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.     

Dimensions of R&D location in the United States

R&D activities in the United States, as in other advanced economies, are geographically concentrated in certain types of locations. This study presents data on the location of four dimensions of R&D in the U.S.: industrial R&D laboratories, scientists and engineers engaged in R&D, scientists and engineers employed by the federal government, and research universities. Industrial R&D is much more concentrated in large urban areas than the other dimensions, and appears to locate more in response to the location of manufacturing activity than to the location of research universities and federal research facilities. The location of R&D employment, which includes government university, and industrial employees, is associated with facilities for all three types of R&D. Because of these factors, R&D in the U.S. is found on a significant per capita basis in 44 of 177 urban areas, most of them in the northeastern portion of the country. When two dimensions, industrial R&D laboratories and R&D employees, are combined as a measure of R&D concentration, the locational pattern is less clustered regionally. Ten urban areas in all regions of the U.S. are identified as important complexes of R&D. Since the location of R&D is a major indicator of comparative advantage for technological activities and the economic potential of urban regions, only a few areas of the U.S. are likely to remain important in the generation of innovations.     

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.     

Space victualling

Victualling in space differs fundamentally from victualling on land or at sea because there is little chance of foraging or of finding local sources of oxygen and water, and all metabolic products have to be carefully collected even if they will ultimately be jettisoned. The need for a deliberate policy for coping with carbon dioxide, faeces, and urine leads naturally, to schemes for recycling. Entropy is increased when food is metabolised: energy will have to be expended for even partial restoration of the status quo.     

The physics of brass wind instruments

The design of musical instruments owes more to art than to science and assessment of their quality is essentially subjective. Nevertheless, the physical principles of their operation are very interesting and may be of practical importance. This article reviews the acoustics of brass wind instruments, regarding the player and his instrument as an entity, and compares experimental and theoretical results.