h-Said-Ball基与h-Said-Ball曲线

h-Bezier曲线是Bezier曲线基于h-微积分意义下的推广模型.为增强Said-Ball曲线的造型能力,提高h-Bezier曲线递归求值速度,该文提出任意次的h-Said-Ball基函数,构造了h-Said-Ball曲线.通过分析Said-Ball曲线递归求值算法与Bezier曲线的转化关系,结合h-Bezier曲线的递归求值算法和h-Bernstein基函数的构造方式,得到任意次h-Said-Ball基函数的表达式.h-Said-Ball基具有非负,单位分解,端点插值等优良性质,和h-Bernstein基之间存在显式转换矩阵.进一步,定义h-Said-Ball曲线并分析其基本性质,推导递归求值算法和包络表示,h-Said-Ball曲线的求值计算量是h-Bezier曲线的一半.借助从h-Said-Ball曲线到h-Bezier曲线的割角算法,证明了h-Said-Ball基是全正基,从而h-Said-Ball曲线具有变差缩减性和保凸性.数值实例显示了h-Said-Ball曲线相比Said-Ball曲线的造型优势和灵活性.

GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N)

In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.

Balanced Fracturing and Cold-welding of Magnesium during Ball Milling Assisted by Carbon Coating:Experimental and Molecular Dynamic Simulation

The lignite-derived carbon from self-protection pyrolysis was employed to balance the fracturing and cold-welding of magnesium during ball milling.Particle size analysis indicates that the introduction of lignite-derived carbon can effectively reduce the particle size of Mg while the introduction of graphite does no help.Besides,the effect of lignite-derived carbon on crystallite size reduction of Mg is also better than graphite.A moderate cold-welding phenomenon was observed after ball-milling Mg with the lignite-derived carbon,suggesting less Mg is wasted on the milling vials and balls.Molecular dynamic simulations reveal that the balanced fracturing and cold-welding of magnesium during ball milling is mainly attributed to the special structure of the lignite-derived carbon:graphitized short-range ordered stacking function as dry lubricant and irregular shape/sharp edge function as milling aid.The preliminary findings in current study are expected to offer implications for designing efficient Mg-based hydrogen storage materials.

ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK

Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure on R^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈R^(d):∣x∣<u})=0}the radius of the largest empty ball centered at the origin of Z_(n).In this work,we prove that after suitable renormalization,Rn converges in law to some non-degenerate distribution as n→∞.Furthermore,our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk.This completes the results of Révész[13]for the critical binary branching Wiener process.

Structural, Magnetic and Heating Efficiency of Ball Milled γ-Fe2O3/Gd2O3 Nanocomposite for Magnetic Hyperthermia

The preparation of γ-Fe2O3/Gd2O3 nanocomposite for possible use in magnetic hyperthermia application was done by ball milling technique. The nanocomposite was characterized by X-ray diffraction (XRD) and vibrating sample magnetometer (VSM). The heating efficiency and the effect of milling time (5 h and 30 h) on the structural and magnetic properties of the nanocomposite were reported. XRD analysis confirms the formation of the nanocomposite, while magnetization measurements show that the milled sample present hysteresis with low coercivity and remanence. The specific absorption rate (SAR) under an alternating magnetic field is investigated as a function of the milling time. A mean heating efficiency of 68 W/g and 28.7 W/g are obtained for 5 h and 30 h milling times respectively at 332 kHz and 170 Oe. The results showed that the obtained nanocomposite for 5 h milling time is a promising candidate for magnetic hyperthermia due to his properties which show an interesting magnetic behavior and high specific absorption rate.

