Search Results (17)

In this paper, we first make and discuss a conjecture concerning Newtonian potentials in Euclidean n space which have all their mass on the unit sphere about the origin and are normalized to be one at the origin. The conjecture essentially divides these potentials into subclasses whose criteria for membership is that a given member has its maximum on the closed unit ball at most M and its minimum at least d. It then lists the extremal potential in each subclass, which is conjectured to solve certain extremal problems. In Theorem 1, we show the existence of these extremal potentials. In Theorem 2, we prove an integral inequality on spheres about the origin, involving so-called extremal potentials, which lends credence to the conjecture. Full article

Studying the Bernstein approximations for fuzzy functions is a new attempt. With the help of considering the support functions of fuzzy sets in which the weak* topology for the normed dual space is involved, we are able to approximate continuous fuzzy functions by considering the Bernstein polynomials for fuzzy functions. We first study the Bernstein approximations for the support functions of fuzzy sets. Using the concept of isometry between the metric spaces of fuzzy sets and the normed spaces of support functions of fuzzy sets, the Bernstein approximations for the support functions of fuzzy sets can naturally lead to the Bernstein approximations for continuous fuzzy functions. Full article

Purpose: Pickleball, the fastest-growing sport in the United States, has seen a rapid increase in participation across all age groups, particularly among older adults. However, the sport introduces specific risks for ocular injuries due to the unique dynamics of gameplay and the physical properties of the pickleball. This study aims to explore the mechanisms of pickleball-related eye injuries, utilizing finite element modeling (FEM) to simulate ocular trauma and better understand injury mechanisms. Methods: A multi-modal approach was employed to investigate pickleball-related ocular injuries. Finite element modeling (FEM) was used to simulate blunt trauma to the eye caused by a pickleball. The FEM incorporated detailed anatomical models of the periorbital structures, cornea, sclera, and vitreous body, using hyperelastic material properties derived from experimental data. The simulations evaluated various impact scenarios, including changes in ball velocity, angle of impact, and material stiffness, to determine the stress distribution, peak strain, and deformation in ocular structures. The FEM outputs were correlated with clinical findings to validate the injury mechanisms. Results: The FE analysis revealed that the rigid, hard-plastic construction of a pickleball results in concentrated stress and strain transfer to ocular structures upon impact. At velocities exceeding 30 mph, simulations showed significant corneal deformation, with peak stresses localized at the limbus and anterior sclera. Moreover, our results show a significant stress applied to lens zonules (as high as 0.35 MPa), leading to potential lens dislocation. Posterior segment deformation was also observed, with high strain levels in the retina and vitreous, consistent with clinical observations of retinal tears and vitreous hemorrhage. Validation against reported injuries confirmed the model’s accuracy in predicting both mild injuries (e.g., corneal abrasions) and severe outcomes (e.g., hyphema, globe rupture). Conclusions: Finite element analysis provides critical insights into the biomechanical mechanisms underlying pickleball-related ocular injuries. The findings underscore the need for preventive measures, particularly among older adults, who exhibit age-related vulnerabilities. Education on the importance of wearing protective eyewear and optimizing game rules to minimize high-risk scenarios, such as close-range volleys, is essential. Further refinement of the FEM, including parametric studies and integration of protective eyewear, can guide the development of safety standards and reduce the socio-economic burden of these injuries. Full article

With the help of support functions of fuzzy sets, we are able to embed some interesting families of fuzzy sets into Banach spaces. It is better to make the embedded Banach spaces as small as possible, which can be achieved by considering the weak* topology. In this case, the weak* continuity of support functions should be studied. The concept of a maximal embedding behavior is also presented in this paper, which shows the maximal subset satisfying the completeness. Full article

Bearings play a crucial role in the complex mechanical systems of ships, and their operational status is closely related to vibration signals. Therefore, analyzing bearing signals plays an important role in the field of fault diagnosis. In order to solve the problems of low accuracy and slow response speed in fault diagnosis through vibration signals at mixed speeds, this paper introduces an improved Simple Window Deep Convolutional Neural Network with Random Forest (SWDCNN-RF) model on traditional Wide Convolutional Neural Network (WDCNN). It was verified through the publicly available dataset of ball bearings from Western Reserve University in the United States. It was found that the improved model increased speed by 38.51% and accuracy from 97.5% to 99.6% at epoch = 50, and also achieved faster convergence and smaller fluctuations during training. This study is of great significance for determining the occurrence time and type of bearing faults, and provides criteria for reliability evaluation and fault diagnosis of equipment using bearings. Full article

