Search Results (756)

We classify the continuous reciprocally symmetric cost functions $J:(0,\infty )\to \mathbb{R}$ with $J\left(1\right)=0$ and strictly convex log-substitution $G\left(t\right):=J\left(e^t\right)$ (admissible costs) for which the symmetric compound $J\left(xy\right)+J(x/y)$ depends on $(x,y)$ only through $\left(J\right(x),J(y\left)\right)$. We first prove that this dependence is automatic: for every admissible J, there exists a unique continuous combiner (the auxiliary function P that encodes the compound) $P:{[0,\infty )}^2\to \mathbb{R}$ with $J\left(xy\right)+J(x/y)=P\left(J\right(x),J(y\left)\right)$ for all $x,y>0$ (Theorem 1); P is symmetric, non-negative, satisfies $P(u,0)=2u$, and inherits monotonicity and coercivity from admissibility. When P is required to be a polynomial, a growth rate comparison between two recursions for G forces $degP\le 2$ (Theorem 4), so $P(u,v)=cuv+2u+2v$ with $c\ge 0$, and the corresponding admissible costs are exhausted by two explicit families (Theorem 8)—the hyperbolic family $J\left(x\right)=c^{-1}(x^{\lambda }+x^{-\lambda })-2c^{-1}$ ($c,\lambda >0$) and the degenerate quadratic family $J\left(x\right)=a{(lnx)}^2$ ($a>0$)—with the latter arising as the Inönü–Wigner contraction $\lambda \to 0^{+}$, ${\lambda }^2/c\to a$ of the former (Theorem 9). Two regularity extensions are obtained: a Lebesgue-measurable cost satisfying explicit regularity hypotheses admits a continuous representative (Theorem 5), and in the entire finite-order regime, the diagonal combiner $Q\left(u\right):=P(u,u)$, when polynomial of degree $d^{\prime }$, obeys the sharp bound $d^{\prime }\ge 2^{\rho }$ (Theorem 6), attained with equality in both classified families. The normalisations $P(1,1)=6$ and $G^{\prime \prime }\left(0\right)=1$ single out the canonical representative $J_{\mathrm{cost}}\left(x\right)=\frac{1}{2}(x+x^{-1})-1$. Full article

This study proposes a vision-based framework for automated inspection and quality grading of beef steaks by integrating fat marbling distribution analysis and lean-meat color evaluation. In frozen beef products, surface frost often generates specular reflections that resemble both fat and lean regions, thereby reducing segmentation accuracy. To address this challenge, a sequential and interpretable analytical framework is developed. First, homomorphic filtering is applied to suppress frost-induced illumination artifacts, followed by curvelet transform combined with square-ring filtering to separate fat and lean regions based on their multi-scale and directional characteristics. For marbling analysis, the convex hull, skeleton, and principal axis of the steak are extracted, and a chi-square goodness-of-fit test is performed within eight predefined regions to quantitatively evaluate marbling distribution uniformity and identify localized fat accumulation. For lean-meat evaluation, RGB color features are extracted and classified using a Support Vector Machine (SVM) to determine redness levels. The resulting marbling and color information are subsequently integrated through a weighted grading strategy to estimate the final quality grade. Experimental results demonstrate a fat detection rate of 92.68%, a false-positive rate of 4.97%, and a correct classification rate of 94.09% for fat segmentation, while the SVM-based lean-meat color classifier achieves an accuracy of 96.67%. Furthermore, the proposed grading framework attains an overall grading accuracy of 90.38%, showing strong agreement with human evaluation. Full article

