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.

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.

Effect of the mixing of s-wave and chiral p-wave pairings on electrical shot noise properties of normal metal/superconductor tunnel junctions

We study theoretically the electrical shot noise properties of tunnel junctions between a normal metal and a superconductor with the mixture of singlet s-wave and chiral triplet p-wave pairing due to broken inversion symmetry. We investigate how the shot noise properties vary as the relative amplitude between the two parity components in the pairing potential is changed. It is demonstrated that some characteristics of the electrical shot noise properties of such tunnel junctions may depend sensitively on the relative amplitude between the two parity components in the pairing potential, and some significant changes may occur in the electrical shot noise properties when the relative amplitude between the two parity components is varied from the singlet s-wave pairing dominated regime to the chiral triplet p-wave pairing dominated regime. In the chiral triplet p-wave pairing dominated regime, the ratio of noise power to electric current is close to 2e both in the in-gap and in the out-gap region. In the singlet s-wave pairing dominated regime, the value of this ratio is close to 4e in the inner gap region but may reduce to about 2e in the outer gap region as the relative amplitude of the chiral triplet pairing component is increased. The variations of the differential shot noise with the bias voltage also exhibit some significantly different features in different regimes. Such different features can serve as useful diagnostic tools for the determination of the relative magnitude of the two parity components in the pairing potential.

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.

Improving hydrogen storage thermodynamics and kinetics of Ce-Mg-Ni-based alloy by mechanical milling with TiF_(3)

Mg-based hydrides are too stable and the kinetics of hydrogen absorption and desorption is not satisfactory.An efficient way to improve these shortcomings is to employ reactive ball milling to synthesize the nanocomposite materials of Mg and additives.In this experiment,TiF_(3)was selected as an additive,and the mechanical milling method was employed to prepare the experimental alloys.The alloys used in this experiment were the as-cast Ce_(5)Mg_(85)Ni_(10),as-milled Ce_(5)Mg_(85)Ni_(10)and Ce_(5)Mg_(85)Ni_(10)+3 wt.%TiF3.The phase transformation,structural evolution,isothermal and non-isothermal hydrogenation and dehydrogenation performances of the alloys were inspected by XRD,SEM,TEM,Sievert apparatus,DSC and TGA.It revealed that nanocrystalline appeared in the as-milled samples.Compared with the as-cast alloy,ball milling made the particle dimension and grain size decrease dramatically and the defect density increase significantly.The addition of TiF_(3)made the surface of ball milling alloy particles markedly coarser and more irregular.Ball milling and adding TiF_(3)distinctly improved the activation and kinetics of the alloys.Moreover,ball milling along with TiF_(3)can decrease the onset dehydrogenation temperature of Mg-based hydrides and slightly ameliorate their thermodynamics.

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.

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.

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".

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.

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.

Shanghai Ballet's Classie Version of Swan Lake Wentto the Netherlands

Invited by the China Arts and Entertainment Group Ltd,Shanghai Ballet has performed the classic version of Swan Lake at the 136-year-old Royal Theatre Carre in Amsterdam on August 31 to start the fourth European tour since 2015.

Comparison of the effects of submerged laser peening,cavitation peening and shot peening on the improvement of the fatigue strength of magnesium alloy AZ31

To investigate the improvement in the fatigue strength of magnesium alloy by peening methods,magnesium alloy AZ31 was treated by submerged laser peening(SLP),cavitation peening(CP),and shot peening(SP),and the fatigue properties were evaluated by a plane bending fatigue test.In the case of SLP,both the impact induced by laser ablation(LA)and that caused by laser cavitation(LC),which developed after LA,were used.In the present study,the fatigue life at a constant bending stress was examined to determine the suitable coverage.It was found that the fatigue strengths at N=10^(7)for the SLP,CP,and SP specimens treated by each optimum condition were 56%,18%,and 16%higher,respectively,than that of the non-peened(NP)specimen,which was 97 MPa.The key factors in the improvement of fatigue strength by peening methods were work hardening and the introduction of compressive residual stress.

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.

