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。

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.

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.

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.

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.

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".

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。

Automatic Team Assignment and Jersey Number Recognition in Football Videos

Football is one of the most-watched sports,but analyzing players’per-formance is currently difficult and labor intensive.Performance analysis is done manually,which means that someone must watch video recordings and then log each player’s performance.This includes the number of passes and shots taken by each player,the location of the action,and whether or not the play had a successful outcome.Due to the time-consuming nature of manual analyses,interest in automatic analysis tools is high despite the many interdependent phases involved,such as pitch segmentation,player and ball detection,assigning players to their teams,identifying individual players,activity recognition,etc.This paper proposes a system for developing an automatic video analysis tool for sports.The proposed system is the first to integrate multiple phases,such as segmenting the field,detecting the players and the ball,assigning players to their teams,and iden-tifying players’jersey numbers.In team assignment,this research employed unsu-pervised learning based on convolutional autoencoders(CAEs)to learn discriminative latent representations and minimize the latent embedding distance between the players on the same team while simultaneously maximizing the dis-tance between those on opposing teams.This paper also created a highly accurate approach for the real-time detection of the ball.Furthermore,it also addressed the lack of jersey number datasets by creating a new dataset with more than 6,500 images for numbers ranging from 0 to 99.Since achieving a high perfor-mance in deep learning requires a large training set,and the collected dataset was not enough,this research utilized transfer learning(TL)to first pretrain the jersey number detection model on another large dataset and then fine-tune it on the target dataset to increase the accuracy.To test the proposed system,this paper presents a comprehensive evaluation of its individual stages as well as of the sys-tem as a whole.

Ball基的推广

构造了一系列次数为n且带有参数k(2≤k≤■n2■+1)的新的广义Ball基,作为Wang-Ball基(k=2)到Said-Ball基(k=■n2■+1)的过渡,并给出新基的一些性质.接着,由新基定义出新的广义Ball曲线,给出曲线的递归求值、升阶和降阶逼近算法.最后,提出相应的三角基,并给出三角曲面的递归求值和升阶算法.

Explanation of Ball Lightning by Plasma Oscillations

Ball Lightning (BL) is a “plasma bubble” that has very remarkable properties. Its membrane contains a higher density of charged particles than the ambient medium. They are held together by mutually attracting surface charges, generated by collective oscillations of all unbound electrons inside the membrane. Energy losses by collisions and emission of radiation, as well as losses of charged particles by recombination, are compensated by extracting other ones from atmospheric air. Since that occurs in a special rhythmic way, this leads to “parametric amplification” of the oscillations of all unbound electrons in the plasma membrane. Moreover, BL is attracted by higher concentrations of charged particles in atmospheric air. Too much of them leads to explosion and too few to extinction of visible BL. Since the electric charge of BL is oscillating, it is also attracted by metals, water and glass. It can then heat, melt and vaporize these materials without stored energy. BL is even able to pass through window panes in 3 different ways, but that can also be explained.

两类形状可调五次广义Ball曲线

定义了两种带形状参数的曲线。第一种曲线包含了五次Wang-Ball和Said-Ball曲线以及介于这两种曲线之间的无数曲线;第二种曲线包含了五次Said-Ball和Bézier曲线以及介于这两种曲线之间的无数曲线。通过分析这两种曲线与五次Bézier曲线之间的关系,得出了形状参数的几何意义,并给出了这两种曲线的几何作图法。

两类新的四次广义Ball曲线

为了实现从四次Wang-Ball到Said-Ball曲线的过渡,以及从四次Said-Ball到Bézier曲线的过渡,定义了2种带形状参数的曲线。第一种曲线包含了四次Wang-Ball和Said-Ball曲线以及介于它们之间的无数曲线;第二种曲线包含了四次Said-Ball和Bézier曲线以及介于它们之间的无数曲线;通过分析新曲线与四次Bézier曲线之间的关系,得出了形状参数的几何意义,并给出了它们的几何作图法。

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.

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.

Water Extract of Rice False Smut Balls Activates Nrf2/HO-1 and Apoptosis Pathways,Causing Liver Injury

