Search Results (371)

This paper investigates the problem of identifying a time-dependent source term in distributed-order time-space fractional diffusion equations (FDEs) based on boundary observation data. Firstly, the existence, uniqueness, and regularity of the solution to the direct problem are proved. Using the regularity of the solution and a Gronwall inequality with a weakly singular kernel, the uniqueness and stability estimates of the solution to the inverse problem are obtained. Subsequently, the inverse source problem is transformed into a minimization problem of a functional using the Tikhonov regularization method, and an approximate solution is obtained by the conjugate gradient method. Numerical experiments confirm that the method provides both accurate and robust results. Full article

The geometric distribution of seabed beacons significantly impacts the positioning accuracy of underwater acoustic navigation systems. To address this challenge, we propose a depth-constrained adaptive stochastic model optimization method based on singular value decomposition (SVD). The method quantifies the contribution weights of each beacon to the dominant navigation direction by performing SVD on the acoustic observation matrix. The acoustic ranging covariance matrix can be dynamically adjusted based on these weights to suppress error propagation. At the same time, the prior depth with centimeter-level accuracy provided by the pressure sensor is used to establish strong constraints in the vertical direction. The experimental results demonstrate that the depth-constrained adaptive stochastic model optimization method reduces three-dimensional RMS errors by 66.65% (300 m depth) and 77.25% (2000 m depth) compared to conventional equal-weight models. Notably, the depth constraint alone achieves 95% vertical error suppression, while combined SVD optimization further enhances horizontal accuracy by 34.2–53.5%. These findings validate that coupling depth constraints with stochastic optimization effectively improves navigation accuracy in complex underwater environments. Full article

Vajrayāna teaching places the guru outside space and time, while simultaneously manifest in the teacher’s physical body. Those who regard Danzanravjaa primarily as a Buddhist teacher even today have his poems as a potent source of his teaching and consequently as a catalyst for their own spiritual development. But what can we hear across two centuries, and how can we actively listen to his religious teaching through his singular, aphoristic, and complex poetics? And to what extent can we understand today his nomadic perspective on Buddhist teaching in order better to understand the particular nature of Mongolian Buddhism? This paper will examine Danzanravjaa’s poetry in both Mongolian and Tibetan through the intertwining outer, inner, and secret levels of Tibeto-Mongolian Vajrayāna Buddhism, listening to how his poetic language and down-to-earth themes might have spoken to his contemporaries, as well as how they might speak to us today. In doing so, it presents Danzanravjaa’s poetry in a different light—not in terms of nineteenth century literature but as actionable spiritual wisdom from a teacher who, like any other, presents his own direct apprehension of Buddha nature in a challenging, personal style. Full article

The central singularity present in black hole (BH) spacetimes arising in the general theory of relativity (GR) can be avoided by using various methods. In the present work we have investigated the gravitational effect of one of such spacetime known as a black-bounce-Reissner–Nordström spacetime. We revisited its horizon structure along with first integrals of its geodesic equations. We derived the expressions for Newtonian radial acceleration for freely infalling neutral test particles. For the description of tidal effects, the geodesic deviation equations are derived and solved analytically as well as numerically. To be specific, in the numerical approach, we have opted for two initial conditions to elaborate on the evolution of geodesic deviation vectors in radial and angular directions. The corresponding nature of geodesic deviation vectors in radial and angular directions is then compared with the standard results such as Schwarzschild and Reissner–Nordström BHs in order to figure out the differences. Full article

