The structure of f(R)f(R)-brane model

Recently, a family of interesting analytical brane solutions were found in $f(R)$ gravity with $f(R)=R+\alpha R^2$ in Ref. [Phys. Lett. B 729, 127 (2014)]. In these solutions, inner brane structure can be turned on by tuning the value of the parameter $\alpha$. In this paper, we investigate how the parameter $\alpha$ affects the localization and the quasilocalization of the tensorial gravitons around these solutions. It is found that, in a range of $\alpha$, despite the brane has an inner structure, there is no graviton resonance. However, in some other regions of the parameter space, although the brane has no internal structure, the effective potential for the graviton KK modes has a singular structure, and there exists a series of graviton resonant modes. The contribution of the massive graviton KK modes to the Newton's law of gravity is discussed shortly.Comment: v2: 10 pages, 8 figures, to be published in EPJ

New generalizations of Browder's variational inequalities and the Ky Fan minimax inequality

AbstractIn the present paper, some new generalized versions of Browder's theorems for variational inequalities and the Ky Fan minimax inequality are obtained

Search for C=+C=+ charmonium and XYZ states in e+e−→γ+He^+e^-\to \gamma+ H at BESIII

Within the framework of nonrelativistic quantum chromodynamics, we study the production of $C=+$ charmonium states $H$ in $e^+e^-\to \gamma~+~H$ at BESIII with $H=\eta_c(nS)$ (n=1, 2, 3, and 4), $\chi_{cJ}(nP)$ (n=1, 2, and 3), and $^1D_2(nD)$ (n=1 and 2). The radiative and relativistic corrections are calculated to next-to-leading order for $S$ and $P$ wave states. We then argue that the search for $C=+$ $XYZ$ states such as $X(3872)$, $X(3940)$, $X(4160)$, and $X(4350)$ in $e^+e^-\to \gamma~+~H$ at BESIII may help clarify the nature of these states. BESIII can search $XYZ$ states through two body process $e^+e^-\to \gamma H$, where $H$ decay to $J/\psi \pi^+\pi^-$, $J/\psi \phi$, or $D \bar D$. This result may be useful in identifying the nature of $C=+$ $XYZ$ states. For completeness, the production of $C=+$ charmonium in $e^+e^-\to \gamma +~H$ at B factories is also discussed.Comment: Comments and suggestions are welcome. References are update

Revealing A Head-on Major Merger in the Nearby NGC 6338 Group with Chandra and VLA observations

By analyzing the Chandra archival data of the nearby NGC 6338 galaxy group, we identify two X-ray bright clumps (N-clump and S-clump) within the central 100 kpc, and detect an arc-like X-ray brightness discontinuity at the south boundary of the N-clump, which is defined as a cold front with a gas flow Mach number of M<0.8. Furthermore, at the north-east boundary of the S-clump (dominated by galaxy NGC 6338) another X-ray edge is detected that corresponds to a weaker cold front. Therefore, the two clumps are approaching each other approximately from opposite directions, and the group is undergoing a head-on collision that is in a stage of pre-core passage. This merger scenario is also supported by the study of the line-of-sight velocity distribution of the group member galaxies. The merger mass ratio is about 1:1.8 as estimated from the central gas temperature of the two clumps, which suggests the merger is most likely to be a major merger. We also analyze the VLA 1.4 and 4.9 GHz radio data, but we do not detect any extended radio emission that is associated with the merger.Comment: Accepted by Ap