Search Results (9,341)

This paper investigates non-fractional operators, a type of nonlocal operator, within the framework of Orlicz spaces. Using inclusions between certain function spaces, we prove the continuity and/or compactness of generalized operators in Orlicz spaces and show that solutions exist for integral equations of fractional order. We also introduce a generalized Hilfer-type derivative and examine the equivalence of differential and integral problems. Finally, we relate these results to the study of compositional p-Laplacian fractional problems involving generalized Hilfer fractional derivatives. Among other things, we prove the existence of solutions to such problems in Orlicz and Orlicz–Sobolev spaces. Full article

Post-quantum cryptography (PQC) artifacts are one to three orders of magnitude larger than their classical counterparts and must be segmented via ISO-TP across a shared CAN-FD bus while coexisting with periodic safety-critical traffic. No prior work has quantitatively mapped the transport-level feasibility of these artifacts under realistic multi-electronic control unit (ECU) contention. This paper presents a validated discrete-event simulator and evaluates 29 parameter sets from nine algorithm families—spanning the KpqC final portfolio, NIST FIPS 203–205 standards, and the draft FIPS 206—across 534 scenarios classified as feasible, borderline, or infeasible. Results show that key encapsulation mechanism (KEM) feasibility is scenario-dependent: domain scale and startup coordination dominate over algorithm choice, with 4-ECU staggered deployments feasible for all Level-1 candidates, while 16-ECU simultaneous startup is universally infeasible. For digital signatures, FN-DSA achieves the best transport feasibility due to its compact signature, while HQC is uniformly infeasible and SLH-DSA is nearly uniformly infeasible, quantifying the CAN-FD bandwidth premium of algorithmic diversity. System-side traffic shaping—staggered startup and reserved bus windows—outperforms algorithm substitution as a mitigation strategy. To the best of our knowledge, these findings constitute the first design-space map of PQC artifact transport on CAN-FD and provide actionable deployment guidelines for post-quantum transition. Full article

By combining hanging-drop self-assembly with melt infiltration and selective inversion, we fabricate millimetric and free-standing curved photonic heterostructures that integrate infiltrated-opal, inverse-opal, embossed, and white-scattering 2.5D metasurface domains within a single continuous body. These architectures enable configurations inaccessible to planar fabrication, including naturally formed concavities within convex inverse-opal films and alternating ordered/single-layer regions that preserve local coherence while introducing disorder at larger scales. Across these heterogeneous curved landscapes, we observe optical phenomena absent in flat photonic structures—spectrally selected lateral collimation, geometry-shifted ghost images, and transmission-derived valleys shaped by curvature-mediated Bragg extraction. Their origin lies in the geometric constraints inherent to curved assemblies, where spatially varying normals, non-parallel lattice orientations, and topologically required defects couple order and disorder into a distributed-coherence regime. This coupling expands the accessible photonic state space, establishing curvature as an active functional degree of freedom rather than a geometric constraint, positioning the self-assembled photonic heterostructures as a scalable route toward multifunctional 3D metasurfaces and new regimes of light–matter interaction. Full article

This article proposes a novel time-space two-grid high-order compact difference scheme for the one-dimensional nonlinear Schrödinger equation subject to Dirichlet boundary conditions. In comparison with the fully nonlinear compact difference scheme, the proposed methodology combines a small-scale nonlinear fourth-order compact difference algorithm on a time-space coarse grid and a large-scale linearized correction compact difference algorithm on a fine grid. In contrast to the time two-grid compact difference method, the proposed scheme applies the two-grid technique in both the spatial and temporal domains, thereby further improving computational efficiency. Solutions from the coarse grid are projected onto the fine grid via a temporally linear and spatially cubic Lagrange interpolation operator. Unconditional stability and optimal convergence rates, which are fourth-order in space and second-order in time, are proven in both the discrete $L^2$ and $L^{\infty }$ norms, without any constraints on the grid ratio. In addition to the standard techniques of the energy method, a discrete Sobolev inequality and an a priori error estimate are employed to demonstrate stability and high-order convergence. Finally, the theoretical results are validated through numerical experiments, which confirm the robustness and reliability of the proposed approach. A single-soliton experiment demonstrates that, compared with the fully nonlinear compact difference scheme, the proposed method achieves a significant reduction in CPU time while maintaining a comparable level of accuracy. Additional experiments further illustrate the algorithm’s effectiveness in simulating two-soliton interactions and soliton birth. These findings establish the proposed scheme as a highly efficient alternative to conventional nonlinear approaches. Full article

