74,383 research outputs found
Fatou and Korányi-Vági type theorems on the minimal ball
Get PDFIn this paper we develop the Hp (p [greater than or equal] 1) theory on the minimal ball. After identifying the admissible approach regions, we establish theorems of Fatou and Korányi-Vági type on this ball
Concentration of the distance between points in the unit ball
No full textWe prove that in every finite dimensional normed space, for “most” pairs (x, y) of points in the unit ball, ║x − y║ is more than √2(1 − ε). As a consequence, we obtain a result proved by Bourgain, using QS-decomposition, that guarantees an exponentially large number of points in the unit ball any two of which are separated by more than √2(1 − ε)
A Study of Diagnostic Signatures of a Deep Groove Ball Bearing Based on a Nonlinear Dynamic Mode
No full textFor accurate fault detection and diagnosis, this paper focuses on the study of bearing vibration responses under increasing radial clearances due to investable wear and different bearing grades. A nonlinear dynamic model incorporating with local defects and clearance increments is developed for a deep groove ball bearing. The model treats the inner race-shaft and outer race-housing as two lumped masses which are coupled by a nonlinear spring formalized by the Hertzian contact deformation between the balls and races. The solution of the nonlinear equation is obtained by a Runge-Kutta method in Matlab. The results show that the vibrations at fault characteristic frequencies exhibit significant changes with increasing clearances. However, an increased vibration is found for the outer race fault whereas a decreased vibration is found for inner race fault. Therefore, it is necessary to take into account these changes in determining the size of faults
The 2010 regulations on golf groove design: impact on ball flight characteristics during a controlled shot.
No full textThe purpose of this study was to investigate the difference in the amount of spin that can be generated during a controlled golf shot, as a result of the 2010 rule change regarding restrictions applied to the design of the grooves on the clubface implemented by the United States Golf Association and the Royal & Ancient Golf Club. Ten experienced golfers (mean ± SD; age, 23.0 ± 0.67 yr; playing experience, 13.2 ± 1.6 yr; handicap, 1.6 ± 1.4) were required to play a total of 120 shots inside a state of the art golf simulator with 3 clubs consisting of ‘old’ pre 2010 U-groove design and ‘new’ post 2010 V-groove design. With the U and V grooved clubs, participants played 10 shots from a fairway mat and 10 shots from a rough mat using a 9 iron, PW and SW. Backspin (RPM) and, as a measure of accuracy, distance landed from the pin (yds) were recorded. Compared to the U-grooves, the newer V-groove design imparted significantly less backspin from both the fairway and rough surfaces (P < 0.05), additionally, shots with all clubs were consistently further away from the pin (P < 0.05). The newer groove design does not enable players to impart as much backspin on the ball as they previously could and our data suggest that the recent change in golf club design might therefore reward driving accuracy
Tracking the soccer ball using multiple fixed cameras
No full textThis paper demonstrates innovative techniques for estimating the trajectory of a soccer ball from multiple fixed cameras. Since the ball is nearly always moving and frequently occluded, its size and shape appearance varies over time and between cameras. Knowledge about the soccer domain is utilized and expressed in terms of field, object and motion models to distinguish the ball from other movements in the tracking and matching processes. Using ground plane velocity, longevity, normalized size and color features, each of the tracks obtained from a Kalman filter is assigned with a likelihood measure that represents the ball. This measure is further refined by reasoning through occlusions and back-tracking in the track history. This can be demonstrated to improve the accuracy and continuity of the results. Finally, a simple 3D trajectory model is presented, and the estimated 3D ball positions are fed back to constrain the 2D processing for more efficient and robust detection and tracking. Experimental results with quantitative evaluations from several long sequences are reported
The specific selection function effect on clinker grinding efficiency in a dry batch ball mill
Get PDFDry grinding experiments on cement clinker were carried out using a laboratory batch ball mill equipped with a torque measurement. The influence of the ball size distribution on the specific selection function can be approached by laboratory runs using mono-size balls. The breakage is more efficient with maximal specific selection functions at the initial size reduction stage. But, in terms of cement finish grinding all stages of grinding are determinant for the production of a required Blaine surface area (3500 cm2/g). So, the choice of ball size according to a maximal specific selection function leads to an increase of the energy consumption. In addition, investigations on the mono-sized fractions and on the crude material (size minus 2.8 mm) demonstrate that the energy efficiency factor can be optimized using ball size corresponding to relatively low specific selection function
Parametric impact characterisation of a solid sports ball, WITH a view to developing a standard core for the GAA Sliotar
Get PDFThe main aim of this research was to characterise the dynamic impact behaviour of the sliotar core. Viscoelastic characterisation of the balls was conducted for a range of impact speeds. Modern polymer balls exhibited strain and strain-rate sensitivity while traditional multi-compositional balls exhibited strain dependency. The non-linear viscoelastic response was defined by two values of stiffness, initial and bulk stiffness.
