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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
  • Language: en
  • Pages: 134

Strengthening the Linkages Between the Sciences and the Mathematical Sciences

Over three hundred years ago, Galileo is reported to have said, "The laws of nature are written in the language of mathematics." Often mathematics and science go hand in hand, with one helping develop and improve the other. Discoveries in science, for example, open up new advances in statistics, computer science, operations research, and pure and applied mathematics which in turn enabled new practical technologies and advanced entirely new frontiers of science. Despite the interdependency that exists between these two disciplines, cooperation and collaboration between mathematical scientists and scientists have only occurred by chance. To encourage new collaboration between the mathematical ...

U.S. Research Institutes in the Mathematical Sciences
  • Language: en
  • Pages: 30

U.S. Research Institutes in the Mathematical Sciences

This report is the result of a fast-track study of U.S. mathematical sciences research institutes done in response to a request from the National Science Foundation (NSF). The task of the Committee on U.S. Mathematical Sciences Research Institutes was to address the following three questions: 1. What are the characteristic features of effective mathematical sciences research institutes in the ways that they further mathematical research in the United States, and are there ways that the current configuration can be improved? 2. What kinds of institutes should there be in the United States, and how many does the nation need? 3. How should U.S. mathematical sciences research institutes be configured (with regard to, for example, diversity of operating formats, distribution of mathematical fields, and interinstitute cooperation or coordination) in order to have the nation's mathematical research enterprise continue to be most productive and successful?

Mathematical Research in Materials Science
  • Language: en
  • Pages: 142

Mathematical Research in Materials Science

This book describes fruitful past collaborations between the mathematical and materials sciences and indicates future challenges. It seeks both to encourage mathematical sciences research that will complement vital research in materials science and to raise awareness of the value of quantitative methods. The volume encourages both communities to increase cross-disciplinary collaborations, emphasizing that each has much to gain from such an increase, and it presents recommendations for facilitating such work. This book is written for both mathematical and materials science researchers interested in advancing research at this interface; for federal and state agency representatives interested in encouraging such collaborations; and for anyone wanting information on how such cross-disciplinary, collaborative efforts can be accomplished successfully.

Mathematical Challenges from Theoretical/Computational Chemistry
  • Language: en
  • Pages: 126

Mathematical Challenges from Theoretical/Computational Chemistry

Computational methods are rapidly becoming major tools of theoretical, pharmaceutical, materials, and biological chemists. Accordingly, the mathematical models and numerical analysis that underlie these methods have an increasingly important and direct role to play in the progress of many areas of chemistry. This book explores the research interface between computational chemistry and the mathematical sciences. In language that is aimed at non-specialists, it documents some prominent examples of past successful cross-fertilizations between the fields and explores the mathematical research opportunities in a broad cross-section of chemical research frontiers. It also discusses cultural differences between the two fields and makes recommendations for overcoming those differences and generally promoting this interdisciplinary work.

Mathematics and Physics of Emerging Biomedical Imaging
  • Language: en
  • Pages: 231

Mathematics and Physics of Emerging Biomedical Imaging

This cross-disciplinary book documents the key research challenges in the mathematical sciences and physics that could enable the economical development of novel biomedical imaging devices. It is hoped that the infusion of new insights from mathematical scientists and physicists will accelerate progress in imaging. Incorporating input from dozens of biomedical researchers who described what they perceived as key open problems of imaging that are amenable to attack by mathematical scientists and physicists, this book introduces the frontiers of biomedical imaging, especially the imaging of dynamic physiological functions, to the educated nonspecialist. Ten imaging modalities are covered, from the well-established (e.g., CAT scanning, MRI) to the more speculative (e.g., electrical and magnetic source imaging). For each modality, mathematics and physics research challenges are identified and a short list of suggested reading offered. Two additional chapters offer visions of the next generation of surgical and interventional techniques and of image processing. A final chapter provides an overview of mathematical issues that cut across the various modalities.

Mathematical Sciences, Technology, and Economic Competitiveness
  • Language: en
  • Pages: 127

Mathematical Sciences, Technology, and Economic Competitiveness

This book describes the contributions of mathematics to the nation's advanced technology and to economic competitiveness. Examples from five industriesâ€"aircraft, petroleum, automotive, semiconductor, and telecommunicationsâ€"illustrate how mathematics enters into and improves industry. Mathematical Sciences, Technology, and Economic Competitiveness addresses these high-technology industries and breadth of mathematical endeavors in the United States as they materially contribute to the technology base from which innovation in these industries flows. The book represents a serious attempt by the mathematics community to bring about an awareness by policymakers of the pervasive influence of mathematics in everyday life.

Motion, Control, and Geometry
  • Language: en
  • Pages: 81

Motion, Control, and Geometry

Some of the modem developments described in Motion, Control, and Geometry include the geometric control of robot motion and craft orientation, how high-power precision micromotors are engineered for less invasive surgery and self-focusing lens applications, what a mobile robot on a surface has in common with one moving in three dimensions, and how the motion-control problem is simplified by a coupled oscillator's geometric grouping of degrees of freedom and motion time scales. The four papers in these proceedings provide a view through the scientific portal of today's motion-control geometric research into tomorrow's technology. The mathematics needed to carry out this research is that of mo...

Preserving Scientific Data on Our Physical Universe
  • Language: en
  • Pages: 59

Preserving Scientific Data on Our Physical Universe

This book advises the National Archives and Records Administration and federal R&D agencies on the long-term retention of scientific and technical data, particularly in electronic formats. It proposes the creation of a National Scientific Information Resource Federation, which would apply a strategic data life-cycle management plan to better link the government's existing scientific data holdings and improve public access to those holdings. The book is expected to draw attention to data management concerns in the context of the current government emphasis on promoting a National Information Infrastructure and to make a significant contribution to improving the inadequate situation regarding our nation's valuable scientific data and information resources.