Search Results (716)

Particle shape analysis is essential in sedimentological research, as it offers vital insights into the sedimentary environment and transport history. However, little is known about the particle shape variation across different sand fractions, as well as the differences between particle shape data based on volume and number weighting. In this study, we investigate the grain shape variation of different sand-sized particles (fine, medium, and coarse sand fractions) in aeolian dune (11 samples) and lake beach (12 samples) environments around Poyang Lake, China, using dynamic image analysis (DIA). The shape data results based on both volume-weighted and number-weighted methods reveal significant differences in shape parameters (circularity, symmetry, aspect ratio, and convexity) among different sand fractions, especially between coarse and fine sand. This highlights the critical need for size-fractionated analysis when employing particle shape as an environmental discriminant. By integrating 86 sets of published particle shape data from different depositional environments, we found that volume-weighted shape data has limited ability to differentiate beach and dune sands, although it distinguished the fluvial, desert dune, and coastal beach sand well. In contrast, number-weighted shape data effectively distinguished the beach and dune sands, as fine sand particles are typically transported in suspension during fluvial processes and in saltation during aeolian processes. This demonstrates the role of integrating both volume-weighted and number-weighted shape data in future studies to accurately distinguish sedimentary environments. Full article

The increasing deployment of islanded microgrids in disaster-prone and infrastructure-constrained regions has elevated the importance of resilient energy storage systems capable of supporting autonomous operation. Grid-forming energy storage (GFES) units—designed to provide frequency reference, voltage regulation, and black-start capabilities—are emerging as critical assets for maintaining both energy adequacy and dynamic stability in isolated environments. However, conventional storage planning models fail to capture the interplay between uncertain renewable generation, time-coupled operational constraints, and control-oriented performance metrics such as virtual inertia and voltage ride-through. To address this gap, this paper proposes a novel distributionally robust optimization (DRO) framework that jointly optimizes the siting and sizing of GFES under renewable and load uncertainty. The model is grounded in Wasserstein-metric DRO, allowing worst-case expectation minimization over an ambiguity set constructed from empirical historical data. A multi-period convex formulation is developed that incorporates energy balance, degradation cost, state-of-charge dynamics, black-start reserve margins, and stability-aware constraints. Frequency sensitivity and voltage compliance metrics are explicitly embedded into the optimization, enabling control-aware dispatch and resilience-informed placement of storage assets. A tractable reformulation is achieved using strong duality and solved via a nested column-and-constraint generation algorithm. The framework is validated on a modified IEEE 33-bus distribution network with high PV penetration and heterogeneous demand profiles. Case study results demonstrate that the proposed model reduces worst-case blackout duration by 17.4%, improves voltage recovery speed by 12.9%, and achieves 22.3% higher SoC utilization efficiency compared to deterministic and stochastic baselines. Furthermore, sensitivity analyses reveal that GFES deployment naturally concentrates at nodes with high dynamic control leverage, confirming the effectiveness of the control-informed robust design. This work provides a scalable, data-driven planning tool for resilient microgrid development in the face of deep temporal and structural uncertainty. Full article

Nonlinear robotic systems often operate under widely varying conditions that challenge traditional linear control approaches. The Linear Parameter-Varying (LPV) paradigm overcomes these limitations and offers a unifying framework by representing the system’s time-varying dynamics as a convex blend of linear models. This enables both controller and observer synthesis through convex optimization, while considering nonlinearities and time-dependent behavior. This paper presents a linear matrix inequality (LMI)-based methodology for simultaneous stabilization control and state estimation in robotic application within the LPV/polytopic setting. Parallel to controller design, the full-state estimation challenge posed by limited sensors in robotics is addressed. An LPV observer architecture, based on the Luemberger observer, is proposed. The simultaneous observer/controller gains synthesis is then reduced to an LMI feasibility problem. The efficacy of our approach is then demonstrated and illustrated through simulations. Full article

In this paper, we introduce two novel subclasses of analytic functions, namely, starlike and convex functions of Ma–Minda-type, associated with a newly proposed domain. We set sharp bounds on the basic coefficients of these classes and provide sharp estimates of the second- and third-order Hankel determinants, demonstrating the power of our analytic approach, the clarity of its results, and its applicability even in unconventional domains. Full article

