Board on Mathematical Sciences – författare

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 modem differential geometry, and the questions raised in the field of motion-control geometry go directly to the research frontier. Geometry is a mathematical area too often neglected nowadays in a student''s education. This publication will help adjust the control initially imposed about 2,300 years ago on one kind of "motion"—that of students entering Plato''s Academy, where the following caveat was inscribed above the doorway: "Let no one ignorant of geometry enter here." Readers of these chapters will gain an appreciation of modem geometry and how it continues to play a crucial role in the context of motion control in cutting-edge science and technology.

Spatial statistics is one of the most rapidly growing areas of statistics, rife with fascinating research opportunities. Yet many statisticians are unaware of those opportunities, and most students in the United States are never exposed to any course work in spatial statistics. Written to be accessible to the nonspecialist, this volume surveys the applications of spatial statistics to a wide range of areas, including image analysis, geosciences, physical chemistry, and ecology.

The book describes the contributions of the mathematical sciences, summarizes the current state of knowledge, and identifies directions for research.

This book focuses on computational methods to determine the dynamics of large-scale electromagnetic, acoustic, and mechanical systems, including those with many substructures and characterized by an extended range of scales. Examples include large naval and maritime vessels, aerospace vehicles, and densely packed microelectronic and optical integrated circuits (VLSI). The interplay of time and frequency-domain computational and experimental procedures was addressed, emphasizing their relationship and synergy, and indicating mathematics research opportunities.

This book describes the contributions of mathematics to the nation''s advanced technology and to economic competitiveness. Examples from five industries—aircraft, petroleum, automotive, semiconductor, and telecommunications—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.

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 modem differential geometry, and the questions raised in the field of motion-control geometry go directly to the research frontier. Geometry is a mathematical area too often neglected nowadays in a student''s education. This publication will help adjust the control initially imposed about 2,300 years ago on one kind of "motion"—that of students entering Plato''s Academy, where the following caveat was inscribed above the doorway: "Let no one ignorant of geometry enter here." Readers of these chapters will gain an appreciation of modem geometry and how it continues to play a crucial role in the context of motion control in cutting-edge science and technology.