Search results for "Mathematical research"
showing 6 items of 6 documents
Frames and representing systems in Fréchet spaces and their duals
2014
[EN] Frames and Bessel sequences in Fr\'echet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of analytic functions, give many examples and consequences about sampling sets and Dirichlet series expansions.
Personal Reflections on Dirk Jan Struik By Joseph W. Dauben
2018
Dirk Jan Struik, who taught for many years at the Massachusetts Institute of Technology and died on 21 October 2000 at the age of 106, was a distinguished mathematician and influential teacher. He was also widely known as a leading Marxist scholar and social activist. His early work on vector and tensor analysis, undertaken together with Jan Arnoldus Schouten, helped impart new mathematical techniques needed to master Einstein’s general theory of relativity. This collaboration lasted for over 20 years, but by the end of the 1930s, Struik came to realize that the heyday of the Ricci calculus had passed. After the Second World War, having now entered his 50s, he gave up mathematical research …
Old mathematical challenges: Precedents to the millennium problems
2018
The millennium problems set out by the Clay Mathematics Institute became a stimulus for mathematical research. The aim of this article is to highlight some previous challenges that were also a stimulus to finding proof for some interesting results. With this pretext, we present three moments in the history of mathematics that were important for the development of new lines of research. We briefly analyse the Tartaglia challenge, which brought about the discovery of a formula for third degree equations; Johan Bernoulli?s problem of the curve of fastest descent, which originated the calculus of variations; and the incidence of the problems posed by David Hilbert in 1900, focusing on the first…
Making Mathematics in an Oral Culture: Göttingen in the Era of Klein and Hilbert
2004
This essay takes a close look at specially selected features of the Göttingen mathematical culture during the period 1895–1920. Drawing heavily on personal accounts and archival resources, it describes the changing roles played by Felix Klein and David Hilbert, as Göttingen's two senior mathematicians, within a fast-growing community that attracted an impressive number of young talents. Within the course of these twenty-five years Göttingen exerted a profound impact on mathematics and physics throughout the world. Many factors contributed to the creation of a special atmosphere that served as a model for several other important centers for mathematical research. Göttingen exemplified a dyna…
Multi-Skill Call Center as a Grading from “Old” Telephony
2009
We explore parallels between the older telephony switches and the multi-skill call centers. The numerical results have shown that a call center with equally distributed skills is preferable compared to traditional grading-type design. The annex contains a short version of mathematical proof on limited availability schemes design for small call flow intensity *** and for large *** . The proof explores one excellent V. Benes' paper (from Bell Labs). On its own merit, the annex could initiate new mathematical research in call center area, more by now the powerful software for numerical analysis is available. Main conclusion is the following: numerical analysis of simple multi-skill call center…
MATHEMATICS AS A QUASI-EMPIRICAL SCIENCE
2006
The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T1, ..., T n in which Ti+1, for 1 ≤ i < n, supersedes T i . This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of t…