The surface texture parameter is a real reflection of the surface topography, which is closely related to the tribological properties of the surface, and the study of the correlation between the surface texture parameter and wear resistance is of great significance in revealing the tribological influence mechanism of the surface and realising the functional manufacturing of the surface. This paper takes the ball-end milling surface as the research object, establishes the three-dimensional simulation model of the surface topography, and analyses the surface topography and the surface texture parameter change rule. Based on the improved correlation analysis model, the correlation characteristics between the surface texture parameters, and between the surface texture parameters and the relative wear rate of per unit sliding distance K_V, were investigated, and the prediction model of K_V was established based on the surface texture parameters Sku, Sa, Sxp, Sp, and Ssk, and the correctness of the model was verified by experiments. The study in this paper provides a new idea to further reveal the relationship between surface topographical features and wear resistance and to guide the functional manufacturing of surfaces. Full article

The Hausdorff distance between two closed sets has important theoretical and practical applications. Yet apart from finite point clouds, there appear to be no generic algorithms for computing this quantity. Because many infinite sets are defined by algebraic equalities and inequalities, this a huge gap. The current paper constructs Frank–Wolfe and projected gradient ascent algorithms for computing the Hausdorff distance between two compact convex sets. Although these algorithms are guaranteed to go uphill, they can become trapped by local maxima. To avoid this defect, we investigate a homotopy method that gradually deforms two balls into the two target sets. The Frank–Wolfe and projected gradient algorithms are tested on two pairs $(A,B)$ of compact convex sets, where: (1) A is the box $[-\mathbf{1},\mathbf{1}]$ translated by $\mathbf{1}$ and B is the intersection of the unit ball and the non-negative orthant; and (2) A is the probability simplex and B is the ${\ell }_1$ unit ball translated by $\mathbf{1}$. For problem (2), we find the Hausdorff distance analytically. Projected gradient ascent is more reliable than the Frank–Wolfe algorithm and finds the exact solution of problem (2). Homotopy improves the performance of both algorithms when the exact solution is unknown or unattained. Full article

Many diseases, such as stroke, arthritis, and spinal cord injury, can cause severe hand impairment. Treatment options for these patients are limited by expensive hand rehabilitation devices and dull treatment procedures. In this study, we present an inexpensive soft robotic glove for hand rehabilitation in virtual reality (VR). Fifteen inertial measurement units are placed on the glove for finger motion tracking, and a motor—tendon actuation system is mounted onto the arm and exerts forces on fingertips via finger-anchoring points, providing force feedback to fingers so that the users can feel the force of a virtual object. A static threshold correction and complementary filter are used to calculate the finger attitude angles, hence computing the postures of five fingers simultaneously. Both static and dynamic tests are performed to validate the accuracy of the finger-motion-tracking algorithm. A field-oriented-control-based angular closed-loop torque control algorithm is adopted to control the force applied to the fingers. It is found that each motor can provide a maximum force of 3.14 N within the tested current limit. Finally, we present an application of the haptic glove in a Unity-based VR interface to provide the operator with haptic feedback while squeezing a soft virtual ball. Full article

The use of fluoride (F) in the prevention of dental caries is established. However, a high amount of F intake during tooth development can cause dental fluorosis The aim of this study was to analyze variations in F concentrations in chocolate bars (CB), chocolate cookies (CC), infant cereals (IC), and chocolate milk drinks (CD) to determine the daily intake of F from different sources by children at the age of risk for developing dental fluorosis. Distinct brands of CB, CC, IC, and CD were analyzed. Fluoride was separated by hexamethyldisiloxane-facilitated diffusion. Analysis was made in triplicate with an F ion-specific electrode. F ingestion (mg/kg body weight) was evaluated with the suggested consumption (0.05–0.07 mg/kg/day) for children aged 24 months (12 kg). The concentrations for all the analyzed products ranged from 0.025 to 1.827 µg/g F. The mean (range) F concentrations were CB= 0.210 ± 0.205 µg/g (0.073–0.698, n = 8), CC = 0.366 ± 0.416 µg/g (0.320–1.827, n = 9), IC = 0.422 ± 0.395 µg/g (0.073–1.061, n = 5), and CD = 0.169 ± 0.170 µg/mL (0.025–0.443, n = 12). The products that had the highest concentration in the categories CB, CC, IC, and CD, respectively, were Nescau-Ball (0.698 µg/g), Passatempo (1.827 µg/g), Milnutri (1.061 µg/g), and Toddynho (0.443 µg/mL). The consumption of only one unit of Toddynho (CD) is equivalent to more than 11% of the maximum suggested daily intake for a 24-month-old child (0.07 mg/kg body weight). When one product from each category is consumed together only once a day, this consumption is equivalent to approximately 24% of the suggested daily intake of fluoride for a 24-month-old child. The presence of high levels of fluoride in certain products suggests that they play a significant role in overall fluoride intake. It is crucial to closely monitor the fluoride content of food and drinks that are consumed by children who are at risk for dental fluorosis, and for product labels to clearly display the fluoride concentrations. Full article

The faces of the unit ball of a finite-dimensional Banach space are automatically closed. The situation is different in the infinite-dimensional case. In fact, under this last condition, the closure of a face may not be a face. In this paper, we discuss these issues in an expository style. In order to illustrate the described situation we consider an equivalent renorming of the Banach space ${\ell }_1.$ Full article

