On Rigidity of hypersurfaces with constant curvature functions in warped product manifolds

In this paper, we first investigate several rigidity problems for hypersurfaces in the warped product manifolds with constant linear combinations of higher order mean curvatures as well as "weighted'' mean curvatures, which extend the work \cite{Mon, Brendle,BE} considering constant mean curvature functions. Secondly, we obtain the rigidity results for hypersurfaces in the space forms with constant linear combinations of intrinsic Gauss-Bonnet curvatures $L_k$. To achieve this, we develop some new kind of Newton-Maclaurin type inequalities on $L_k$ which may have independent interest.Comment: 24 pages, Ann. Glob. Anal. Geom. to appea

A Generic Transformation to Enable Optimal Repair in MDS Codes for Distributed Storage Systems

We propose a generic transformation that can convert any nonbinary $(n=k+r,k)$ maximum distance separable (MDS) code into another $(n,k)$ MDS code over the same field such that 1) some arbitrarily chosen $r$ nodes have the optimal repair bandwidth and the optimal rebuilding access, 2) for the remaining $k$ nodes, the normalized repair bandwidth and the normalized rebuilding access (over the file size) are preserved, 3) the sub-packetization level is increased only by a factor of $r$. Two immediate applications of this generic transformation are then presented. The first application is that we can transform any nonbinary MDS code with the optimal repair bandwidth or the optimal rebuilding access for the systematic nodes only, into a new MDS code which possesses the corresponding repair optimality for all nodes. The second application is that by applying the transformation multiple times, any nonbinary $(n,k)$ scalar MDS code can be converted into an $(n,k)$ MDS code with the optimal repair bandwidth and the optimal rebuilding access for all nodes, or only a subset of nodes, whose sub-packetization level is also optimal.Comment: This paper has been published in IEEE Transactions on Information Theor

Exploring Lexical, Syntactic, and Semantic Features for Chinese Textual Entailment in NTCIR RITE Evaluation Tasks

We computed linguistic information at the lexical, syntactic, and semantic levels for Recognizing Inference in Text (RITE) tasks for both traditional and simplified Chinese in NTCIR-9 and NTCIR-10. Techniques for syntactic parsing, named-entity recognition, and near synonym recognition were employed, and features like counts of common words, statement lengths, negation words, and antonyms were considered to judge the entailment relationships of two statements, while we explored both heuristics-based functions and machine-learning approaches. The reported systems showed robustness by simultaneously achieving second positions in the binary-classification subtasks for both simplified and traditional Chinese in NTCIR-10 RITE-2. We conducted more experiments with the test data of NTCIR-9 RITE, with good results. We also extended our work to search for better configurations of our classifiers and investigated contributions of individual features. This extended work showed interesting results and should encourage further discussion.Comment: 20 pages, 1 figure, 26 tables, Journal article in Soft Computing (Spinger). Soft Computing, online. Springer, Germany, 201

Perturbative QCD analysis of Dalitz decays J/ψ→η(′)ℓ+ℓ−J/\psi\rightarrow\eta^{(\prime)}\ell^{+}\ell^{-}

In the framework of perturbative QCD, we study the Dalitz decays $J/\psi\rightarrow\eta^{(\prime)}e^{+}e^{-}$ with large recoil momentum. Meanwhile, the soft contributions from the small recoil momentum region and the VMD corrections have also been taken into account. The transition form factors $f_{\psi\eta^{(\prime)}}(q^{2})$ including the hard and soft contributions as well as the VMD corrections are calculated for the first time. By analytical evaluation of the involved one-loop integrals, we find that the transition form factors are insensitive to both the light quark masses and the shapes of $\eta^{(\prime)}$ distribution amplitudes. With the normalized transition form factors, our results of the branching ratios $\mathcal{B}(J/\psi\rightarrow\eta^{(\prime)}e^{+}e^{-})$ and their ratio $R_{J/\psi}^{e}=\mathcal{B}(J/\psi\rightarrow\eta e^{+}e^{-})/\mathcal{B}(J/\psi\rightarrow\eta^{\prime}e^{+}e^{-})$ are in good agreement with their experimental data. Furthermore, by the ratio $R_{J/\psi}^{e}$, we extract the mixing angle of $\eta-\eta^{\prime}$ system $\phi=34.0^{\circ}\pm0.6^{\circ}$ and comment on this result briefly. Inputting the mixing angle $\phi$ extracted from $R_{J/\psi}^{e}$, we predict the branching ratios $\mathcal{B}(J/\psi\rightarrow\eta\mu^{+}\mu^{-})=3.64\times10^{-6}$, $\mathcal{B}(J/\psi\rightarrow\eta^{\prime}\mu^{+}\mu^{-})=1.52\times10^{-5}$ and their ratio $R_{J/\psi}^{\mu}=23.9\%$.Comment: 14 pages, 9 figures and 5 table

Wannier-type photonic higher-order topological corner states induced solely by gain and loss

