Search Results (53)

Real-time precise point positioning (RT-PPP) has enabled a wide range of high-precision positioning and navigation applications, while its reliability strongly depends on the availability and continuity of precise satellite clock products. In the third-generation BeiDou Navigation Satellite System (BDS-3), interruptions or gaps in real-time precise clock products can significantly degrade the continuity and performance of precise positioning services. Therefore, accurate and robust satellite clock bias (SCB) prediction is essential for supporting reliable RT-PPP applications under product outage conditions. To address this problem, this study proposes a hybrid physics-informed and data-driven framework for BDS-3 SCB prediction. The proposed method sequentially integrates a physics-informed neural network (PINN) and a long short-term memory (LSTM) network. Specifically, the PINN is used to model and extrapolate the physically consistent trend component of SCB increments by embedding clock dynamical constraints through automatic differentiation, while the LSTM is employed to learn and predict the residual sequence containing short-term stochastic variations that cannot be fully captured by the physical model. The final SCB prediction is obtained by reconstructing the trend and residual components and recovering the original clock bias series. The proposed framework is evaluated using BDS-3 precise clock products and compared with conventional models, including quadratic polynomial (QP), autoregressive integrated moving average (ARIMA), convolutional neural network–long short-term memory (CNN-LSTM), and attention-enhanced long short-term memory (LSTM-Attention). Experimental results show that the proposed PINN-LSTM framework consistently achieves superior prediction accuracy and stability at both 12 h and 24 h forecasting horizons. Specifically, compared with QP, ARIMA, CNN-LSTM, and LSTM-Attention, the proposed method improves prediction accuracy by 18.4%, 52.8%, 32.3%, and 33.8%, respectively, for the 12 h forecasting task, and by 34.8%, 58.5%, 41.8%, and 43.8%, respectively, for the 24 h forecasting task. The results further demonstrate reduced long-horizon error accumulation, improved robustness across satellites equipped with different atomic clock types, and stronger generalization across observation days. These findings indicate that the proposed framework can provide effective support for maintaining the continuity and reliability of BDS-3 precise clock products and has strong potential for improving real-time precise positioning applications. Full article

Deploying post-quantum cryptography on highly constrained devices remains challenging due to the large key sizes and substantial storage and memory-traffic demands of leading lattice-based schemes. Although constructions such as Kyber, Dilithium, and NTRU offer strong resistance against quantum adversaries, their multi-kilobyte public keys and intensive memory access patterns limit practical adoption in microcontrollers, smart cards, and low-power edge environments. This work proposes a hybrid key-encapsulation mechanism that integrates a compact, seed-generated Module-LWE structure with a quantum-secure hash-based authentication layer. The design employs a small public seed to instantiate lattice matrices on demand via a lightweight pseudorandom generator and incorporates a Merkle-tree commitment to represent compressed auxiliary error information. Additional design considerations—including sparsity-aware secret keys, SIMD-friendly polynomial operations, and cache-efficient decryption paths—are intended to reduce runtime memory usage and computational overhead. The security of the proposed construction is analysed under both Module-LWE and hash-based one-way assumptions, with further consideration of constant-time execution and cache-line alignment to mitigate side-channel risks. This hybrid approach outlines a design pathway toward post-quantum key-encapsulation mechanisms suitable for deployment on memory-limited and energy-constrained platforms. Full article

We study a modified-degenerate version of the $W_{\alpha ,\beta ,\nu }$-factorial and the associated exponential, trigonometric, and hyperbolic families obtained by replacing the Euler gamma function with the modified-degenerate gamma function ${\Gamma }_{\lambda }^{*}$, where $\lambda \in (0,1)$. A main conclusion of this paper is that this construction does not generate a genuinely new transcendental family. Indeed, since ${\Gamma }_{\lambda }^{*}\left(s\right)=b_{\lambda }^s\Gamma \left(s\right),b_{\lambda }={\displaystyle \frac{\lambda }{\log (1+\lambda )}},$ all modified-degenerate W-functions reduce to exact rescalings of their non-degenerate counterparts. The novelty of the present work is therefore operational rather than structural. We formulate this transport principle explicitly, derive the corresponding modified-degenerate Laplace-transform identities directly in the spectral variable s, establish the induced convolution rule, and obtain first-order asymptotic expansions as $\lambda \to 0^{+}$. We further show that the associated W-derivative is a formal coefficient-shift operator, and conjugate it to the non-degenerate one under the scaling map. As an application, we present a complete Volterra integral-equation example with polynomial memory, including an explicit resolvent representation for the case $m=1$, together with convergence and residual-error checks supporting the numerical illustrations. Full article

