11,719 research outputs found
On the F.Smarandache LCM Ratio Sequence
In this paper, we use the elementary methods to study the F.Smarandache LCM
ratio sequence, and obtain three interesting recurrence relations for it
Decomposing Overcomplete 3rd Order Tensors using Sum-of-Squares Algorithms
Tensor rank and low-rank tensor decompositions have many applications in
learning and complexity theory. Most known algorithms use unfoldings of tensors
and can only handle rank up to for a -th order
tensor in . Previously no efficient algorithm can decompose
3rd order tensors when the rank is super-linear in the dimension. Using ideas
from sum-of-squares hierarchy, we give the first quasi-polynomial time
algorithm that can decompose a random 3rd order tensor decomposition when the
rank is as large as .
We also give a polynomial time algorithm for certifying the injective norm of
random low rank tensors. Our tensor decomposition algorithm exploits the
relationship between injective norm and the tensor components. The proof relies
on interesting tools for decoupling random variables to prove better matrix
concentration bounds, which can be useful in other settings
Nucleon sea in the effective chiral quark model
The asymmetries of both light-flavor antiquark and
strange-antistrange distributions of the nucleon sea are
considered with more details in the effective chiral quark model. We find that
the asymmetric distribution of light-flavor antiquarks
matches the experiment data well and that the asymmetry of strange and
antistrange distributions can bring about 60-100% correction to the NuTeV
anomaly of , which are three standard deviations from the
world average value measured in other electroweak processes. The results on the
correction to the NuTeV anomaly are insensitive to the inputs of the
constituent quark distributions and the cut-off parameters. The ratios of
and are also discussed, and it is
found that the ratio is compatible with the available
experiments with an additional symmetric sea contribution being considered
effectively.Comment: 24 Latex pages, 8 figure
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