Traditional balls were up to 2.5 times stiffer than the modern types, with this magnitude being rate-dependent. The greater rate of increase of traditional ball stiffness produced a more non-linear COR velocity-dependence compared to modern balls. The dynamic stiffness results demonstrated limited applicability of quasi-static testing and springtheory equations. Analysis of ball deformation behaviour demonstrated that centre-of mass displacement and diameter compression values were not consistently equivalent for all ball types. The contribution of manufacturing conditions to ball performance was investigated by conducting extensive prototyping experiments. Manufacturing parameters of temperature, pressure and material composition were varied to produce a range of balls. Polymer hardness affected stiffness but not energy dissipation, with increased hardness increasing ball stiffness. The nucleating additive influenced ball COR, with increased additive tending to reduce ball COR, but this effect was sensitive to polymer grade. The impact response of the ball was simulated using three mathematical models. The first model was shown to replicate ball behaviour to only a limited degree, despite being used previously with reported success for other ball types. The second model exhibited a reasonable representation of ball impact response that was universally applicable to all tested ball types; however, the accuracy in terms of predicting force-displacement response was not as high as required for broad range implementation. The third model exhibited significantly better accuracy in simulating ball response. The force values generated from this model exhibited up to 95% agreement with experimental data
Stability of a spherical flame ball in a porous medium
Get PDFGaseous flame balls and their stability to symmetric disturbances are studied numerically and asymptotically, for large activation temperature, within a porous medium that serves only to exchange heat with the gas. Heat losses to a distant ambient environment, affecting only the gas, are taken to be radiative in nature and are represented using two alternative models. One of these treats the heat loss as being constant in the burnt gases and linearizes the radiative law in the unburnt gas (as has been studied elsewhere without the presence of a solid). The other does not distinguish between burnt and unburnt gas and is a continuous dimensionless form of Stefan's law, having a linear part that dominates close to ambient temperatures and a fourth power that dominates at higher temperatures.Numerical results are found to require unusually large activation temperatures in order to approach the asymptotic results. The latter involve two branches of solution, a smaller and a larger flame ball, provided heat losses are not too high. The two radiative heat loss models give completely analogous steady asymptotic solutions, to leading order, that are also unaffected by the presence of the solid which therefore only influences their stability. For moderate values of the dimensionless heat-transfer time between the solid and gas all flame balls are unstable for Lewis numbers greater than unity. At Lewis numbers less than unity, part of the branch of larger flame balls becomes stable, solutions with the continuous radiative law being stable over a narrower range of parameters. In both cases, for moderate heat-transfer times, the stable region is increased by the heat capacity of the solid in a way that amounts, simply, to decreasing an effective Lewis number for determining stability, just as if the heat-transfer time was zero
On homogeneous polynomials on a complex ball
No full textWe prove that there exist
n
n
-homogeneous polynomials
p
n
{p_n}
on a complex
d
d
-dimensional ball such that
‖
p
n
‖
∞
=
1
{\left \| {{p_n}} \right \|_\infty } = 1
and
‖
p
n
‖
2
⩾
π
2
−
d
{\left \| {{p_n}} \right \|_2} \geqslant \sqrt \pi {2^{- d}}
. This enables us to answer some questions about
H
p
{H_p}
and Bloch spaces on a complex ball. We also investigate interpolation by
n
n
-homogeneous polynomials on a
2
2
-dimensional complex ball.</p
prolifera
No full textPetrorhagia prolifera (Linnaeus) P. Ball & HeywoodProliferous or childing pinkTunica proliferaCa. 12 mi n of Chico, at junction of Hwy 99E and Broyles Road.Layia fremontii, Achyrachaena mollis, Lasthenia fremontiiCorolla rose-pink, produces new fl every day
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