Weather–yield relationships in arid agricultural regions are shaped jointly by temperature and precipitation exposure, irrigation conditions, crop choice, and management under water constraints. This study combines county-level cotton yield and maize grain-yield data for Xinjiang, China, from 2000 to 2020 with daily meteorological station records assigned to county-level weather exposures. We estimate two-way fixed-effects models that include temperature degree-day indicators and a quadratic precipitation term to examine crop-specific weather–yield associations in irrigation-intensive oasis agriculture. The baseline two-way fixed-effects estimates indicate that a 100 °C d increase in growing degree days is associated with a 2.85% increase in cotton yield and a 1.88% decrease in maize yield. For cotton, the baseline and common-trend specifications indicate a convex precipitation–yield association, with an estimated turning point of 141.07 mm (95% CI: 27.75–225.63 mm), while the pattern is less stable under prefecture-by-year fixed effects. Maize yield is more consistently negatively associated with growing-season heat accumulation. Post-2010 interaction terms indicate crop-differentiated changes in heat sensitivity, consistent with different temporal evolution of weather–yield associations across cotton and maize. Overall, the results show that climate-risk assessment in irrigation-intensive arid agriculture should distinguish between crop types, precipitation regimes, and the management conditions under which weather exposure is translated into yield outcomes. Full article

This paper investigates the optimal control problem of time-delay backward doubly stochastic systems under partial information. Partial information widely exists in practical control systems due to monitoring constraints, communication delays, and data acquisition costs. Combined with inherent system time delays, it greatly complicates state estimation and decision-making, which requires research. A new type of anticipated backward doubly stochastic differential equations is introduced to describe the system dynamics. Using stochastic analysis and the variational methods, the corresponding maximum principle for optimal control is derived. Furthermore, a verification theorem is established that provides rigorous sufficient optimality conditions: any admissible control satisfying the necessary conditions, along with reasonable convexity assumptions, indeed optimizes the cost functional, thereby bridging the gap between necessary and sufficient optimality criteria. As an application, we solve a time-delay linear-quadratic optimal control problem and obtain explicit analytical expressions; the results demonstrate the validity of the established theoretical framework. Full article

A second-order cone programming support vector machine (SOCP-SVM) method is proposed to realize the binary classification faster and better. This method combines the advantages of better classification performance of nonparallel hyperplane second-order cone programming support vector machine (SOCP-NHSVM), and represents SOCP-NHSVM as a convex quadratic nonparallel hyperplane circular cone programming support vector machine (CQCCP-NHSVM), and finally uses the projection and contraction method to solve it. Experiments on the benchmark dataset of the UCI repository show that the proposed method can improve the computational efficiency and obtain the accuracy value, F-measure value and G-mean value, which are similar to the SOCP-NHSVM of the linear classifier. In the case of kernel-based nonlinear classification, the proposed method can achieve similar performance under three model evaluation indexes, and greatly shorten the running time of the program. Full article

In this paper, we introduce and study a Szász-type family of positive linear operators generated by Euler polynomials of negative order on $[0,\infty )$. The construction is based on an explicit finite representation of these polynomials with non-negative terms, which ensures the positivity of the corresponding kernel. We prove the basic properties of the operators and show that they can be represented as finite convex combinations of shifted classical Szász operators. We also provide a probabilistic representation of the kernel as a finite mixture of Poisson distributions, which clarifies the role of the parameter k and the resulting moment structure. The corresponding algebraic and central moment identities are derived and used to establish convergence on compact intervals and to obtain quantitative estimates in terms of the modulus of continuity, Lipschitz-type classes, and Peetre’s K-functional. Furthermore, Voronovskaya-type asymptotic results are obtained, including a quantitative form and a second-order asymptotic formula. Numerical tables and a graphical illustration are presented for selected test functions and parameter values, and the results are consistent with the theoretical convergence behaviour. The paper shows that Euler polynomials of negative order provide a positive and structurally tractable framework for constructing Szász-type approximation operators on the positive real axis. Full article