The deployment of Federated Learning (FL) in edge environments is often impeded by system heterogeneity, non-independent and identically distributed (non-IID) data, and constrained communication resources, which collectively hinder training efficiency and scalability. To address these challenges, this paper presents FLEX-SFL, a flexible and efficient split federated learning framework that jointly optimizes model partitioning, client selection, and communication scheduling. FLEX-SFL incorporates three coordinated mechanisms: a device-aware adaptive segmentation strategy that dynamically adjusts model partition points based on client computational capacity to mitigate straggler effects; an entropy-driven client selection algorithm that promotes data representativeness by leveraging label distribution entropy; and a hierarchical local asynchronous aggregation scheme that enables asynchronous intra-cluster and inter-cluster model updates to improve training throughput and reduce communication latency. We theoretically establish the convergence properties of FLEX-SFL under convex settings and analyze the influence of local update frequency and client participation on convergence bounds. Extensive experiments on benchmark datasets including FMNIST, CIFAR-10, and CIFAR-100 demonstrate that FLEX-SFL consistently outperforms state-of-the-art FL and split FL baselines in terms of model accuracy, convergence speed, and resource efficiency, particularly under high degrees of statistical and system heterogeneity. These results validate the effectiveness and practicality of FLEX-SFL for real-world edge intelligent systems. Full article

In modern livestock production, obtaining accurate body weight measurements for pigs is essential for feeding management and economic assessment, yet conventional weighing is laborious and can stress animals. To address these limitations, we developed a contactless image-based pipeline that first uses BiRefNet for high-precision background removal and YOLOv11-seg to extract the pig dorsal mask from top-view RGB images; from these masks we designed and extracted 17 representative phenotypic features (for example, dorsal area, convex hull area, major/minor axes, curvature metrics and Hu moments) and included camera height as a calibration input. We then compared eight machine-learning and deep-learning regressors to map features to body weight. The segmentation pipeline achieved mAP₅₀–₉₅ = 0.995 on the validation set, and the XGBoost regressor gave the best test performance (MAE = 3.9350 kg, RMSE = 5.2372 kg, R² = 0.9814). These results indicate the method provides accurate, low-cost and computationally efficient weight prediction from simple RGB images, supporting frequent, noninvasive monitoring and practical deployment in smart-farming settings. Full article

The Yang local fractional setting provides the generalized framework to explore the non-differentiable mappings considering the local properties. Due to the dominance of these concepts, mathematicians have investigated multiple problems, including mathematical modelling, optimization, and inequalities. Incorporating these useful concepts, this study aims to derive Weddle-type integral inequalities within the context of fractal space. To achieve the intended results, we establish a new local fractional identity. By using this identity, the convexity property, the bounded property of mappings, the L-Lipschitzian property of mappings, and other famous inequalities, we develop numerous upper bounds. Additionally, we provide 2D and 3D graphical representations and numerous applications, which show the significance of our main findings. To the best of our knowledge, this is the first study concerning error inequalities of Weddle’s quadrature formulation within the fractal space. Full article

This paper examines the relationship between weak orthogonality and almost orthogonality for complete non-algebraic 1-types in weakly ordered minimal theories. A central element of our approach is the concept of neighborhoods, which encapsulate local properties of type realizations. This work contributes to a deeper understanding of the geometry of types in weakly ordered minimal theories and provides tools that may be applied in related model-theoretic contexts. Full article

This paper aims to discuss the positive mild solutions for nonlocal fractional variable exponent differential equations with concave and convex coefficients. Based on a specifically defined order cone, even under the influence of the $p(t)$-Laplacian operator and the fractional integral operator, we avoid making many assumptions on the nonlocal coefficient $\mathcal{A}$ and just require that $\mathcal{A}>0$ on a set of positive measures. Utilizing the fixed-point index theory on cones, some new results on the existence and multiplicity of positive mild solutions were obtained, which extend and enrich some previous research findings. Finally, numerical examples are used to verify the feasibility of our main results. Full article

In this paper, we study a class of optimization problems with separable constraint structures, characterized by a combination of convex and nonconvex constraints. To handle these two distinct types of constraints, we introduce a partial augmented Lagrangian function by retaining nonconvex constraints while relaxing convex constraints into the objective function. Specifically, we employ the Moreau envelope for the convex term and apply second-order variational geometry to analyze the nonconvex term. For this partial augmented Lagrangian function, we study its saddle points and establish their relationship with KKT conditions. Furthermore, second-order optimality conditions are developed by employing tools such as second-order subdifferentials, asymptotic second-order tangent cones, and second-order tangent sets. Full article

