Search Results (11)

The medial longitudinal arch is fundamental to weight distribution, balance, and lower limb biomechanics, and its evaluation is important for identifying abnormalities such as flatfoot or high arch. Traditional clinical methods for assessing the foot arch index (FAI) are often constrained by limited accessibility and inconsistent accuracy. To overcome these limitations, this study proposes a deep learning-based plantar pressure measurement system (DLPPMS) designed for accurate and affordable static foot arch evaluation. The system integrates two resistive pressure sensor arrays combined into a 24 × 24 matrix to acquire plantar pressure data in real time. To enhance spatial resolution and improve the fidelity of pressure distribution, Bessel interpolation is employed to generate smooth, high-resolution plantar pressure maps. Deep learning-based pose estimation and instance segmentation models are further applied to isolate the plantar region and identify anatomical keypoints relevant for FAI computation. The system was validated on participants with flatfoot, normal arch, and high arch conditions, demonstrating high segmentation accuracy, reliable keypoint localization, and consistent FAI estimation with minimal error compared to reference values. These results confirm that the DLPPMS provides accurate, repeatable, and low-cost assessment of the medial longitudinal arch under static conditions. Overall, this work highlights the potential of combining pressure sensing, interpolation algorithms, and deep learning into a portable and scalable system, offering promising applications not only for clinical diagnostics but also for biomechanical research, preventive healthcare, and rehabilitation monitoring. Full article

This paper develops novel results in the harmonic analysis of Bessel operators, extending their theory to higher-dimensional and non-Euclidean spaces. We present a refined framework for Hardy spaces associated with Bessel operators, emphasizing atomic decompositions, dual spaces, and connections to Sobolev and Besov spaces. The spectral theory of families of boundary-interpolating operators is also expanded, offering precise eigenvalue estimates and functional calculus applications. Furthermore, we explore Bessel operators under non-standard measures, such as fractal and weighted geometries, uncovering new analytical phenomena. Key implications include advanced insights into singular integrals, heat kernel behavior, and the boundedness of Riesz transforms, with potential applications in fractal geometry, constrained wave propagation, and mathematical physics. Full article

Traditional spherical sector microphone arrays using omnidirectional microphones face limitations in modal strength and spatial resolution, especially within spherical sector configurations. This study aims to enhance array performance by developing a spherical sector array employing first-order cardioid microphones. A model based on spherical sector harmonic (SSH) functions is introduced to extend the benefits of spherical harmonics to sector arrays. Modal strength analysis demonstrates that cardioid microphones in open spherical sectors enhance nonzero-order strengths and eliminate the nulls associated with spherical Bessel functions. We find that the spatial resolution of spherical cap arrays depends on the array’s maximum order and the limiting polar angle, but is independent of the microphone gain pattern. We assess direction-of-arrival (DOA) estimation performance for coherent wideband sources using the array manifold interpolation method, and compare cardioid and omnidirectional arrays through simulations in both open and rigid hemispherical configurations. The results indicate that cardioid arrays outperform omnidirectional ones on DOA estimation tasks, with performance improving alongside increased microphone directivity in the open hemispherical configuration. Specifically, hypercardioid microphones yielded the best results in the open configuration, while subcardioid microphones (without nulls) were optimal in rigid configurations. These findings demonstrate that spherical sector arrays of first-order cardioid microphones offer improved modal strength and DOA estimation capabilities over traditional omnidirectional arrays, providing significantly enhancing performance in spherical sector array processing. Full article

This paper introduces a novel approach to bipedal robot gait generation by proposing a higher-order form through the parameter equation of first-order Bessel interpolation. The trajectory planning for the bipedal robot, specifically for stepping up or down stairs, is established based on a three-dimensional interpolation equation. The experimental prototype, Roban, is utilized for the study, and the structural sketch of a single leg is presented. The inverse kinematics expression for the leg is derived using kinematic methods. Employing a position control method, the angle information is transmitted to the robot’s joints, enabling the completion of both downstairs simulation experiments and physical experiments with the Roban prototype. The analysis of the experimental process reveals a noticeable phenomenon of hip and ankle joint tilting in the robot. This observation suggests that low-cost bipedal robots driven by servo motors exhibit low stiffness characteristics in their joints. Full article

Providing an accurate spatiotemporal distribution of rainfall and filling data gaps are pivotal for effective water resource management. This study focuses on the Asir region in the southwest of Saudi Arabia. Given the limited accuracy of satellite data in this arid/mountain-dominated study area, geospatial interpolation has emerged as a viable alternative approach for filling terrestrial records data gaps. Furthermore, the irregularity in rain gauge data and the yearly spatial variation in data gaps hinder the creation of a coherent distribution pattern. To address this, the Centered Root Mean Square Error (CRMSE) is employed as a criterion to select the most appropriate geospatial interpolation technique among 51 evaluated methods for maximum and total yearly precipitation data. This study produced gap-free maps of total and maximum yearly precipitation from 1966 to 2013. Beyond 2013, it is recommended to utilize ordinary Kriging with a J-Bessel semivariogram and simple Kriging with a K-Bessel semivariogram to estimate the spatial distribution of maximum and total yearly rainfall depth, respectively. Additionally, a proposed methodology for allocating additional rain gauges to improve the accuracy of rainfall spatial distribution is introduced based on a cross-validation error (CVE) assessment. Newly proposed gauges in the study area resulted in a significant 21% CVE reduction. Full article