In this study, ruled surfaces are examined where the direction vectors are unit vectors derived from Smarandache curves, and the base curve is taken as an adjoint curve constructed using the integral curve of a Smarandache-type curve generated from the first and second Bishop normal vectors. The newly generated ruled surfaces will be referred to as Bishop adjoint ruled surfaces. Explicit expressions for the Gaussian and mean curvatures of these surfaces have been obtained, and their fundamental geometric properties have been analyzed in detail. Additionally, the conditions for developability, minimality, and singularities have been investigated. The asymptotic and geodesic behaviors of parametric curves have been examined, and the necessary and sufficient conditions for their characterization have been derived. Furthermore, the geometric properties of the surface generated by the Bishop adjoint curve and its relationship with the choice of the original curve have been established. The constructed ruled surfaces exhibit a notable degree of geometric regularity and symmetry, which naturally arise from the structural behavior of the associated adjoint curves and direction fields. This underlying symmetry plays a central role in their formulation and classification within the broader context of differential geometry. Finally, the obtained surfaces are illustrated with figures. Full article

In time-sensitive aerial missions such as urban surveillance, emergency response, and adversarial airspace operations, achieving rapid and reliable formation control of multi-UAV systems is crucial. This paper addresses the challenge of ensuring robust and efficient formation control under stringent time constraints. The proposed singularity-free prescribed-time formation (PTF) control scheme guarantees task completion within a user-defined time, independent of initial conditions and control parameters. Unlike existing scaling-based prescribed-time methods plagued by unbounded gains and fixed-time strategies with non-tunable convergence bounds, the proposed scheme uses fixed-time stability theory and systematic parameter tuning to avoid singularity issues while ensuring robustness and predictable convergence. The method also accommodates directed communication topologies and unknown external disturbances, allowing follower UAVs to track a dynamic leader and maintain the desired geometric formation. Finally, some simulation results demonstrate the effectiveness of the proposed control strategy, showcasing its superiority over existing methods and validating its potential for practical applications. Full article

Global High-Resolution Land Cover Maps (GHRLCs), characterized by spatial resolutions higher than 30 m per pixel, have become essential tools for environmental monitoring, urban planning, and climate modeling. Over the past two decades, new GHRLCs have emerged, offering increasingly detailed and timely representations of Earth’s surface. This review provides an in-depth analysis of recent developments by examining the data sources, methodologies, and validation techniques utilized in 19 global binary and multi-class land cover products. The evolution of GHRLC production techniques is analyzed, starting from the use of singular source input data, such as multi-temporal remotely sensed optical imagery, to the integration of satellite radar and other geospatial data. The article highlights significant advances in data pre-processing and processing, showcasing a shift from classical methods to modern approaches, including machine learning (ML) and deep learning techniques (e.g., neural networks and transformers), and their direct application on powerful cloud-computing platforms. A comprehensive analysis of the temporal dimension of land cover products, where available, is conducted, highlighting a shift from decadal intervals to production intervals of less than a month. This review also addresses the ongoing challenge of land cover legend harmonization, a topic that remains crucial for ensuring consistency and comparability across datasets. Validation remains another critical aspect of GHRLC production. The methods used to assess map accuracy and reliability, including statistical techniques and visual inspections, are briefly discussed. The validation approaches adopted in recent studies are summarized, with an emphasis on their importance in maintaining data integrity and addressing emerging needs, such as the development of common validation datasets. Ultimately, this review aims to provide a comprehensive overview of the current state and future directions of GHRLC production and validation, highlighting the advancements that have shaped this rapidly evolving field. Full article

This paper proposes a weak Galerkin (WG) finite element method for solving a multi-dimensional evolution equation with a weakly singular kernel. The temporal discretization employs the backward Euler scheme, while the fractional integral term is approximated via a piecewise constant function method. A fully discrete scheme is constructed by integrating the WG finite element approach for spatial discretization. $L^2$-norm stability and convergence analysis of the fully discrete scheme are rigorously established. Numerical experiments are conducted to validate the theoretical findings and demonstrate optimal convergence order in both spatial and temporal directions. The numerical results confirm that the proposed method achieves an accuracy of the order $O\left(\tau +h^{k+1}\right)$, where $\tau$ and h represent the time step and spatial mesh size, respectively. This work extends previous studies on one-dimensional problems to higher spatial dimensions, providing a robust framework for handling evolution equations with a weakly singular kernel. Full article

