The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form

Let $M=S^n/ \Gamma$ and $h$ be a nontrivial element of finite order $p$ in $\pi_1(M)$, where the integer $n\geq2$, $\Gamma$ is a finite group which acts freely and isometrically on the $n$-sphere and therefore $M$ is diffeomorphic to a compact space form. In this paper, we establish first the resonance identity for non-contractible homologically visible minimal closed geodesics of the class $[h]$ on every Finsler compact space form $(M, F)$ when there exist only finitely many distinct non-contractible closed geodesics of the class $[h]$ on $(M, F)$. Then as an application of this resonance identity, we prove the existence of at least two distinct non-contractible closed geodesics of the class $[h]$ on $(M, F)$ with a bumpy Finsler metric, which improves a result of Taimanov in [Taimanov 2016] by removing some additional conditions. Also our results extend the resonance identity and multiplicity results on $\mathcal{R}P^n$ in [arXiv:1607.02746] to general compact space forms.Comment: 33 pages, All comments are welcome. arXiv admin note: substantial text overlap with arXiv:1607.0274

Charm-strange baryon strong decays in a chiral quark model

The strong decays of charm-strange baryons up to N=2 shell are studied in a chiral quark model. The theoretical predictions for the well determined charm-strange baryons, $\Xi_c^*(2645)$, $\Xi_c(2790)$ and $\Xi_c(2815)$, are in good agreement with the experimental data. This model is also extended to analyze the strong decays of the other newly observed charm-strange baryons $\Xi_c(2930)$, $\Xi_c(2980)$, $\Xi_c(3055)$, $\Xi_c(3080)$ and $\Xi_c(3123)$. Our predictions are given as follows. (i) $\Xi_c(2930)$ might be the first $P$-wave excitation of $\Xi_c'$ with $J^P=1/2^-$, favors the $|\Xi_c'\ ^2P_\lambda 1/2^->$or$|\Xi_c'\ ^4P_\lambda 1/2^->$state. (ii)$\Xi_c(2980)$might correspond to two overlapping$P$-wave states$|\Xi_c'\ ^2P_\rho 1/2^->$and$|\Xi_c'\ ^2P_\rho 3/2^->$, respectively. The$\Xi_c(2980)$observed in the$\Lambda_c^+\bar{K}\pi$final state is most likely to be the$|\Xi_c'\ ^2P_\rho 1/2^->$state, while the narrower resonance with a mass$m\simeq 2.97$GeV observed in the$\Xi_c^*(2645)\pi$channel favors to be assigned to the$|\Xi_c'\ ^2P_\rho 3/2^->$state. (iii)$\Xi_c(3080)$favors to be classified as the$|\Xi_c\ S_{\rho\rho} 1/2^+>$state, i.e., the first radial excitation (2S) of$\Xi_c$. (iv)$\Xi_c(3055)$is most likely to be the first$D$-wave excitation of$\Xi_c$with$J^P=3/2^+$, favors the$|\Xi_c\ ^2D_{\lambda\lambda} 3/2^+>$state. (v)$\Xi_c(3123)$might be assigned to the$|\Xi_c'\ ^4D_{\lambda\lambda} 3/2^+>$,$|\Xi_c'\ ^4D_{\lambda\lambda} 5/2^+>$, or$|\Xi_c\ ^2D_{\rho\rho} 5/2^+>$state. As a by-product, we calculate the strong decays of the bottom baryons$\Sigma_b^{\pm}$,$\Sigma_b^{*\pm}$and$\Xi_b^*$, which are in good agreement with the recent observations as well.Comment: 15 pages, 9 figure

Potential therapeutic effects of pigment epithelium-derived factor for treatment of diabetic retinopathy

Diabetic retinopathy (DR), a major micro-vascular complication of diabetes, has emerged as a leading cause of visual impairment and blindness among working adults in the worldwide. The pathobiology of DR involves multiple molecular pathways and is characterized chronic neurovascular degeneration. Current approaches to prevent or to treat DR are still far from satisfactory. Therefore, it is important to develop new therapeutic strategies for the prevention and treatment to DR. Pigment epithelium-derived factor (PEDF), a 50-kDa secreted glycoprotein, has been described as a multi-functional protein. Some emerging evidences indicate that PEDF are able to target multiple pathways exerting neurotropic, neuroprotective, anti-angiogenic, antivasopermeability, anti-inflammation, anti-thrombogenic and anti-oxidative effects in DR. In this review, we addressed the functions of PEDF in different pathways, which could lead to potential therapeutics on the treatment to DR