Globally F-regular type of moduli spaces and Verlinde formula

We prove that moduli spaces of semistable parabolic bundles and generalized parabolic sheaves (GPS) with a fixed determinant on a smooth projective curve are globally F-regular type. As an application, we prove vanishing theorems on the moduli spaces of semistable parabolic sheaves on a singular curve, which combining with Factorization theorems in [24] and [25] give two recurrence relations among dimensions of spaces of generalized theta functions. By using of these recurrence relations, we prove an explicit formula (Verlinde formula) for the dimension of spaces of generalized theta functions.Comment: 43 page

All fractional (g,f)-factors in graphs

Let $G$ be a graph, and $g,f:V(G)\rightarrow N$ be two functions with $g(x)\leq f(x)$ for each vertex $x$ in $G$. We say that $G$ has all fractional $(g,f)$-factors if $G$ includes a fractional $r$-factor for every $r:V(G)\rightarrow N$ such that $g(x)\leq r(x)\leq f(x)$ for each vertex $x$ in $G$. Let $H$ be a subgraph of $G$. We say that $G$ admits all fractional $(g,f)$-factors including $H$ if for every $r:V(G)\rightarrow N$ with $g(x)\leq r(x)\leq f(x)$ for each vertex $x$ in $G$, $G$ includes a fractional $r$-factor $F_h$ with $h(e)=1$ for any $e\in E(H)$, then we say that $G$ admits all fractional $(g,f)$-factors including $H$, where $h:E(G)\rightarrow [0,1]$ is the indicator function of $F_h$. In this paper, we obtain a characterization for the existence of all fractional $(g,f)$-factors including $H$ and pose a sufficient condition for a graph to have all fractional $(g,f)$-factors including $H$.Comment: 5 page

A Gromov-Hausdorff convergence theorem of surfaces in Rn\mathbb{R}^n with small total curvature

In this paper, we mainly study the compactness and local structure of immersing surfaces in $\mathbb{R}^n$ with local uniform bounded area and small total curvature $\int_{\Sigma\cap B_1(0)} |A|^2$. A key ingredient is a new quantity which we call isothermal radius. Using the estimate of the isothermal radius we establish a compactness theorem of such surfaces in intrinsic $L^p$-topology and extrinsic $W^{2,2}$-weak topology. As applications, we can explain Leon Simon's decomposition theorem\cite{LS} in the viewpoint of convergence and prove a non-collapsing version of H\'{e}lein's convergence theorem\cite{H}\cite{KL12}

Recurrent Meta-Structure for Robust Similarity Measure in Heterogeneous Information Networks

Similarity measure as a fundamental task in heterogeneous information network analysis has been applied to many areas, e.g., product recommendation, clustering and Web search. Most of the existing metrics depend on the meta-path or meta-structure specified by users in advance. These metrics are thus sensitive to the pre-specified meta-path or meta-structure. In this paper, a novel similarity measure in heterogeneous information networks, called Recurrent Meta-Structure-based Similarity (RMSS), is proposed. The recurrent meta-structure as a schematic structure in heterogeneous information networks provides a unified framework to integrate all of the meta-paths and meta-structures. Therefore, RMSS is robust to the meta-paths and meta-structures. We devise an approach to automatically constructing the recurrent meta-structure. In order to formalize the semantics, the recurrent meta-structure is decomposed into several recurrent meta-paths and recurrent meta-trees, and we then define the commuting matrices of the recurrent meta-paths and meta-trees. All of the commuting matrices of the recurrent meta-paths and meta-trees are combined according to different weights. Note that the weights can be determined by two kinds of weighting strategies: local weighting strategy and global weighting strategy. As a result, RMSS is defined by virtue of the final commuting matrix. Experimental evaluations show that the existing metrics are sensitive to different meta-paths or meta-structures and that the proposed RMSS outperforms the existing metrics in terms of ranking and clustering tasks

3d Transition Metal Adsorption Induced Vally-polarized Anomalous Hall Effect in Germanene

Based on DFT+U and Berry curvature calculations, we study the electronic structures and topological properties of 3d transition metal (TM) atom (from Ti to Co) adsorbed germanene (TM-germanene). We find that valley-polarized anomalous hall effect (VAHE) can be realized in germanene by adsorbing Cr, Mn, or Co atom on its surface. A finite valley hall voltage can be easily detected in its nanoribbon, which is important for valleytronics devices. Moreover, different valley-polarized current and even reversible valley Hall voltage can be archived by shifting the Fermi energy of the systems. Such versatile features of the systems show potential in next generation electronics devices.Comment: 8 pages, 7 figure

Enhancement of Loop induced 125GeV Higgs pair production through Large-Extra-Dimensions model at the LHC