The rapid emergence of the platform economy has accelerated the practice of embedded innovation, with ecosystem partner selection serving as a critical first step in platform enterprises’ innovation collaborations and playing a key role in enhancing innovation efficiency and outcomes. Based on the theory of embedded innovation, this study identifies the core innovation demands of platform enterprises at distinct stages. It then employs QFD to quantify decision indicator weights for ecosystem partner selection. By integrating Prospect Theory with Field Theory, this study develops both a decision evaluation model and an optimization model to achieve the optimal screening of ecosystem partners. Specifically, this study contributes in the following ways: (1) It constructs an embedded innovation direction selection model to uncover the evolving innovation demands at each stage. Within the QFD framework, we map these demands onto selection evaluation indicators, assess their importance via the maximum entropy principle, and determine indicator weights through a correlation matrix. (2) It proposes a Prospect Theory-based TOPSIS evaluation model, incorporating decision-makers’ psychological preferences to mitigate bias arising from singular or excessive risk attitudes. This model ranks potential partners according to their closeness to an ideal solution. Finally, (3) it designs a Field Theory-based optimization model that accounts for the platform enterprise’s perspective, partner-matching rationality, and continuity of interaction. This model emphasizes the complementarity and synergy of innovation resources to enhance cooperation fit and strategic alignment between the platform and its partners. Finally, this study conducts an empirical analysis on platform enterprise XM and validates the model’s feasibility and stability through sensitivity testing and comparative analyses. This study enriches the understanding of ecosystem partner selection within platform ecosystems by advancing methods for quantifying partner demands and refining the selection of evaluation indicators. It also deepens the depiction of non-rational characteristics in behavioral decision-making and elucidates the mechanisms underlying the ongoing interactions between platform enterprises and their ecosystem partners. These theoretical contributions not only extend the scope of research on platform ecosystems and embedded innovation but also provide feasible approaches for platform enterprises to improve partner governance and foster collaborative innovation in dynamic and complex environments. Ultimately, the findings offer strong support for enhancing innovation performance and building sustainable competitive advantages. Full article

An estimate of the trigger effect of the proton flux on seismicity was obtained. The proton flux time series with a time step of 5 min, 2000–2024, was analyzed. In each time interval of 5 days, statistics of the proton flux time series were calculated: mean values, logarithm of kurtosis, spectral slope, singularities spectrum support width, wavelet-based entropy, and the Donoho–Johnston wavelet-based index. For each of the used statistics, time points of local extrema were found, and for each pair of time sequences of proton flux statistics and earthquakes with a magnitude of at least 6.5 in sliding time windows, the “advance measures” of each time sequence relative to the other were estimated using a model of the intensity of interacting point processes. The difference between the “direct” measure of the advance of time points of local extrema of proton flux statistics relative to the time moments of earthquakes and the “inverse” measure of the advance was calculated. The maximum proportion of the intensity of seismic events for which the proton flux was a trigger was estimated as 0.28 for using the points of the local minima of the singularities spectrum support width. Full article

Task prioritization for inverse kinematics can be a powerful tool for realizing objectives in robot manipulation. This is particularly true for robots with redundant degrees of freedom, but it can also help address a debilitating singularity in six-axis robots. A roll-pitch-roll wrist is especially problematic for any six-axis robot because it produces a “gimbal-lock” singularity in the middle of the wrist workspace when the roll axes align. A task priority methodology can be used to realize only the achievable components of the commanded motion in the reduced operational space of a manipulator near singularities while phasing out the uncontrollable direction. In addition, this approach allows the operator to prioritize translation and rotation in the region of singularities. This methodology overcomes a significant drawback to the damped least-squares method, which can produce tool motion that deviates significantly from the desired path even in directions that are controllable. The approach used here reduces the operational space near the wrist singularity while maintaining full command authority over tool translation. The methodology is demonstrated in simulations conducted on a six degree-of-freedom Motoman MH250 manipulator. Full article