Unmanned aerial vehicle (UAV)-assisted millimeter-wave (mmWave) and terahertz (THz) communications are promising enablers of ultra-reliable and low-latency communication in next-generation wireless networks. However, the initial access and beam alignment process remains challenging because highly directional beams must be rapidly aligned in a three-dimensional environment. In this paper, we investigate a risk-aware beam alignment framework for UAV-assisted mmWave/THz systems, where user equipment scans a 3D spherical region to detect UAV base stations. The objective is to jointly minimize the expected cell-search latency and its variance while satisfying detection-failure and link-quality constraints. To solve this non-convex optimization problem efficiently, we employ the Lévy Self-Renewable Flow Direction Algorithm (LSRFDA), which combines Lévy-flight exploration with self-renewal to improve convergence robustness. A unified propagation model is adopted to cover both mmWave and THz regimes by incorporating free-space spreading loss and frequency-dependent molecular absorption. Extensive Monte Carlo simulations compare the proposed approach with Particle Swarm Optimization, Random Search, Reinforcement Learning, and PPO-Lagrangian methods. The results show that LSRFDA achieves lower latency, lower latency variation, more reliable detection, and lower energy consumption across a wide range of UAV densities and coverage radii. These outcomes highlight the effectiveness of risk-aware geometric optimization for fast and dependable initial access in UAV-assisted 5G mmWave and 6G THz networks. Full article

Compressed sensing (CS) and matrix completion algorithms (MCA) have each introduced sparse and low-rank priors into synthetic aperture radar (SAR) imaging. However, their combined use reveals a fundamental zero-sum trade-off: enhancing spatial continuity tends to obscure weak targets, while strengthening sparse recovery amplifies off-grid artifacts. This inherent conflict is further exacerbated by static regularization, which imposes a rigid global compromise and prevents genuine synergy between the two priors. To overcome this limitation, this paper proposes a Spatio-Temporal Adaptive Synergistic Constraint Imaging (STASCI) algorithm, which dynamically balances the two priors in a scene-aware manner. The core of STASCI is a unified regularization framework. The low-rank constraint models’ spatial continuity in the background to suppress off-grid artifacts. The sparse constraint, enhanced by a non-convex Geman-McClure function, is employed to detect weak targets and compensate for detail loss. A key innovation is a spatio-temporal dual-dimensional regularization mechanism that employs Sobel operators to probe local spatial gradients and dynamically adjusts the strength of each prior according to regional scene characteristics. This enables adaptive synergy rather than a fixed trade-off. The optimization is solved via the alternating direction method of multipliers (ADMM), with the low-rank subproblem accelerated by randomized singular value decomposition (RSVD). Final imaging is performed using the Range Migration Algorithm (RMA). Experiments on real measurements and public datasets demonstrate that STASCI breaks the conventional detail-background trade-off. It effectively suppresses off-grid artifacts while retaining weak targets, leading to significant improvements in imaging accuracy and robustness across complex scenarios. Full article

Low Earth orbit (LEO) satellite systems provide ubiquitous global connectivity for massive grant-free random access Internet of Things (IoT) applications. Full frequency reuse (FFR) improves spectrum efficiency in spectrum sharing scenarios but introduces severe adjacent beam and cross-system co-channel interference. Meanwhile, the high mobility of LEO satellites hinders accurate instantaneous channel state information (iCSI) acquisition, and random direction-of-arrival (DOA) estimation errors cause statistical CSI (sCSI) mismatch, which degrades beamforming performance and makes it difficult to balance transmission robustness, user fairness, and onboard computational complexity. To address these issues, we propose a low-complexity Hybrid Optimized Robust Beamforming (HORBA) algorithm. We first construct a robust joint optimization model to characterize the coupling effects of DOA errors, outdated CSI, and multi-dimensional interference, with constraints on per-user minimum SINR and cross-system interference temperature. Then, based on the block coordinate descent framework, we decouple the original non-convex problem into two convex subproblems, which are solved via generalized eigenvalue decomposition and first-order Taylor expansion, combined with an adaptive sampling mechanism that balances accuracy and complexity. Simulation results verify that our algorithm outperforms typical benchmarks in sum rate and robustness, maintains low onboard processing complexity, and effectively alleviates edge user rate polarization. Full article

