Special populations: the female player and the youth player

Females and youth are frequently described as "special" populations in football literature, but together these two populations outnumber male players. What makes females "special" is that they tend to eat less when training and competing than their male counterparts, leading to lower intakes of energy, carbohydrate, and some nutrients. Youth football players are special in regard to energy and nutrient requirements to promote growth and development, as well as to fuel sport. There is limited research on the dietary habits of these two populations, but the available literature suggests that many female and youth players need to increase carbohydrate intake, increase fluid intake, and develop dietary habits to sustain the demands of training and competition.     

The mathematical education of engineers

Mathematics has always played an important role in the education of engineers and production managers. At the present time, the importance of mathematics has increased significantly and it is quite natural that in universities around the world engineering students are taking courses in mathematics which constitute, as a rule, a significant portion of their programme. At the same time, however, the mathematical education of the engineer is far from ideal and its improvement deserves the closest scrutiny. The present article deals with several general aspects of this problem.     

The origin and direction of industrial R&D in India

This paper surveys the trends in industrial R&D in India over the last two decades. It shows that there has been a rapid rise in R&D expenditure and a shift in its composition towards in-house corporate R&D and away from R&D in government laboratories, which is explained by the laboratories' lack of market orientation and manufacturing experience. According to cross-section studies of corporate R&D, larger companies aim towards larger technological advances and take a longer view; but the overall composition of corporate R&D shows no discernible change. This apparent inconsistency is explained by the development of the technology market. Much R&D was triggered off by the need for import replacement arising from import controls till 1965 and later by the need for product diversification in the recession. But construction of new plants and mechanization for speeding up operations, activities where sustained R&D can yield large firms a steady flow of innovations, were unimportant or infrequent, and the demand for technology they gave rise to was largely met by imports.     

Ladder realizations of multivariable positive real functions

Necessary and sufficient conditions are obtained for the realization of an m-variable positive real function (PRF) as the impedence function of a resistively-terminated ladder network of m lossless two-ports connected in cascade. Each two-port is a single-variable lossless ladder with all of its transmission zeros either at the origin or at finity. Conditions are also obtained when each of the two-ports is a Fujisawa-type lowpass ladder.     

Buckling of a continuous beam resting on a tensionless elastic foundation

In this paper, a solution is presented to the buckling problem of a continuous beam resting on a tensionless foundation model that was proposed by Winkler and by Reissner.     

An initial value method for solving Fredholm integral equation of the first kind

The difficulties in solving Fredholm integral equations of the first kind are well known. A classical method has been to convert the equation into a set of m linear algebraic equations in n unknowns (m?n). For computational convenience, it is customary to force m = n and solve the resulting ill-conditioned system using one technique or other. In the general case, a feasible solution, if it exists, can be found by determining the generalized inverse of the coefficient matrix. One method of finding the generalized inverse is to reformulate the problem and observe the steady state response of a system of ordinary differential equations with prescribed initial conditions. Results obtained from this reformulation are found to be comparable in quality to those obtained earlier by other methods. Analog and digital computer implementations are discussed.