The Impact and Intervention of Handheld Tai Chi Water-Resistance Fitness Ball on Middle-Aged and Elderly Patients with Parkinson’s Disease

Through the use of a survey and statistical methods, this study explores the effects and interventions of handheld Tai Chi water resistance fitness balls on the elderly with Parkinson’s disease. Firstly, a questionnaire on exercise compliance for patients with Parkinson’s disease was developed, and its reliability and validity were tested. Then, a survey was conducted to investigate the current status of exercise compliance among Parkinson’s disease patients, including general information, scoring status, and single and multiple factor analyses of influencing factors [1]. The results of the study show that through qualitative research, the dimensions and item pools of the questionnaire were initially constructed, and the reliability analysis of the questionnaire was conducted through Delphi expert consultation, with favorable results in terms of its reliability and validity [2]. Regarding the current status of exercise compliance among Parkinson’s disease patients, the study found that the level of exercise compliance needs improvement, and there are significant differences in exercise compliance levels among patients under different circumstances. Finally, the research results were discussed and conclusions were drawn. The innovation of this study lies in the development of a questionnaire on exercise compliance for patients with Parkinson’s disease and the preliminary qualitative research and Delphi expert consultation conducted on it, providing new ideas and methods for the study of exercise compliance. However, the study also has limitations as it did not examine the effects of other interventions on Parkinson’s disease, so further research should be conducted [3].

Existence of a Hölder Continuous Extension on Embedded Balls of the 3-Torus for the Periodic Navier Stokes Equations

This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of cells of the 3-Torus. Satisfying a divergence-free vector field and periodic boundary conditions respectively with a general spatio-temporal forcing term which is smooth and spatially periodic, the existence of solutions which have finite time singularities can occur starting with the first derivative and higher with respect to time. The existence of a subspace of the solution space where v3 is continuous and {C, y1, y12}, is linearly independent in the additive argument of the solution in terms of the Lambert W function, (y12=y2, C∈R) together with the condition v2=-2y1v1. On this subspace, the Biot Savart Law holds exactly [see Section 2 (Equation (13))]. Also on this subspace, an expression X (part of PNS equations) vanishes which contains all the expressions in derivatives of v1 and v2 and the forcing terms in the plane which are related as with the cancellation of all such terms in governing PDE. The y3 component forcing term is arbitrarily small in ε ball where Weierstrass P functions touch the center of the ball both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3 only governing PDE resulting. With viscosity present as v changes from zero to the fully viscous case at v =1 the solution for v3 reaches a peak in the third component y3. Consequently, there exists a dipole which is not centered at the center of the cell of the Lattice. Hence since the dipole by definition has an equal in magnitude positive and negative peak in y3, then the dipole Riemann cut-off surface is covered by a closed surface which is the sphere and where a given cell of dimensions [-1, 1]3 is circumscribed on a sphere of radius 1. For such a closed surface containing a dipole it necessarily follows that the flux at the surface of the sphere of v3 wrt to surface normal n is zero including at the points where the surface of sphere touches the cube walls. At the finite time singularity on the sphere a rotation boundary condition is deduced. It is shown that v3 is spatially finite on the Riemann Sphere and the forcing is oscillatory in y3 component if the velocity v3 is. It is true that . A boundary condition on the sphere shows the rotation of a sphere of viscous fluid. Finally on the sphere a solution for v3 is obtained which is proven to be Hölder continuous and it is shown that it is possible to extend Hölder continuity on the sphere uniquely to all of the interior of the ball.

Improved length of calcium sulfate crystal seeds and whiskers via ball milling and hydration treatment

Elucidating the effect of growth periods on the quality of calcium sulfate whiskers(CSWs)prepared from calcium sulfate dihydrate(DH)is imperative.Herein,crystal seeds and whiskers were prepared from DH in a water–glycerol system.Longer whiskers were obtained from crystal seeds prepared via hydration of DH for 30 s than via ball milling for 5 min followed by hydration for 20 s.The attachment of cetyltrimethyl ammonium bromide and glycerol additives to the whisker tops promoted whisker growth.The whisker sponges exhibited good thermal barrier properties and compression cycle stability.

