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.

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".

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.

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.

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].

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.

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.

Balls into bins分配器算法

针对传统的bitmap分配器算法中没有反馈机制,导致搜索不能很好地适应各种情况的问题。分析得到bitmap分配器算法中空闲块的搜索问题实际上是一个负载平衡的问题,因此将ballsintobins的负载平衡问题的研究结果应用在bitmap分配器上。将bitmap分成不同的区,从中选出负载量小的区进行分析,经对比分析和对C3I系统的实际检验表明,这种分配器算法的确优于传统的bitmap分配器算法。

基于非对称balls-into-bins的高效平衡负载分配模型

在大规模数据中心和P2P覆盖网络等复杂网络负载平衡分配中,前人提出了多种多样的负载分配方法,但许多方法为了达到更好的平衡负载指标,追求越来越复杂的算法,使得时间复杂度和算法复杂度很难控制在合理的范围之内。本文在研究了经典balls-into-bins、Azar balls-into-bins和balls into non-uniformbins等模型的基础上,提出了一种新颖高效的非对称balls-into-bins平衡负载分配模型,该模型具有异构的balls、异构的bins,以及不同的bin选择概率,能以很高的概率将最大负载均衡地控制在合理的范围内,通信负载很小,且具有很好的可扩展性,通过拓展,该模型在负载平衡的诸多领域都将有广阔的应用空间。

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。

Effects of austempering temperature on microstructure and surface residual stress of carbidic austempered ductile iron(CADI) grinding balls

The effects of austempering temperature on microstructure and surface residual stress of carbidic austempered ductile iron(CADI) grinding balls were systematically investigated in this work. The microstructures were oberserved by optical metallography and analyized by X-ray diffraction. The surface residual stress measured by the cutting method is mainly composed of thermal stress and phase transformation stress. The thermal stress in grinding balls was determined by ANSYS simulation technique, and the surface phase transformation stress was obtained by subtracting the simulated surface thermal stress from the measured surface residual stress. Results show that all microstructures consist of ausferrite, white-bright zones(mixture of martensite and austenite), nodular graphite, and carbides. The distribution of ausferrite shows uniform. With the increase of austempering temperature, the volume fraction and carbon content of austenite increase, whereas the amount of white-bright zone decreases. In addition, the surface residual stress increases with the increase of austempering temperature. Only the tension exists at the austempering temperature of 200 ℃, and the pressure exists at the austempering temperature of 220-260 ℃. The thermal stress changes from the tension on the inside with the radius of 0-35 mm to the pressure on the outside with the radius of 35-62.5 mm, and the stress balance state presents at the radius of 35 mm. It is also found that the transformation stress is related to the content of carbon-rich austenite, and will reduce by 5.03 MPa accompanied with 1 vol.% increase of the austenite. The thermal compressive stress and the transformation tensile stress on the surface both decrease with the increase of the austempering temperature.

Research on Abrasives in the Chemical Mechanical Polishing Process for Silicon Nitride Balls

Silicon nitride (Si 3N 4) has been the main material for balls in ceramic ball bearings, for its lower density, high strength, high hardness, fine thermal stability and anticorrosive, and is widely used in various fields, such as high speed and high temperature areojet engines, precision machine tools and chemical engineer machines. Silicon nitride ceramics is a kind of brittle and hard material that is difficult to machining. In the traditional finishing process of silicon nitride balls, balls are lapped by expensive diamond abrasive. The machining is inefficiency and the cost is high, but also lots of pits, scratch subsurface micro crazes and dislocations will be caused on the surface of the balls, the performance of the ball bearings would be declined seriously. In these year, a kind of new technology known as chemical mechanical polishing is introduced in the ultraprecision machining process of ceramic balls. In this technology, abrasives such as ZrO 2, CeO 2 whose hardness is close to or lower than the work material (Si 3N 4) are used to polishing the balls. In special slurry, these abrasives can chemo-mechanically react with the work material and environment (air or water) to generate softer material (SiO 2). And the resultants will be removed easily at 0.1 nm level. So the surface defects can be minimized, very smooth surface (Ra=4 nm) and fine sphericity (0.15～0.25 μm ) can be obtained, and the machining efficiency is also improved. The action mechanism of the abrasives in the chemical mechanical polishing process in finishing of silicon nitride ball will be introduced in this paper.

LINEAR SINGULAR INTEGRAL EQUATION ON DOMAINS COMPOSED BY BALLS

For domains composed by balls in C^n, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smooth lower dimensional edges on the boundary of the domain.

WEARING PERFORMANCE OF STEEL BALLS IN WET GRINDING

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Rolling contact fatigue of silicon nitride bearing balls under pure rolling condition

A newly developed pure rolling fatigue test rig with three contact points for bearing bails was used to perform rolling contact fatigue （RCF） tests. The fatigue properties of GCrl5 steel bails and two kinds of Si3N4 ceramic balls （GSN-200 and NBD-200） produced with different technologies were compared. Ball surfaces were examined after failure with optical microscope and scanning electron microscope （SEM）. It was identified by tests that the failure mode of ceramic balls was surface spail. The main factor of ceramic bail failure was principal tensile stress. Life tests data, summarized in accordance with the Weibull theory, showed that the life of GSN-200 balls was close to that of GCrl5 balls, whereas the life of NBD-200 balls was much longer than those of GSN-200 and GCr15. Under the same working condition, the temperature rise of all ceramic bails was lower than that of steel balls, and their crack propagation rates were slower than that of steel balls.

THE WEAR PERFORMANCES OF FINE GRAINED ALUMINA BALLS

The wear performance of fine grain alumina ball adding diopside as fluxing agent are reported for the first time in this paper. The ball (average grain size 3 mum) exhibits excellent toughness and low wear rates. Ploughing grooves and traces of micro-cutting occur at the place with no pore. And the wear process is mainly caused by plastic deformation mechanism. Yet, the ordinary alumina balls (average grain size 6 and 15 mum) are brittle and the wear rates are high. The intergranular and transgranular dropping pits occur, and the wear process in mainly caused by brittle fracture mechanism.