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The decrease in kinetic energy of a ball incident vertically on a rigid horizontal surface depends on the normal coefficient of restitution, ey. It is shown in the present paper that if the ball is incident obliquely on the surface then the total decrease in kinetic energy has two independent contributions, one depending on ey, the other depending on the tangential coefficient of restitution, ex.

A ball incident on a horizontal surface with backspin can rebound forwards or backwards depending on the angle of incidence and the amount of backspin. The ball can also bounce forwards several times before it bounces backwards. The outcome depends on whether the ball slides throughout the impact or whether the ball grips the surface during the impact. The physics of the bounce of a golf ball on a green is described in the present article and estimates are given of the stopping distance after the ball first lands on the green, based on experimental bounce data.

Experimental results are presented to show how the speed and spin of a billiard ball vary as the impact point of the cue is varied above and below the center of the ball. The results are compared with a simple impact model to estimate how the normal and tangential impact forces vary with impact location.

Data from Grand Slam men's singles matches is presented for the period 1995 to 2009 showing how set score distributions have varied with time and across the four events. The relative number of tie-break sets provides a good indication of court speed, and so does the number of 6-0 or 6-4 sets. We show (a) how serve point probabilities vary between match winners and losers, (b) that match winners win about 9 out of 10 service games on average, while losers win about 7 out of 10 service games, (c) about 1/3 of all points are won by a player hitting a winner, (d) about 78% of match winners win the first set and (e) a player who wins the first set 7-6 is 2.5 times more likely to win the match than his opponent. [ABSTRACT FROM AUTHOR]

The mathematical definition of systems withhysteresis, that is nonlinear input-output systemswith memory, is different from the definition usuallyapplied to economic systems. Economic theory andmodelling practice have almost always specified simpledynamic systems with regular leads and lags in theirresponses, corresponding to input-output systems withunit or zero (or at least stable) roots. These modelscannot capture the ‘selective memory’ feature ofhysteretic behaviour, that is, the influence only ofcertain past events (typically, non-dominatedsequences of previous peaks and troughs). There istherefore a difficulty in testing for and validatingeconomic models containing hysteretic behaviour;appropriate empirical tests have not been developed.In particular, the usual unit vs. zero (or stable)root tests used in econometric analysis are unable todetect hysteretic behaviour or to distinguish it frommore conventional economic behaviour. The purpose ofthis paper is to propose a new way of testing forhysteresis, by drawing on some ideas in themathematical/control theory literature and adaptingthem to fit into the economic frameworks with elementsof hysteresis.

ABSTRACTThis study examines the time constraints faced by the junior school teacher taking on the dual role of student mentor and class‐teacher and seeks to discover whether it is possible to fulfil both roles effectively. It begins by looking at recent developments in teacher training and considers the role of the mentor in the training of students from a local college of education. It also examines the traditional role of the class‐teacher and the current statutory conditions of employment. To discover whether there is a conflict between the two roles, a diary was maintained of all activities relating to mentoring and teaching during three selected seven‐day periods. An analysis was made of the amount of time devoted to each. This revealed that the student mentor with a full‐time class‐teaching commitment may well encounter difficulties in doing full justice to both roles at once. Where there was a conflict of interest, it tended to be the students, rather than the pupils, that suffered. The author suggests ways in which this particular mentoring scheme might be adapted to take this into account. The preferred option is for mentors to work in pairs, each supervising the other's student. It is shown how this would reduce the time pressures on the mentor and, at the same time, benefit both the class and the student teacher.

Until recently, the new teacher in school received no formal induction and support was haphazard. There was an obvious need for the establishment of a structure to support new teachers during the initial stages of their teaching career. In 1992, new government legislation declared that headteachers must identify a member of staff to act as mentor to the new teacher. For the mentor to play a positive role, s/he would need to work within the context of a support system composed of staff colleagues, headteacher, governors, advisers and the local authority. This study examines the role and function of the mentor; analyses the needs of the new teacher; and shows how the mentor can best meet these needs. It recognises the constraints within which the mentor might have to operate but concludes that the role of mentor is crucial in helping the new teacher become established within the school.

Conclusion: The point of this note has been to appraise different accounts of the relationship between prices and unemployment in relation to the test of explaining the time series data for prices and unemployment in the U.S. and U.K. over the last century or more. The procedure adopted was to fix a specification of the different hypotheses before looking at the data, not to pursue a specification search for the “best” description of the data generation processes in the U.S. and the U.K. The hypothesis which outperforms the others in relation to tests employed is the hysteresis hypothesis, there being some support for the original Phillips Curve hypothesis (which belongs to the same species), but none for the natural rate hypothesis. Given the Duhem problem, it is not possible to assert conclusively that the natural rate hypothesis cannot be saved by the re-specification of auxiliary hypotheses, but this is in need of demonstration. The estimates of the general unrestricted form of the prices-unemployment relationship suggest that the conditions necessary for estimating relationships in the first and second differences of the price level are violated. Possibly as a result of this, the estimates of the natural rate and hysteresis relationships are unsatisfactory in that the residuals contain autocorrelation and heteroscedasticity. Given this, it would not be in order to draw strong conclusions from the results reported. What can be said is that the evidence in this note gives more support to the hysteresis hypothesis that the change in unemployment, rather than the level effect of the natural rate hypothesis, stimulates changes in the rate of inflation.

Without Abstract:

This paper deals with the way metaphors carried over from physical or biological systems condition the analysis of economic systems. The metaphors drawn from Newtonian mechanics, or from conservative fields of force, by neoclassical economists are discussed. Alternative metaphors which involve non-homeostasis and time irreversible processes are then outlined. Particular attention is paid to thermodynamics, evolutionary biology, and non-conservative or hysteretic force fields as sources of such metaphors. It is argued that these metaphors provide illumination to aspects of economic systems which are not consistent with the homeostatic, time reversible metaphors conventionally employed in economics.

Copyright of Coaching & Sport Science Review (Spanish Version) is the property of International Tennis Federation and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Coaching & Sport Science Review (Spanish Version) is the property of International Tennis Federation and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Discusses the results of a survey which reveals children's perception of mathematics and how acquire their mathematical skills. Fun and enjoyment among seven to eight year olds; Acceptance of math as a skill; Understanding the importance of math in education.

Presents a learning activity for use in teaching mathematics focusing on the use of multiples, prime numbers and factors. Use of a combination of formal discussion with individuals; Creation of a student activity based on the Pythagorean Square; Children's achievement of learning objectives. INSET: The mystery of mathematics, by Laurie, Buxton..

The article features Appian Way Tennis Club in Burwood in New South Wales. It mentions that the development of the club was initiated by businessman George Hoskins in 1903. It states that it is surrounded by very tall trees and is not in such excellent condition due to water restrictions and problems related to its natural environment. In the meantime, it only offers limited formal competition opportunities especially in summer since it is wet due to the winter months.

Describes the use of a school's physical environment for teaching mathematics to ten-year-olds in an English school by the creation of mathematics trails. Positive aspects of the activity; Planning of the trail; Implementation.

The article offers techniques and tips for mastering the kick serve in tennis including hitting the ball early from a large height, striking the ball with a topspin, and having a high ball toss.

The article provides a scientific explanation on the importance of using the right string in increasing the amount of topspin made by tennis players.