4,546 research outputs found
On multigraded generalizations of Kirillov-Reshetikhin modules
We study the category of Z^l-graded modules with finite-dimensional graded
pieces for certain Z+^l-graded Lie algebras. We also consider certain Serre
subcategories with finitely many isomorphism classes of simple objects. We
construct projective resolutions for the simple modules in these categories and
compute the Ext groups between simple modules. We show that the projective
covers of the simple modules in these Serre subcategories can be regarded as
multigraded generalizations of Kirillov-Reshetikhin modules and give a
recursive formula for computing their graded characters
Random-mass Dirac fermions in an imaginary vector potential: Delocalization transition and localization length
One dimensional system of Dirac fermions with a random-varying mass is
studied by the transfer-matrix methods which we developed recently. We
investigate the effects of nonlocal correlation of the spatial-varying Dirac
mass on the delocalization transition. Especially we numerically calculate both
the "typical" and "mean" localization lengths as a function of energy and the
correlation length of the random mass. To this end we introduce an imaginary
vector potential as suggested by Hatano and Nelson and solve the eigenvalue
problem. Numerical calculations are in good agreement with the results of the
analytical calculations.Comment: 4 page
Localization properties of a one-dimensional tight-binding model with non-random long-range inter-site interactions
We perform both analytical and numerical studies of the one-dimensional
tight-binding Hamiltonian with stochastic uncorrelated on-site energies and
non-fluctuating long-range hopping integrals . It was argued recently [A.
Rodriguez at al., J. Phys. A: Math. Gen. 33, L161 (2000)] that this model
reveals a localization-delocalization transition with respect to the disorder
magnitude provided . The transition occurs at one of the band edges (the upper
one for and the lower one for). The states at the other band edge are always
localized, which hints on the existence of a single mobility edge. We analyze
the mobility edge and show that, although the number of delocalized states
tends to infinity, they form a set of null measure in the thermodynamic limit,
i.e. the mobility edge tends to the band edge. The critical magnitude of
disorder for the band edge states is computed versus the interaction exponent
by making use of the conjecture on the universality of the normalized
participation number distribution at transition.Comment: 7 pages, 6 postscript figures, uses revtex
Reachability in Parametric Interval Markov Chains using Constraints
Parametric Interval Markov Chains (pIMCs) are a specification formalism that
extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into
account imprecision in the transition probability values: transitions in pIMCs
are labeled with parametric intervals of probabilities. In this work, we study
the difference between pIMCs and other Markov Chain abstractions models and
investigate the two usual semantics for IMCs: once-and-for-all and
at-every-step. In particular, we prove that both semantics agree on the
maximal/minimal reachability probabilities of a given IMC. We then investigate
solutions to several parameter synthesis problems in the context of pIMCs --
consistency, qualitative reachability and quantitative reachability -- that
rely on constraint encodings. Finally, we propose a prototype implementation of
our constraint encodings with promising results
Splitting Proofs for Interpolation
We study interpolant extraction from local first-order refutations. We
present a new theoretical perspective on interpolation based on clearly
separating the condition on logical strength of the formula from the
requirement on the com- mon signature. This allows us to highlight the space of
all interpolants that can be extracted from a refutation as a space of simple
choices on how to split the refuta- tion into two parts. We use this new
insight to develop an algorithm for extracting interpolants which are linear in
the size of the input refutation and can be further optimized using metrics
such as number of non-logical symbols or quantifiers. We implemented the new
algorithm in first-order theorem prover VAMPIRE and evaluated it on a large
number of examples coming from the first-order proving community. Our
experiments give practical evidence that our work improves the state-of-the-art
in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201
Realization of Rectangular Artificial Spin Ice and Direct Observation of High Energy Topology
In this letter, we have constructed and experimentally investigated
frustrated arrays of dipoles forming two-dimensional artificial spin ices with
different lattice parameters (rectangular arrays with horizontal and vertical
lattice spacings denoted by and respectively). Arrays with three
different ratios , and are
studied. Theoretical calculations of low-energy demagnetized configurations for
these same parameters are also presented. Experimental data for demagnetized
samples confirm most of the theoretical results. However, the highest energy
topology (doubly-charged monopoles) does not emerge in our theoretical model,
while they are seen in experiments for large enough . Our results also
insinuate that magnetic monopoles may be almost free in rectangular lattices
with a critical ratio , supporting previous
theoretical predictions
Comportamento do Ãndice de clorofila a, b e total na cultura da soja em sucessão a cultivos de outono-inverno.
JIPE 2013
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