Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching

In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the population model. Finally, we illustrate our conclusions through two examples

Assessing the effect of lens mass model in cosmological application with updated galaxy-scale strong gravitational lensing sample

By comparing the dynamical and lensing masses of early-type lens galaxies, one can constrain both the cosmological parameters and the density profiles of galaxies. We explore the constraining power on cosmological parameters and the effect of the lens mass model in this method with 161 galaxy-scale strong lensing systems, which is currently the largest sample with both high resolution imaging and stellar dynamical data. We assume a power-law mass model for the lenses, and consider three different parameterizations for $\gamma$ (i.e., the slope of the total mass density profile) to include the effect of the dependence of $\gamma$ on redshift and surface mass density. When treating $\delta$ (i.e., the slope of the luminosity density profile) as a universal parameter for all lens galaxies, we find the limits on the cosmological parameter $\Omega_m$ are quite weak and biased, and also heavily dependent on the lens mass model in the scenarios of parameterizing $\gamma$ with three different forms. When treating $\delta$ as an observable for each lens, the unbiased estimate of $\Omega_m$ can be obtained only in the scenario of including the dependence of $\gamma$ on both the redshift and the surface mass density, that is $\Omega_m = 0.381^{+0.185}_{-0.154}$ at 68\% confidence level in the framework of a flat $\Lambda$CDM model. We conclude that the significant dependencies of $\gamma$ on both the redshift and the surface mass density, as well as the intrinsic scatter of $\delta$ among the lenses, need to be properly taken into account in this method.Comment: Accepted for publication in MNRAS; 17 pages, 5 figures, 2 table

Mo Yan’s \u3cem\u3eRadish\u3c/em\u3e: Between the Real and the Surreal

In their article “Mo Yan’s Radish: Between the Real and the Surreal” Xiaoyue Li and Xuefang Feng argue that Radish, a novella written by Nobel Prize winner Mo Yan skillfully combines realism with surrealism, the flexible swing between which is made possible by the choice of children’s perspective, and the effect is too significant to be ignored. Their analysis concludes that the transparent golden radish symbolizes humanity, the lack of which projects the protagonist’ sufferings, and that the surrealist description of the radish reveals the magic function of humanity in brightening up life in times of miseries

Existence and uniqueness of solutions for singular fourth-order boundary value problems

AbstractBy mixed monotone method, the existence and uniqueness are established for singular fourth-order boundary value problems. The theorems obtained are very general and complement previous known results