to elementary arithmetic for rational model primitives and is verified against $2\times {10}^5$ Monte Carlo trajectories in a worked example. Full article

This paper advances a comprehensive controllability framework for Prabhakar fractional differential systems ($\mathcal{PFDS}$s) of order $\eta \in (1,2)$ with nonlocal initial conditions, where the second-order setting requires the joint specification of both an initial state and an initial velocity. Explicit solution representations for four structurally distinct classes of second-order Prabhakar systems are derived via the Laplace transform method and Neumann series expansions, revealing that the placement of the forcing term directly in the system or under the Prabhakar fractional integral operator produces fundamentally different convolution kernels. For linear integro-differential systems, necessary and sufficient controllability conditions are established through a Gramian rank criterion with an explicit norm-bounded control law, while for nonlinear systems, sufficient conditions are obtained via the Schauder fixed-point theorem under an asymptotic growth condition. Three numerical examples validate the theory: a three-dimensional linear system and a two-dimensional nonlinear integro-differential system achieve terminal errors of order ${10}^{-12}$ and ${10}^{-7}$, respectively, and a Prabhakar fractional mass–spring–damper system with viscoelastic hereditary damping demonstrates direct physical relevance, with all theoretical conditions verified and a terminal error of $7.42\times {10}^{-5}$ confirming precise rest-position steering by the Gramian-based control law. Full article

The responses of a very large floating structure (VLFS), which is modeled as a thin viscoelastic plate floating on a fluid of finite depth, are analytically studied within the framework of the nonlinear potential flow theory. We use the Laplace equation with the dynamical boundary condition to express a balance among the hydrodynamic, inertial, and viscoelastic forces. For the case of steady-state incident waves, we obtain convergent series solutions for plate deflection and velocity potential by choosing the optimal convergence-control parameter $C_0$ and proper auxiliary linear operators in the homotopy analysis method (HAM). The strain relaxation time for the viscoelastic plate is studied, and the result shows that the plate deflection decreases when the retardation time increases. The influences of other physical parameters on the viscoelastic plate are also discussed. The nonlinearity of dispersion relation and the retardation time of the plate have important and non-negligible effects on the responses of the VLFS. The results obtained here may be helpful in understanding the different physical parameters to model hydroelastic responses of a VLFS in the real ocean. Full article

This paper presents a hybrid numerical approach, termed the Radial Basis Function–Finite Difference Matrix Operator (RBF–FDMO) method, to enhance the accuracy and flexibility of the conventional FDMO technique for three-dimensional (3D) electromagnetic field analysis governed by the Laplace–Poisson equation. Conventional numerical methods often face challenges related to computational complexity and limited flexibility when handling non-uniform discretization and complex geometries. In the proposed method, spatial derivatives are approximated using RBF-based interpolation rather than finite difference schemes derived from Taylor series expansion. This formulation enables the construction of high-accuracy derivative operators on both uniform and non-uniform FD grids, thereby improving numerical robustness and adaptability to complex geometries. The performance of the proposed method is first compared with the FDMO in a 3D benchmark problem, with reductions of more than two orders of magnitude in both RMS and maximum errors. Furthermore, the RBF-FDMO approach is developed and, for the first time, applied to the analysis of grounding system (GS) configurations specified in IEEE Std. 80™, as well as a practical 110 kV substation GS in Vietnam. The obtained potential distributions, grounding resistances, and touch and step voltages confirm the effectiveness and reliability of the method. The results indicate that the proposed approach features a simple formulation and competitive computational efficiency, positioning it as a practical alternative to conventional methods like the finite element method (FEM) and the boundary element method (BEM) for GS analysis and design. Full article

This paper revisits the use of the Laplace transform in the study of Bessel and modified Bessel differential equations. Rather than presenting the method as a new alternative to the classical Frobenius approach, the paper is organized as a pedagogical review of how standard operational rules for the Laplace transform lead to transform-domain differential equations for the regular solutions of these variable-coefficient problems. For Bessel’s equation, the transformed equation yields the classical Laplace transform of $J_{\nu }\left(x\right)$; for the modified Bessel equation, the same procedure yields the corresponding transform of $I_{\nu }\left(x\right)$. These formulas are then used to recover standard recurrence and derivative identities and to derive several illustrative transform evaluations. The paper also explains why the singular companion solutions $Y_{\nu }\left(x\right)$ and $K_{\nu }\left(x\right)$ are not obtained directly from the regular Laplace-transform framework and must instead be introduced through classical connection formulas. Particular attention is given to placing the calculations in the context of the earlier literature, especially the classical treatise of Watson and later work on Laplace and Lipschitz–Hankel integrals. In this form, the paper is intended as a self-contained review and tutorial on a useful operational approach to Bessel-type equations. Full article