Photonic crystals have provided a controllable platform to examine excitingly new topological states in open systems. In this work, we reveal photonic topological corner states in a photonic graphene with mirror-symmetrically patterned gain and loss. Such a nontrivial Wannier-type higher-order topological phase is achieved through solely tuning on-site gain/loss strengths, which leads to annihilation of the two valley Dirac cones at a time-reversal-symmetric point, as the gain and loss change the effective tunneling between adjacent sites. We find that the symmetry-protected photonic corner modes exhibit purely imaginary energies and the role of the Wannier center as the topological invariant is illustrated. For experimental considerations, we also examine the topological interface states near a domain wall. Our work introduces an interesting platform for non-Hermiticity-induced photonic higher-order topological insulators, which, with current experimental technologies, can be readily accessed.Comment: 7 pages, 5 figure

Liquid Metal as Connecting or Functional Recovery Channel for the Transected Sciatic Nerve

In this article, the liquid metal GaInSn alloy (67% Ga, 20.5% In, and 12.5% Sn by volume) is proposed for the first time to repair the peripheral neurotmesis as connecting or functional recovery channel. Such material owns a group of unique merits in many aspects, such as favorable fluidity, super compliance, high electrical conductivity, which are rather beneficial for conducting the excited signal of nerve during the regeneration process in vivo. It was found that the measured electroneurographic signal from the transected bullfrog sciatic nerve reconnected by the liquid metal after the electrical stimulation was close to that from the intact sciatic nerve. The control experiments through replacement of GaInSn with the conventionally used Riger Solution revealed that Riger Solution could not be competitive with the liquid metal in the performance as functional recovery channel. In addition, through evaluation of the basic electrical property, the material GaInSn works more suitable for the conduction of the weak electroneurographic signal as its impedance was several orders lower than that of the well-known Riger Solution. Further, the visibility under the plain radiograph of such material revealed the high convenience in performing secondary surgery. This new generation nerve connecting material is expected to be important for the functional recovery during regeneration of the injured peripheral nerve and the optimization of neurosurgery in the near future

A penrose inequality for graphs over Kottler space

In this work, we prove an optimal Penrose inequality for asymptotically locally hyperbolic manifolds which can be realized as graphs over Kottler space. Such inequality relies heavily on an optimal weighted Alexandrov-Fenchel inequality for the mean convex star shaped hypersurfaces in Kottler space

Radiative decays of bottomonia into charmonia and light mesons

In the framework of nonrelativistic QCD, we study the radiative decays of bottomonia into charmonia, including $\Upsilon\to \chi_{cJ}\gamma$, $\Upsilon\to \eta_c\gamma$, $\eta_b\to J/\psi\gamma$, and $\chi_{bJ}\to J/\psi\gamma$. We give predictions for their branching ratios with numerical calculations. E.g., we predict the branching ratio for $\eta_b\to J/\psi\gamma$ is about $1\times 10^{-7}$. As a phenomenological model study, we further extend our calculation to the radiative decays of bottomonia into light mesons by assuming the $f_2(1270)$, $f_2'(1525)$ and other light mesons to be described by nonrelativistic $q\bar q ~(q=u,d,s)$ bound states with constituent quark masses. The calculated branching ratios for $\Upsilon\to f_2(1270)\gamma$ and $\Upsilon\to f_2'(1525)\gamma$ are roughly consistent with the CLEO data. Comparisons with radiative decays of charmonium into light mesons such as $J/\psi\to f_2(1270)\gamma$ are also given. In all calculations the QED contributions are taken into account and found to be significant in some processes

Spectral operators of matrices: semismoothness and characterizations of the generalized Jacobian

Spectral operators of matrices proposed recently in [C. Ding, D.F. Sun, J. Sun, and K.C. Toh, Math. Program. {\bf 168}, 509--531 (2018)] are a class of matrix valued functions, which map matrices to matrices by applying a vector-to-vector function to all eigenvalues/singular values of the underlying matrices. Spectral operators play a crucial role in the study of various applications involving matrices such as matrix optimization problems (MOPs) {that include semidefinite programming as one of the most important example classes}. In this paper, we will study more fundamental first- and second-order properties of spectral operators, including the Lipschitz continuity, $\rho$-order B(ouligand)-differentiability ($0<\rho\le 1$), $\rho$-order G-semismoothness ($0<\rho\le 1$), and characterization of generalized Jacobians.Comment: 25 pages. arXiv admin note: substantial text overlap with arXiv:1401.226

Graphic Method for Arbitrary nn-body Phase Space

In quantum field theory, the phase space integration is an essential part in all theoretical calculations of cross sections and decay widths. It is also needed for computing the imaginary part of a physical amplitude. A key problem is to get the phase space formula expressed in terms of any chosen invariant masses in an $n$-body system. We propose a graphic method to quickly get the phase space formula of any given invariant masses intuitively for an arbitrary $n$-body system in general $D$-dimensional spacetime, with the involved momenta in any reference frame. The method also greatly simplifies the phase space calculation just as what Feynman diagrams do in calculating scattering amplitudes.Comment: More explanations, generalization to the general spacetime dimensions include