12,623 research outputs found

### Relative Generalized Hamming Weights of Cyclic Codes

Relative generalized Hamming weights (RGHWs) of a linear code respect to a
linear subcode determine the security of the linear ramp secret sharing scheme
based on the code. They can be used to express the information leakage of the
secret when some keepers of shares are corrupted. Cyclic codes are an
interesting type of linear codes and have wide applications in communication
and storage systems. In this paper, we investigate the RGHWs of cyclic codes
with two nonzeros respect to any of its irreducible cyclic subcodes. Applying
the method in the paper [arxiv.org/abs/1410.2702], we give two formulae for
RGHWs of the cyclic codes. As applications of the formulae, explicit examples
are computed.Comment: 14 page

### Optimal laser pulse design for transferring the coherent nuclear wave packet of H$_2^+$

Within the Franck-Condon approximation, the single ionization of H$_2$ leaves
H$_2^+$ in a coherent superposition of 19 nuclear vibrational states. We
numerically design an optimal laser pulse train to transfer such a coherent
nuclear wave packet to the ground vibrational state of H$_2^+$. The simulation
results show that the population of the ground state after the transfer is more
than 91%. Frequency analysis of the designed optimal pulse reveals that the
transfer principle is mainly an anti-Stokes transition, i.e., the H$_2^+$ in
$1s\sigma_g$ with excited nuclear vibrational states is first pumped to
$2p\sigma_g$ state by the pulse at an appropriate time, and then dumped back to
$1s\sigma_g$ with lower excited or ground vibrational states

### On $L$-functions of certain exponential sums

Let $\mathbb{F}_{q}$ denote the finite field of order $q$ (a power of a prime
$p$). We study the $p$-adic valuations for zeros of $L$-functions associated
with exponential sums of the following family of Laurent polynomials
f(x_1,x_2,...,x_{n+1})=a_1x_{n+1}(x_1+{1\over
x_1})+...+a_{n}x_{n+1}(x_{n}+{1\over x_{n}})+a_{n+1}x_{n+1}+{1\over x_{n+1}}
where $a_i\in \mathbb{F}_{q}^*,\,i=1,2,...,n+1$. When n=2, the estimate of the
associated exponential sum appears in Iwaniec's work, and Adolphson and Sperber
gave complex absolute values for zeros of the corresponding $L$-function. Using
the decomposition theory of Wan, we determine the generic Newton polygon
($q$-adic values of the reciprocal zeros) of the $L$-function. Working on the
chain level version of Dwork's trace formula and using Wan's decomposition
theory, we are able to give an explicit Hasse polynomial for the generic Newton
polygon in low dimensions, i.e., $n\leq 3$.Comment: 27 pages. arXiv admin note: text overlap with arXiv:1208.4590,
arXiv:math/9905216 by other author

### Anomalous Josephson Effect in magnetic Josephson junctions with noncentrosymmetric superconductors

We show that the two-band nature of noncentrosymmetric superconductors leads
naturally to an anomalous Josephson current appearing at zero phase difference
in a clean noncentrosymmetric superconductor/ferromagnet/noncentrosymmetric
superconductor junction. The two-band nature provides two sets of Andreev bound
states which carry two supercurrents with different amplitudes. When the
magnetization direction of the ferromagnet is suitably chosen, two
supercurrents experience opposite phase shifts from the conventional sinusoidal
current-phase relation. Then the total Josephson current results in a
continuously tunable ground-state phase difference by adjusting the ferromagnet
parameters and the triplet-singlet ratio of noncentrosymmetric superconductors.
The physics picture and analytical results are given on the basis of the
$s$+$p$ wave, while the numerical results are reported on both $s$+$p$ and
$d$+$p$ waves. For the $d$+$p$ wave, we find novel states in which the
supercurrents are totally carried by continuous propagating states instead of
discrete Andreev bound states. Instead of carrying supercurrent, the Andreev
bound states which here only appear above the Fermi energy block the
supercurrent flowing along the opposite direction. These novel states advance
the understaning of the relation between Andreev bound states and the Josephson
current. And the ground-state phase difference serves as a tool to determine
the triplet-singlet ratio of noncentrosymmetric superconductors.Comment: 10pages, 6figure

### Multi-channel Weighted Nuclear Norm Minimization for Real Color Image Denoising

Most of the existing denoising algorithms are developed for grayscale images,
while it is not a trivial work to extend them for color image denoising because
the noise statistics in R, G, B channels can be very different for real noisy
images. In this paper, we propose a multi-channel (MC) optimization model for
real color image denoising under the weighted nuclear norm minimization (WNNM)
framework. We concatenate the RGB patches to make use of the channel
redundancy, and introduce a weight matrix to balance the data fidelity of the
three channels in consideration of their different noise statistics. The
proposed MC-WNNM model does not have an analytical solution. We reformulate it
into a linear equality-constrained problem and solve it with the alternating
direction method of multipliers. Each alternative updating step has closed-form
solution and the convergence can be guaranteed. Extensive experiments on both
synthetic and real noisy image datasets demonstrate the superiority of the
proposed MC-WNNM over state-of-the-art denoising methods.Comment: 9 pages, ICCV 201