Based on the analysis of 5 fb^-1 of data at the LHC, the ATLAS and CMS collaborations have presented evidence for a Higgs boson with a mass in the 125 GeV range. We consider the 125 GeV neutral Higgs pair production process in the context of large-extra-dimensions(LED) model including the Kaluza-Klein(KK) excited gravitons at the LHC. We take into account the LED effects coming from gluon-gluon fusion and quark-antiquark collision channels as well as their corresponding next-to-leading order(NLO) QCD loop induced corrections. We analyse their impacts on both the total cross section and some key distributions. Indeed,pp -> HH has the clear advantage of a lower standard model(SM) background compare to process like pp -> jj, though its SM prediction is very small, it is shown that the LED model raises the cross section of Higgs pair production compare to its SM prediction and enhance the transverse momentum(pHT) and invariant mass(MHH) Distributions especially at high scales of pH T and MHH. By including the NLO QCD loop corrections, the scale dependence of total cross section can be reduced obviously. Choose suitable decay modes like HH -> bbrr or HH -> bbmumu and some simple cuts, we can strongly reduce the SM background but keep most of the LED effects, leading Higgs pair production a promising channel to search LED effects

Neutral Triple Gauge Boson production in the large extra dimensions model at linear colliders

We consider the neutral triple gauge boson production process in the context of large extra dimensions (LED) model including the Kaluza-Klein (KK) excited gravitons at future linear colliders, say ILC(CLIC). We consider $\gamma\gamma\gamma, \gamma\gamma Z, \gamma Z Z$ and $ZZZ$ production processes, and analyse their impacts on both the total cross section and some key distributions. These processes are important for new physics searches at linear colliders. Our results show that KK graviton exchange has the most significant effect on \eerzz among the four processes with relatively small $M_S$, while it has the largest effect on \eerrr with larger $M_S$. By using the neutral triple gauge boson production we could set the discovery limit on the fundamental Plank scale $M_S$ up to around 6-9 TeV for $\delta$ = 4 at the 3 TeV CLIC.Comment: 17 pages,8 figures, accepted by Phys. Rev.

Two Dimensional Antiferromagnetic Chern Insulator NiRuCl6

Based on DFT and Berry curvature calculations, we predict that quantum anomalous hall effect (QAHE) can be realized in two dimensional anti-ferromagnetic (AFM) NiRuCl6 with zero net magnetic moment. By tuning spin-orbits coupling (SOC), we find that the topological properties of NiRuCl6 come from its energy band reversal. The results indicate that NiRuCl6 behaves as AFM Chern insulator and its spin-polarized electronic structure and strong spin-orbits coupling (SOC) are the origin of QAHE. Considering the compatibility between AFM and insulator, AFM Chern insulator is more suitable to realize high temperature QAHE because generally Neel temperature of AFM systems is more easily improved than Curie temperature of ferromagnetic (FM) systems. Due to the different magnetic coupling mechanism between FM and AFM Chern insulator, AFM Chern insulator provides a new way to archive high temperature QAHE in experiments.Comment: 6 pages, 6 figure

On the spectral radius of nonregular uniform hypergraphs

Let $G$ be a connected uniform hypergraphs with maximum degree $\Delta$, spectral radius $\lambda$ and minimum H-eigenvalue $\mu$. In this paper, we give some lower bounds for $\Delta-\lambda$, which extend the result of [S.M. Cioab\u{a}, D.A. Gregory, V. Nikiforov, Extreme eigenvalues of nonregular graphs, J. Combin. Theory, Ser. B 97 (2007) 483-486] to hypergraphs. Applying these bounds, we also obtain a lower bound for $\Delta+\mu$

Practical Design and Implementation of Metamaterial-Enhanced Magnetic Induction Communication

Although wireless communications in complex environments, such as underground, underwater, and indoor, can enable a large number of novel applications, their performances are constrained by lossy media and complicated structures. Magnetic Induction (MI) has been proved to be an efficient solution to achieve reliable communication in such environments. However, due to the small coil antenna's physical limitation, MI's communication range is still very limited if devices are required to be portable. To this end, Metamaterial-enhanced Magnetic Induction (M$^2$I) communication has been proposed and the theoretical results predict that it can significantly increase the communication performance, namely, data rate and communication range. Nevertheless, currently, the real implementation of M$^2$I is still a challenge and there is no guideline on design and fabrication of spherical metamaterials. In this paper, a practical design is proposed by leveraging a spherical coil array to realize M$^2$I. We prove that the effectively negative permeability can be achieved and there exists a resonance condition where the radiated magnetic field can be significantly amplified. The radiation and communication performances are evaluated and full-wave simulation is conducted to validate the design objectives. By using the spherical coil array-based M$^2$I, the communication range can be significantly extended, exactly as we predicted in the ideal M$^2$I model. Finally, the proposed M$^2$I antenna is implemented and tested in various environments.Comment: arXiv admin note: text overlap with arXiv:1510.0846