Mocposite functions

Traditional mathematical notation can lead to confusion. Expressions that appear to define composite functions sometimes do not. A particular example with engineering applications is studied in detail.Comment: To appear in the American Mathematical Monthl

The football player and the infinite series

This is the text of an expository talk given at the May 1997 Detroit meeting of the American Mathematical Society. It is a tale of a famous football player and a subtle problem he posed about the uniform convergence of Dirichlet series. Hiding in the background is the theory of analytic functions of an infinite number of variables

Continuing the biological exploration of Mars

Mars has been an object of interest for the better part of this century. To a biologist, Mars assumes special importance because many aspects of the theory of chemical evolution for the origin of life can be tested there. The central idea of this theory is that life on a suitable planet arises through a process in which the so-called biogenic elements combine to form increasingly more complex molecules under the influence of naturally-occurring energy sources ultimately resulting in the formation of replicating organic molecules. The biogenic elements are present on Mars today. Furthermore, the available evidence also strongly suggests that Mars may have had an early history similar to that of the Earth, including a period in which large amounts of liquid water once flowed on its surface and a denser atmosphere and higher global temperatures prevailed. This is important since many lines of evidence indicate that living organisms were already present on the Earth within the first billion years after its formation at a time when the environment on Mars may have closely resembled that of Earth. Our current knowledge of the state of chemical evolution on Mars can best be described as paradoxical. Most of what we have learned has come from experiments performed on the Viking landers. The combination of planned investigations covered a broad range of techniques to detect signs of chemical evolution. The most surprising data from all of these was the absence of any detectable quantities of organic compounds at the two landing sites. On the other hand, the Viking experiments did indicate that the Martian surface samples contained unidentified strong oxidant(s) that could account for their absence

The solar system: Importance of research to the biological sciences

An attempt is made to describe the scope of scientific areas that comprise the current field of exobiology in the United States. From investigations of astrophysical phenomena that deal with the birth of stars and planetary systems to questions of molecular biology involving phylogenetic relationships among organisms, from attempts to simulate the synthesis of biological precursor molecules in the chemistry laboratory to making measurements of the organic constituents of Titan's atmosphere, these researches all converge toward a common objective--answering the question of how life came about in the universe

Control system software, simulation, and robotic applications

All essential existing capabilities needed to create a man-machine interaction dynamics and performance (MMIDAP) capability are reviewed. The multibody system dynamics software program Order N DISCOS will be used for machine and musculo-skeletal dynamics modeling. The program JACK will be used for estimating and animating whole body human response to given loading situations and motion constraints. The basic elements of performance (BEP) task decomposition methodologies associated with the Human Performance Institute database will be used for performance assessment. Techniques for resolving the statically indeterminant muscular load sharing problem will be used for a detailed understanding of potential musculotendon or ligamentous fatigue, pain, discomfort, and trauma. The envisioned capacity is to be used for mechanical system design, human performance assessment, extrapolation of man/machine interaction test data, biomedical engineering, and soft prototyping within a concurrent engineering (CE) system