### The obstacle problem for nonlinear degenerate equations with $L^{1}$-data

The aim of this paper is to study the obstacle problem with an elliptic
operator having degenerate coercivity. We prove the existence of an entropy
solution to the obstacle problem under the assumption of $L^{1}-$summability on
the data. Meanwhile, we prove that every entropy solution belongs to some
Sobolev space $W^{1,q}(\Omega)$.Comment: 21 pages. arXiv admin note: text overlap with arXiv:1003.2305 by
other author

### On the 2-Adic Complexity of the Ding-Helleseth-Martinsen Binary Sequences

We determine the 2-adic complexity of the Ding-Helleseth-Martinsen (DHM)
binary sequences by using cyclotomic numbers of order four, "Gauss periods" and
"quadratic Gauss sum" on finite field $\mathbb{F}_q$ and valued in
$\mathbb{Z}_{2^N-1}$ where $q \equiv 5\pmod 8$ is a prime number and $N=2q$ is
the period of the DHM sequences.Comment: 16 page

### Double sneutrino inflation and its phenomenologies

In this paper we study double scalar neutrino inflation in the minimal
supersymmetric seesaw model in light of WMAP. Inflation in this model is
firstly driven by the heavier sneutrino field $\tilde{N}_2$ and then the
lighter field $\tilde{N}_1$. we will show that with the mass ratio $6\lesssim
M_2/M_1 \lesssim 10$ the model predicts a suppressed primordial scalar spectrum
around the largest scales and the predicted CMB TT quadrupole is much better
suppressed than the single sneutrino model. So this model is more favored than
the single sneutrino inflation model. We then consider the implications of the
model on the reheating temperature, leptogenesis and lepton flavor violation.
Our results show that the seesaw parameters are constrained strongly by the
reheating temperature, together with the requirement by a successful inflation.
The mixing between the first generation and the other two generations in the
right-handed neutrino sector is tiny. The rates of lepton flavor violating
processes in our scenario depend on only 4 unknown seesaw parameters through a
'reduced' seesaw formula, besides $U_{e3}$ and the supersymmetric parameters.
We find that the branching ratio of $\mu \to e \gamma$ is generally near the
present experimental limit, while ${\rm Br}(\tau \to \mu \gamma)$ is around
$\mathcal{O}(10^{-10} - 10^{-9})$.Comment: 28 pages, 12 figures; new references adde

### $K^{*0}$ and $\Sigma^*$ production in Au+Au collisions at $\sqrt{s_{NN}}=$ 200 GeV and 62.4 GeV

Applying a quark combination model for the hadronization of Quark Gluon
Plasma (QGP) and A Relativistic Transport (ART) model for the subsequent
hadronic rescattering process, we investigate the production of $K^{*0}$ and
$\Sigma^*$ resonances in central Au+Au collisions at $\sqrt{s_{NN}}=$ 200 GeV
and 62.4 GeV. The initial $K^{*0}$ produced via hadronization is higher than
the experimental data in the low $p_T$ region and is close to the data at 2-3
GeV/c. We take into account the hadronic rescattering effects which lead to a
strong suppression of $K^{*0}$ with low $p_T$, and find that the $p_T$ spectrum
of $K^{*0}$ can be well described. According to the suppressed magnitude of
$K^{*0}$ yield, the time span of hadronic rescattering stage is estimated to be
about 13 fm/c at 200 GeV and 5 fm/c at 62.4 GeV. The $p_T$ spectrum of
$\Sigma^*$ directly obtained by quark combination hadronization in central
Au+Au collisions at 200 GeV is in well agreement with the experimental data,
which shows a weak hadronic rescattering effects. The elliptic flow v2 of
$\Sigma^*$ in minimum bias Au+Au collisions at 200 GeV and $p_T$ spectrum of
$\Sigma^*$ at lower 62.4 GeV are predicted.Comment: 12 pages, 6 figure

### On the Degree of Freedom for Multi-Source Multi-Destination Wireless Network with Multi-layer Relays

Degree of freedom (DoF) region provides an approximation of capacity region
in high signal-to-noise ratio (SNR) regime, while sum DoF gives the scaling
factor. In this correspondence, we analyse the DoF region and sum DoF for
unicast layered multi-hop relay wireless networks with arbitrary number of
source/destination/relay nodes, arbitrary number of hops and arbitrary number
of antennas at each node. The result is valid for quite a few message
topologies. We reveal the limitation on capacity of multi-hop network due to
the concatenation structure and show the similarity with capacitor network.
From the analysis on bound gap and optimality condition, the ultimate capacity
of multi-hop network is shown to be strictly inferior to that of single-hop
network. Linear scaling law can be established when the number of hops is
fixed. At cost of channel state information at transmitters (CSIT) for each
component single-hop network, our achievable scheme avoids routing and
simplifies scheduling.Comment: 15 pages, 2 figure

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