Tangential Markov Inequalities on Transcendental Curves

   Abstract. We show that on the curves γ:=(x,e ^t(x) ) , x∈ [a,b] , where t(x) is a fixed polynomial, there holds a tangential Markov inequality of exponent four for algebraic polynomials P _N (x,y) of degree at most N in each variable x,y: ||(P _N (x,e ^t(x) ))'|| _[a,b] ≤ CN ⁴ ||P _N || _γ , and the exponent four is sharp. On the other hand, the corresponding tangential Markov factors on curves y=x ^α with irrational α grow exponentially in the degree of the polynomials.     

Decay of a potential vortex in a Maxwell fluid

The velocity field and the associated tangential tension corresponding to a potential vortex in a Maxwell fluid are determined by means of the Hankel transform. The similar solutions for a Newtonian fluid appear as a limiting case of our solutions.     

零像散宽波段平场全息凹面光栅的优化设计

平场全息凹面光栅的理想像面应为一平面,此时子午焦线与弧矢焦线均位于像面内且彼此重合,形成接近理想像点的光谱像。但子午焦线总是存在弯曲,只有弧矢焦线在满足一定条件的情况下可以成为直线。鉴于此,提出一种满足平场弧矢焦线条件的平场全息凹面光栅设计方法。利用光学设计软件ZEMAX研究了运用此方法设计的零像散光栅的成像特性,并与原有设计方法得到的结果进行比较。模拟结果显示,满足平场弧矢焦线条件的光栅能够达到与原有方法所设计光栅相当的光谱分辨率,而其全波段零像散特性使其拥有更加出色的弧矢方向聚焦性能,显著提高平场光谱仪的信噪比。     

2D FE–DEM analysis of contact stress and tractive performance of a tire driven on dry sand

Normal and tangential stresses acting over a contact interface of a tire driven on dry sand were investigated to expand the applicability of our model incorporating 2D FE–DEM with proportional–integral–derivative (PID) control. A simple averaging method for contact reaction was introduced: computational segments were defined over the lower half part of the tire circumference that translates without rotation with the tire; then the contact stresses were calculated segment by segment. For the analysis, it was assumed that the tire was in rigid contact mode and that it would travel on the model sand terrain in stationary condition. The integration of normal and tangential contact stresses with respect to the angle of rotation was then applied to calculate the vertical contact load, gross tractive effort, net traction, and running resistance of the tire by parametric (or semi-empirical) analysis. The result of tractive performance obtained through the parametric analysis was found to be similar to the result of tractive performance obtained directly using FE–DEM analysis. A forward shift of the consistent angle of rotation for maximum normal contact stress and that for maximum tangential contact stress with the increase of slip from 22% was also observed in the FE–DEM result.     

On the use of digital image correlation for slip measurement during coupon scale fretting fatigue experiments

Digital image correlation (DIC) is a full field three dimensional measurement technique that can quantify displacements and strains of a surface. In this paper, digital image correlation is used as a slip measurement technique during coupon scale fretting fatigue experiments. Slip measured with the novel DIC technique is compared to conventional slip measurement techniques as clip gauges and modified clip gauge measurements proposed by Wittkowsky et al. Slip measurements with the DIC system show lower slip values and higher tangential contact stiffness’s compared to (modified) clip gauge measurements. Slip measured with DIC is obtained closer to the contact compared to clip gauges, eliminating the influence of elastic deformations or fitting parameters. During the fretting fatigue experiments are two equal contacts simultaneously tested. However, the slip of both contacts is not identical with outliers of more than 10% difference in slip amplitude.     

Dynamic Contact Behavior of a Golf Ball during an Oblique Impact

The oblique impact between a golf ball and a rigid steel target was studied using a high-speed video camera. Video images recorded before and after the impact were used to determine the inbound velocity v _i, rebound velocity v _r, inbound angle θ_i, rebound angle θ_r, and the coefficient of restitution e. The results showed that θ_r and e decreased as v _i increased. The maximum compression ratio η_c, contact time t _c, average angular velocity , and tangential velocity , along the target were determined from images obtained during the impact. The images demonstrated that η_c increased with v _i while t _c decreased. In addition, and increased almost linearly as v _i increased. A rigid body model was used to estimate the final angular velocity ω* and tangential velocity ν_t* at the end of the impact; these results were then compared with experimental data.     

Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.     

Dynamic Contact Behavior of a Golf Ball during Oblique Impact: Effect of Friction between the Ball and Target

The oblique impact between a golf ball and a polymethyl methacrylate (PMMA) target with smooth transparent surfaces was studied using a high-speed video camera. Video images of the impact were recorded from the backside of the target and were used to determine the contact time, contact area, and the displacement and rotation of the ball along the target. The average tangential and angular velocities were determined as functions of the inbound ball velocity. As the inbound ball velocity increased, the contact area and average tangential and angular velocities also increased while the contact time decreased. An oiled PMMA target was used to study the effect of reduced friction between the ball and target. The results were compared with earlier data for a steel target with relatively rough surfaces. The contact area and time were unaffected by friction, but the average tangential velocity increased while the average angular velocity decreased as the friction decreased.