An On-line Search for Optimum Operating Conditions of Noisy Systems

Optimum process operating conditions are often achieved by on-line computer programming. A general method has been developed which is capable of optimizing processes whose responses are corrupted by random error. The method is particularly useful for application to processes whose response functions contain sharp ridges. Application to ridge and non-ridge systems gives the same results in each case showing that the rate of convergence of the search is totally unaffected by the presence of a ridge. An accelarated gradient method is used which obtains its derivatives from a quadratic interpolation. The inability of the gradient method to move along a ridge is overcome by projecting a straight line through points on the ridge to obtain new starting points for a gradient search. Points on the ridge are located by finding the stationary point of the polynomial which is constructed by regression through points found by the gradient search. The method is applied to several test functions known to the literature—a fast convergence rate is obtained for a wide range of noise levels.     

Short texts to explain problem — Solution structures — and vice versa

Linguistic analysis of short published reports leads to the presentation of an aigorithm that depicts the problem-solving process in terms of a series of evaluative questions. The work shows how reports enable us to define in detail the various stages of problem solving, and it shows that an understanding of these various stages enables us to recognise information structures in written texts; the writing of brief reports of high-priority information on which the whole thinking process is based is thus seen as a vital part of the problem-solving process. One report is analysed in detail to demonstrate the close relationship between information structures in the text and the real-life thought'action process it describes. There is discussion of how paragraphs, sentences and signals within the sentences enable the writer to communicate the information in a conceptual array that represents the actual thought/action process it describes. Educational implications for inter-sentential coherence, discourse analysis, and writing structures, and control of research through written reports are all discussed.     

Distributed-parameter optimal control via mathematical programming

In this paper a variety of optimal control (OC) problems for distributed- parameter (DP) systems are approached using mathematical programming (MP). First, the principal DP models in current use are given, a variety of DP objective functions is provided, and the OC problems based on them are formulated. Second, these models and objective functions are converted in algebraic form, as required by MP, and the solution procedure of the OC problems via MP is outlined. Third, a representative set of nonlinear programming results applied to DP systems is presented, and finally, a numvber of application examples is given.     

A control problem with structural choices

The case is considered in which, during the operation of an optimal control system, the optimizer, in addition to applying his usual control, may switch structures. Necessary and sufficient conditions are derived and emphasis is placed on the special characteristics of this problem. Continuous and discrete time set-ups are considered and the separation principle is shown not to hold for the linear quadratic case in the presence of noise.     

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.