4,614 research outputs found
Webliography of African-American Champaign-Urbana
This Lab Note reflects one part of a year-long project called eBlackChampaign-Urbana. Our interest here is to provide better access to the dispersed documentation of local African-American history and culture in ChampaignUrbana, using digital technology to aggregate and enliven historical and contemporary information. Although this
webliography focuses primarily on substantial, in-depth texts documenting local African-American life, we are also
aggregating into the eBlackCU.net website URLs for local African-American websites, facebook pages, photographs,
newspaper clippings, flyers, posters and other ephemeral documentation of Champaign-Urbana's Black heritage.published or submitted for publicationnot peer reviewe
Algorithms in algebraic number theory
In this paper we discuss the basic problems of algorithmic algebraic number
theory. The emphasis is on aspects that are of interest from a purely
mathematical point of view, and practical issues are largely disregarded. We
describe what has been done and, more importantly, what remains to be done in
the area. We hope to show that the study of algorithms not only increases our
understanding of algebraic number fields but also stimulates our curiosity
about them. The discussion is concentrated of three topics: the determination
of Galois groups, the determination of the ring of integers of an algebraic
number field, and the computation of the group of units and the class group of
that ring of integers.Comment: 34 page
The least common multiple of a quadratic sequence
For any irreducible quadratic polynomial f(x) in Z[x] we obtain the estimate
log l.c.m.(f(1),...,f(n))= n log n + Bn + o(n) where B is a constant depending
on f.Comment: 26 page
Addendum: an analogue of Artin reciprocity for closed orbits of skew products
One of the unfulfilled aims of the authors of the preceding paper [W. Parry and M. Pollicott. An analogue of Bauer’s theorem for closed orbits of skew products. Ergod. Th. & Dynam. Sys. 28 (2008), 535–546] was to find a dynamical analogue of Artin reciprocity. In this addendum, we present one such version, suggested by work of Sunada
Unnested islands of period-doublings in an injected semiconductor laser
We present a theoretical study of unnested period-doubling islands in three-dimensional rate equations modeling a semiconductor laser subject to external optical injection. In this phenomenon successive curves of period doublings are not arranged in nicely nested islands, but intersect each other. This overall structure is globally organized by several codimension-2 bifurcations. As a consequence, the chaotic region existing inside an unnested island of period doublings can be entered not only via a period-doubling cascade but also via the breakup of a torus, and even via the sudden appearance of a chaotic attractor. In order to fully understand these different chaotic transitions we reveal underlying global bifurcations and we show how they are connected to codimension-2 bifurcation points. Unnested islands of period doublings appear to be generic and hence must be expected in a large class of dynamical systems
- …