While Graph Autoencoders (GAEs) have become a standard for unsupervised representation learning, their reliance on integer-order convolutions inherently restricts information propagation to immediate local neighborhoods. This paper introduces the Fractional Graph Autoencoder (FGAE) and its variational extension (FVGAE) to move beyond these local constraints. By integrating fractional Laplace operators, our framework generalizes conventional GAEs and enables tunable non-local propagation. We show that the fractional order $\alpha$ acts as a structural regularizer, utilizing the Green’s function of anomalous diffusion to induce a form of structural memory within the latent space. This allows the model to recover long-range dependencies that are typically lost in standard architectures. Systematic benchmarking across eight datasets—ranging from homophilic citation networks to heterophilic and dense product graphs—shows that these fractional variants consistently outperform both foundational and state-of-the-art baselines (ARGA, SIG-VAE, and GraphMAE). Notably, on the Amazon Computers and Citeseer datasets, our methods achieve relative increases in Normalized Mutual Information (NMI) of 77.55% and 67.28%, respectively. Statistical analysis confirms these gains are robust, with large effect sizes (Cohen’s $d>0.80$) and significance at $p<0.05$. These findings suggest that fractional graph autoencoding offers a mathematically grounded inductive bias for capturing the complex, multi-scale dynamics of real-world networked systems. Full article

Self-collision detection has become the dominant computational bottleneck in GPU-accelerated cloth simulation, as modern parallel solvers such as XPBD have drastically reduced the cost of position updates while leaving collision resolution largely unoptimized. Existing spatial partitioning methods treat all cloth regions uniformly, saturating GPU memory bandwidth despite the fact that the vast majority of the mesh surface remains geometrically flat and collision-free at any given frame. We propose a hierarchical self-collision culling framework built upon a resolution-independent discrete curvature metric derived from the $h^2$-normalized Laplace-Beltrami operator, integrated with a discrete Kirchhoff–Love shell model combining distance and dihedral bending constraints within XPBD. Unlike prior cache-dependent acceleration strategies, our method tightly couples curvature-driven geometric pruning with a fused GPU kernel design and shows that this stateless formulation is both faster and physically more reliable. Evaluated on meshes of $512\times 512$ and $1024\times 1024$ particles, our method achieves a $5.5\%$ and $9.7\%$ FPS improvement alongside a $34.9\%$ and $28.4\%$ reduction in active collision pairs, respectively, with qualitative validation via high-fidelity rendering confirming artifact-free self-contact and strict ground-plane non-penetration. Ablation results further reveal that temporal coherence, conventionally regarded as an optimization standard, strictly degrades both performance (FPS decrease of $1.4\%p$ to $1.9\%p$) and physical accuracy (penetration depth increase of $36.1\%$ to $100.0\%$ relative to the curvature-only stage) on RTX 3070 GPU, advocating for stateless per-frame geometric evaluation as the preferred design paradigm. Full article

We study the phase-space dynamics of quantum systems with $\mathrm{SU}(1,1)$ group symmetry using coherent-state representations on the Poincaré disk. The resulting evolution equation combines transport terms with nonlocal contributions generated with the spectral functions of the Casimir operator, which admit a natural interpretation as pseudodifferential operators associated with the hyperbolic Laplace–Beltrami operator. Using this pseudodifferential structure, we classify the phase-space generators according to the type of the underlying PDE: compact quadratic dynamics ($\widehat{H}\propto {\widehat{K}}_0^2$) yield a degenerate hyperbolic operator of the transport type, and noncompact dynamics ($\widehat{H}\propto {\widehat{K}}_2^2$) give rise to a mixed-order differential–pseudodifferential operator. For numerical evaluation, we reformulate the propagator as an oscillatory integral and develop two complementary strategies: a Fourier-series reduction exploiting the periodicity of compact orbits and a Levin-type spectral collocation method for the noncompact case. Both approaches are stable, accurate, and free of the stiffness issues that afflict direct PDE evolution on the Poincaré disk. Full article