Mathematical Sciences, Technology, and Economic Competitiveness (1991) / Chapter Skim
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4 THE TECHNOLOGY BASE
4 THE TECHNOLOGY BASE
Pages 55-87
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From page 55... ...
Economic competitiveness, among other factors, requires a broad technology base from which to derive new methods of production, quantitative information (data) and analysis, and quality control methodology.
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From page 56... ...
In a series of cases, one finds the same subjects moving back and forth between theory and applications, and becoming richer with each transition, as the following examples illustrate: · Nearly integrable systems of differential equations and fiber optics; · Geometrical optics and the asymptotic solutions of differential equations; · Fourier analysis, group symmetries, and special functions; · Covariant differential geometry and elastic deformations; and · Fourier analysis on finite groups and the fast-Fourier-transform (FFT) algorithm.
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From page 57... ...
Rather, the point of this chapter is to analyze areas of the mathematical sciences and to document their close connection to economic competitiveness, thereby establishing the importance of the technology base. 57 4.1 Technology Transfer The technology transfer of importance to this report is the transfer of ideas, methods, and results from the mathematical sciences community to engineering and industrial groups for the purpose of improving the technical operation and economic competitiveness of U.S.
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From page 58... ...
His influence on Japanese manufacturing, and notably on the Japanese engineer Taguchi, was profound and was an important reason for the success Japan has had in industrial competition. Taguchi's contribution was to adapt the experimental design methodology, developed earlier in the United Kingdom and the United States, to problems of reducing variability in the performance of products, thereby increasing their quality.
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From page 59... ...
. Applied mathematics is a research field that develops and uses new or existing mathematical theory to solve problems of importance to society.
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accumulates near the electric image of the dark spots of the document. The boundary of the toner's region is a "free boundary." The electric potential satisfies one partial differential equation outside the toner and another partial differential equation inside the toner.
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A consortium of industrial sponsors has been organized by the Institute for Oil Recovery and the Department of Mathematics at the University of Wyoming. The scientific program of the institute follows the research interests of its faculty in petroleum reservoir modeling and numerical simulation.
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A portable translator was distributed within the Bell Laboratories and to universities for a nominal cost, thereby encouraging experimentation by users and feedback to the designer. Today the estimated number of C++ users is 100,000.
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Highly efficient methods of computational fluid dynamics lead to airplane geometries with optimal flight characteristics and lower fuel consumption (see Figure 4.~. Complex processes are characterized by their many interacting subprocesses.
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These composite overlapping grids are used in modeling fluid flow around objects with complex geometrical structure. Some of their advantages over other methods are their smoothness and their ability to provide high resolution where it is needed, both of which are important for accurate modeling.
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From page 65... ...
mandated by Congress identified 20 critical technologies, including the following five: · Simulation and modeling · Software producibility · Parallel computer architectures · Computational fluid dynamics · Semiconductor devices and microelectronic circuits Simulation and modeling have a critical role among the remaining fifteen identified technologies. Simulation has been at the heart of progress in technology and science for many reasons, including the following: Necessity.
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From page 66... ...
At the same time, powerful workstations provide desktop computational capability formerly available only on mainframes at a limited number of central locations. Of equal importance to the raw computing power are advances being made in mathematical sciences, including the development of algorithms for parallel processing.
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Computer simulation is an increasingly important method for determining the shape and structure of biological molecules and will be an increasingly powerful tool in biotechnology. Reprinted, by permission, from [13]
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From page 68... ...
Finally, efficient and eFective numerical methods for solving the equations must be developed and tested in each case. Modeling is more than mathematical and numerical analysis it must of necessity be an interdisciplinary effort requiring the cooperai;ion of engineers and scientists who understand the problems and mathematicians who understand the computational and mathematical modeling process.
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~< ~ ~ v w v ^ ~ ~ ~ ~v 4 - -w V a_ ~ ~ 1 ~ 1 1 V JO I J O vv w AL G O W 1 1 1 4.3 Statistical Quality Improvement The methods and concepts of quality control and statistical design ~_ 1~` . ~ ~ of experiments began in the 1920s.
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From page 70... ...