The convergence of optical transport and wireless access in next- and future-generation networks imposes strict QoS demands, particularly end-to-end reliability, which conventional redundancy approaches cannot meet. The paper presents an architectural framework integrating three aspects: a risk-diverse route-computation algorithm with shared-risk link group constraints that achieve polynomial complexity and overcome memory constraints. Secondly, it presents a self-optimising signal-control bus modelled as a closed-loop queueing system that maintains 95% throughput under an offered load of 400%, thereby representing a statistically significant improvement over static configurations. Lastly, it presents an adaptive multipath communication framework formalised as a multi-objective optimisation that enables application-specific trade-offs among reliability, latency, and bandwidth. Performance evaluation demonstrates polynomial versus exponential memory scaling, control-plane resilience under signalling storms, and sub-10 ms latency at 10% packet loss. As such, the discussed aspects establish design principles for reliable, resilient, and robust converged optical–wireless networks. In addition to formal architectural modelling and algorithm design, this study independently validates the proposed framework through original simulations conducted in OMNeT++ and ns-3. Full article

This work investigates a sophisticated class of neutral fuzzy fractional functional differential equations (N3FDEs), where the fractional order $\alpha$ satisfies $0<\alpha \le 1$. We present a comprehensive analysis of the existence, uniqueness, and well-posedness of solutions under the generalized Hukuhara framework. First, we examine the existence and uniqueness of solutions under the generalized Hukuhara framework, providing an refined iterative formula for linear systems. We further verify the system’s well-posedness, proving that solutions remain stable and respond continuously to changes in initial data and parameters. Second, we introduce a novel spectral Vieta–Lucas projection method to approximate the solution. By leveraging the unique properties of Vieta–Lucas polynomials, we transform complex memory-dependent fuzzy equations into a streamlined algebraic system. Finally, numerical examples and error analysis show the method is accurate and efficient. Full article

Fractional differential equations provide a flexible framework for describing evolutionary processes in complex media, where nonlocality and memory effects play central roles, and classical integer-order models are frequently inadequate to capture these behaviors. In this work, we revisit the time-fractional Harry Dym (HD) evolution equation in the Caputo sense and construct high-precision analytical approximations using the recently developed Tantawy technique (TT). The method generates a rapidly convergent fractional-power series in time without resorting to perturbative assumptions, auxiliary decomposition polynomials, linearization procedures, or integral transforms, and it remains computationally economical even at high approximation orders. Closed, compact expressions are derived up to the fifth-order approximation and can be systematically extended, yielding excellent agreement with the known exact solution of the classical/integer HD model and with approximations obtained via the new iterative method. A detailed error analysis is carried out by computing absolute and maximum residual errors over the entire computational domain, demonstrating the accuracy, stability, and robustness of the TT for the HD-type fractional nonlinear evolution equation. From a physical perspective, the proposed framework offers a reliable tool for modeling nonlinear wave structures in dispersive media with significant memory and, more generally, for treating a broad class of fractional nonlinear wave equations arising in physics and engineering. Full article

This work constructs an orthogonal function system on bounded intervals $[0,R]$ associated with the Atangana–Baleanu–Caputo (ABC) fractional derivative for $\alpha \in (1/2,1)$. Starting from a fractional Laguerre-type equation involving the ABC operator, solutions are obtained via a generalized Frobenius method, yielding series representations with characteristic exponent $\alpha -1$. Rather than postulating a weight function by analogy with classical or Caputo settings, the weight is derived directly from the requirement that the underlying fractional operator be formally self-adjoint on a suitable admissible domain. This operator-theoretic approach leads to the explicit Mittag–Leffler weight $w_{\alpha }\left(x\right)=x^{-(2\alpha -1)}{E}_{\alpha }(-x^{\alpha })$, which intrinsically reflects the nonlocal memory structure of the ABC kernel. A similarity transformation removes the universal singular factor and produces regularized eigenfunctions that are continuous on $[0,R]$ and orthogonal in the weighted $L^2$ space. The weight identity and formal self-adjointness are rigorously verified through a right-Volterra uniqueness argument. Numerical experiments confirm orthogonality up to machine precision, demonstrate spectral convergence for a model ABC differential equation, and illustrate consistency with classical Laguerre polynomials in the limit $\alpha \to 1^{-}$. The resulting framework provides a self-consistent orthogonal system suitable for spectral approximations of problems governed by the ABC operator on bounded domains. Full article