Ustiloxins are vital cyclopeptide mycotoxins originally isolated from rice false smut balls that form in rice spikelets infected by the fungal pathogen Ustilaginoidea virens.The toxicity of the water extract of rice false smut balls(RBWE) remains to be investigated.Studies have shown that RBWE may be toxic to animals,but toxicological evidence is still lacking.In this study,we found that the IC50 values of RBWE to BNL CL.2 cells at 24 and 48 h were 40.02 and 30.11 μg/m L,respectively,with positive correlations with dose toxicity and time toxicity.After treatment with RBWE,the number of BNL CL.2 cells decreased significantly,and the morphology of BNL CL.2 cells showed atrophy and wall detachment.RBWE induced DNA presynthesis phase arrest of BNL CL.2 cells,increased the proportion of apoptotic cells and inhibited cell proliferation.RBWE up-regulated reactive oxygen species(ROS) levels and lowered mitochondrial membrane potentials.Additionally,Western blot and q RT-PCR results suggested that RBWE exerted the above effects by promoting the Nrf2/HO-1 and caspase-induced apoptosis pathways in vitro and in vivo.The contents of alanine aminotransferase,aspartate aminotransferase,alkaline phosphatase,and total bile acids in the serum of mice from Institute of Cancer were significantly up-regulated by RBWE.At the same time,RBWE can lead to increases in ROS and malondialdehyde contents,decreases in contents of oxidized glutathione,glutathione and reduced glutathione,as well as decrease in catalase and superoxide dismutase activities in mouse liver tissues,demonstrating that oxidative stress occurred in mice.Moreover,liver damage was further detected by haematoxylin-eosin staining and electron microscopy to verify the damage to the mice caused by RBWE.In general,RBWE may cause hepatotoxicity in vivo and in vitro via the apoptosis pathway,which provides a reference for hepatotoxicity and its mechanism of action.

Reactive ball-milling synthesis of Co-Fe bimetallic catalyst for efficient hydrogenation of carbon dioxide to value-added hydrocarbons

Catalytic hydrogenation of CO_(2) using renewable hydrogen not only reduces greenhouse gas emissions,but also provides industrial chemicals.Herein,a Co-Fe bimetallic catalyst was developed by a facile reactive ball-milling method for highly active and selective hydrogenation of CO_(2) to value-added hydrocarbons.When reacted at 320℃,1.0 MPa and 9600 mL h^(-1) g_(cat)^(-1),the selectivity to light olefin(C_(2)^(=)-C_(4)^(=)) and C_(5)+ species achieves 57.3% and 22.3%,respectively,at a CO_(2) co nversion of 31.4%,which is superior to previous Fe-based catalysts.The CO_(2) activation can be promoted by the CoFe phase formed by reactive ball milling of the Fe-Co_(3)O_(4) mixture,and the in-situ Co_(2)C and Fe_(5)C_(2) formed during hydrogenation are beneficial for the C-C coupling reaction.The initial C-C coupling is related to the combination of CO species with the surface carbon of Fe/Co carbides,and the sustained C-C coupling is maintained by self-recovery of defective carbides.This new strategy contributes to the development of efficient catalysts for the hydrogenation of CO_(2) to value-added hydrocarbons.

Research and experimental analysis of precision degradation method based on the ball screw mechanism

As a key transmission component in computer numerical control(CNC) machine tools,the ball screw mechanism(BSM) is usually investigated under working load conditions. Its accuracy degradation process is relatively long,which is not conducive to the design and development of new products. In this paper,the normal wear depth of the BSM nut raceway is calculated under the variable speed operation condition using the fractal wear analysis method and the BSM’s accelerated degradation proportional wear model. Parameters of the acceleration degradation model of the double-nut preloaded ball screw pair are calculated based on the physical simulation results. The accelerated degradation test platform of the BSM is designed and manufactured to calculate the raceway wear model when the lubrication condition is broken under the variable-speed inertial load and the boundary lubrication condition under the uniform speed state. Three load forces and two samples are selected for the accelerated degradation test of the BSM. The measured friction torque of the BSM is employed as the evaluation index of the accuracy degradation test. In addition,the life cycle of the accuracy retention is accurately calculated by employing the parameters of the physical simulation model of the BSM. The calculations mentioned above can be used to estimate BSM’s accuracy performance degradation law under normal operating conditions. The application of the proposed model provides a new research method for researching the precision retention of the BSM.

双曲混合多项式形式的Ball曲线

Ball曲线在多项式空间中得到了广泛的研究,而且在CAD系统中也有着广泛应用.详细讨论了双曲混合多项式空间Kn=span{1,t,t2,…,tn-2,sht,cht}中的Ball基和Ball曲线.在H-Bézier基的基础上构造的一组新的基称为空间Kn的H-Ball基,用这组H-Ball基定义的曲线称为H-Ball曲线.H-Ball曲线继承了Bézier曲线的很好的几何性质,而且在曲线升阶和降阶上比Bézier曲线更加快速方便.另外H-Ball曲线不仅可以通过调整控制多边形来控制曲线形状,还可以通过调整形状因子来调节曲线对控制多边形的逼近程度.H-Ball曲线在CAD系统和相关领域的曲线设计和建模中得到了重要的应用.