3,280 research outputs found
With a Little Help from my Friends: How a US Judicial International Comity Balancing Test Can Foster Global Antitrust Redress
Noncommuting Coordinates and Magnetic Monopoles
The appearance of noncommuting spatial coordinates is studied in quantum
systems containing a magnetic monopole and under the influence of a radial
potential. We derive expressions for the commutators of the coordinates that
have been restricted to the lowest energy level. Quantum corrections are found
to previous results by Frenkel and Pereira based on quantizing the Dirac
brackets of the classical theory. For two different potentials, the modified
harmonic oscillator potential and the modified Coulomb potential, we also
calculate the commutators for a projection to a fixed energy level.Comment: 8 pages, Late
Noncommutative Spherically Symmetric Spaces
We examine some noncommutative spherically symmetric spaces in three space
dimensions. A generalization of Snyder's noncommutative (Euclidean) space
allows the inclusion of the generator of dilations into the defining algebra of
the coordinate and rotation operators. We then construct a spherically
symmetric noncommutative Laplacian on this space having the correct limiting
spectrum. This is presented via a creation and annihilation operator
realization of the algebra, which may lend itself to a truncation of the
Hilbert space.Comment: 9 pages, revtex, matches Phys.Rev.D versio
The word problem distinguishes counter languages
Counter automata are more powerful versions of finite-state automata where
addition and subtraction operations are permitted on a set of n integer
registers, called counters. We show that the word problem of is accepted
by a nondeterministic -counter automaton if and only if .Comment: 8 page
Cone types and geodesic languages for lamplighter groups and Thompson's group F
We study languages of geodesics in lamplighter groups and Thompson's group F.
We show that the lamplighter groups have infinitely many cone types, have
no regular geodesic languages, and have 1-counter, context-free and counter
geodesic languages with respect to certain generating sets. We show that the
full language of geodesics with respect to one generating set for the
lamplighter group is not counter but is context-free, while with respect to
another generating set the full language of geodesics is counter and
context-free. In Thompson's group F with respect to the standard finite
generating set, we show there are infinitely many cone types and no regular
language of geodesics with respect to the standard finite generating set. We
show that the existence of families of "seesaw" elements with respect to a
given generating set in a finitely generated infinite group precludes a regular
language of geodesics and guarantees infinitely many cone types with respect to
that generating set.Comment: 30 pages, 13 figure
Buying a Better World: Students as Conscious Consumers
Conscious consumer movements have given people opportunities to “vote with their dollars” – that is, buy from companies with values matching their own, and forgo products from businesses with questionable policies and practices. After providing brief context about consumerism and conscious consumption, I focus on a Conscious Consumer Project that I teach in my First Year Writing courses at St. John’s University. Excerpts of student writing emphasizing labor issues, as well as student reflections on the project, are shared as I discuss possibilities for revising and improving the assignment. The possibilities discussed include increasing opportunities for students to do academic service-learning and connect the project to their spirituality
Random subgroups of Thompson's group
We consider random subgroups of Thompson's group with respect to two
natural stratifications of the set of all generator subgroups. We find that
the isomorphism classes of subgroups which occur with positive density are not
the same for the two stratifications.
We give the first known examples of {\em persistent} subgroups, whose
isomorphism classes occur with positive density within the set of -generator
subgroups, for all sufficiently large . Additionally, Thompson's group
provides the first example of a group without a generic isomorphism class of
subgroup. Elements of are represented uniquely by reduced pairs of finite
rooted binary trees.
We compute the asymptotic growth rate and a generating function for the
number of reduced pairs of trees, which we show is D-finite and not algebraic.
We then use the asymptotic growth to prove our density results.Comment: 37 pages, 11 figure
Ireland\u27s fight for freedom and the Irish in the U.S.A:
https://stars.library.ucf.edu/prism/1331/thumbnail.jp
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