Cageless ball bearings with discrete grooves in the outer raceway enable the dispersion of rolling elements. Once worn, the discrete groove can cause the rolling element to discretely fail. This paper presents the discrete element method to investigate the wear of discrete grooves in cageless bearings from the standpoint of bond fracture. In conjunction with the structural characteristics of bearing races with discrete slots, we propose a hexagonal close-spaced spherical particle arrangement, in which the discrete slots are discretized into particles of the same size that are connected by bonds. The contact model and contact force equation between the rolling elements and the aggregate elements are established, and the external force on the aggregate elements is calculated. Under the influence of an external force and the arrangement of particles in the aggregate element, the internal force transfer equation of different layers and different particles is derived, and the internal force of the particles in the aggregate unit is calculated. In accordance with Hertz–Mindline theory, the bonding model of discrete groove particles is established, the size of the particle shedding cohesive force during bond fracture is determined, and the wear degree of discrete grooves is characterized by comparing the cohesive force and internal force. Numerical solutions and wear tests are combined. Bond fracture can accurately characterize the wear of discrete grooves. This approach offers theoretical guidance for cageless bearing design. Full article

To solve the trajectory tracking control problem for a class of nonlinear systems with time-varying parameter uncertainties and unknown control directions, this paper proposed a neural sliding mode control strategy with prescribed performance against event-triggered disturbance. First, an enhanced finite-time prescribed performance function and a compensation term containing the Hyperbolic Tangent function are introduced to design a non-singular fast terminal sliding mode (NFTSM) surface to eliminate the singularity in the terminal sliding mode control and speed up the convergence in the balanced unit-loop neighborhood. This sliding surface guarantees arbitrarily small overshoot and fast convergence speed even when triggering mistakes. Meanwhile, we utilize the Nussbaum gain function to solve the problem of unknown control directions and unknown time-varying parameters and design a self-recurrent wavelet neural network (SRWNN) to handle the uncertainty terms in the system. In addition, we use a non-periodic relative threshold event-triggered mechanism to design a new trajectory tracking control law so that the conventional time-triggered mechanism has overcome a significant resource consumption problem. Finally, we proved that all the closed-loop signals are eventually uniformly bounded according to the stability analysis theory, and the Zeno phenomenon can be eliminated. The method in this paper has a better tracking effect and faster response and can obtain better control performance with lower control energy than the traditional NFTSM method, which is verified in inverted pendulum and ball and plate system. Full article

We characterize the extreme points of the closed unit ball of the dual of a Banach space which are preserved by the adjoint of any extreme operator. The result is related to the structure topology introduced by Alfsen and Effros on the set of all extreme points in the dual of any Banach space. As a consequence, we prove that $c_0\left(I\right)$ is the only Banach space such that the adjoint of every extreme operator taking values into it preserves extreme points. Full article

Bacillus cereus foodborne intoxications and toxicoinfections are on a rise. Usually, symptoms are self-limiting but occasionally hospitalization is necessary. Severe intoxications with the emetic Bacillus cereus toxin cereulide, which is notably resistant heat and acid during cooking, can cause acute liver failure and encephalopathy. We here present a case series of food poisonings in five immunocompetent adults after ingestion of fried rice balls, which were massively contaminated with Bacillus cereus. The patients developed a broad clinical spectrum, ranging from emesis and diarrhoea to life-threatening acute liver failure and acute tubular necrosis of the kidney in the index patient. In the left-over rice ball, we detected 8 × 10⁶Bacillus cereus colony-forming units/g foodstuff, and cereulide in a concentration of 37 μg/g foodstuff, which is one of the highest cereulide toxin contaminations reported so far from foodborne outbreaks. This report emphasizes the potential biological hazard of contaminated rice meals that are not freshly prepared. It exemplifies the necessity of a multidisciplinary approach in cases of Bacillus cereus associated food poisonings to rapidly establish the diagnosis, to closely monitor critically ill patients, and to provide supportive measures for acute liver failure and—whenever necessary—urgent liver transplantation. Full article

In this work, we introduced fabrication and interrogation of simple and highly sensitive fiber-optic refractive index (RI) sensors based on ball resonators built on the tip of single-mode fibers. The probes have been fabricated through a CO₂ fiber splicer, with a fast (~600 s) and repeatable method. The ball resonator acted as a weak interferometer with a return loss below −50 dB and was interrogated with an optical backscatter reflectometer measuring the reflection spectrum. The ball resonators behaved as weak interferometers with a shallow fringe and a spectrum that appeared close to a random signal, and RI sensitivity could be measured either through wavelength shift or amplitude change. In this work, we reported four samples having sensitivity ranges 48.9–403.3 nm/RIU and 256.0–566.2 dB/RIU (RIU = refractive index unit). Ball resonators appeared as a sensitive and robust platform for RI sensing in liquid and can be further functionalized for biosensing. Full article