Dense Video Captioning (DVC) represents the cutting edge of advanced multimedia tasks, focusing on generating a series of temporally precise descriptions for events unfolding within a video. In contrast to traditional video captioning, which usually offers a singular summary or caption for an entire video, DVC demands the identification of multiple events within a video, the determination of their exact temporal boundaries, and the production of natural language descriptions for each event. This review paper presents a thorough examination of the latest techniques, datasets, and evaluation protocols in the field of DVC. We categorize and assess existing methodologies, delve into the characteristics, strengths, and limitations of widely utilized datasets, and underscore the challenges and opportunities associated with evaluating DVC models. Furthermore, we pinpoint current research trends, open challenges, and potential avenues for future exploration in this domain. The primary contributions of this review encompass: (1) a comprehensive survey of state-of-the-art DVC techniques, (2) an extensive review of commonly employed datasets, (3) a discussion on evaluation metrics and protocols, and (4) the identification of emerging trends and future directions. Full article

Compared to conventional single-aperture infrared cameras, the bio-inspired infrared compound eye camera integrates the advantages of infrared imaging technology with the benefits of multi-aperture systems, enabling simultaneous information acquisition from multiple perspectives. This enhanced detection capability demonstrates unique performance in applications such as autonomous driving, surveillance, and unmanned aerial vehicle reconnaissance. Current single-aperture small target detection algorithms fail to exploit the spatial relationships among compound eye apertures, thereby underutilizing the inherent advantages of compound eye imaging systems. This paper proposes a low-rank and sparse decomposition method based on bio-inspired infrared compound eye image features for small target detection. Initially, a compound eye structural weighting operator is designed according to image characteristics, which enhances the sparsity of target points when combined with the reweighted $l_1$-norm. Furthermore, to improve detection speed, the structural tensor of the effective imaging region in infrared compound eye images is reconstructed, and the Representative Coefficient Total Variation method is employed to avoid complex singular value decomposition and regularization optimization computations. Our model is efficiently solved using the Alternating Direction Method of Multipliers (ADMM). Experimental results demonstrate that the proposed model can rapidly and accurately detect small infrared targets in bio-inspired compound eye image sequences, outperforming other comparative algorithms. Full article

This paper presents a Finite Element Method (FEM) framework for solving the screened Poisson equation with a Dirac delta function as the forcing term. The singularity introduced by the delta function poses challenges for standard numerical methods, particularly in higher dimensions. To address this, we employ integrated Legendre basis functions, which yield sparse and structured system matrices characterized by a Banded-Block-Banded-Arrowhead ($B^3$-Arrowhead) form. In one dimension, the resulting linear system can be solved directly. In two and three dimensions, the equation can be efficiently solved using a generalized Alternating Direction Implicit (ADI) method combined with reverse Cholesky factorization. Numerical results in 1D, 2D, and 3D confirm that the method accurately captures the localized impulse response and reproduces the expected Green’s function behavior. The proposed approach offers a robust and scalable solution framework for partial differential equations with singular source terms and has potential applications in physics, engineering, and computational science. Full article

The planar parallel robots are widely employed in industrial applications due to simple geometry, few linkage interferences, and a large, reachable workspace. The symmetric geometry can bring significant convenience to parallel robots. The complexity of the mathematic models can be simplified since only one calculation method can be proposed to deal with various kinematic limbs in a parallel manipulator. The symmetric geometry can ease the assembly and maintenance procedures due to the modular design of linkages/joints. A novel 2-translation and 1-rotation (2T1R) parallel robot with symmetric geometry is proposed in this research. There is one closed loop in each kinematic limb, and 18 revolute joints are applied in its planar structure. Both the inverse and direct kinematic models are explored. The first-order relationship between robot inputs and outputs are constructed. Various singularity configurations are obtained based on the Jacobian matrix. The reachable workspace is resolved by the discrete spatial searching methodology, followed by the impacts originating from various linkages. The dexterity analysis of the parallel robot is conducted. Full article