Against the background of highly interconnected global capital markets and rapidly propagating cross-lingual information streams, traditional anomaly detection paradigms based solely on single-modality numerical time-series sensors are insufficient for forward-looking risk sensing. From the perspective of artificial intelligence-driven sensing, this study proposes a multilingual semantic–numerical collaborative Transformer framework to construct a unified multimodal financial sensing architecture for intelligent anomaly sensing and risk perception. Within the proposed sensing paradigm, multilingual texts are conceptualized as semantic sensors that continuously emit event-driven sensing signals, while market prices, trading volumes, and order book dynamics are modeled as heterogeneous numerical sensor streams reflecting behavioral market sensing responses. These heterogeneous sensors are jointly integrated through a cross-modal sensor fusion architecture. A cross-modal temporal alignment attention mechanism is designed to explicitly model dynamic lag structures between semantic sensing signals and numerical sensor responses, enabling temporally adaptive sensor-level alignment and fusion. To enhance sensing robustness, a multilingual semantic noise-robust encoding module is introduced to suppress unreliable textual sensor noise and stabilize cross-lingual semantic sensing representations. Furthermore, a semantic–numerical collaborative risk fusion module is constructed within a shared latent sensing space to achieve adaptive sensor contribution weighting and cross-sensor feature coupling, thereby improving anomaly sensing accuracy and robustness under complex multimodal sensing environments. Extensive experiments conducted on real-world multi-market financial sensing datasets demonstrate that the proposed artificial intelligence-driven sensing framework significantly outperforms representative statistical and deep learning baselines. The framework achieves a Precision of $0.852$, Recall of $0.781$, F1-score of $0.815$, and an AUC of $0.892$, while substantially improving early warning time in practical risk sensing scenarios. In cross-market transfer settings, the proposed sensing architecture maintains stable anomaly sensing performance under bidirectional domain shifts, with AUC consistently exceeding $0.86$, indicating strong structural generalization across heterogeneous sensing environments. Ablation analysis further verifies that temporal sensor alignment, semantic sensor denoising, and collaborative cross-sensor risk coupling contribute independently and synergistically to the overall sensing performance. Overall, this study establishes a scalable multimodal intelligent sensing framework for dynamic financial anomaly sensing, providing an effective artificial intelligence-driven sensing solution for cross-market risk surveillance and adaptive financial signal sensing. Full article

CuCo-based catalysts are promising candidates for higher alcohol synthesis from syngas, yet their performance is often limited by poor metal dispersion and insufficient Cu-Co synergy. In this work, a series of ordered mesoporous CuCoAl catalysts with varying Cu/Co atomic ratios were synthesized via the evaporation-induced self-assembly (EISA) method. The structural, electronic, and catalytic properties were systematically investigated using N₂ physisorption, XRD, TEM, H₂-TPR, CO-TPD, XPS, and fixed-bed reactor evaluation. The results show that all CuCoAl catalysts prepared by the EISA method possess well-ordered mesoporous structures with high surface areas (up to 235 m²/g) and narrow pore size distributions. The interaction between Cu and Co stabilizes the mesoporous framework, inhibits Cu particle growth, and induces electron transfer from Cu to Co as evidenced by XPS. Among the catalysts tested, Cu₁Co₁Al (Cu/Co = 1:1) exhibits the highest strong CO adsorption capacity (1.54 mmol/g) and surface hydroxyl content (63.29%), achieving a CO conversion of 32.9% with a C₂⁺ alcohol space–time yield of 20.5 mg·gcat⁻¹·h⁻¹. These findings establish clear structure–performance relationships for ordered mesoporous CuCoAl catalysts and provide fundamental guidance for the rational design of efficient catalysts for higher alcohol synthesis. Full article