This paper presents a mathematical reinterpretation of virtual multi-vector synthesis defined over finite vector sets. Unlike conventional approaches that treat multi-vector synthesis as an algorithmic technique, the proposed framework characterizes it as a structured problem combining convex geometry, combinatorial selection, and probabilistic averaging. First, it is shown that the set of all realizable virtual vectors coincides with the convex hull of a finite vector set, providing a geometric interpretation of the synthesis process. Based on this observation, a subset-based formulation is introduced, in which virtual vectors are constructed as averages over selected subsets. This formulation allows the synthesis problem to be interpreted as a combinatorial selection problem. Under a uniform subset selection model, closed-form expressions for the expectation and variance of the synthesized vectors are derived. In particular, it is demonstrated that the approximation behavior can be interpreted through the variance structure of subset-averaged vectors, and that increasing the subset size leads to a systematic reduction in variance. Furthermore, the trade-off between approximation accuracy and combinatorial complexity is analyzed, and the existence of an optimal subset size is established. The proposed framework provides a theoretical foundation for understanding multi-vector synthesis as a structured mathematical process, and offers a general perspective applicable to a wide class of approximation problems over finite vector sets. Full article

Operational Technology (OT) and Industrial Control Systems (ICSs) along the NATO-EU eastern flank face escalating hybrid threats, yet existing cyber-resilience metrics remain IT-centric, lacking OT-specific constraints and geopolitical exposure dimensions. This paper presents a Design Science Research contribution: the development and simulation-based feasibility demonstration of two interconnected artefacts. The first is the AI-enabled Cyber-Resilience Index (ACRI)—a composite 0–100 metric operationalized through 16 indicators across four domains (detection performance, operational continuity, governance maturity, supply-chain risk), aggregated as a three-term convex combination of capability domains with a linear subtractive supply-chain exposure penalty, weighted via AHP-based illustrative sector-reference profiles. The second is the Unified Compliance Framework (UCF), a structured R → C → E → SLO mapping linking 47 atomic regulatory requirements (NIS2, DORA, CER, AI Act, CRA) to standards (IEC 62443, ISO/IEC 27001) and auditable evidence artifacts, with a Continuous Assurance Loop operationalizing continuous control monitoring. Feasibility is demonstrated through digital twin simulation under three OT-representative threat scenarios (energy SCADA APT, railway supply-chain compromise, manufacturing ransomware). Results in simulated environments show ACRI improvement from Moderate-Risk baselines (45–61) to Adequate-Resilience thresholds (65–73); the proposed federated autoencoder–LSTM detector attains a composite $D_{perf}$ of 0.883 versus 0.510 for a static ±3$\sigma$ threshold baseline (a 73% relative improvement at the domain level). Sensitivity analysis confirms classification robustness ($\pm 7.3\%$ weight perturbation; coefficient of variation below 9.1% across 10,000 Monte Carlo iterations). Critical limitations are explicit: simulation-only evidence ($n=12$ scenario instances), illustrative (non-empirical) AHP weights, no operational field validation, and limited inferential statistical power. instances), illustrative (non-empirical) AHP weights, no operational field validation, and limited inferential statistical power. The contribution is positioned as a proof-of-concept design artifact establishing methodological foundations for OT-centric resilience assessment and compliance-to-engineering traceability, not as a field-validated operational system. Full article