We consider first-order impulses for impulsive stochastic differential equations driven by fractional Brownian motion (fBm) with Hurst parameter $H\in ({\displaystyle \frac{1}{2}},1)$ involving a nonlinear $\varphi$-Laplacian operator. The system incorporates both state and derivative impulses at fixed time instants. First, we establish the existence of at least one mild solution under appropriate conditions in terms of nonlinearities, impulses, and diffusion coefficients. We achieve this by applying a nonlinear alternative of the Leray–Schauder fixed-point theorem in a generalized Banach space setting. The topological structure of the solution set is established, showing that the set of all solutions is compact, closed, and convex in the function space considered. Our results extend existing impulsive differential equation frameworks to include fractional stochastic perturbations (via fBm) and general $\varphi$-Laplacian dynamics, which have not been addressed previously in tandem. These contributions provide a new existence framework for impulsive systems with memory and hereditary properties, modeled in stochastic environments with long-range dependence. Full article

The theory of stochastic processes is the prominent part of advanced probability theory and very influential in various mathematical models having randomness. One of the potential aspects is to investigate the stochastic convex processes. Working in the following direction, this study explores the set-valued super-quadratic processes through a unified approach under the centre-radius order relation, which is a totally ordered relation. First, we discuss some captivating properties and important results, which serve as a criterion. Relying on the newly proposed class of super-quadratic processes, we develop several fundamental inequalities within the fractional framework. Moreover, we present some novel deductions to complement the theoretical results with the existing literature. Also, we have provided the graphical breakdown, applications to the means, information theory, and divergence measures of the main inequalities. Full article

In this paper, we extend the concept of dimension of sets to some general frameworks relative to a gauge function $\phi$, where two simultaneous dimensions are introduced. Unlike the classical cases where one dimension function is introduced based on the diameter power relative to the associated measure power, and where the gauge is a set-valued function or a measure in the majority of cases, we no longer assume this hypothesis. The introduced variant generalizes many existing cases, such as Haudorff, packing, Carathéodory, and Billingsley original variants. Many characteristics of the dimensions are investigated, such as bijectivity, convexity, monotony, asymptotic behavior, and fixed points. Full article

To meet the dual demands of 6G cellular networks for high spectral efficiency and environmental sensing, this paper proposes a full-duplex (FD) integrated sensing and communication (ISAC) dynamic resource allocation framework. At the heart of the framework lies a dynamic frame structure that can self-adapt the time-domain resource ratio between sensing and communication, designed to flexibly handle complex traffic demands. In FD mode, however, the trade-off between communication and sensing performance, exacerbated by severe self-interference (SI), morphs into a non-convex, NP-hard multi-objective optimization problem (MOP). To tackle this, we propose an Adaptive Hybrid Memetic Multi-Objective Grey Wolf Optimizer (AM-MOGWO). Finally, simulations were conducted on a high-fidelity platform that integrates 3GPP-standardized channels, which was further extended to a challenging multi-cell interference scenario to validate the algorithm’s robustness. AM-MOGWO was systematically benchmarked against standard Grey Wolf Optimizer (GWO), random search (RS), and the genetic algorithm (GA). Simulation results demonstrate that in both the single-cell and the more complex multi-cell environments, the proposed algorithm excels in locating the Pareto-optimal solution set, where its solution set significantly outperforms the baseline methods. Its hypervolume (HV) metric surpasses the second-best approach by more than 93%. This result quantitatively demonstrates the algorithm’s superiority in finding a high-quality set of trade-off solutions, confirming the framework’s high efficiency in complex interference environments. Full article

Quadratic programming (QP) formulations are widely used in optimal investment portfolio selection, a central problem in financial decision-making. In practice, asset allocation decisions operate at two interconnected levels: the strategic level, which allocates the budget across major asset classes, and the tactical level, which distributes the allocation within each class to individual securities or instruments. This study evaluates the Frank–Wolfe (FW) algorithm as a computationally alternative to a QP formulation implemented in CVXPY and solved using OSQP (CVXPY–OSQP solver) for tactical investment portfolio optimization. By iteratively solving a linear approximation of the convex objective function, FW offers a distinct approach to portfolio construction. A comparative analysis was conducted using a tactical portfolio model with a small number of stock assets, assessing solution similarity, computational running time, and memory usage. The results demonstrate a clear trade-off between the two methods. While FW can produce portfolio weights closely matching those of the CVXPY–OSQP solver at lower and feasible target returns, its solutions differ at higher returns near the limits of the feasible set. However, FW consistently achieved shorter execution times and lower memory consumption. This study quantifies the trade-offs between accuracy and efficiency and identifies opportunities to improve FW’s accuracy through adaptive iteration strategies under more challenging optimization conditions. Full article