Geometric problem-solving has always been a great challenge in the field of deductive reasoning and artificial intelligence. Symmetry is a defining characteristic of geometric shapes and properties. Consequently, the application of symmetry principles to geometric reasoning arises as a natural choice. To address the efficiency degradation and limited generalization, we propose FGeo-ISRL, a neural-symbolic inverse search framework whose core is the synergistic integration of a task-fine-tuned large language model and Monte Carlo Tree Search. Under the formal framework of FormalGeo, geometric theorems are iteratively applied starting from the given conditions and the target conclusion, in order to infer the necessary supporting premises. The large language model simultaneously serves as a policy network and a value network, guiding theorem application decisions and evaluating intermediate proof states, whereas the Monte Carlo Tree Search performs structured exploration over the state space, both training for policy refinement and inference for online search. The reinforcement learning agent is trained with a hybrid reward scheme, combining immediate feedback from the value difference and a sparse success reward. Experiments demonstrate the effectiveness and correctness of FGeo-ISRL. It not only achieves a Single-Step Theorem Accuracy of 90.2% and a Geometric Problem-Solving Accuracy of 83.14%, but also ensures that every step of the proof process remains readable, verifiable, and traceable. Full article

This study details the design and development of an ultra-sensitive microwave sensor for non-invasive blood glucose monitoring, achieved by analyzing variations in the response of a split-ring resonator (SRR) through advanced engineering methodologies. There were three design phases in the development process. In the first phase, a standard SRR design was used. It had a resonant frequency of 2.975 GHz in S₂₁ and a sensitivity of only 0.0032 dB/(mg/dL). In the second phase, an interdigital capacitor (IDC) was added to the SRR structure. This made it work better and made it more sensitive, with a sensitivity of 0.015 dB/(mg/dL) at 4.1 GHz. The third phase was to use a fourth-order Moore fractal geometry to improve the resonance properties of the design a lot. From the obtained S₁₁, the maximum sensitivity was 0.042 dB/(mg/dL), which was a huge improvement in sensing efficiency compared to earlier designs. Several resonant frequencies were recorded between 4.84 and 7.56 GHz. The addition of the fractal structure made the electromagnetic field stronger in the resonant space and made the waves interact more with small changes in the biological medium, all without changing the sensor’s size (80 mm × 40 mm). These results show that fractal architecture is a promising way to create non-invasive, accurate, and easily integrated sensors in biological systems that can continuously measure blood glucose levels. Full article

This study presents a unified mechanics-based framework for evaluating bonded composite patch repairs. Discrete fracture, fatigue, and adhesive responses are transformed into continuous master equations over the design space. Low-order polynomial surfaces model stress intensity and concentration responses, enabling continuous prediction of repair performance without repeated finite-element analyses. A fracture-based repair efficiency index is derived from the analytical master surface. This index quantifies the average reduction in crack-driving force across the domain. Combined with adhesive stiffness and strength, it defines an adhesive-based repair efficiency index (A-REI), providing a direct link between structural response and material properties. The results show that repair effectiveness is strongly influenced by both geometric severity and adhesive properties. Fatigue performance decreases significantly with increasing notch ratio in single-sided repairs. Double-sided configurations maintain consistently higher efficiency. Symmetric reinforcement more effectively reduces stress concentration, with improvements exceeding 40% at intermediate notch ratios. Adhesive selection is governed by stiffness and strength. Structural adhesives achieve significantly higher A-REI values, whereas compliant adhesives contribute negligibly. Overall, repair symmetry controls the magnitude of improvement, while adhesive properties determine performance ranking. This framework provides a clear, practical basis for design and material selection. Full article

