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The aim of this study was to compare the pre- and post-impact three-dimensional kinematics of the ball and racquet during first and second serves performed by elite tennis players. Data were collected from four male and four female right-handed professional players during competition using two high-speed cameras (200 Hz). For each player, one first serve and one second serve from the 'deuce' or right service court that landed within the specified target area were analysed. To test for significant differences between the first and second serves, Wilcoxon tests (P < or = 0.05) were performed on selected parameters. The results indicate that the ball travelled forward and to the left during the flight phase of the toss in all but one trial. The average pre-impact ball forward location for the first serve was significantly more in front and had a higher associated forward ball velocity than the corresponding values for the second serve. On average, the decrease in post-impact ball speed from the first to the second serve was 24.1%. No significant differences between the first and second serves were found in the pre-impact racquet head speed and orientation, which was represented as a unit vector perpendicular to the racquet face. The major adjustments made by the players when going from the first to second serve were a decrease in pre-impact ball forward location (P < or = 0.01) and an increase in the pre-impact racquet vertical and lateral velocities (both P < or = 0.05). This implies that the players tossed the ball closer to the body and imparted topspin and sidespin on the ball by changing the racquet vertical and lateral velocities when going from the first to the second serve.  相似文献   
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The report is a translation of part of a Swedish paper entitled “On Students' Achievement in Mathematics after Finishing Comprehensive School”. The intention of the investigation was to

  • - diagnose the retention of some basic skills in some topics in algebra and geometry,
  • - reveal difficult steps in the learning processes in these topics.
  • Starting with a complicated question, e.g. the equation \(\frac{{3x - 2}}{2} = \frac{x}{3}\) a sequence consisting of 5–15 problems were constructed. Each new problem followed by the preceding one by taking away one or two details. \(\begin{gathered} 3(3x - 2) = 2x \\ {\text{ 9}}x - 6 = 2x \\ {\text{ 7}}x - 6 = 0 \\ {\text{ 7}}x = 6 \\ \end{gathered} \) is an example of a sequence belonging to the equation above. From about 10 complicated problems (“top-items”) and their sequences, in all 130 items, 10 sub-tests were put together in such a way that the pupils who took the test were not aware of the sequences but found no connection between the problems. Many surprising results were found, e.g., that the students scored higher on 14/(x+2)=2 than on 4/x=3, that the difficulty in finding the area of a triangle depended on the position of the triangle and that the problems “Simplify a/a 2, a2/a, a/a” were of quite unequal difficulty. A discussion about the students' thinking in patterns and mechanically learning ends the report.  相似文献   
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