52,623 research outputs found
q-Deformation of the Krichever-Novikov Algebra
The recent focus on deformations of algebras called quantum algebras can be
attributed to the fact that they appear to be the basic algebraic structures
underlying an amazingly diverse set of physical situations. To date many
interesting features of these algebras have been found and they are now known
to belong to a class of algebras called Hopf algebras [1]. The remarkable
aspect of these structures is that they can be regarded as deformations of the
usual Lie algebras. Of late, there has been a considerable interest in the
deformation of the Virasoro algebra and the underlying Heisenberg algebra
[2-11]. In this letter we focus our attention on deforming generalizations of
these algebras, namely the Krichever-Novikov (KN) algebra and its associated
Heisenberg algebra.Comment: AmsTex. To appear in Letters in Mathematical Physic
Klein tunneling through an oblique barrier in graphene ribbons
We study a transmission coefficient of graphene nanoribbons with a top gate
which acts as an oblique barrier. Using a Green function method based on the
Dirac-like equation, scattering among transverse modes due to the oblique
barrier is taken into account numerically. In contrast to the 2-dimensional
graphene sheet, we find that the pattern of transmission in graphene ribbons
depends strongly on the electronic structure in the region of the barrier.
Consequently, irregular structures in the transmission coefficient are
predicted while perfect transmission is still calculated in the case of
metallic graphene independently of angle and length of the oblique barrier
A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion
We consider the problem of reconstructing a low-rank matrix from a small
subset of its entries. In this paper, we describe the implementation of an
efficient algorithm called OptSpace, based on singular value decomposition
followed by local manifold optimization, for solving the low-rank matrix
completion problem. It has been shown that if the number of revealed entries is
large enough, the output of singular value decomposition gives a good estimate
for the original matrix, so that local optimization reconstructs the correct
matrix with high probability. We present numerical results which show that this
algorithm can reconstruct the low rank matrix exactly from a very small subset
of its entries. We further study the robustness of the algorithm with respect
to noise, and its performance on actual collaborative filtering datasets.Comment: 26 pages, 15 figure
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