Tennis ball cord combined with endoscopy for giant gastric phytobezoar:A case report

BACKGROUND Due to the specificity of Chinese food types,gastric phytobezoars are relatively common in China.Most gastric phytobezoars can be removed by chemical enzyme lysis and endoscopic fragmentation,but the treatment for large phytobezoars is limited,and surgical procedures are often required for this difficult problem.CASE SUMMARY For giant gastric phytobezoars that cannot be dissolved and fragmented by conventional treatment,we have invented a new lithotripsy technique(tennis ball cord combined with endoscopy)for these phytobezoars.This non-interventional treatment was successful in a patient whose abdominal pain was immediately relieved,and the gastroscope-induced ulcer healed well 3 d after lithotripsy.The patient was followed-up for 8 wk postoperatively and showed no discomfort such as abdominal pain.CONCLUSION The combination of tennis ball cord and endoscopy for the treatment of giant gastric phytobezoars is feasible and showed high safety and effectiveness,and can be widely applied in hospitals of all sizes.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

Enhancing Fire Safety in Commercial Vehicles: Assessing the Efficacy and Advantages of Exploding Fire Extinguishing Balls

Fire incidents in commercial vehicles pose significant risks to passengers, drivers, and cargo. Traditional fire extinguishing systems, while effective, may have limitations in terms of response time, coverage, and human intervention [1]. This study investigates the efficacy of a novel fire suppression technology—the Exploding Fire Extinguishing Ball (EFEB) —as an alternative and complementary fire safety solution for commercial vehicles. The research employs a multidisciplinary approach, encompassing engineering, materials science, fire safety, and human factors analysis. A systematic literature review establishes a comprehensive understanding of existing fire suppression technologies, including EFEBs. Subsequently, this study analyzes the unique features of EFEBs, such as automatic activation, as well as manual activation upon exposure to fire, and their potential to provide rapid, localized, and autonomous fire suppression. The study presents original experimental investigations to assess the performance and effectiveness of EFEBs in various fire scenarios representative of commercial vehicles. Experiments include controlled fires in confined spaces and dynamic simulations to emulate real-world fire incidents. Data on activation times, extinguishing capability, and coverage area are collected and analyzed to compare the efficacy of EFEBs with traditional fire extinguishing methods. Furthermore, this research shows the practical aspects of implementing EFEBs in commercial vehicles. A feasibility study examines the integration challenges, cost-benefit analysis, and potential regulatory implications. The study also addresses the impact of EFEBs on vehicle weight, stability, and overall safety. Human factors and user acceptance are crucial elements in adopting new safety technologies. Therefore, this research utilizes an experimental design to assess the performance and effectiveness of EFEBs in various fire scenarios representative of commercial vehicles. This dissertation presents original controlled experiments to emulate real-world fire incidents, including controlled fires in confined spaces and dynamic simulations. The experimental approach ensures rigorous evaluation and objective insights into EFEBs’ potential as an autonomous fire suppression system for commercial vehicles. This includes the perspectives of drivers, passengers, fleet operators, insurance agencies, and regulatory bodies. Factors influencing trust, perceived safety, and willingness to adopt EFEBs are analyzed to provide insights into the successful integration of this technology. The findings of this research will contribute to the knowledge of fire safety technology and expand the understanding of the applicability of EFEBs in commercial vehicles.

Ex⁃situ Measurement of Internal Deformation in Ball Grid Array Package with Digital Volume Correlation

In spacecraft electronic devices,the deformation of solder balls within ball grid array(BGA)packages poses a significant risk of system failure.Therefore,accurately measuring the mechanical behavior of solder balls is crucial for ensuring the safety and reliability of spacecraft.Although finite element simulations have been extensively used to study solder ball deformation,there is a significant lack of experimental validation,particularly under thermal cycling conditions.This is due to the challenges in accurately measuring the internal deformations of solder balls and eliminating the rigid body displacement introduced during ex-situ thermal cycling tests.In this work,an ex-situ three-dimensional deformation measurement method using X-ray computed tomography(CT)and digital volume correlation(DVC)is proposed to overcome these obstacles.By incorporating the layer-wise reliability-guided displacement tracking(LW-RGDT)DVC with a singular value decomposition(SVD)method,this method enables accurate assessment of solder ball mechanical behavior in BGA packages without the influence of rigid body displacement.Experimental results reveal that BGA structures exhibit progressive convex deformation with increased thermal cycling,particularly in peripheral solder balls.This method provides a reliable and effective tool for assessing internal deformations in electronic packages under ex-situ conditions,which is crucial for their design optimization and lifespan predictions.

