262,880 research outputs found
A strong operator topology adiabatic theorem
We prove an adiabatic theorem for the evolution of spectral data under a weak
additive perturbation in the context of a system without an intrinsic time
scale. For continuous functions of the unperturbed Hamiltonian the convergence
is in norm while for a larger class functions, including the spectral
projections associated to embedded eigenvalues, the convergence is in the
strong operator topology.Comment: 15 pages, no figure
Adaptive Gibbs samplers
We consider various versions of adaptive Gibbs and Metropolis-
within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the
fly during a run, by learning
as they go in an attempt to optimise the algorithm. We present a cautionary
example of how even a simple-seeming adaptive Gibbs sampler may fail to
converge. We then present various positive results guaranteeing convergence
of adaptive Gibbs samplers under certain conditions
Generating functions for Wilf equivalence under generalized factor order
Kitaev, Liese, Remmel, and Sagan recently defined generalized factor order on
words comprised of letters from a partially ordered set by
setting if there is a subword of of the same length as
such that the -th character of is greater than or equal to the -th
character of for all . This subword is called an embedding of
into . For the case where is the positive integers with the usual
ordering, they defined the weight of a word to be
, and the corresponding weight
generating function . They then
defined two words and to be Wilf equivalent, denoted , if
and only if . They also defined the related generating
function where
is the set of all words such that the only embedding of
into is a suffix of , and showed that if and only if
. We continue this study by giving an explicit formula for
if factors into a weakly increasing word followed by a weakly
decreasing word. We use this formula as an aid to classify Wilf equivalence for
all words of length 3. We also show that coefficients of related generating
functions are well-known sequences in several special cases. Finally, we
discuss a conjecture that if then and must be
rearrangements, and the stronger conjecture that there also must be a
weight-preserving bijection such
that is a rearrangement of for all .Comment: 23 page
The quantum bit commitment theorem
Unconditionally secure two-party bit commitment based solely on the
principles of quantum mechanics (without exploiting special relativistic
signalling constraints, or principles of general relativity or thermodynamics)
has been shown to be impossible, but the claim is repeatedly challenged. The
quantum bit commitment theorem is reviewed here and the central conceptual
point, that an `Einstein-Podolsky-Rosen' attack or cheating strategy can always
be applied, is clarified. The question of whether following such a cheating
strategy can ever be disadvantageous to the cheater is considered and answered
in the negative. There is, indeed, no loophole in the theorem.Comment: LaTeX, 25 pages. Forthcoming in Foundations of Physics, May 200
Unions Impose Stability on a Turbulent Construction Industry
Grabelsky31_Unions_Impose_Stability_on_a_Turbulent_Construction_Industry.pdf: 133 downloads, before Oct. 1, 2020
Quivers and Three-Dimensional Lie Algebras
We study a family of three-dimensional Lie algebras that depend on a
continuous parameter . We introduce certain quivers, which we denote by
and , and prove that
idempotented versions of the enveloping algebras of the Lie algebras
are isomorphic to the path algebras of these quivers modulo certain ideals in
the case that is rational and non-rational, respectively. We then show
how the representation theory of the quivers and
can be related to the representation theory of quivers
of affine type , and use this relationship to study representations of the
Lie algebras . In particular, though it is known that the Lie algebras
are of wild representation type, we show that if we impose certain
restrictions on weight decompositions, we obtain full subcategories of the
category of representations of that are of finite or tame
representation type.Comment: 18 page
Motivation and Performance
Faculty reflection on VCU Great Bike Race Book course.
Course Description: This track will explore how motivation links to learning and performance
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