Fully Homomorphic Encryption (FHE) provides strong data confidentiality during computation but often suffers from high latency on Central Processing Units (CPUs). This study evaluates Graphics Processing Unit (GPU) acceleration for modern FHE libraries across a laptop (NVIDIA GTX 1650 Ti), a server (NVIDIA RTX 4060), and a Jetson Nano 2 GB embedded GPU. We benchmark key generation, arithmetic operations, Boolean-gate evaluation and scheme-specific tasks such as relinearization and key switching, using library-provided benchmarks with an explicit baseline (operation scope, timing boundaries, and parameter tuples). Moreover, we compare GPU-native libraries (NuFHE, Phantom-FHE, and Troy-Nova) with CPU-oriented ones (Microsoft SEAL, HElib, OpenFHE, Cupcake, and TFHE-rs). Results show GPUs deliver significant speedups for targeted operations. For example, NuFHE’s NVIDIA CUDA (Compute Unified Device Architecture) backend achieves about 1.4× faster Boolean-gate evaluation on the laptop and 3.4× faster on the server compared to its OpenCL backend. Likewise, RLWE (Ring Learning With Errors)-based schemes (BFV, CKKS, and BGV) see marked gains for polynomial arithmetic such as Number Theoretic Transform (NTT) when executed via Phantom-FHE. However, attempts to add CUDA support to Microsoft SEAL reveal four main challenges: high-precision modular arithmetic on GPUs, sequential dependencies in SEAL’s design, limited GPU memory and complex build-system changes. In light of these findings, we propose revised guidelines for GPU-first FHE libraries and practical recommendations for deploying high-throughput, privacy-preserving solutions on modern GPUs. Full article

Kolmogorov–Arnold Networks employ learnable univariate activation functions on edges rather than fixed node nonlinearities. Standard B-spline implementations require $O\left(3KW\right)$ parameters per layer (K basis functions, W connections). We introduce shared Gaussian radial basis functions with learnable centers ${\mu }_k^{\left(l\right)}$ and widths ${\sigma }_k^{\left(l\right)}$ maintained globally per layer, reducing parameter complexity to $O(KW+2LK)$ for L layers—a threefold reduction, while preserving Sobolev convergence rates $O\left(h^{s-\mathrm{\Omega }}\right)$. Width clamping at ${\sigma }_{min}={10}^{-6}$ and tripartite regularization ensure numerical stability. On MNIST with architecture $[784,128,10]$ and $K=5$, RBF-KAN achieves $87.8\%$ test accuracy versus $89.1\%$ for B-spline KAN with $1.4\times$ speedup and 33% memory reduction, though generalization gap increases from $1.1\%$ to $2.7\%$ due to global Gaussian support. Physics-informed neural networks demonstrate substantial improvements on partial differential equations: elliptic problems exhibit a $45\times$ reduction in PDE residual and maximum pointwise error, decreasing from $1.32$ to $0.18$; parabolic problems achieve a $2.1\times$ accuracy gain; hyperbolic wave equations show a $19.3\times$ improvement in maximum error and a $6.25\times$ reduction in $L^2$ norm. Superior hyperbolic performance derives from infinite differentiability of Gaussian bases, enabling accurate high-order derivatives without polynomial dissipation. Ablation studies confirm that coefficient regularization reduces mean error by 40%, while center diversity prevents basis collapse. Optimal basis count $K\in [3,5]$ balances expressiveness and overfitting. The architecture establishes Gaussian RBFs as efficient alternatives to B-splines for learnable activation networks with advantages in scientific computing. Full article

This paper presents a novel high-order numerical method. The proposed scheme utilizes polynomial generating functions to achieve p order accuracy in time for the Grünwald–Letnikov fractional derivatives, while maintaining second-order spatial accuracy. By incorporating a short-memory principle, the method remains computationally efficient for long-time simulations. The authors rigorously analyze the stability of equilibrium points for the fractional vegetation–water model and perform a weakly nonlinear analysis to derive amplitude equations. Convergence analysis confirms the scheme’s consistency, stability, and convergence. Numerical simulations demonstrate the method’s effectiveness in exploring how different fractional derivative orders influence system dynamics and pattern formation, providing a robust tool for studying complex fractional systems in theoretical ecology. Full article

This paper introduces a fractional generalization of the classical Legendre differential equation based on the Atangana–Baleanu–Caputo (ABC) derivative. A novel fractional Legendre-type operator is rigorously defined within a functional framework of continuously differentiable functions with absolutely continuous derivatives. The associated initial value problem is reformulated as an equivalent Volterra integral equation, and existence and uniqueness of classical solutions are established via the Banach fixed-point theorem, supported by a proved Lipschitz estimate for the ABC derivative. A constructive solution representation is obtained through a Volterra–Neumann series, explicitly revealing the role of Mittag–Leffler functions. We prove that the fractional solutions converge uniformly to the classical Legendre polynomials as the fractional order approaches unity, with a quantitative convergence rate of order $O(1-\alpha )$ under mild regularity assumptions on the Volterra kernel. A fully reproducible quadrature-based numerical scheme is developed, with explicit kernel formulas and implementation algorithms provided in appendices. Numerical experiments for the quadratic Legendre mode confirm the theoretical convergence and illustrate the smooth interpolation between fractional and classical regimes. An application to time-fractional diffusion in spherical coordinates demonstrates that the operator arises naturally in physical models, providing a mathematically consistent tool for extending classical angular analysis to fractional settings with memory. Full article

