Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras

In this paper, we introduce the concepts of Rota-Baxter operators and differential operators with weights on a multiplicative $n$-ary Hom-algebra. We then focus on Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras and show that they can be derived from Rota-Baxter Hom-Lie algebras, Hom-preLie algebras and Rota-Baxter commutative Hom-associative algebras. We also explore the connections between these Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras.Comment: arXiv admin note: substantial text overlap with arXiv:1306.1990, arXiv:1004.4795 by other author

A Study of deuteron electromagnetic form factors with light-front approach

The electromagnetic form factors and low-energy observables of deuteron are studied with the help of the light-front approach, where the deuteron is regarded as a weekly bound state of a proton and a neutron. Both the $S-$ and $D-$wave interacting vertexes among deuteron, proton, and neutron are taken into account. Moreover, the regularization functions are also introduced. In our calculations, the vertex and the regularization functions are employed to simulate the momentum distribution inside the deuteron. Our numerical results show that the light-front approach can roughly reproduce the deuteron electromagnetic form factors, like charge $G_0$, magnetic $G_1$, and quadrupole $G_2$, in the low $Q^2$ region. The important role of the $D-$wave vertex on $G_2$ is also addressed

K\"ahler-Ricci flow, K\"ahler-Einstein metric, and K-stability

We prove the existence of Kahler-Einstein metric on a K-stable Fano manifold using the recent compactness result on Kahler-Ricci flows. The key ingredient is an algebro-geometric description of the asymptotic behavior of Kahler-Ricci flow on Fano manifolds. This is in turn based on a general finite dimensional discussion, which is interesting in its own and could potentially apply to other problems. As one application, we relate the asymptotics of the Calabi flow on a polarized Kahler manifold to K-stability assuming bounds on geometry

Entanglement Entropy of A Simple Non-minimal Coupling Model

We evaluate the entanglement entropy of a non-minimal coupling Einstein-scalar theory with two approaches in classical Euclidean gravity. By analysing the equation of motion, we find that the entangled surface is restricted to be a minimal surface. The entanglement entropy formula is derived directly from the approach of regularized conical singularity. On the other hand, by expressing Ricci scalar of the conical spacetime, we obtain the same result. In addition, we generalize the reduced geometric approach to Riemann tensor and its derivations.Comment: 6 pages, some parts rewritte

The construction and deformation of Hom-Novikov superalgebras

We study a twisted generalization of Novikov superalgebras, called Hom-Novikov superalgebras. It is shown that two classes of Hom-Novikov superalgebras can be constructed from Hom-supercommutative algebras together with derivations and Hom-Novikov superalgebras with Rota-Baxter operators, respectively. We show that quadratic Hom-Novikov superalgebras are Hom-associative superalgebras and the sub-adjacent Hom-Lie superalgebras of Hom-Novikov superalgebras are 2-step nilpotent. Moreover, we develop the 1-parameter formal deformation theory of Hom-Novikov superalgebras

3-ary Hom-Lie superalgebras induced Hom-Lie superalgebras

The purpose of this paper is to study the relationships between a Hom-Lie superalgebra and its induced 3-ary-Hom-Lie superalgebra. We provide an overview of the theory and explore the structure properties such as ideals, center, derived series, solvability, nilpotency, central extensions, and the cohomology.Comment: 23pages. arXiv admin note: substantial text overlap with arXiv:1504.06980 by other author

Polarized GPDs and structure functions of ρ\rho meson

The $\rho$ meson polarized generalized parton distribution functions, its structure functions $g_1$ and $g_2$ and its axial form factors ${\tilde G}_{1,2}$ are studied based on a light-front quark model for the first time. Comparing our obtained moments of $g_1$ to lattice QCD calculation, we find that our results are reasonably consistent to the Lattice predictions

On universal α\alpha-central extensions of Hom-preLie algebras

We introduce the notion of Hom-co-represention and low-dimensional chain complex. We study universal central extensions of Hom-preLie algebras and generlize some classical results. As the same time, we introduce $\alpha$-central extensions, universal $\alpha$-central extensions and $\alpha$-perfect Hom-preLie algebras. We construct universal ($\alpha$)-central extensions of Hom-preLie algebras.Comment: arXiv admin note: substantial text overlap with arXiv:1209.5887 and arXiv:1209.6266 by other author

Effect of orbital-overlap dependence in density functionals

The semilocal meta generalized gradient approximation (MGGA) for the exchange-correlation functional of Kohn-Sham (KS) density functional theory can yield accurate ground-state energies simultaneously for atoms, molecules, surfaces, and solids, due to the inclusion of kinetic energy density as an input. We study for the first time the effect and importance of the dependence of MGGA on the kinetic energy density through the dimensionless inhomogeneity parameter, $\alpha$, that characterizes the extent of orbital overlap. This leads to a simple and wholly new MGGA exchange functional, which interpolates between the single-orbital regime, where $\alpha=0$, and the slowly varying density regime, where $\alpha \approx 1$, and then extrapolates to $\alpha \to \infty$. When combined with a variant of the Perdew-Burke-Erzerhof (PBE) GGA correlation, the resulting MGGA performs equally well for atoms, molecules, surfaces, and solids

O(α3αs)\mathcal O(\alpha^{3}\alpha_s) Study on the yields and polarizations of J/ψ(Υ)J/\psi(\Upsilon) within the framework of non-relativistic QCD via γγ→J/ψ(Υ)+γ+X\gamma\gamma \to J/\psi(\Upsilon)+\gamma+X at CEPC

Within the framework of the non-relativistic QCD (NRQCD), we make a systematical study of the yields and polarizations of $J/\psi$ and $\Upsilon$ via $\gamma \gamma \to J/\psi(\Upsilon)+\gamma+X$ in photon-photon collisions at the Circular Electron Positron Collider (CEPC), up to $\mathcal O(\alpha^{3}\alpha_s)$. We find that this process at CEPC is quite "clean", namely the direct photoproduction absolutely dominate over the single- and double- resolved processes, at least 2 orders of magnitude larger. It is found that the next-to-leading order (NLO) QCD corrections will significantly reduce the results due to that the virtual corrections to $^3S_1^1$ is large and negative. For $J/\psi$, as $p_t$ increases, the color octet (CO) processes will provide increasingly important contributions to the total NLO results. Moreover the inclusion of CO contributions will dramatically change the polarizations of $J/\psi$ from toally transverse to longitudinal, which can be regarded as a distinct signal for the CO mechanism. However, for the case of $\Upsilon$, the effects of the CO processes are negligible, both for yields and polarizations. For $J/\psi$, the dependence of the yields on the value of the renormalization scale $\mu_r$ is moderate, while significant for the polarization. The impact of the variation of $\mu_{\lambda}$ is found to be relatively slight. As for the case of $\Upsilon$, the uncertainties of $\mu_{r}$ and $\mu_{\lambda}$ just bring about negligible effects. The future measurements on this semi-inclusive photoproductions of $J/\psi(\Upsilon)+\gamma+X$, especially on the polarization parameters of $J/\psi$, will be a good laboratory for the study of heavy quarkonium production mechanism and helpful to clarify the problems of the $J/\psi$ polarization puzzle