Silicon micromachining serves as the foundational enabling technology for high-precision MEMS inertial sensors. However, the relentless pursuit of enhanced sensitivity and multi-functionality in emerging applications encounters a fundamental bottleneck when confined to two-dimensional scaling. The evolution toward complex three-dimensional (3D) stacking architectures is an inevitable trajectory for devices including MEMS inertial sensors, yet performance is constrained by the limitations of conventional processes in fabricating and integrating intricate 3D hollow structures. Specifically, uniformity in large-area deep silicon etching, structural integrity of convex corners in wet etching, and residual stress induced by multi-layer wafer bonding have emerged as critical, shared challenges. To address these issues, this paper proposes a triple-layer wafer-level stacking scheme that synergistically combines wet/dry hybrid etching with low-temperature adhesive bonding. This stacking scheme incorporates an innovative linear compensation model for wet-etched convex corners, enabling high-precision fabrication of complex corner structures under deep etching conditions. Furthermore, a collaborative strategy involving temporary bonding and plasma flow-field optimization improves the uniformity and integrity of dry etching for large perforated structures. A low-temperature triple-layer wafer-level stacking process is developed, encompassing precise adhesive dispensing, optical alignment, and a stepped low-temperature curing profile, thereby achieving highly symmetric 3D integration with controlled adhesive distribution. The efficacy of this stacking scheme is validated through the fabrication of a symmetrically stacked triple-layer MOEMS accelerometer sensing element. Test results demonstrate a noise floor as low as 0.40 µg/√Hz and a bias instability of 1.81 µg over 10 min. Compared with a double-layer counterpart, improved performance is obtained. The wafer-level stacking scheme established in this work not only provides a viable pathway for pushing the manufacturing limits of high-precision inertial devices but also offers a generic methodology for tackling complex hollow structure formation and low-temperature integration, holding referential value for broader applications in high-precision 3D microsystems. Full article

Reconfigurable intelligent surface (RIS)-assisted unmanned aerial vehicle (UAV)-enabled mobile edge computing (MEC) has become an effective architecture for supporting computation-intensive and latency-sensitive applications by enabling flexible deployment and enhanced wireless coverage. However, when non-orthogonal multiple access (NOMA) is incorporated, the joint optimization of computation offloading, wireless resource allocation, RIS phase configuration, and UAV trajectory design becomes highly challenging owing to the strong coupling among decision variables, problem non-convexity, and time-varying system dynamics. To address these challenges, this paper investigates the energy consumption minimization problem in a NOMA-based RIS-assisted UAV-MEC system by jointly optimizing user offloading ratios, transmit power, UAV computing resource allocation, and flight trajectory. A long short-term memory (LSTM)-embedded proximal policy optimization (PPO) algorithm is developed to capture the temporal dependencies of system states and enable adaptive decision-making in dynamic environments. In addition, a closed-form phase conjugation-based optimal RIS configuration is derived and incorporated into the environment model to reduce the action space and improve training efficiency. The simulation results show that the proposed LSTM-PPO method converges faster and achieves lower energy consumption than conventional PPO, deep deterministic policy gradient (DDPG), and fixed offloading schemes, while exhibiting improved stability and scalability in the tested multi-user scenarios. These results demonstrate the effectiveness of combining temporal learning and model-assisted RIS optimization for energy efficient resource management in RIS-assisted UAV-MEC systems. Full article

In this paper, we investigate secrecy energy efficiency (SEE) maximization in a rate-splitting multiple access (RSMA)-enabled UAV communication system, which consists of a communication UAV serving legitimate ground users (GUs) and a cooperative jamming UAV transmitting jamming signals to degrade the channel of the eavesdropper (Eve). Taking into account the propulsion energy consumption of fixed-wing UAVs, we formulate a non-convex SEE maximization problem by jointly optimizing communication scheduling, CUAV transmit power, and the trajectories of both UAVs. To tackle the non-convex problem, an iterative optimization algorithm combined with the Dinkelbach method and successive convex approximation (SCA) is developed to obtain a suboptimal solution. Simulation results demonstrate the convergence of the proposed algorithm and show the proposed joint optimization scheme significantly improves SEE compared with benchmark schemes. Full article

In this paper, certain subclasses of meromorphic harmonic functions which are formulated using a q-differential operator are meticulously analyzed. Initially, two new subclasses $W_H^q(k;E,F)$ and $W_{\eta }^q(k;E,F)$ associated with the Janowski function with relevance to the idea of weak subordination are defined. These classes are further studied through their various analytical and geometric properties. Some of these explored properties include the necessary and sufficient coefficient condition, the radii of starlikeness, characterizations of extreme points, distortion estimation, closeness under convolution, and convex combination features. Additionally, the asymptotic behavior of the coefficients is also examined, and to express the findings, the Big-O, little-o, and asymptotic equivalency notations are used. These findings significantly represent the interaction between the growth, dominant terms, and limiting behavior of functions within these subclasses. Full article