Abnormal electrolyte levels can lead to failures in lead-acid batteries. The capacitive method, as a non-invasive liquid level inspection technique, can be applied to the nondestructive detection of electrolyte level abnormalities in lead-acid batteries. However, due to the high viscosity of sulfuric acid in lead-acid batteries, residual liquid films are easily adhered to the tube walls during rapid liquid level drops, resulting in significant dynamic measurement errors in capacitive methods. To eliminate dynamic measurement errors caused by residual liquid film adhesion, this study proposes a hybrid deep learning model—Poly-LSTM. This model combines polynomial feature generation with a Long Short-Term Memory (LSTM) network. First, polynomial features are generated to explicitly capture the complex nonlinear and coupling effects in the sensor inputs. Subsequently, the LSTM network processes these features to model their temporal dependencies. Finally, the time information encoded by the LSTM is used to generate accurate liquid level predictions. Experimental results show that this method outperforms other comparative models in terms of liquid level estimation accuracy. At a rapid drop rate of 0.12 mm/s, the average absolute error (MAE) is 0.5319 mm, the root mean square error (RMSE) is 0.7180 mm, and the mean absolute percentage error (MAPE) is 0.1320%. Full article

Nonlinear signal models are widely used in power amplifier predistortion, full-duplex self-interference cancellation, and other scenarios. The parallel Hammerstein (PH) model is a typical nonlinear signal model, but its serial and parallel hybrid architecture brings difficulties in performance analysis and coefficient estimation. This paper focuses on the performance analysis and coefficient estimation of the PH model for nonlinear systems with memory effects, such as power amplifiers. By comparing the PH model with the memory polynomial (MP) model under identical basis functions, we analyze its performance across varying numbers of parallel branches, nonlinear orders, and memory depths. Using singular value decomposition (SVD), we derive a closed-form expression for the PH model’s performance under underdetermined conditions, establishing its relationship to the non-zero singular values of the MP model’s coefficient matrix. Based on this, we propose a coefficient generation method combining SVD and least squares (LS), which directly computes coefficients and assesses performance during execution. Simulations confirm the method’s effectiveness, showing that selecting branches associated with larger singular values achieves near-optimal performance with reduced complexity. Full article

In-band full-duplex (IBFD) communication systems offer a promising means of improving spectral efficiency by enabling simultaneous transmission and reception on the same frequency channel. Despite this advantage, self-interference (SI) remains a major challenge to their practical deployment. Among the different SI cancellation (SIC) techniques, this paper focuses on digital SIC methodologies tailored for multiple-input multiple-output (MIMO) wireless transceivers operating under digital beamforming architectures. Two distinct digital SIC approaches are evaluated, employing a generalized memory polynomial (GMP) model augmented with Itô–Hermite polynomial basis functions and a phase-normalized neural network (PNN) to effectively model the nonlinearities and memory effects introduced by transmitter and receiver hardware impairments. The robustness of the SIC is further evaluated under both single off-line training and closed-loop real-time adaptation, employing estimation techniques such as least squares (LS), least mean squares (LMS), and fast Kalman (FK) for model coefficient estimation. The performance of the proposed digital SIC techniques is evaluated through detailed simulations that incorporate realistic power amplifier (PA) characteristics, channel conditions, and high-order modulation schemes. Metrics such as error vector magnitude (EVM) and total bit error rate (BER) are used to assess the quality of the received signal after SIC under different signal-to-interference ratio (SIR) and signal-to-noise ratio (SNR) conditions. The results show that, for time-variant scenarios, a low-complexity adaptive SIC can be realized using a GMP model with FK parameter estimation. However, in time-invariant scenarios, an open-loop SIC approach based on PNN offers superior performance and maintains robustness across various modulation schemes. Full article

This paper studies a one-dimensional thermoelastic Bresse beam model, in which thermal effects governed by the Green–Naghdi theory of heat conduction are coupled specifically with the longitudinal displacement. Assuming appropriate conditions on the memory kernel and by defining a key stability parameter, we prove a unified decay estimate for the system’s energy. This general result includes both exponential and polynomial decay rates as special instances, offering a comprehensive framework for characterizing the system’s long-term behavior. Full article