7,451 research outputs found
On Kostant's partial order on hyperbolic elements
We study Kostant's partial order on the elements of a semisimple Lie group in
relations with the finite dimensional representations. In particular, we prove
the converse statement of [3, Theorem 6.1] on hyperbolic elements.Comment: 7 page
Log-Euclidean Bag of Words for Human Action Recognition
Representing videos by densely extracted local space-time features has
recently become a popular approach for analysing actions. In this paper, we
tackle the problem of categorising human actions by devising Bag of Words (BoW)
models based on covariance matrices of spatio-temporal features, with the
features formed from histograms of optical flow. Since covariance matrices form
a special type of Riemannian manifold, the space of Symmetric Positive Definite
(SPD) matrices, non-Euclidean geometry should be taken into account while
discriminating between covariance matrices. To this end, we propose to embed
SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW
approach to its Riemannian version. The proposed BoW approach takes into
account the manifold geometry of SPD matrices during the generation of the
codebook and histograms. Experiments on challenging human action datasets show
that the proposed method obtains notable improvements in discrimination
accuracy, in comparison to several state-of-the-art methods
Generalized Induced Norms
Let ||.|| be a norm on the algebra M_n of all n-by-n matrices over the
complex field C. An interesting problem in matrix theory is that "are there two
norms ||.||_1 and ||.||_2 on C^n such that ||A||=max{||Ax||_2: ||x||_1=1} for
all A in M_n. We will investigate this problem and its various aspects and will
discuss under which conditions ||.||_1=||.||_2.Comment: 8 page
Entanglement of pure states for a single copy
An optimal local conversion strategy between any two pure states of a
bipartite system is presented. It is optimal in that the probability of success
is the largest achievable if the parties which share the system, and which can
communicate classically, are only allowed to act locally on it. The study of
optimal local conversions sheds some light on the entanglement of a single copy
of a pure state. We propose a quantification of such an entanglement by means
of a finite minimal set of new measures from which the optimal probability of
conversion follows.Comment: Revtex, 4 pages, no figures. Minor changes. Appendix remove
Heat Transfer in a Second Order Fluid with Suction and Constant Heat Sources
The heat transfer in the laminar boundary layer due to the flow of
a second order fluid over a flat plate subjected to suction in the presence
of constant heat sources has been discussed. The solution
of the problem is sought by expanding the flow and temperature
functions in powers of 1/λ, λ being the suction parameter. Besides
other results it is interesting to observe that an increase in elasticoviscous parameter, γ,decreases the temperature near the plate irrespective of suction
Tobacco and health: What can the medical profession do?
Tobacco consumption, that leads to three million
deaths every year of which about one million occur in
developing countries is a social evil(1). Tobacco smoke
is a complex mixture of as many as 4700 individual
constituents including carcinogens, irritants, ciliotoxic
substances and poisonous gases. There is no dearth of
information about the health hazards to smokers. it has
been implicated as a major risk factor in a variety of
chronic diseases including cardiac, cerebrovascular,
malignant, respiratory and other diseases (2), Most of
the smoking related lung diseases (e.g. chronic obstructive
lung disease and lung carcinoma) are dose dependent.
it is often the cumulative dose of smoking which
determines the risk. Parameters like pack-year (PY)
have been used to express exposure to tobacco smoke.
One PY implies one packet of cigarettes (or 20 gms.
tobacco) smoked each day over a course of one year (3).
In India the number of cigarettes and bidis per packet is
quite variable. A standard packet of cigarette and bidis
per packet is quite variable
Catalytic Conversion Probabilities for Bipartite Pure States
For two given bipartite-entangled pure states, an expression is obtained for
the least upper bound of conversion probabilities using catalysis. The
attainability of the upper bound can also be decided if that bound is less than
one.Comment: 4 pages; comments appreciated; the article is a modified version of
this preprint combined with arXiv:0707.044
Extremal extensions of entanglement witnesses: Unearthing new bound entangled states
In this paper, we discuss extremal extensions of entanglement witnesses based
on Choi's map. The constructions are based on a generalization of the Choi map
due to Osaka, from which we construct entanglement witnesses. These extremal
extensions are powerful in terms of their capacity to detect entanglement of
positive under partial transpose (PPT) entangled states and lead to unearthing
of entanglement of new PPT states. We also use the Cholesky-like decomposition
to construct entangled states which are revealed by these extremal entanglement
witnesses.Comment: 8 pages 6 figures revtex4-
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