Few-Shot Object Detection Based on the Transformer and High-Resolution Network

Now object detection based on deep learning tries different strategies.It uses fewer data training networks to achieve the effect of large dataset training.However,the existing methods usually do not achieve the balance between network parameters and training data.It makes the information provided by a small amount of picture data insufficient to optimize model parameters,resulting in unsatisfactory detection results.To improve the accuracy of few shot object detection,this paper proposes a network based on the transformer and high-resolution feature extraction(THR).High-resolution feature extractionmaintains the resolution representation of the image.Channels and spatial attention are used to make the network focus on features that are more useful to the object.In addition,the recently popular transformer is used to fuse the features of the existing object.This compensates for the previous network failure by making full use of existing object features.Experiments on the Pascal VOC and MS-COCO datasets prove that the THR network has achieved better results than previous mainstream few shot object detection.

New Method to Measure the Fill Level of the Ball Mill I——Theoretical Analysis and DEM Simulation

The accurate measurement of the fill level in the ball mill has not been resolved because of the interplay of many variable factors, which led the mill to be operated under the uneconomical condition and lost a lot of energy. At present, some methods, such as vibration method and acoustic method, have been applied for measuring the fill level by the researchers. Aiming at the problem of the traditional methods for measuring the fill level, that is, the feature variables of the fill level suffer the influences of the ball load and the water content of the coal, a novel method to measure the fill level is proposed and a possible relation between the fill level and the angular position of the maximum vibration point on the mill shell is investigated. The angular positions of the maximum vibration point on the mill shell for different fill level cases are calculated theoretically under two assumptions, respectively. Meanwhile the charge motions of the mill for different fill level cases are simulated with the discrete element method （DEM）. And the simulation results are verified by comparing the motion trajectories of steel balls and power draft of the mill. The simulated movement trajectories of the outmost layer steel balls in the mill are monitored and analyzed to obtain the angular positions of the maximum vibration point on the mill shell. Both the results of the theoretical calculation and the 3D DEM simulation show that the position of the maximum vibration point on the mill shell moves to a lower angular positions as the fill level decreasing, which provides a new idea for measuring the filllevel accurately.

Weighted composition operators from F(p,q,s) spaces to Bers-type spaces in the unit ball

This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.

Anatomical Structures of " Lepidodendron " pulchrum Zhang in Coal-balls from the Taiyuan Formation (Lower Lower Permian) in Shandong Province, North China

This study reports the anatomical structures of a kind of lepidodendralean stem in coal balls from the early Early Permian Taiyuan Formation in Yanzhou Mining District, southwestern Shandong Province, North China. The leaf cushion is slightly rhomboid in outline with a height of 9 - 10 mm and a width of 7.5 9.0 mm and its lower sides are slightly longer than the upper ones. The top and basic angles of the leaf cushion are truncate and the basic angle is slightly elongate. The upper part of the leaf cushion is strongly high-rising. The leaf sear is large and lenticular in shape. The leaf trace is wide and V-shaped in the leaf scar, and horizontally elongate within the leaf cushion. The leaf trace and lateral parichnos strand extend at a nearly horizontal course outward within the leaf cushion. The ligular pit is deep and extends outward at an oblique course and its aperture is located near the top angle of the leaf scar. No infrafoliar parichnos strands are present. The stem is probably siphonostelic and its pith is probably parenchymatous. The primary xylem is exarch with a nearly smooth outer margin. Only the outer cortex is present and it consists of alternately-arranged radial cell bands and gaps within which the are-shaped or V-shaped leaf traces can be seen. The concave side of the leaf trace is toward the center of the stem. No bundle sheath is developed. Periderm is well-developed and consists of phelloderm and phellem in nearly equal thickness. Compared with the lepidodendralean stems of the Cathaysian and Euramerican Floras, the present specimens are most close to an impression-compression species Lepidodendron pulchrum Zhang in morphology of the leaf cushion and they are put into this species temporarily. Whether the present specimens or the type specimens of L. pulchrum are very different from Lepidodendron Sternburg sensu DiMichele, thus the correct nomenclature and classification of L. pulchrum needs to be reconsidered based on the study of better- and anatomically-preserved stems and fertile organs in the future. Because 'L'. pulchrum possesses the mixed features of several genera of Euramerican lepidodendralean stems, it bears significance to study the origin and evolution of the Cathaysian lepidodendralean lycopods.