Quenching depends on morphologies: implications from the ultraviolet-optical radial color distributions in Green Valley Galaxies

In this Letter, we analyse the radial UV-optical color distributions in a sample of low redshift green valley (GV) galaxies, with the Galaxy Evolution Explorer (GALEX)+Sloan Digital Sky Survey (SDSS) images, to investigate how the residual recent star formation distribute in these galaxies. We find that the dust-corrected $u-r$ colors of early-type galaxies (ETGs) are flat out to $R_{90}$, while the colors turn blue monotonously when $r>0.5R_{50}$ for late-type galaxies (LTGs). More than a half of the ETGs are blue-cored and have remarkable positive NUV$-r$ color gradients, suggesting that their star formation are centrally concentrated; the rest have flat color distributions out to $R_{90}$. The centrally concentrated star formation activity in a large portion of ETGs is confirmed by the SDSS spectroscopy, showing that $\sim$50 % ETGs have EW(H$\rm \alpha$)$>6.0$ \AA. For the LTGs, 95% of them show uniform radial color profiles, which can be interpreted as a red bulge plus an extended blue disk. The links between the two kinds of ETGs, e.g., those objects having remarkable "blue-cored" and those having flat color gradients, are less known and require future investigations. It is suggested that the LTGs follow a general picture that quenching first occur in the core regions, and then finally extend to the rest of the galaxy. Our results can be re-examined and have important implications for the IFU surveys, such as MaNGA and SAMI.Comment: ApJ Letter, accepted. Five figure

Existence and Ulam-Hyers Stability of ODEs Involving Two Caputo Fractional Derivatives

In this paper, we study existence of solutions to a Cauchy problem for nonlinear ordinary differential equations involving two Caputo fractional derivatives. The existence and uniqueness of solutions are obtained by using monotonicity, continuity and explicit estimation of Mittag-Leffler functions via fixed point theorems. Further, we present Ulam-Hyers stability results by using direct analysis methods. Finally, examples are given to illustrate our theoretical results

Relative controllability of multiagent systems with pairwise different delays in states

In this manuscript, relative controllability of leader–follower multiagent systems with pairwise different delays in states and fixed interaction topology is considered. The interaction topology of the group of agents is modeled by a directed graph. The agents with unidirectional information flows are selected as leaders, and the others are followers. Dynamics of each follower obeys a generic time-invariant delay differential equation, and the delays of agents, which satisfy a specified condition, are different one another because of the degeneration or burn-in of sensors. With a neighbor-based protocol steering, the dynamics of followers become a compact form with multiple delays. Solution of the multidelayed system without pairwise matrices permutation is obtained by improving the method in the references, and relative controllability is established via Gramian criterion. Further rank criterion of a single delay system is dealt with. Simulation illustrates the theoretical deduction

Stability of solutions of Caputo fractional stochastic differential equations

In this paper, we study the stability of Caputo-type fractional stochastic differential equations. Stochastic stability and stochastic asymptotical stability are shown by stopping time technique. Almost surly exponential stability and pth moment exponentially stability are derived by a new established Itô’s formula of Caputo version. Numerical examples are given to illustrate the main results