What Makes a Theory of Infinitesimals Useful? A View by Klein and Fraenkel

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein

A note on the strong law of large numbers

identically distributed (i.i.d.) random variables. Let Sn-t^Xk (fl » 1, 2, • • •)• J f e- 1 A long standing problem in probability theory has been to find neces

Where Is Science Going?

Do researchers produce scientific and technical knowledge differently than they did ten years ago? What will scientific research look like ten years from now? Addressing such questions means looking at science from a dynamic systems perspective. Two recent books about the social system of science, by Ziman and by Gibbons, Limoges, Nowotny, Schwartzman, Scott, and Trow, accept this challenge and argue that the research enterprise is changing. This article uses bibliometric data to examine the extent and nature of changes identified by these authors, taking as an example British research. We use their theoretical frameworks to investigate five characteristics of research said to be increasingly pervasive-namely, application, interdisciplinarity, networking, internationalization, and concentration of resources. Results indicate that research may be becoming more interdisciplinary and that research is increasingly conducted more in networks, both domestic and international; but the data are more ambiguous regarding application and concentration. CR - Copyright © 1996 Sage Publications, Inc

Surface interactions and high-voltage current collection

Spacecraft of the future will be larger and have higher power requirements than any flown to date. For several reasons, it is desirable to operate a high power system at high voltage. While the optimal voltages for many future missions are in the range 500 to 5000 volts, the highest voltage yet flown is approximately 100 volts. The NASCAP/LEO code is being developed to embody the phenomenology needed to model the environmental interactions of high voltage spacecraft. Some plasma environment are discussed. The treatment of the surface conductivity associated with emitted electrons and some simulations by NASCAP/LEO of ground based high voltage interaction experiments are described

Equity and Excellence in Research Funding

The tension between equity and excellence is fundamental in science policy. This tension might appear to be resolved through the use of merit-based evaluation as a criterion for research funding. This is not the case. Merit-based decision making alone is insufficient because of inequality aversion, a fundamental tendency of people to avoid extremely unequal distributions. The distribution of performance in science is extremely unequal, and no decision maker with the power to establish a distribution of public money would dare to match the level of inequality in research performance. We argue that decision makers who increase concentration of resources because they accept that research resources should be distributed according to merit probably implement less inequality than would be justified by differences in research performance. Here we show that the consequences are likely to be suppression of incentives for the very best scientists. The consequences for the performance of a national research system may be substantial. Decision makers are unaware of the issue, as they operate with distributional assumptions of normality that guide our everyday intuitions

A Rigid Local System with Monodromy Group 2.J_2

We exhibit a rigid local system of rank six on the affine line in characteristic $p=5$ whose arithmetic and geometric monodromy groups are the finite group $2.J_2$ ($J_2$ the Hall-Janko sporadic group) in one of its two (Galois-conjugate) irreducible representation of degree six