133 research outputs found
Non-commutative connections of the second kind
A connection-like objects, termed {\em hom-connections} are defined in the
realm of non-commutative geometry. The definition is based on the use of
homomorphisms rather than tensor products. It is shown that hom-connections
arise naturally from (strong) connections in non-commutative principal bundles.
The induction procedure of hom-connections via a map of differential graded
algebras or a differentiable bimodule is described. The curvature for a
hom-connection is defined, and it is shown that flat hom-connections give rise
to a chain complex.Comment: 13 pages, LaTe
A Class of Bicovariant Differential Calculi on Hopf Algebras
We introduce a large class of bicovariant differential calculi on any quantum
group , associated to -invariant elements. For example, the deformed
trace element on recovers Woronowicz' calculus. More
generally, we obtain a sequence of differential calculi on each quantum group
, based on the theory of the corresponding braided groups . Here
is any regular solution of the QYBE.Comment: 16 page
Quantum teardrops
Algebras of functions on quantum weighted projective spaces are introduced,
and the structure of quantum weighted projective lines or quantum teardrops are
described in detail. In particular the presentation of the coordinate algebra
of the quantum teardrop in terms of generators and relations and classification
of irreducible *-representations are derived. The algebras are then analysed
from the point of view of Hopf-Galois theory or the theory of quantum principal
bundles. Fredholm modules and associated traces are constructed. C*-algebras of
continuous functions on quantum weighted projective lines are described and
their K-groups computed.Comment: 18 page
The Serre spectral sequence of a noncommutative fibration for de Rham cohomology
For differential calculi on noncommutative algebras, we construct a twisted
de Rham cohomology using flat connections on modules. This has properties
similar, in some respects, to sheaf cohomology on topological spaces. We also
discuss generalised mapping properties of these theories, and relations of
these properties to corings. Using this, we give conditions for the Serre
spectral sequence to hold for a noncommutative fibration. This might be better
read as giving the definition of a fibration in noncommutative differential
geometry. We also study the multiplicative structure of such spectral
sequences. Finally we show that some noncommutative homogeneous spaces satisfy
the conditions to be such a fibration, and in the process clarify the
differential structure on these homogeneous spaces. We also give two explicit
examples of differential fibrations: these are built on the quantum Hopf
fibration with two different differential structures.Comment: LaTeX, 33 page
Obturator Artery Aneurysm
AbstractWe present a case of a symptomatic obturator artery aneurysm. The patient was investigated for a possible rectal tumor. The final diagnosis was made during surgery, despite the presence of imaging studies. The operation consisted of simple ligation of inflow and outflow of the aneurysm. Satisfying early and long term result indicates that this is a sufficient operative procedure in such an aneurysm
Direct measurement of diurnal polar motion by ring laser gyroscopes
We report the first direct measurements of the very small effect of forced
diurnal polar motion, successfully observed on three of our large ring lasers,
which now measure the instantaneous direction of Earth's rotation axis to a
precision of 1 part in 10^8 when averaged over a time interval of several
hours. Ring laser gyroscopes provide a new viable technique for directly and
continuously measuring the position of the instantaneous rotation axis of the
Earth and the amplitudes of the Oppolzer modes. In contrast, the space geodetic
techniques (VLBI, SLR, GPS, etc.) contain no information about the position of
the instantaneous axis of rotation of the Earth, but are sensitive to the
complete transformation matrix between the Earth-fixed and inertial reference
frame. Further improvements of gyroscopes will provide a powerful new tool for
studying the Earth's interior.Comment: 5 pages, 4 figures, agu2001.cl
On Iterated Twisted Tensor Products of Algebras
We introduce and study the definition, main properties and applications of
iterated twisted tensor products of algebras, motivated by the problem of
defining a suitable representative for the product of spaces in noncommutative
geometry. We find conditions for constructing an iterated product of three
factors, and prove that they are enough for building an iterated product of any
number of factors. As an example of the geometrical aspects of our
construction, we show how to construct differential forms and involutions on
iterated products starting from the corresponding structures on the factors,
and give some examples of algebras that can be described within our theory. We
prove a certain result (called ``invariance under twisting'') for a twisted
tensor product of two algebras, stating that the twisted tensor product does
not change when we apply certain kind of deformation. Under certain conditions,
this invariance can be iterated, containing as particular cases a number of
independent and previously unrelated results from Hopf algebra theory.Comment: 44 pages, 21 figures. More minor typos corrections, one more example
and some references adde
Analysis of the Accuracy of Prediction of the Celestial Pole Motion
VLBI observations carried out by global networks provide the most accurate
values of the precession-nutation angles determining the position of the
celestial pole; as a rule, these results become available two to four weeks
after the observations. Therefore, numerous applications, such as satellite
navigation systems, operational determination of Universal Time, and space
navigation, use predictions of the coordinates of the celestial pole. In
connection with this, the accuracy of predictions of the precession- nutation
angles based on observational data obtained over the last three years is
analyzed for the first time, using three empiric nutation models---namely,
those developed at the US Naval Observatory, the Paris Observatory, and the
Pulkovo Observatory. This analysis shows that the last model has the best of
accuracy in predicting the coordinates of the celestial pole. The rms error for
a one-month prediction proposed by this model is below 100 microarcsecond.Comment: 13 p
Fairness-enhancing interventions in stream classification
The wide spread usage of automated data-driven decision support systems has
raised a lot of concerns regarding accountability and fairness of the employed
models in the absence of human supervision. Existing fairness-aware approaches
tackle fairness as a batch learning problem and aim at learning a fair model
which can then be applied to future instances of the problem. In many
applications, however, the data comes sequentially and its characteristics
might evolve with time. In such a setting, it is counter-intuitive to "fix" a
(fair) model over the data stream as changes in the data might incur changes in
the underlying model therefore, affecting its fairness. In this work, we
propose fairness-enhancing interventions that modify the input data so that the
outcome of any stream classifier applied to that data will be fair. Experiments
on real and synthetic data show that our approach achieves good predictive
performance and low discrimination scores over the course of the stream.Comment: 15 pages, 7 figures. To appear in the proceedings of 30th
International Conference on Database and Expert Systems Applications, Linz,
Austria August 26 - 29, 201
Morita base change in Hopf-cyclic (co)homology
In this paper, we establish the invariance of cyclic (co)homology of left
Hopf algebroids under the change of Morita equivalent base algebras. The
classical result on Morita invariance for cyclic homology of associative
algebras appears as a special example of this theory. In our main application
we consider the Morita equivalence between the algebra of complex-valued smooth
functions on the classical 2-torus and the coordinate algebra of the
noncommutative 2-torus with rational parameter. We then construct a Morita base
change left Hopf algebroid over this noncommutative 2-torus and show that its
cyclic (co)homology can be computed by means of the homology of the Lie
algebroid of vector fields on the classical 2-torus.Comment: Final version to appear in Lett. Math. Phy
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