Preparation and Properties of Spray Polyurea Elastomer for Aquaculture Foam Floating Balls

[Objectives] This study was conducted to develop a polyurea elastomer which can be sprayed on the surface of expanded polystyrene (EPS) floating balls, so as to improve the surface strength and service life of the floating balls. [Methods] The effects of the types and amounts of isocyanate, chain extenders and polyether polyols on the gelation rate, adhesion and wear resistance of polyurea elastomer were investigated, and it was finally determined the preparation process of polyurea elastomer using liquid isophorone diisocyanate (IPDI) and amino-terminated polyether (D2000) as the main raw materials, dimethylthiotoluene diamine (E300) as the chain extender and silica as the wear resistance modifier through two-step solution polymerization of prepolymerization and chain extension. [Results] The physical properties and chemical resistance tests of spray polyurea elastomer showed that it had good physical properties and acid and alkali resistance, and could meet the requirements of spraying and protection of EPS floating ball surface in marine environment. [Conclusions] Polyurea elastomer coating can improve the aging resistance, wear resistance and acid and alkali resistance of EPS floating balls, and prevent them from being fragile and floating randomly to form marine floating garbage which results in "white pollution".

七次广义Ball曲线的两种扩展

构造了两组含形状参数的多项式基函数:第一组基既是七次Wang-Ball基的扩展,又是七次Said-Ball基的扩展;第二组基既是七次Said-Ball基的扩展,又是七次Bernstein基的扩展。并由此定义了两种新的七次广义Ball曲线:前者不仅包括了七次Wang-Ball和Said-Ball曲线,还涵盖了无数条处于这两种曲线之间的曲线;后者不仅包括了七次Said-Ball和Bézier曲线,还涵盖了无数条处于这两种曲线之间的曲线。依次分析了两种新的广义Ball曲线与七次Bézier曲线之间的关系后明确了每个形状参数的几何意义,并给出了其几何作图法。

Research on the Influence of Raceway Waviness on the Vibration Characteristics of Deep Groove Ball Bearings

The dynamics model of a 2-degree-of-freedom deep groove ball bearing is established by incorporating the raceway surface waviness model comprising multiple sinusoidal functions superposition.The model is solved using the fourth-order Runge-Kutta method to obtain the vibration characteristics including displacement,velocity,acceleration,and frequency of the bearing.Validation of the model is accomplished through comparison with theoretical vibration frequencies.The influence of the amplitude of waviness of the inner and outer ring raceway surfaces of deep groove ball bearings on the vibration displacement,peak-to-peak vibration displacement and root-mean-square vibration acceleration is analyzed,and the results show that as the amplitude of the inner and outer ring raceway surfaces waviness increases,all the vibration characteristic indexes increase,indicating that the vibration amplitude of the bearings as well as the energy of the waviness-induced shock waveforms increase with the increase of the amplitude of the waviness.

ball tree优化的自动驾驶仿真测试场景生成方法

基于场景的仿真测试方法可以有效加速自动驾驶汽车的测试进程,但是传统的采样方法面对高维度采样空间时无法维持高效性,提出了一种ball tree优化的仿真测试场景采样方法,并基于Carla模拟器构建了仿真测试场景自动化生成框架验证算法的有效性。分别使用随机采样方法、基于KD tree结构的最近邻采样方法与基于ball tree结构的最近邻采样方法进行场景参数采样,并生成不同天气要素下的仿真测试场景进行验证。最后将仿真过程与人工方法进行对比。结果表明,提出方法相对于人工方法具有11.38倍场景制作速度的提升,且相对于KD tree结构的采样方法的场景生成速度提升了27.97%。

影响Ball公式法估算热杀菌F值的因素研究

传统的Ball公式法在罐头企业热杀菌应用过程中由于采用纯人工制图并计算相关参数,过程较复杂。对于影响F值预测的准确性因素未见有研究。实验采用Ball公式法通过计算机辅助计算#9121罐型紫薯泥罐头热杀菌。过程选取12、15、18、21、24、27 min作为升温斜率计算起点和按照不同的时间间隔采集温度数据,分成0.5、1、2、3、4 min间隔等若干组进行采集数据,以考查不同的升温起点选择和不同的时间间隔所获取数据对预测F值的影响。结果表明:#9121罐型紫薯泥罐头杀菌属于简单型传热类型,建议选择温度采集时间间隔在3 min以内的,且满足预测F值与实际累计F值相对误差小于5%的升温起始点,其得到的传热参数值准确性较高,预测F值准确度较好。这点可以为企业今后使用Ball公式法进行热杀菌F值预测提供参考。