In modern applications such as robotics, autonomous vehicles, and speaker localization, the computational power for sound source localization applications can be limited when other functionalities get more complex. In such application fields, there is a need to maintain high localization accuracy for several sound sources while reducing computational complexity. The array manifold interpolation (AMI) method applied with the Multiple Signal Classification (MUSIC) algorithm enables sound source localization of multiple sources with high accuracy. However, the computational complexity has so far been relatively high. This paper presents a modified AMI for uniform circular array (UCA) that offers reduced computational complexity compared to the original AMI. The complexity reduction is based on the proposed UCA-specific focusing matrix which eliminates the calculation of the Bessel function. The simulation comparison is done with the existing methods of iMUSIC, the Weighted Squared Test of Orthogonality of Projected Subspaces (WS-TOPS), and the original AMI. The experiment result under different scenarios shows that the proposed algorithm outperforms the original AMI method in terms of estimation accuracy and up to a 30% reduction in computation time. An advantage offered by this proposed method is the ability to implement wideband array processing on low-end microprocessors. Full article

A study was conducted at Kalamandari Tanda-1 micro-watershed, Karnataka, India, to assess the spatio-temporal variability of surface soil properties sampled from 23 varied soil-phase units, delineated using IRS P6 LISS-IV merged Cartosat-I imagery (2.5 m spatial resolution). Three sets of surface soil samples (231 in each set) were collected, analyzed, and interpolated to evaluate the soil spatio-temporal variability. Further soil-phase-wise composite representative samples (23 in each set) were collected before the sowing and after the harvest of pigeon peasin January 2019 and 2020. Results showed that the soil OC with N, Mg with Ca, exchangeable sodium percentage (ESP), and cation exchange capacity (CEC) with Mn and K₂O have a significantly positive association (p < 0.01) during both years. Similarly, a significantly positive association (p < 0.05) was observed among soil OC and N with Cu, Mn with CEC, and Zn with Fe, while a negative association was seen between available P₂O₅ and Na. Skewness from descriptive statistics revealed that pH, EC, Cu, Mg, B, and ESP distribution varied temporally, whereas other parameters remained almost unchanged. Geo-statistically, the spatial distribution of measured soil properties was best fitted to exponential, stable, and K-Bessel models. The available N in 2018 and the ESP in 2019 have shown weak spatial dependency, whereas the rest of the soil parameters showed moderate and strong spatial dependency. These interpolated maps were exported as vector layers to quantify soil-phase-wise spatio-temporal variability of soil properties. Full article

The article describes a multi-grid algorithm for integrating the Reynolds equation for hydrodynamic pressures in the lubricating film of a heavy-loaded journal bearing. This equation is the basic one in solving the tasks of designing friction units of piston- and rotary machines. Lubrication sources of various configurations in the form of grooves and holes located on the friction surfaces were taken into account. The version of the multi-grid algorithm developed by the authors is based on Brandt’s work. At each level of grids, not only the convergence of the solution is controlled, but also the rate of convergence. The pressure equation was approximated by finite differences using the control volume method and passed to a system of algebraic equations, which were solved by the Seidel method. Bessel formulas were used as the interpolation operator. The function for taking into account the non-Newtonian properties of the lubricant is based on the power law. Comparison of the developed algorithm with other versions showed high efficiency. The use of multi-grid algorithms makes it possible to perform multi-variant calculations of the dynamics of heavily loaded bearings. As a result of the calculations, the characteristics of the connecting rod bearing of the heat engine, as well as the multilayer bearing of the turbocharger, are presented. Full article

In this paper, through complex analysis, the convergence rate is given on a quadrature of a Fourier integral with symmetrical Jacobi weight. The interpolation nodes of this quadrature formula are expressed by the frequency, and the coefficients can be expressed by the Bessel function. When the frequency is close to 0, the nodes are close to those in the Gauss quadrature. When the frequency tends to infinity, the nodes tend symmetrically to the two ends of the integrand. The higher the frequency is, the higher the accuracy of this quadrature will be. Numerical examples are provided to illustrate the theoretical results. Full article

A predictive guidance obstacle avoidance algorithm (PGOA) in unknown environments is proposed for autonomous underwater vehicle (AUV) that must adapt to multiple complex obstacle environments. Using the environmental information collected by the Forward-looking Sonar (FLS), the obstacle boundary is simplified by the convex algorithm and Bessel interpolation. Combining the predictive control secondary optimization function and the obstacle avoidance weight function, the predicting obstacle avoidance trajectory parameters are obtained. According to different types of obstacle environments, the corresponding obstacle avoidance rules are formulated. Lastly, combining with the obstacle avoidance parameters and rules, the AUV’s predicting obstacle avoidance trajectory point is obtained. Then AUV can successfully achieve obstacle avoidance using the guidance algorithm. The simulation results show that the PGOA algorithm can better predict the trajectory point of the obstacle avoidance path of AUV, and the secondary optimization function can successfully achieve collision avoidance for different complex obstacle environments. Lastly, comparing the execution efficiency and cost of different algorithms, which deal with various complex obstacle environments, simulation experiment results indicate the high efficiency and great adaptability of the proposed algorithm. Full article

In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods. Full article