Accuracy in fractional numerical integration is often limited by the regularity of the integrand. This work proposes a flexible error estimation framework for proportional Caputo-hybrid integral operators based on $\mathfrak{s}$-convexity. We introduce a parametric Newton–Cotes formula ($\nu \in [0,1]$) that bridges the gap between classical quadrature rules, recovering the fractional Trapezoidal, Midpoint, and Simpson’s methods as specific instances. In order to confirm the correctness of our results, we provide an illustrative example with graphical representations. Furthermore, we provide some additional results using Hölder’s and power mean inequalities and employ a verification strategy based on an Artificial Neural Networks (ANNs) model. The ANN approach allows for high-dimensional parameter space exploration, demonstrating that the proposed inequalities provide robust and precise error estimates. Full article

Spectrum scarcity has become a critical issue due to the rapid deployment of fifth-generation (5G) networks and the explosive growth of future wireless data traffic. Spectrally Efficient Frequency Division Multiplexing (SEFDM) is a promising technique to enhance spectral efficiency by compressing subcarrier spacing and allowing spectral overlap; however, it suffers from severe inter-carrier interference (ICI) caused by the loss of orthogonality. In particular, under Rayleigh fading channels, the combined effects of ICI and multipath fading lead to significant degradation in bit error rate (BER) performance. Conventional SEFDM systems employing a cyclic prefix (CP) encounter an unavoidable error floor due to residual interference stemming from non-orthogonality. On the other hand, while zero-padding (ZP)-based SEFDM offers superior multipath tolerance, further enhancement in communication quality is still desired. This paper proposes a novel receiver architecture utilizing sector antennas to spatially separate multipath components based on the angle of arrival (AoA). Furthermore, we investigate and compare sector selection algorithms specifically tailored for SEFDM systems. Simulation results demonstrate that the proposed method, employing a sector selection scheme based on the maximum channel response power, effectively suppresses inter-symbol interference (ISI) and improves BER performance for both CP-SEFDM and ZP-SEFDM. Furthermore, our quantitative evaluations confirm that the proposed architecture successfully achieves the theoretical maximum spectral efficiency even in higher-order modulation schemes (16QAM), while maintaining a low computational complexity compared to conventional spatial diversity techniques. Full article

This paper is a contribution to Einstein’s general relativity theory and is mostly a review of known work. It concentrates attention on four fourth-order tensors which arise on the space-time manifold describing this theory and which are very useful. These are the (Riemann) curvature tensor, the Weyl conformal tensor, the “E” tensor and the Weyl projective tensor. The first of these, the curvature tensor, plays an important role in the formulation and interpretation of Einstein’s theory. Next, the Weyl conformal tensor is introduced and its conformal properties described and with it, the Petrov classification of gravitational fields which arises from this tensor. This, in turn, gives rise to the Bel criteria for distinguishing Petrov types at a point by an alignment of certain null directions at that point. The third of these tensors, the “E” tensor, is an important tensor in calculations due to its close connection to the Ricci tensor. The fourth tensor, the Weyl projective tensor, is then described together with its properties relating to the geodesic structure of space-time. As examples of the combined usefulness of these tensors, pp-waves and generalised pp-waves are discussed and related, and a review of the geodesic structure of vacuum metrics is given. Full article

