2,487 research outputs found
The Chow ring for the classifying space of
Let be the general orthogonal group scheme (the group of orthogonal
similitudes). In the topological category, Y. Holla and N. Nitsure determined
the singular cohomology ring of
the classifying space of the corresponding complex Lie
group in terms of explicit generators and relations. The
author of the present note showed that over any algebraically closed field of
characteristic not equal to , the smooth-\'etale cohomology ring of the classifying algebraic stack
has the same description in terms of generators and relations as the singular
cohomology ring . Totaro defined
for any reductive group over a field, the Chow ring , which is
canonically identified with the ring of characteristic classes in the sense of
intersection theory, for principal -bundles, locally trivial in \'etale
topology. In this paper, we calculate the Chow group over any
field of characteristic different from in terms of generators and
relations.Comment: 11 page
Atomistic aspects of ductile responses of cubic silicon carbide during nanometric cutting
Cubic silicon carbide (SiC) is an extremely hard and brittle material having unique blend of material properties which makes it suitable candidate for microelectromechanical systems and nanoelectromechanical systems applications. Although, SiC can be machined in ductile regime at nanoscale through single-point diamond turning process, the root cause of the ductile response of SiC has not been understood yet which impedes significant exploitation of this ceramic material. In this paper, molecular dynamics simulation has been carried out to investigate the atomistic aspects of ductile response of SiC during nanometric cutting process. Simulation results show that cubic SiC undergoes sp3-sp2 order-disorder transition resulting in the formation of SiC-graphene-like substance with a growth rate dependent on the cutting conditions. The disorder transition of SiC causes the ductile response during its nanometric cutting operations. It was further found out that the continuous abrasive action between the diamond tool and SiC causes simultaneous sp3-sp2 order-disorder transition of diamond tool which results in graphitization of diamond and consequent tool wear
Harder-Narasimhan Filtrations which are not split by the Frobenius maps
Let be a smooth projective variety over a perfect field of
characteristic , and be a vector bundle over . It is well known
that if is a curve and is not strongly semistable, then some Frobenius
pullback is a direct sum of strongly semistable bundles. A natural
question to ask is whether this still holds in higher dimension. Indranil
Biswas, Yogish I. Holla, A.J. Parameswaran, and S. Subramanian showed that
there is always a counterexample to this over any algebraically closed field of
positive characteristic which is uncountable. However, we will produce a smooth
projective variety over and a rank 2 vector bundle on it, which,
restricted to each prime in a nonempty open subset of \spec\mathbb Z,
constitutes a counterexample over . Indeed, given any split semisimple
simply connected algebraic group of semisimple rank over ,
we will show that there exists a smooth projective homogeneous space over
and a vector bundle on of rank 2 such that for each prime
in a nonempty open subset of \spec\mathbb Z, the restriction
as a vector bundle over is a
counterexample. We only use the Borel-Weil-Bott theorem in characteristic 0 and
Frobenius Splitting of in characteristic .Comment: 3 page
Text segmentation on multilabel documents: A distant-supervised approach
Segmenting text into semantically coherent segments is an important task with
applications in information retrieval and text summarization. Developing
accurate topical segmentation requires the availability of training data with
ground truth information at the segment level. However, generating such labeled
datasets, especially for applications in which the meaning of the labels is
user-defined, is expensive and time-consuming. In this paper, we develop an
approach that instead of using segment-level ground truth information, it
instead uses the set of labels that are associated with a document and are
easier to obtain as the training data essentially corresponds to a multilabel
dataset. Our method, which can be thought of as an instance of distant
supervision, improves upon the previous approaches by exploiting the fact that
consecutive sentences in a document tend to talk about the same topic, and
hence, probably belong to the same class. Experiments on the text segmentation
task on a variety of datasets show that the segmentation produced by our method
beats the competing approaches on four out of five datasets and performs at par
on the fifth dataset. On the multilabel text classification task, our method
performs at par with the competing approaches, while requiring significantly
less time to estimate than the competing approaches.Comment: Accepted in 2018 IEEE International Conference on Data Mining (ICDM
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