The facility had a product failure rate of 146 percent, meaning that most television sets required repair, and some required multiple repairs, before manufacture was complete. After introduction of quality improvement methods, the failure rate was reduced to 2 percent, with an increase in product quality and a decrease in manufacturing costs.
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Thus it is no surprise that they play a central role in the technology base required for economic competitiveness. Asymptotics Early in this century, boundary layer theory was developed as a powerful too!
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Numerical algorithms, mathematical theory, and excellent software packages have been developed. Engineering-based CAD/CAM packages and computer codes depend on numerical algorithms based on the theory of stiff ordinary differential equations.
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It is an area to which mathematicians have contributed extensively. Similarly, image processing and pattern recognition ideas often draw from methods in differential equations.
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. This improvement is based on new mathematical ideas and algorithms, which transform the unknown density function by a pseudodifferential operator and render the inverse problem local in terms of the tomographic data.
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~ ~0100Y BOSE 75 FICCRE 4.3b Improved image reconstruction methods for same image ~ in Figure 4.3a. Reprinted, by permission' Tom )
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Similar issues arise in many other technological contexts, such as the relation of material strength to microscopic descriptions involving lattice defects, voids, and microfractures and in the derivation of flow equations through porous media. To ciate, substantial progress has been made in the understanding of viscous flow through porous media, a necessary precondition for meaningful attempts at secondary and tertiary oil recovery.
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Copyright Q1988 by the Society for Computer Simulation.
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A measure of lithe enormous progress in opl;imizal;ion algorithms since that time is that algorithmic improvements in many areas have matched or even exceeded gains in computing power. For example, quasi-Newton methods, developed in the 1960s, require only first-derivative information but, close to the solution, converge very rapidly, whereas the only method previously available could display arbitrarily slow convergence or fail to converge even on simple problems.
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Sequential Quadratic Programming Methods Enormous progress has been made within the past 15 years in the development of algorithms for solving optimization problems that include nonlinear constraints. A great step forward has been the (levelopment of sequential quadratic programming (SQP)
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For example, one power company reduced the power loss in its system by 3 percent per year, leading to an estimated annual savings of $2.5 million. The scenario just described for the OPF problem illustrates a frequent pattern in the successful application of mathematical sciences: once a previously intractable problem has been solved, expectations rise accordingly.
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Discrete Optimization Applications of discrete optimization are revolutionizing the way products are manufactured, ordered, stored, and delivered. With proper mathematical scheduling techniques, one has prompt fulfillment of orders, with striking economic consequences.
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The simulator provides the user with a way to cut and allocate tree stems, receive immediate feedback on the economic consequences of the decisions, and see for comparison the dynamic programming decisions and their economic consequences. Workers on site in forests and at mills quickly became comfortable with the system.
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as input, instead of the model being treated deterministically. Stochastic modeling areas such as simulation, queuing theory, dynamic programming, statistical quality control, and reliability have aIreacly been alluder]
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One of these recommendations stated that "Operations re 1 ~ 1. 1 1 1 1 · 1 1 1 1 ~ 1 ~ searcn lapped matnemat~cs methods and mockers tor solving complex optimization oroblemsl should be recognized as a standard approach for problem solving in the FAA." As an example, when the safety of navigation standarcis over the North Atlantic was questioned by the International Federation of Airline Pilots Association in the 1960s, an operations research stucly, which included the assessment of collision risk, resulted in a resolution that troth minimized cost and maximized safety.
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From page 85... ...
4.7 Manpower, Education, and Training The mathematical sciences community has the primary responsibility for the collegiate mathematics education of engineers and scientists. It has provided significant portions of the intellectual leadership in efforts to revitalize education at the K-12 levels and has sole responsibility for graduate- and professional-level education in the mathematical sciences.
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From page 86... ...
Indeed, what was once considered advanced mathematical training is now becoming essential knowledge for many future blue-collar jobs. In Japan, working on an automobile assembly line requires that employees with only a high school diploma perform statistical quality control calculations.
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From page 87... ...
Because the mathematical sciences community has only recently returned to these educational issues in a serious way, because of the great importance of science and technical education to economic competitiveness and other important national issues, and because of the sizable fraction that mathematics occupies within science and technical education as a whole, there is a strong need for the mathematical sciences community to recognize the seriousness of the issues described in this report and to assume responsibility for further action.
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