11,013 research outputs found
An extension of an inequality for ratios of gamma functions
In this paper, we prove that for and the inequality
{equation*}
\frac{[\Gamma(x+y+1)/\Gamma(y+1)]^{1/x}}{[\Gamma(x+y+2)/\Gamma(y+1)]^{1/(x+1)}}
1x<1\frac12\Gamma(x)$ is the Euler gamma function. This extends the result in [Y. Yu,
\textit{An inequality for ratios of gamma functions}, J. Math. Anal. Appl.
\textbf{352} (2009), no.~2, 967\nobreakdash--970.] and resolves an open problem
posed in [B.-N. Guo and F. Qi, \emph{Inequalities and monotonicity for the
ratio of gamma functions}, Taiwanese J. Math. \textbf{7} (2003), no.~2,
239\nobreakdash--247.].Comment: 8 page
QCD corrections to single slepton production at hadron colliders
We evaluate the cross section for single slepton production at hadron
colliders in supersymmetric theories with R-parity violating interactions to
the next-to-leading order in QCD. We obtain fully differential cross section by
using the phase space slicing method. We also perform soft-gluon resummation to
all order in of leading logarithm to obtain a complete transverse
momentum spectrum of the slepton. We find that the full transverse momentum
spectrum is peaked at a few GeV, consistent with the early results for
Drell-Yan production of lepton pairs. We also consider the contribution from
gluon fusion via quark-triangle loop diagrams dominated by the -quark loop.
The cross section of this process is significantly smaller than that of the
tree-level process induced by the initial annihilation.Comment: one new reference is adde
Easing Embedding Learning by Comprehensive Transcription of Heterogeneous Information Networks
Heterogeneous information networks (HINs) are ubiquitous in real-world
applications. In the meantime, network embedding has emerged as a convenient
tool to mine and learn from networked data. As a result, it is of interest to
develop HIN embedding methods. However, the heterogeneity in HINs introduces
not only rich information but also potentially incompatible semantics, which
poses special challenges to embedding learning in HINs. With the intention to
preserve the rich yet potentially incompatible information in HIN embedding, we
propose to study the problem of comprehensive transcription of heterogeneous
information networks. The comprehensive transcription of HINs also provides an
easy-to-use approach to unleash the power of HINs, since it requires no
additional supervision, expertise, or feature engineering. To cope with the
challenges in the comprehensive transcription of HINs, we propose the HEER
algorithm, which embeds HINs via edge representations that are further coupled
with properly-learned heterogeneous metrics. To corroborate the efficacy of
HEER, we conducted experiments on two large-scale real-words datasets with an
edge reconstruction task and multiple case studies. Experiment results
demonstrate the effectiveness of the proposed HEER model and the utility of
edge representations and heterogeneous metrics. The code and data are available
at https://github.com/GentleZhu/HEER.Comment: 10 pages. In Proceedings of the 24th ACM SIGKDD International
Conference on Knowledge Discovery and Data Mining, London, United Kingdom,
ACM, 201
A Note on Symplectic, Multisymplectic Scheme in Finite Element Method
We find that with uniform mesh, the numerical schemes derived from finite
element method can keep a preserved symplectic structure in one-dimensional
case and a preserved multisymplectic structure in two-dimentional case in
certain discrete version respectively. These results are in fact the intrinsic
reason that the numerical experiments indicate that such finite element
algorithms are accurate in practice.Comment: 7 pages, 3 figure
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