Long-term safety assessment of deep geological repositories for spent nuclear fuel requires explicit evaluation of thermo-mechanical (TM) processes induced by decay heat and their influence on fractured host rock. A safety-relevant, though low-probability, scenario concerns shear reactivation of fractures intersecting deposition holes, which could compromise canister integrity if displacement exceeds design limits. This study presents a three-dimensional discrete element modelling approach to analyze the thermal evolution of the Forsmark repository (Sweden) and the associated long-term response of a discrete fracture network (DFN) during the post-closure phase. The model explicitly represents repository panel, deterministic deformation zones, and a stochastically generated fracture network embedded in a bonded particle assembly representing the rock for Particle Flow Code (PFC) numerical simulations. Time-dependent heat release from spent nuclear fuel canisters is implemented using a physically based decay power function. A deposition panel-scale heat-loading formulation accounts for deposition-hole and tunnel spacing. Two emplacement scenarios are analyzed: (a) a simultaneous all-panel heating scenario, used as a conservative bounding case, and (b) a sequential panel heating scenario representing staged emplacement and closure. The simulations show that temperature and thermally induced stress evolution are sensitive to the emplacement and closure sequence. Sequential heating produces a more gradual thermal build-up and lower peak temperatures than simultaneous heating, indicating that thermal and stress perturbations in the host rock can be influenced not only through repository design, but also by operational strategy. Thermally induced fracture shear displacement displays a systematic temporal response. Fractures located within the deposition panel footprint develop shear displacement rapidly during the early post-closure period, reaching peak values at approximately 200 years, followed by gradual relaxation as temperatures decline. The average peak shear displacement on fractures is on the order of 2–3 mm, while fractures outside the panel footprint show smaller early-time displacements and a more prolonged long-term response. All simulated shear displacements remain more than one order of magnitude below the commonly cited canister damage threshold for Forsmark of approximately 50 mm, even for the conservative simultaneous heating case. These results indicate that thermally induced fracture shear is unlikely to cause direct mechanical damage to canisters. At the same time, the persistence of residual shear displacement after heating implies permanent fracture dilation, which may influence long-term hydraulic properties and indirectly affect processes such as groundwater flow and canister corrosion. The modelling framework and results presented here were conducted for review purposes independently from the Swedish safety case, and provide a mechanistic basis for evaluating thermally induced fracture deformation in crystalline rock repositories and contribute to bounding the role of thermo-mechanical processes in the safety assessment of spent nuclear fuel disposal at Forsmark. Full article

We develop a unified Koopman–von Neumann (KvN) operator and Weyl–Wigner phase-space framework for inviscid ideal (barotropic) Euler flows. Our approach reformulates the nonlinear fluid dynamics as a linear KvN evolution on an enlarged field phase space, thereby enabling us to apply tools developed for quantum mechanics (Weyl quantization, Moyal ⋆-products, and Wigner functionals) to a classical fluid. We construct the appropriate KvN generator (including the required Jacobian term for unitarity) and derive the evolution equation for the corresponding Wigner functional. This framework clarifies when the classical Liouville (Vlasov) description is exact—namely, in quadratic or linear regimes where the Moyal bracket reduces to the Poisson bracket—and when higher-order quantum-like corrections become significant in fully nonlinear regimes. As an analytic example, we obtain a closed-form Wigner solution for a one-dimensional Burgers flow (pressureless Euler) and verify, term by term, that it reproduces the expected Liouville transport (with distributional contributions at the shock). We also compare the phase-space approach with a kinetic (Vlasov–monokinetic) formulation and outline the extension of the framework to three-dimensional flows using a Clebsch variable representation. Full article

Additive manufacturing in construction is expanding production possibilities for housing, however its integration into architectural design workflows remains limited. This research proposes a computational workflow for the early-stage form-finding of housing volumes intended for additive construction. A parametric design system was developed to generate a wide range of residential volumetric configurations based on geometric parameters derived from conventional housing typologies and emerging 3D-printed construction practices. The design space was explored through user-driven experimentation and automated evolutionary optimization targeting predefined surface area conditions. Besides design alternatives were visualized using AI-assisted image generation to support comparative evaluation, translated into BIM models for further architectural development, and tested through physical 3D-printed scale models to assess material expression and constructability. Five design exploration activities involving architects and graduate students produced nearly 200 volumetric alternatives, in order to review its use and possibilities. The results show that the parametric system enables efficient exploration of both conventional and novel housing forms potentially compatible with additive construction. Vertically articulated volumes with curved envelopes and spatial variation emerged as promising alternatives. The study demonstrates the potential of integrating parametric modeling, evolutionary search, AI-assisted visualization, and physical prototyping to support architectural decision-making and facilitate the incorporation of 3D printing into housing design processes. Full article