Effect of ball milling time on the microstructure and compressive properties of the Fe–Mn–Al porous steel

In the present work,Fe–Mn–Al–C powder mixtures were manufactured by elemental powders with different ball milling time,and the porous high-Mn and high-Al steel was fabricated by powder sintering.The results indicated that the powder size significantly decreased,and the morphology of the Fe powder tended to be increasingly flat as the milling time increased.However,the prolonged milling duration had limited impact on the phase transition of the powder mixture.The main phases of all the samples sintered at 640℃ were α-Fe,α-Mn and Al,and a small amount of Fe2Al5 and Al8Mn5.When the sintering temperature increased to 1200℃,the phase composition was mainly comprised of γ-Fe and α-Fe.The weight loss fraction of the sintered sample decreased with milling time,i.e.,8.3wt% after 20 h milling compared to15.3wt% for 10 h.The Mn depletion region(MDR) for the 10,15,and 20 h milled samples was about 780,600,and 370 μm,respectively.The total porosity of samples sintered at 640℃ decreased from ~46.6vol% for the 10 h milled powder to ~44.2vol% for 20 h milled powder.After sintering at 1200℃,the total porosity of sintered samples prepared by 10 and 20 h milled powder was ~58.3vol% and ~51.3vol%,respectively.The compressive strength and ductility of the 1200℃ sintered porous steel increased as the milling time increased.

PID and Fuzzy Logic Control of Ball and Beam System Using Particle Swarm Optimization

In this research, we carried out the modeling of the ball and beam system (BBS) within the MATLAB/Simulink framework by applying both proportional-integral-derivative (PID) and fuzzy logic control strategies to govern the dynamics of this constructed model. The underlying non-linear dynamic equations adjusting the behavior of the BBS system are based on Newton’s second law of motion. The physical installation of the BBS, designed for potential real-time application, comprises a lengthy beam subject to movement through the action of a DC servomotor, with a ball traversing the beam in a reciprocating manner. A distance sensor is strategically placed in front of the beam to determine the exact position of the ball. In this system, an electrical control signal applied to the DC servomotor causes the beam to pivot about its horizontal axis, thereby enabling the ball to move freely along the beam's length. To avoid the risk of losing the ball equilibrium on the beam and to achieve precise system control, a mathematical model was devised and implemented within the MATLAB/Simulink environment. The use of the particle swarm optimization (PSO) algorithm was aimed at tackling the task of refining and optimizing the PID controller specifically designed for the linearized ball and beam control system. The presented system is controlled using both PID and fuzzy logic, and the use of the PSO algorithm enhances the system’s responsiveness efficiency.

Numerical study on erosion behavior of sliding sleeve ball seat for hydraulic fracturing based on experimental data

The sleeve sealing ball seat is one of the important components in the multistage fracturing process of horizontal wells.The erosion and wear of the surface will decrease the sealing performance of the fracturing ball and the ball seat.This leads to pressure leakage during the fracturing process and fracturing failure.In this paper,combined with the actual ball seat materials and working conditions during the fracturing process,the erosion tests of ductile iron and tungsten carbide materials under different erosion speeds,angles,and mortar concentrations are carried out.Then the erosion test results were analyzed by mathematical fitting,and a set of erosion models suitable for sliding sleeve setting ball seat materials were innovatively established.For the first time,this paper combines the erosion model obtained from the experiment and the computational fluid dynamics(CFD)with Fluent software to simulate the erosion of the ball seat.Based on the simulation results,the morphology of the sliding sleeve seat ball after erosion is predicted.Through analysis of the test and simulation results,it is showed that the erosion rate of tungsten carbide material is lower and the wear resistance is better under the condition of small angle erosion.This research can offer a strong basis for fracturing site selection,surface treatment methods,and prediction of failure time of ball seats.