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We analyze the stellar initial mass functions (IMF) of a large sample of early type galaxies (ETGs) provided by MaNGA. The large number of IFU spectra of individual galaxies provide high signal-to-noise composite spectra that are essential for constraining IMF and to investigate possible radial gradients of the IMF within individual galaxies. The large sample of ETGs also make it possible to study how the IMF shape depends on various properties of galaxies. We adopt a novel approach to study IMF variations in ETGs, use Bayesian inferences based on full spectrum fitting. The Bayesian method provides a statistically rigorous way to explore potential degeneracy in spectrum fitting, and to distinguish different IMF models with Bayesian evidence. We find that the IMF slope depends systematically on galaxy velocity dispersion, in that galaxies of higher velocity dispersion prefer a more bottom-heavy IMF, but the dependence is almost entirely due to the change of metallicity, $Z$, with velocity dispersion. The IMF shape also depends on stellar age, $A$, but the dependence is completely degenerate with that on metallicity through a combination $AZ^{-1.42}$. Using independent age and metallicity estimates we find that the IMF variation is produced by metallicity instead of age. The IMF near the centers of massive ETGs appears more bottom-heavy than that in the outer parts, while a weak opposite trend is seen for low-mass ETGs. Uncertainties produced by star formation history, dust extinction, $\alpha$-element abundance enhancement and noise in the spectra are tested., Comment: 21 pages,20 figures, accepted for publication in MNRAS

The propagation of a dissipative solitary wave across an interface is studied in a binary complex plasma. The experiments were performed under microgravity conditions in the PK-3 Plus Laboratory on board the International Space Station using microparticles with diameters of 1.55 micrometre and 2.55 micrometre immersed in a low-temperature plasma. The solitary wave was excited at the edge of a particle-free region and propagated from the sub-cloud of small particles into that of big particles. The interfacial effect was observed by measuring the deceleration of particles in the wave crest. The results are compared with a Langevin dynamics simulation, where the waves were excited by a gentle push on the edge of the sub-cloud of small particles. Reflection of the wave at the interface is induced by increasing the strength of the push. By tuning the ion drag force exerted on big particles in the simulation, the effective width of the interface is adjusted. We show that the strength of reflection increases with narrower interfaces.

In this letter, we present the first numerical study on the structural and dynamical properties of a quasi-two-dimensional (q2D) binary complex plasma with Langevin dynamics simulation. The effect of interaction with non-reciprocity on the structure is investigated by comparing systems with pure Yukawa and with point-wake Yukawa interactions. The long-time alpha-relaxation for the latter system is revealed by plotting and analyzing the intermediate scattering function. The results clearly indicate that a q2D binary complex plasma is a suitable model system to study the dynamics of a glass former. The non-reciprocity of the interactions shifts the glass formation significantly but leads to the same qualitative signatures as in the reciprocal case.

In this paper we construct two groupoids from morphisms of groupoids, with one from a categorical viewpoint and the other from a geometric viewpoint. We show that for each pair of groupoids, the two kinds of groupoids of morphisms are equivalent. Then we study the automorphism groupoid of a groupoid., Comment: 28 pages; Final version, to appear in JGP; An appendix is added to discuss the topology of the morphism groupoid; Title changed

It was proved by Fan--Lee and Fan that the absolute Gromov--Witten invariants of two projective bundles $\mathbb P(V_i)\rightarrow X$ are identified canonically when the total Chern classes $c(V_1)=c(V_2)$ for two bundles $V_1$ and $V_2$ over a smooth projective variety $X$. In this note we show that for the two projective completions $\mathbb P(V_i\oplus\mathcal O)$ of $V_i$ and their infinity divisors $\mathbb P(V_i)$, the relative Gromov--Witten invariants of $(\mathbb P(V_i\oplus\mathcal O),\mathbb P(V_i))$ are identified canonically when $c(V_1)=c(V_2)$., Comment: 14pages; accepted for publication in SCIENCE CHINA Mathematics

Let $\sf X$ be a symplectic orbifold groupoid with $\sf S$ being a symplectic sub-orbifold groupoid, and $\sf X_{\mathfrak a}$ be the weight-$\mathfrak a$ blowup of $\sf X$ along $\sf S$ with $\sf Z$ being the corresponding exceptional divisor. We show that there is a weighted blowup correspondence between some certain absolute orbifold Gromov--Witten invariants of $\sf X$ relative to $\sf S$ and some certain relative orbifold Gromov--Witten invariants of the pair $(\sf X_{\mathfrak a}|Z)$. As an application, we prove that the symplectic uniruledness of symplectic orbifold groupoids is a weighted blowup invariant., Comment: 50 pages; typos are fixed, the concept of symplectic uniruledness is modified; final version, to appear in Math. Ann; comments are welcome

An orbital-angular-momentum (OAM) mode-group multiplexing (MGM) scheme based on a graded-index ring-core fiber (GIRCF) is proposed, in which a single-input two-output (or receive diversity) architecture is designed for each MG channel and simple digital signal processing (DSP) is utilized to adaptively resist the mode partition noise resulting from random intra-group mode crosstalk. There is no need of complex multiple-input multiple-output (MIMO) equalization in this scheme. Furthermore, the signal-to-noise ratio (SNR) of the received signals can be improved if a simple maximal ratio combining (MRC) technique is employed on the receiver side to efficiently take advantage of the diversity gain of receiver. Intensity-modulated direct-detection (IM-DD) systems transmitting three OAM mode groups with total 100-Gb/s discrete multi-tone (DMT) signals over a 1-km GIRCF and two OAM mode groups with total 40-Gb/s DMT signals over an 18-km GIRCF are experimentally demonstrated, respectively, to confirm the feasibility of our proposed OAM-MGM scheme., Comment: 13 pages, 6 figures

Good atlases are defined for effective orbifolds, and a spark complex is constructed on each good atlas. It is proved that this process is 2-functorial with compatible systems playing as morphisms between good atlases, and that the spark character 2-functor factors through this 2-functor., Comment: 29 pages, final version